Parsing THF and adding several regressions (#3131)

diff --git a/src/options/options.h b/src/options/options.h
index 56b92359b60a22175bca47277341d30c8ca88cc1..020350c496751b265524b2af4062bf737f861254 100644 (file)
--- a/src/options/options.h
+++ b/src/options/options.h
@@ -242,7 +242,6 @@ public:
   unsigned getThreadStackSize() const;
   unsigned getThreads() const;
 
-
   // TODO: Document these.
   void setInputLanguage(InputLanguage);
   void setInteractive(bool);

diff --git a/src/parser/parser.cpp b/src/parser/parser.cpp
index 5e036ee69ea46e004c2197ef05c57f34dfc91ae5..dec4ebc978bdc63a24d6a90bc541bc9698003f0e 100644 (file)
--- a/src/parser/parser.cpp
+++ b/src/parser/parser.cpp
@@ -492,6 +492,15 @@ Type Parser::mkFlatFunctionType(std::vector<Type>& sorts, Type range)
     // no difference
     return range;
   }
+  if (Debug.isOn("parser"))
+  {
+    Debug("parser") << "mkFlatFunctionType: range " << range << " and domains ";
+    for (Type t : sorts)
+    {
+      Debug("parser") << " " << t;
+    }
+    Debug("parser") << "\n";
+  }
   while (range.isFunction())
   {
     std::vector<Type> domainTypes =

diff --git a/src/parser/tptp/Tptp.g b/src/parser/tptp/Tptp.g
index 758198e0d68ad778856b7332bb08396c1f38ed0b..599b3bbe15393c2063c6097d801ce17938c0d360 100644 (file)
--- a/src/parser/tptp/Tptp.g
+++ b/src/parser/tptp/Tptp.g
@@ -148,7 +148,6 @@ parseCommand returns [CVC4::Command* cmd = NULL]
   Tptp::FormulaRole fr;
   std::string name, inclSymbol;
 }
-//  : LPAREN_TOK c = command RPAREN_TOK { $cmd = c; }
   : CNF_TOK LPAREN_TOK nameN[name] COMMA_TOK formulaRole[fr] COMMA_TOK
   { PARSER_STATE->setCnf(true);
     PARSER_STATE->setFof(false);
@@ -203,6 +202,26 @@ parseCommand returns [CVC4::Command* cmd = NULL]
         cmd = PARSER_STATE->makeAssertCommand(fr, aexpr, /* cnf == */ false, true);
       }
     ) RPAREN_TOK DOT_TOK
+  | THF_TOK LPAREN_TOK nameN[name] COMMA_TOK
+    // Supported THF formulas: either a logic formula or a typing atom (i.e. we
+    // ignore subtyping and logic sequents). Also, only TH0
+    ( TYPE_TOK COMMA_TOK thfAtomTyping[cmd]
+    | formulaRole[fr] COMMA_TOK
+      { PARSER_STATE->setCnf(false); PARSER_STATE->setFof(false); }
+      thfLogicFormula[expr] (COMMA_TOK anything*)?
+      {
+        Expr aexpr = PARSER_STATE->getAssertionExpr(fr,expr);
+        if (!aexpr.isNull())
+        {
+          // set the expression name (e.g. used with unsat core printing)
+          Command* csen = new SetExpressionNameCommand(aexpr, name);
+          csen->setMuted(true);
+          PARSER_STATE->preemptCommand(csen);
+        }
+        // make the command to assert the formula
+        cmd = PARSER_STATE->makeAssertCommand(fr, aexpr, /* cnf == */ false, true);
+      }
+    ) RPAREN_TOK DOT_TOK
   | INCLUDE_TOK LPAREN_TOK unquotedFileName[name]
     ( COMMA_TOK LBRACK_TOK nameN[inclSymbol]
       ( COMMA_TOK nameN[inclSymbol] )* RBRACK_TOK )?
@@ -226,13 +245,13 @@ parseCommand returns [CVC4::Command* cmd = NULL]
   | EOF
     {
       CommandSequence* seq = new CommandSequence();
-      // assert that all distinct constants are distinct 
+      // assert that all distinct constants are distinct
       Expr aexpr = PARSER_STATE->getAssertionDistinctConstants();
       if( !aexpr.isNull() )
       {
         seq->addCommand(new AssertCommand(aexpr, false));
       }
-      
+
       std::string filename = PARSER_STATE->getInput()->getInputStreamName();
       size_t i = filename.find_last_of('/');
       if(i != std::string::npos) {
@@ -284,7 +303,6 @@ formulaRole[CVC4::parser::Tptp::FormulaRole& role]
 cnfFormula[CVC4::Expr& expr]
   : LPAREN_TOK cnfDisjunction[expr] RPAREN_TOK
   | cnfDisjunction[expr]
-//| FALSE_TOK { expr = MK_CONST(bool(false)); }
 ;
 
 cnfDisjunction[CVC4::Expr& expr]
@@ -302,7 +320,6 @@ cnfDisjunction[CVC4::Expr& expr]
 cnfLiteral[CVC4::Expr& expr]
   : atomicFormula[expr]
   | NOT_TOK atomicFormula[expr] { expr = MK_EXPR(kind::NOT, expr); }
-//| folInfixUnary[expr]
   ;
 
 atomicFormula[CVC4::Expr& expr]
@@ -323,22 +340,77 @@ atomicFormula[CVC4::Expr& expr]
         PARSER_STATE->makeApplication(expr, name, args, false);
       }
     )
-  | definedFun[expr] LPAREN_TOK arguments[args] RPAREN_TOK
-    equalOp[equal] term[expr2]
-    { expr = EXPR_MANAGER->mkExpr(expr, args);
-      expr = MK_EXPR(kind::EQUAL, expr, expr2);
-      if(!equal) expr = MK_EXPR(kind::NOT, expr);
-    }
+  | definedFun[expr]
+    (
+     LPAREN_TOK arguments[args] RPAREN_TOK
+     equalOp[equal] term[expr2]
+     {
+       expr = EXPR_MANAGER->mkExpr(expr, args);
+       expr = MK_EXPR(kind::EQUAL, expr, expr2);
+       if (!equal)
+       {
+         expr = MK_EXPR(kind::NOT, expr);
+       }
+     }
+    )?
   | (simpleTerm[expr] | letTerm[expr] | conditionalTerm[expr])
-    equalOp[equal] term[expr2]
-    { // equality/disequality between terms
-      expr = MK_EXPR(kind::EQUAL, expr, expr2);
-      if(!equal) expr = MK_EXPR(kind::NOT, expr);
+    (
+      equalOp[equal] term[expr2]
+      { // equality/disequality between terms
+        expr = MK_EXPR(kind::EQUAL, expr, expr2);
+        if (!equal)
+        {
+          expr = MK_EXPR(kind::NOT, expr);
+        }
+      }
+    )?
+  | definedPred[expr] (LPAREN_TOK arguments[args] RPAREN_TOK)?
+    {
+      if (!args.empty())
+      {
+        expr = EXPR_MANAGER->mkExpr(expr, args);
+      }
     }
-  | definedPred[expr] LPAREN_TOK arguments[args] RPAREN_TOK
-    { expr = EXPR_MANAGER->mkExpr(expr, args); }
   | definedProp[expr]
   ;
+
+thfAtomicFormula[CVC4::Expr& expr]
+@declarations {
+  Expr expr2;
+  std::string name;
+  std::vector<CVC4::Expr> args;
+  bool equal;
+}
+  : atomicWord[name] (LPAREN_TOK arguments[args] RPAREN_TOK)?
+    {
+      PARSER_STATE->makeApplication(expr, name, args, true);
+    }
+  | definedFun[expr]
+    (
+      LPAREN_TOK arguments[args] RPAREN_TOK
+      equalOp[equal] term[expr2]
+      {
+        expr = EXPR_MANAGER->mkExpr(expr, args);
+        expr = MK_EXPR(kind::EQUAL, expr, expr2);
+        if (!equal)
+        {
+          expr = MK_EXPR(kind::NOT, expr);
+        }
+      }
+    )?
+  | thfSimpleTerm[expr]
+  | letTerm[expr]
+  | conditionalTerm[expr]
+  | thfDefinedPred[expr] (LPAREN_TOK arguments[args] RPAREN_TOK)?
+    {
+      if (!args.empty())
+      {
+        expr = EXPR_MANAGER->mkExpr(expr, args);
+      }
+    }
+  | definedProp[expr]
+  ;
+
 //%----Using <plain_term> removes a reduce/reduce ambiguity in lex/yacc.
 //%----Note: "defined" means a word starting with one $ and "system" means $$.
 
@@ -373,6 +445,45 @@ definedPred[CVC4::Expr& expr]
     }
   | '$is_int' { expr = EXPR_MANAGER->operatorOf(CVC4::kind::IS_INTEGER); }
   | '$distinct' { expr = EXPR_MANAGER->operatorOf(CVC4::kind::DISTINCT); }
+  | AND_TOK { expr = EXPR_MANAGER->operatorOf(CVC4::kind::AND); }
+  | IMPLIES_TOK { expr = EXPR_MANAGER->operatorOf(CVC4::kind::IMPLIES); }
+  | OR_TOK { expr = EXPR_MANAGER->operatorOf(CVC4::kind::OR); }
+  ;
+
+thfDefinedPred[CVC4::Expr& expr]
+  : '$less' { expr = EXPR_MANAGER->operatorOf(CVC4::kind::LT); }
+  | '$lesseq' { expr = EXPR_MANAGER->operatorOf(CVC4::kind::LEQ); }
+  | '$greater' { expr = EXPR_MANAGER->operatorOf(CVC4::kind::GT); }
+  | '$greatereq' { expr = EXPR_MANAGER->operatorOf(CVC4::kind::GEQ); }
+  | '$is_rat'
+    // a real n is a rational if there exists q,r integers such that
+    //   to_real(q) = n*to_real(r),
+    // where r is non-zero.
+    {
+      Expr n = EXPR_MANAGER->mkBoundVar("N", EXPR_MANAGER->realType());
+      Expr q = EXPR_MANAGER->mkBoundVar("Q", EXPR_MANAGER->integerType());
+      Expr qr = MK_EXPR(CVC4::kind::TO_REAL, q);
+      Expr r = EXPR_MANAGER->mkBoundVar("R", EXPR_MANAGER->integerType());
+      Expr rr = MK_EXPR(CVC4::kind::TO_REAL, r);
+      Expr body = MK_EXPR(
+          CVC4::kind::AND,
+          MK_EXPR(CVC4::kind::NOT,
+                  MK_EXPR(CVC4::kind::EQUAL, r, MK_CONST(Rational(0)))),
+          MK_EXPR(CVC4::kind::EQUAL, qr, MK_EXPR(CVC4::kind::MULT, n, rr)));
+      Expr bvl = MK_EXPR(CVC4::kind::BOUND_VAR_LIST, q, r);
+      body = MK_EXPR(CVC4::kind::EXISTS, bvl, body);
+      Expr lbvl = MK_EXPR(CVC4::kind::BOUND_VAR_LIST, n);
+      expr = MK_EXPR(CVC4::kind::LAMBDA, lbvl, body);
+    }
+  | '$is_int' { expr = EXPR_MANAGER->operatorOf(CVC4::kind::IS_INTEGER); }
+  | '$distinct' { expr = EXPR_MANAGER->operatorOf(CVC4::kind::DISTINCT); }
+  | LPAREN_TOK
+    (
+      AND_TOK { expr = EXPR_MANAGER->operatorOf(CVC4::kind::AND); }
+    | OR_TOK { expr = EXPR_MANAGER->operatorOf(CVC4::kind::OR); }
+    | IMPLIES_TOK { expr = EXPR_MANAGER->operatorOf(CVC4::kind::IMPLIES); }
+    )
+    RPAREN_TOK
   ;
 
 definedFun[CVC4::Expr& expr]
@@ -504,6 +615,16 @@ simpleTerm[CVC4::Expr& expr]
   | DISTINCT_OBJECT { expr = PARSER_STATE->convertStrToUnsorted(AntlrInput::tokenText($DISTINCT_OBJECT)); }
   ;
 
+/* Not an application */
+thfSimpleTerm[CVC4::Expr& expr]
+  : NUMBER { expr = PARSER_STATE->d_tmp_expr; }
+  | DISTINCT_OBJECT
+    {
+      expr = PARSER_STATE->convertStrToUnsorted(
+          AntlrInput::tokenText($DISTINCT_OBJECT));
+    }
+  ;
+
 functionTerm[CVC4::Expr& expr]
 @declarations {
   std::vector<CVC4::Expr> args;
@@ -637,8 +758,283 @@ fofBinaryNonAssoc[CVC4::parser::tptp::NonAssoc& na]
   ;
 
 folQuantifier[CVC4::Kind& kind]
-  : BANG_TOK { kind = kind::FORALL; }
-  | MARK_TOK { kind = kind::EXISTS; }
+  : FORALL_TOK { kind = kind::FORALL; }
+  | EXISTS_TOK { kind = kind::EXISTS; }
+  ;
+
+/*******/
+/* THF */
+
+thfQuantifier[CVC4::Kind& kind]
+  : FORALL_TOK { kind = kind::FORALL; }
+  | EXISTS_TOK { kind = kind::EXISTS; }
+  | LAMBDA_TOK { kind = kind::LAMBDA; }
+  | CHOICE_TOK { kind = kind::CHOICE; }
+  | DEF_DESC_TOK
+    {
+      UNSUPPORTED("Description quantifier");
+    }
+  | (TH1_UN_A | TH1_UN_E)
+    {
+      UNSUPPORTED("TH1 operator");
+    }
+  ;
+
+thfAtomTyping[CVC4::Command*& cmd]
+// for now only supports mapping types (i.e. no applied types)
+@declarations {
+  CVC4::Expr expr;
+  CVC4::Type type;
+  std::string name;
+}
+  : LPAREN_TOK thfAtomTyping[cmd] RPAREN_TOK
+  | nameN[name] COLON_TOK
+    ( '$tType'
+      {
+        if (PARSER_STATE->isDeclared(name, SYM_SORT))
+        {
+          // duplicate declaration is fine, they're compatible
+          cmd = new EmptyCommand("compatible redeclaration of sort " + name);
+        }
+        else if (PARSER_STATE->isDeclared(name, SYM_VARIABLE))
+        {
+          // error: cannot be both sort and constant
+          PARSER_STATE->parseError(
+              "Symbol `" + name
+              + "' previously declared as a constant; cannot also be a sort");
+        }
+        else
+        {
+          // as yet, it's undeclared
+          Type type = PARSER_STATE->mkSort(name);
+          cmd = new DeclareTypeCommand(name, 0, type);
+        }
+      }
+    | parseThfType[type]
+      {
+        if (PARSER_STATE->isDeclared(name, SYM_SORT))
+        {
+          // error: cannot be both sort and constant
+          PARSER_STATE->parseError("Symbol `" + name
+                                   + "' previously declared as a sort");
+          cmd = new EmptyCommand("compatible redeclaration of sort " + name);
+        }
+        else if (PARSER_STATE->isDeclared(name, SYM_VARIABLE))
+        {
+          if (type == PARSER_STATE->getVariable(name).getType())
+          {
+            // duplicate declaration is fine, they're compatible
+            cmd = new EmptyCommand("compatible redeclaration of constant "
+                                   + name);
+          }
+          else
+          {
+            // error: sorts incompatible
+            PARSER_STATE->parseError(
+                "Symbol `" + name
+                + "' declared previously with a different sort");
+          }
+        }
+        else
+        {
+          // as yet, it's undeclared
+          CVC4::Expr freshExpr;
+          if (type.isFunction())
+          {
+            freshExpr = PARSER_STATE->mkFunction(name, type);
+          }
+          else
+          {
+            freshExpr = PARSER_STATE->mkVar(name, type);
+          }
+          cmd = new DeclareFunctionCommand(name, freshExpr, type);
+        }
+      }
+    )
+  ;
+
+thfLogicFormula[CVC4::Expr& expr]
+@declarations {
+  tptp::NonAssoc na;
+  std::vector< Expr > args;
+  Expr expr2;
+  bool equal;
+}
+  //prefix unary formula case
+  // ~
+  : thfUnitaryFormula[expr]
+    ( // Equality: =
+      equalOp[equal]
+      thfUnitaryFormula[expr2]
+      {
+        if (expr.getKind() == kind::BUILTIN && expr2.getKind() != kind::BUILTIN)
+        {
+          // make expr with a lambda of the same type as expr
+          PARSER_STATE->mkLambdaWrapper(expr, expr2.getType());
+        }
+        else if (expr2.getKind() == kind::BUILTIN
+                 && expr.getKind() != kind::BUILTIN)
+        {
+          // make expr2 with a lambda of the same type as expr
+          PARSER_STATE->mkLambdaWrapper(expr2, expr.getType());
+        }
+        else if (expr.getKind() == kind::BUILTIN
+                 && expr2.getKind() == kind::BUILTIN)
+        {
+          // TODO create whatever lambda
+        }
+        expr = MK_EXPR(kind::EQUAL, expr, expr2);
+        if (!equal)
+        {
+          expr = MK_EXPR(kind::NOT, expr);
+        }
+      }
+    | // Non-associative: <=> <~> ~& ~|
+      fofBinaryNonAssoc[na] thfUnitaryFormula[expr2]
+      {
+        switch(na) {
+         case tptp::NA_IFF:
+           expr = MK_EXPR(kind::EQUAL,expr,expr2);
+           break;
+         case tptp::NA_REVIFF:
+           expr = MK_EXPR(kind::XOR,expr,expr2);
+           break;
+         case tptp::NA_IMPLIES:
+           expr = MK_EXPR(kind::IMPLIES,expr,expr2);
+           break;
+         case tptp::NA_REVIMPLIES:
+           expr = MK_EXPR(kind::IMPLIES,expr2,expr);
+           break;
+         case tptp::NA_REVOR:
+           expr = MK_EXPR(kind::NOT,MK_EXPR(kind::OR,expr,expr2));
+           break;
+         case tptp::NA_REVAND:
+           expr = MK_EXPR(kind::NOT,MK_EXPR(kind::AND,expr,expr2));
+           break;
+        }
+      }
+    | // N-ary and &
+      ( { args.push_back(expr); }
+        ( AND_TOK thfUnitaryFormula[expr] { args.push_back(expr); } )+
+        {
+          expr = MK_EXPR_ASSOCIATIVE(kind::AND, args);
+        }
+      )
+    | // N-ary or |
+      ( { args.push_back(expr); }
+        ( OR_TOK thfUnitaryFormula[expr] { args.push_back(expr); } )+
+        {
+          expr = MK_EXPR_ASSOCIATIVE(kind::OR, args);
+        }
+      )
+    | // N-ary @ |
+      //
+      // @ (denoting apply) is left-associative and lambda is right-associative.
+      // ^ [X] : ^ [Y] : f @ g (where f is a <thf_apply_formula> and g is a
+      // <thf_unitary_formula>) should be parsed as: (^ [X] : (^ [Y] : f)) @ g.
+      // That is, g is not in the scope of either lambda.
+      { args.push_back(expr); }
+      ( APP_TOK
+        (
+         thfUnitaryFormula[expr] { args.push_back(expr); }
+         | LBRACK_TOK
+           { UNSUPPORTED("Tuple terms"); }
+           thfTupleForm[args]
+           RBRACK_TOK
+        )
+      )+
+      {
+        expr = args[0];
+        // also add case for total applications
+        if (expr.getKind() == kind::BUILTIN)
+        {
+          args.erase(args.begin());
+          expr = EXPR_MANAGER->mkExpr(expr, args);
+        }
+        else
+        {
+          // check if any argument is a bultin node, e.g. "~", and create a
+          // lambda wrapper then, e.g. (\lambda x. ~ x)
+          for (unsigned i = 1; i < args.size(); ++i)
+          {
+            // create a lambda wrapper, e.g. (\lambda x. ~ x)
+            if (args[i].getKind() != kind::BUILTIN)
+            {
+              continue;
+            }
+            PARSER_STATE->mkLambdaWrapper(
+                args[i],
+                (static_cast<FunctionType>(args[0].getType()))
+                    .getArgTypes()[i - 1]);
+          }
+          for (unsigned i = 1; i < args.size(); ++i)
+          {
+            expr = MK_EXPR(kind::HO_APPLY, expr, args[i]);
+          }
+        }
+      }
+    )?
+  ;
+
+thfTupleForm[std::vector<CVC4::Expr>& args]
+@declarations {
+  Expr expr;
+}
+  : thfUnitaryFormula[expr]
+   { args.push_back(expr); }
+   ( COMMA_TOK thfUnitaryFormula[expr] { args.push_back(expr); } )+
+;
+
+thfUnitaryFormula[CVC4::Expr& expr]
+@declarations {
+  Kind kind;
+  std::vector< Expr > bv;
+  Expr expr2;
+  bool equal;
+}
+  : variable[expr]
+  | thfAtomicFormula[expr]
+  | LPAREN_TOK
+    thfLogicFormula[expr]
+    RPAREN_TOK
+  | NOT_TOK
+    { expr = EXPR_MANAGER->operatorOf(CVC4::kind::NOT); }
+    (thfUnitaryFormula[expr2] { expr = MK_EXPR(expr,expr2); })?
+  | // Quantified
+    thfQuantifier[kind]
+    LBRACK_TOK {PARSER_STATE->pushScope();}
+    thfBindVariable[expr]
+    {
+      bv.push_back(expr);
+    }
+    ( COMMA_TOK thfBindVariable[expr]
+     {
+       bv.push_back(expr);
+     }
+     )*
+    RBRACK_TOK COLON_TOK
+    thfUnitaryFormula[expr]
+    {
+      PARSER_STATE->popScope();
+      // handle lambda case, in which return type must be flattened and the
+      // auxiliary variables introduced in the proccess must be added no the
+      // variable list
+      //
+      // see documentation of mkFlatFunctionType for how it's done
+      //
+      // flatten body via flattening its type
+      std::vector<Type> sorts;
+      std::vector<Expr> flattenVars;
+      PARSER_STATE->mkFlatFunctionType(sorts, expr.getType(), flattenVars);
+      if (!flattenVars.empty())
+      {
+        // apply body of lambda to flatten vars
+        expr = PARSER_STATE->mkHoApply(expr, flattenVars);
+        // add variables to BOUND_VAR_LIST
+        bv.insert(bv.end(), flattenVars.begin(), flattenVars.end());
+      }
+      expr = MK_EXPR(kind, MK_EXPR(kind::BOUND_VAR_LIST, bv), expr);
+    }
   ;
 
 /*******/
@@ -776,7 +1172,7 @@ tffLetTermDefn[CVC4::Expr& lhs, CVC4::Expr& rhs]
 @declarations {
   std::vector<CVC4::Expr> bvlist;
 }
-  : (BANG_TOK LBRACK_TOK tffVariableList[bvlist] RBRACK_TOK COLON_TOK)*
+  : (FORALL_TOK LBRACK_TOK tffVariableList[bvlist] RBRACK_TOK COLON_TOK)*
     tffLetTermBinding[bvlist, lhs, rhs]
   ;
 
@@ -793,7 +1189,7 @@ tffLetFormulaDefn[CVC4::Expr& lhs, CVC4::Expr& rhs]
 @declarations {
   std::vector<CVC4::Expr> bvlist;
 }
-  : (BANG_TOK LBRACK_TOK tffVariableList[bvlist] RBRACK_TOK COLON_TOK)*
+  : (FORALL_TOK LBRACK_TOK tffVariableList[bvlist] RBRACK_TOK COLON_TOK)*
     tffLetFormulaBinding[bvlist, lhs, rhs]
   ;
 
@@ -806,6 +1202,20 @@ tffLetFormulaBinding[std::vector<CVC4::Expr>& bvlist, CVC4::Expr& lhs, CVC4::Exp
   | LPAREN_TOK tffLetFormulaBinding[bvlist, lhs, rhs] RPAREN_TOK
   ;
 
+thfBindVariable[CVC4::Expr& expr]
+@declarations {
+  std::string name;
+  CVC4::Type type = PARSER_STATE->d_unsorted;
+}
+  : UPPER_WORD
+    { name = AntlrInput::tokenText($UPPER_WORD); }
+    ( COLON_TOK parseThfType[type] )?
+    {
+      expr = PARSER_STATE->mkBoundVar(name, type);
+    }
+  ;
+
+
 tffbindvariable[CVC4::Expr& expr]
 @declarations {
   CVC4::Type type = PARSER_STATE->d_unsorted;
@@ -827,8 +1237,39 @@ tffVariableList[std::vector<CVC4::Expr>& bvlist]
     ( COMMA_TOK tffbindvariable[e] { bvlist.push_back(e); } )*
   ;
 
-parseType[CVC4::Type& type]
+parseThfType[CVC4::Type& type]
+// assumes only mapping types (arrows), no tuple type
 @declarations {
+  std::vector<CVC4::Type> sorts;
+}
+  : thfType[type] { sorts.push_back(type); }
+    (
+     (ARROW_TOK | TIMES_TOK) thfType[type] { sorts.push_back(type); }
+    )*
+    {
+      if (sorts.size() < 1)
+      {
+        type = sorts[0];
+      }
+      else
+      {
+        Type range = sorts.back();
+        sorts.pop_back();
+        type = PARSER_STATE->mkFlatFunctionType(sorts, range);
+      }
+    }
+  ;
+
+thfType[CVC4::Type& type]
+// assumes only mapping types (arrows), no tuple type
+  : simpleType[type]
+    | LPAREN_TOK parseThfType[type] RPAREN_TOK
+    | LBRACK_TOK { UNSUPPORTED("Tuple types"); } parseThfType[type] RBRACK_TOK
+  ;
+
+parseType[CVC4::Type & type]
+@declarations
+{
   std::vector<CVC4::Type> v;
 }
   : simpleType[type]
@@ -837,7 +1278,7 @@ parseType[CVC4::Type& type]
       ( TIMES_TOK simpleType[type] { v.push_back(type); } )+
       RPAREN_TOK
     )
-    GREATER_TOK simpleType[type]
+    ARROW_TOK simpleType[type]
     { v.push_back(type);
       type = EXPR_MANAGER->mkFunctionType(v);
     }
@@ -873,8 +1314,8 @@ anything
   | COLON_TOK
   | OR_TOK
   | NOT_TOK
-  | BANG_TOK
-  | MARK_TOK
+  | FORALL_TOK
+  | EXISTS_TOK
   | AND_TOK
   | IFF_TOK
   | IMPLIES_TOK
@@ -914,23 +1355,32 @@ LBRACK_TOK : '[';
 RBRACK_TOK : ']';
 COLON_TOK  : ':';
 
-GREATER_TOK  : '>';
+// typing
+ARROW_TOK   : '>';
+SUBTYPE_TOK : '>>';
 
 //operator
-OR_TOK       : '|';
-NOT_TOK      : '~';
-BANG_TOK     : '!';
-MARK_TOK     : '?';
-AND_TOK      : '&';
-IFF_TOK      : '<=>';
+OR_TOK         : '|';
+NOT_TOK        : '~';
+FORALL_TOK     : '!';
+EXISTS_TOK     : '?';
+LAMBDA_TOK     : '^';
+CHOICE_TOK     : '@+';
+DEF_DESC_TOK   : '@-';
+AND_TOK        : '&';
+IFF_TOK        : '<=>';
 IMPLIES_TOK    : '=>';
 REVIMPLIES_TOK : '<=';
-REVIFF_TOK   : '<~>';
-REVOR_TOK    : '~|';
-REVAND_TOK   : '~&';
-TIMES_TOK    : '*';
-PLUS_TOK     : '+';
-MINUS_TOK    : '-';
+REVIFF_TOK     : '<~>';
+REVOR_TOK      : '~|';
+REVAND_TOK     : '~&';
+TIMES_TOK      : '*';
+PLUS_TOK       : '+';
+MINUS_TOK      : '-';
+APP_TOK        : '@';
+
+TH1_UN_A       : '!!';
+TH1_UN_E       : '??';
 
 //predicate
 TRUE_TOK     : '$true';
@@ -1076,4 +1526,3 @@ COMMENT
   : '%' (~('\n' | '\r'))*     { SKIP(); }     //comment line
   | '/*'  ( options {greedy=false;} : . )*  '*/' { SKIP(); } //comment block
   ;
-

diff --git a/src/parser/tptp/tptp.cpp b/src/parser/tptp/tptp.cpp
index c4efe5e09e5f9cb050b23f277a5d295d579a47a0..694369429b0936d2aab50393790a4970e0c1193e 100644 (file)
--- a/src/parser/tptp/tptp.cpp
+++ b/src/parser/tptp/tptp.cpp
@@ -121,7 +121,7 @@ bool newInputStream(std::string fileName, pANTLR3_LEXER lexer, std::vector< pANT
   // Same thing as the predefined PUSHSTREAM(in);
   lexer->pushCharStream(lexer,in);
   // restart it
-  //lexer->rec->state->tokenStartCharIndex     = -10;
+  //lexer->rec->state->tokenStartCharIndex  = -10;
   //lexer->emit(lexer);
 
   // Note that the input stream is not closed when it EOFs, I don't bother
@@ -301,6 +301,27 @@ void Tptp::makeApplication(Expr& expr, std::string& name,
   }
 }
 
+void Tptp::mkLambdaWrapper(Expr& expr, Type argType)
+{
+  std::vector<Expr> lvars;
+  std::vector<Type> domainTypes =
+      (static_cast<FunctionType>(argType)).getArgTypes();
+  for (unsigned i = 0, size = domainTypes.size(); i < size; ++i)
+  {
+    // the introduced variable is internal (not parsable)
+    std::stringstream ss;
+    ss << "_lvar_" << i;
+    Expr v = getExprManager()->mkBoundVar(ss.str(), domainTypes[i]);
+    lvars.push_back(v);
+  }
+  // apply body of lambda to variables
+  Expr wrapper = getExprManager()->mkExpr(
+      kind::LAMBDA,
+      getExprManager()->mkExpr(kind::BOUND_VAR_LIST, lvars),
+      getExprManager()->mkExpr(expr, lvars));
+
+  expr = wrapper;
+}
 
 Expr Tptp::getAssertionExpr(FormulaRole fr, Expr expr) {
   switch (fr) {

diff --git a/src/parser/tptp/tptp.h b/src/parser/tptp/tptp.h
index 605748d88021308273e5d22826e8e098b7144d97..5b3ed08074a868855c03db2c9c593d5eb8d8dae7 100644 (file)
--- a/src/parser/tptp/tptp.h
+++ b/src/parser/tptp/tptp.h
@@ -105,6 +105,14 @@ class Tptp : public Parser {
   void makeApplication(Expr& expr, std::string& name, std::vector<Expr>& args,
                        bool term);
 
+  /** creates a lambda abstraction around expression
+   *
+   * Given an expression expr of type argType = t1...tn -> t, creates a lambda
+   * expression
+   *  (lambda x1:t1,...,xn:tn . (expr x)) : t
+   */
+  void mkLambdaWrapper(Expr& expr, Type argType);
+
   /** get assertion expression, based on the formula role.
   * expr should have Boolean type.
   * This returns the expression that should be asserted, given the formula role fr.
@@ -159,7 +167,7 @@ class Tptp : public Parser {
   // TPTP directory where to find includes;
   // empty if none could be determined
   std::string d_tptpDir;
-  
+
   // the null expression
   Expr d_nullExpr;
 

diff --git a/test/regress/CMakeLists.txt b/test/regress/CMakeLists.txt
index 0ac2d4142f3334d7494ec26cf19d37560dfe0757..df278ba5a249fcddb759539bacbd35298742a03d 100644 (file)
--- a/test/regress/CMakeLists.txt
+++ b/test/regress/CMakeLists.txt
@@ -467,6 +467,7 @@ set(regress_0_tests
   regress0/get-value-reals.smt2
   regress0/ho/apply-collapse-sat.smt2
   regress0/ho/apply-collapse-unsat.smt2
+  regress0/ho/bug_nodbuilding_interpreted_SYO042^1.p
   regress0/ho/cong-full-apply.smt2
   regress0/ho/cong.smt2
   regress0/ho/declare-fun-variants.smt2
@@ -478,11 +479,17 @@ set(regress_0_tests
   regress0/ho/ext-sat.smt2
   regress0/ho/finite-fun-ext.smt2
   regress0/ho/fta0144-alpha-eq.smt2
+  regress0/ho/fta0210.smt2
+  regress0/ho/ho-exponential-model.smt2
   regress0/ho/ho-match-fun-suffix.smt2
   regress0/ho/ho-matching-enum.smt2
+  regress0/ho/ho-matching-enum-2.smt2
   regress0/ho/ho-matching-nested-app.smt2
+  regress0/ho/ho-std-fmf.smt2
+  regress0/ho/hoa0008.smt2
   regress0/ho/ite-apply-eq.smt2
   regress0/ho/lambda-equality-non-canon.smt2
+  regress0/ho/match-middle.smt2
   regress0/ho/modulo-func-equality.smt2
   regress0/ho/shadowing-defs.smt2
   regress0/ho/simple-matching-partial.smt2
@@ -1182,14 +1189,14 @@ set(regress_1_tests
   regress1/fmf/sort-inf-int.smt2
   regress1/fmf/with-ind-104-core.smt2
   regress1/gensys_brn001.smt2
-  regress1/ho/auth0068.smt2
-  regress1/ho/fta0210.smt2
-  regress1/ho/fta0409.smt2
-  regress1/ho/ho-exponential-model.smt2
-  regress1/ho/ho-matching-enum-2.smt2
-  regress1/ho/ho-std-fmf.smt2
-  regress1/ho/hoa0008.smt2
-  regress1/ho/match-middle.smt2
+  regress1/ho/fta0328.lfho.p
+  regress1/ho/nested_lambdas-AGT034^2.smt2
+  regress1/ho/nested_lambdas-sat-SYO056^1-delta.smt2
+  regress1/ho/NUM638^1.smt2
+  regress1/ho/NUM925^1.p
+  regress1/ho/soundness_fmf_SYO362^5-delta.p
+  regress1/ho/store-ax-min.p
+  regress1/ho/SYO056^1.p
   regress1/hole6.cvc
   regress1/ite5.smt2
   regress1/lemmas/clocksynchro_5clocks.main_invar.base.smt
@@ -1766,6 +1773,12 @@ set(regress_2_tests
   regress2/hash_sat_07_17.smt2
   regress2/hash_sat_09_09.smt2
   regress2/hash_sat_10_09.smt2
+  regress2/ho/auth0068.smt2
+  regress2/ho/bug_instfalse_SEU882^5.p
+  regress2/ho/fta0409.smt2
+  regress2/ho/involved_parsing_ALG248^3.p
+  regress2/ho/partial_app_interpreted_SWW474^2.p
+  regress2/ho/SYO362^5.p
   regress2/hole7.cvc
   regress2/hole8.cvc
   regress2/instance_1444.smt

diff --git a/test/regress/regress0/ho/bug_nodbuilding_interpreted_SYO042^1.p b/test/regress/regress0/ho/bug_nodbuilding_interpreted_SYO042^1.p
new file mode 100644 (file)
index 0000000..0ed7fe4
--- /dev/null
+++ b/test/regress/regress0/ho/bug_nodbuilding_interpreted_SYO042^1.p
@@ -0,0 +1,56 @@
+% COMMAND-LINE:  --uf-ho
+% EXPECT: % SZS status Unsatisfiable for bug_nodbuilding_interpreted_SYO042^1
+
+%------------------------------------------------------------------------------
+% File     : SYO042^1 : TPTP v7.2.0. Released v4.0.0.
+% Domain   : Syntactic
+% Problem  : Unsatisfiable basic formula 4
+% Version  : Especial.
+% English  :
+
+% Refs     : [BS09a] Brown E. & Smolka (2009), Terminating Tableaux for the
+%          : [BS09b] Brown E. & Smolka (2009), Extended First-Order Logic
+% Source   : [BS09a]
+% Names    :
+
+% Status   : Unsatisfiable
+% Rating   : 0.00 v5.4.0, 0.33 v5.3.0, 0.67 v5.0.0, 0.33 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
+% Syntax   : Number of formulae    :    5 (   0 unit;   4 type;   0 defn)
+%            Number of atoms       :   15 (   3 equality;   0 variable)
+%            Maximal formula depth :    7 (   4 average)
+%            Number of connectives :   10 (   2   ~;   0   |;   4   &;   4   @)
+%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
+%                                         (   0  ~|;   0  ~&)
+%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
+%            Number of symbols     :    6 (   4   :;   0   =)
+%            Number of variables   :    0 (   0 sgn;   0   !;   0   ?;   0   ^)
+%                                         (   0   :;   0  !>;   0  ?*)
+%                                         (   0  @-;   0  @+)
+% SPC      : TH0_UNS_EQU_NAR
+
+% Comments : The fragment of simple type theory that restricts equations to
+%            base types and disallows lambda abstraction and quantification is
+%            decidable. This is an example.
+%------------------------------------------------------------------------------
+thf(g,type,(
+    g: $o > $o )).
+
+thf(p,type,(
+    p: ( $o > $o ) > $o )).
+
+thf(x,type,(
+    x: $o )).
+
+thf(y,type,(
+    y: $o )).
+
+thf(4,axiom,
+    ( ( x != y )
+    & ( ( g @ x )
+      = y )
+    & ( ( g @ y )
+      = x )
+    & ( p @ g )
+    & ~ ( p @ (~) ) )).
+
+%------------------------------------------------------------------------------

diff --git a/test/regress/regress0/ho/fta0210.smt2 b/test/regress/regress0/ho/fta0210.smt2
new file mode 100644 (file)
index 0000000..9f0a39f
--- /dev/null
+++ b/test/regress/regress0/ho/fta0210.smt2
@@ -0,0 +1,64 @@
+; COMMAND-LINE: --uf-ho
+; EXPECT: unsat
+(set-logic ALL)
+(declare-sort A$ 0)
+(declare-sort Nat$ 0)
+(declare-sort A_poly$ 0)
+(declare-sort Nat_poly$ 0)
+(declare-sort A_poly_poly$ 0)
+(declare-fun p$ () A_poly$)
+(declare-fun uu$ (A_poly$ (-> A_poly$ A_poly$) A_poly$) A_poly$)
+(declare-fun one$ () Nat$)
+(declare-fun suc$ (Nat$) Nat$)
+(declare-fun uua$ (A_poly$) A_poly$)
+(declare-fun uub$ (A$ (-> A$ A$) A$) A$)
+(declare-fun uuc$ (A$) A$)
+(declare-fun uud$ (Nat$ (-> Nat$ Nat$) Nat$) Nat$)
+(declare-fun uue$ (Nat$) Nat$)
+(declare-fun one$a () Nat_poly$)
+(declare-fun one$b () A$)
+(declare-fun one$c () A_poly$)
+(declare-fun plus$ (A_poly$ A_poly$) A_poly$)
+(declare-fun poly$ (A_poly$ A$) A$)
+(declare-fun zero$ () A_poly$)
+(declare-fun pCons$ (A$ A_poly$) A_poly$)
+(declare-fun plus$a (Nat$ Nat$) Nat$)
+(declare-fun plus$b (A$ A$) A$)
+(declare-fun plus$c (Nat_poly$ Nat_poly$) Nat_poly$)
+(declare-fun poly$a (Nat_poly$ Nat$) Nat$)
+(declare-fun poly$b (A_poly_poly$ A_poly$) A_poly$)
+(declare-fun power$ (A$ Nat$) A$)
+(declare-fun psize$ (A_poly$) Nat$)
+(declare-fun times$ (A_poly$ A_poly$) A_poly$)
+(declare-fun zero$a () Nat$)
+(declare-fun zero$b () A$)
+(declare-fun zero$c () Nat_poly$)
+(declare-fun zero$d () A_poly_poly$)
+(declare-fun pCons$a (Nat$ Nat_poly$) Nat_poly$)
+(declare-fun pCons$b (A_poly$ A_poly_poly$) A_poly_poly$)
+(declare-fun power$a (A_poly$ Nat$) A_poly$)
+(declare-fun power$b (Nat_poly$ Nat$) Nat_poly$)
+(declare-fun power$c (Nat$ Nat$) Nat$)
+(declare-fun psize$a (A_poly_poly$) Nat$)
+(declare-fun times$a (Nat$ Nat$) Nat$)
+(declare-fun times$b (A$ A$) A$)
+(declare-fun times$c (Nat_poly$ Nat_poly$) Nat_poly$)
+(declare-fun times$d (A_poly_poly$ A_poly_poly$) A_poly_poly$)
+(declare-fun uminus$ (A_poly$) A_poly$)
+(declare-fun uminus$a (A$) A$)
+(declare-fun constant$ ((-> A$ A$)) Bool)
+(declare-fun pcompose$ (A_poly$ A_poly$) A_poly$)
+(declare-fun pcompose$a (Nat_poly$ Nat_poly$) Nat_poly$)
+(declare-fun pcompose$b (A_poly_poly$ A_poly_poly$) A_poly_poly$)
+(declare-fun poly_shift$ (Nat$ A_poly$) A_poly$)
+(declare-fun fold_coeffs$ ((-> A_poly$ (-> (-> A_poly$ A_poly$) (-> A_poly$ A_poly$))) A_poly_poly$ (-> A_poly$ A_poly$)) (-> A_poly$ A_poly$))
+(declare-fun poly_cutoff$ (Nat$ A_poly$) A_poly$)
+(declare-fun fold_coeffs$a ((-> A$ (-> (-> A$ A$) (-> A$ A$))) A_poly$ (-> A$ A$)) (-> A$ A$))
+(declare-fun fold_coeffs$b ((-> Nat$ (-> (-> Nat$ Nat$) (-> Nat$ Nat$))) Nat_poly$ (-> Nat$ Nat$)) (-> Nat$ Nat$))
+
+(assert (! (forall ((?v0 A$)) (= (poly$ zero$ ?v0) zero$b)) :named a14))
+(assert (! (forall ((?v0 (-> A$ A$))) (= (constant$ ?v0) (forall ((?v1 A$) (?v2 A$)) (= (?v0 ?v1) (?v0 ?v2))))) :named a69))
+(assert (! (not (constant$ (poly$ zero$))) :named a206))
+
+(check-sat)
+;(get-proof)

diff --git a/test/regress/regress0/ho/ho-exponential-model.smt2 b/test/regress/regress0/ho/ho-exponential-model.smt2
new file mode 100644 (file)
index 0000000..3f00118
--- /dev/null
+++ b/test/regress/regress0/ho/ho-exponential-model.smt2
@@ -0,0 +1,40 @@
+; COMMAND-LINE: --uf-ho
+; EXPECT: sat
+(set-logic UFLIA)
+(set-info :status sat)
+(declare-fun f1 (Int Int Int Int) Int)
+(declare-fun f2 (Int Int Int) Int)
+(declare-fun f3 (Int Int) Int)
+(declare-fun f4 (Int) Int)
+(declare-fun f5 (Int Int Int) Int)
+(declare-fun f6 (Int Int) Int)
+(declare-fun f7 (Int) Int)
+
+
+(assert (= (f1 0) (f1 1)))
+(assert (= (f1 1) f2))
+
+(assert (= (f2 0) (f2 1)))
+(assert (= (f2 1) f3))
+
+(assert (= (f3 0) (f3 1)))
+(assert (= (f3 1) f4))
+
+(assert (= (f4 0) (f4 1)))
+(assert (= (f4 1) 2))
+
+
+(assert (= (f1 3) (f1 4)))
+(assert (= (f1 4) f5))
+
+(assert (= (f5 3) (f5 4)))
+(assert (= (f5 4) f6))
+
+(assert (= (f6 3) (f6 4)))
+(assert (= (f6 4) f7))
+
+(assert (= (f7 3) (f7 4)))
+(assert (= (f7 4) 5))
+
+; this benchmark has a concise model representation for f1 if we use curried (tree-like) models for UF
+(check-sat)

diff --git a/test/regress/regress0/ho/ho-matching-enum-2.smt2 b/test/regress/regress0/ho/ho-matching-enum-2.smt2
new file mode 100644 (file)
index 0000000..9581e4c
--- /dev/null
+++ b/test/regress/regress0/ho/ho-matching-enum-2.smt2
@@ -0,0 +1,18 @@
+; COMMAND-LINE: --uf-ho
+; EXPECT: unsat
+(set-logic ALL)
+(set-info :status unsat)
+
+(declare-sort U 0)
+
+(declare-fun p (Int) Bool)
+(declare-fun q (Int) Bool)
+(declare-fun k (Int Int) Int)
+
+(assert (q (k 0 1)))
+(assert (not (p (k 0 0))))
+
+(assert (forall ((f (-> Int Int Int)) (y Int) (z Int)) (or (p (f y z)) (not (q (f z y))))))
+
+(check-sat)
+(exit)

diff --git a/test/regress/regress0/ho/ho-std-fmf.smt2 b/test/regress/regress0/ho/ho-std-fmf.smt2
new file mode 100644 (file)
index 0000000..61d82d0
--- /dev/null
+++ b/test/regress/regress0/ho/ho-std-fmf.smt2
@@ -0,0 +1,18 @@
+; COMMAND-LINE: --uf-ho --finite-model-find
+; EXPECT: sat
+(set-logic UF)
+(set-info :status sat)
+(declare-sort U 0)
+(declare-fun P (U U) Bool)
+(declare-fun Q (U U) Bool)
+(declare-fun R (U U) Bool)
+(declare-fun a () U)
+(declare-fun b () U)
+
+; can solve this using standard MBQI model for P = \ xy true
+(assert (forall ((x U) (y U)) (or (P x y) (Q x y))))
+(assert (forall ((x U) (y U)) (or (P x y) (R x y))))
+
+(assert (not (= a b)))
+(assert (= (Q a) (R b)))
+(check-sat)

diff --git a/test/regress/regress0/ho/hoa0008.smt2 b/test/regress/regress0/ho/hoa0008.smt2
new file mode 100644 (file)
index 0000000..f4833aa
--- /dev/null
+++ b/test/regress/regress0/ho/hoa0008.smt2
@@ -0,0 +1,68 @@
+; COMMAND-LINE: --uf-ho
+; EXPECT: unsat
+(set-logic ALL)
+(declare-sort A$ 0)
+(declare-sort Com$ 0)
+(declare-sort Loc$ 0)
+(declare-sort Nat$ 0)
+(declare-sort Pname$ 0)
+(declare-sort State$ 0)
+(declare-sort Vname$ 0)
+(declare-sort Literal$ 0)
+(declare-sort Natural$ 0)
+(declare-sort Typerep$ 0)
+(declare-sort A_triple$ 0)
+(declare-sort Com_option$ 0)
+(declare-fun p$ () (-> A$ (-> State$ Bool)))
+(declare-fun q$ () (-> A$ (-> State$ Bool)))
+(declare-fun pn$ () Pname$)
+(declare-fun wt$ (Com$) Bool)
+(declare-fun ass$ (Vname$ (-> State$ Nat$)) Com$)
+(declare-fun suc$ (Nat$) Nat$)
+(declare-fun the$ (Com_option$) Com$)
+(declare-fun body$ (Pname$) Com$)
+(declare-fun call$ (Vname$ Pname$ (-> State$ Nat$)) Com$)
+(declare-fun cond$ ((-> State$ Bool) Com$ Com$) Com$)
+(declare-fun none$ () Com_option$)
+(declare-fun plus$ (Nat$ Nat$) Nat$)
+(declare-fun semi$ (Com$ Com$) Com$)
+(declare-fun size$ (A_triple$) Nat$)
+(declare-fun skip$ () Com$)
+(declare-fun some$ (Com$) Com_option$)
+(declare-fun suc$a (Natural$) Natural$)
+(declare-fun zero$ () Nat$)
+(declare-fun body$a (Pname$) Com_option$)
+(declare-fun evalc$ (Com$ State$ State$) Bool)
+(declare-fun evaln$ (Com$ State$ Nat$ State$) Bool)
+(declare-fun local$ (Loc$ (-> State$ Nat$) Com$) Com$)
+(declare-fun plus$a (Natural$ Natural$) Natural$)
+(declare-fun size$a (Com$) Nat$)
+(declare-fun size$b (Natural$) Nat$)
+(declare-fun size$c (Bool) Nat$)
+(declare-fun size$d (Com_option$) Nat$)
+(declare-fun size$e (Typerep$) Nat$)
+(declare-fun size$f (Literal$) Nat$)
+(declare-fun while$ ((-> State$ Bool) Com$) Com$)
+(declare-fun zero$a () Natural$)
+(declare-fun triple$ ((-> A$ (-> State$ Bool)) Com$ (-> A$ (-> State$ Bool))) A_triple$)
+(declare-fun rec_bool$ (Nat$ Nat$) (-> Bool Nat$))
+(declare-fun size_com$ (Com$) Nat$)
+(declare-fun size_bool$ (Bool) Nat$)
+(declare-fun wT_bodies$ () Bool)
+(declare-fun size_option$ ((-> Com$ Nat$)) (-> Com_option$ Nat$))
+(declare-fun size_triple$ ((-> A$ Nat$) A_triple$) Nat$)
+(declare-fun size_natural$ (Natural$) Nat$)
+(declare-fun triple_valid$ (Nat$ A_triple$) Bool)
+(assert (! (not (triple_valid$ zero$ (triple$ p$ (body$ pn$) q$))) :named a0))
+
+(assert (! (forall ((?v0 Nat$) (?v1 (-> A$ (-> State$ Bool))) (?v2 Com$) (?v3 (-> A$ (-> State$ Bool)))) (= (triple_valid$ ?v0 (triple$ ?v1 ?v2 ?v3)) (forall ((?v4 A$) (?v5 State$)) (=> (?v1 ?v4 ?v5) (forall ((?v6 State$)) (=> (evaln$ ?v2 ?v5 ?v0 ?v6) (?v3 ?v4 ?v6))))))) :named a6))
+
+(assert (! (= (size_bool$ true) zero$) :named a13))
+(assert (! (= size_bool$ (rec_bool$ zero$ zero$)) :named a14))
+
+(assert (! (forall ((?v0 Nat$)) (not (= zero$ (suc$ ?v0)))) :named a37))
+
+(assert (! (forall ((?v0 Pname$) (?v1 State$) (?v2 Nat$) (?v3 State$)) (=> (and (evaln$ (body$ ?v0) ?v1 ?v2 ?v3) (forall ((?v4 Nat$)) (=> (and (= ?v2 (suc$ ?v4)) (evaln$ (the$ (body$a ?v0)) ?v1 ?v4 ?v3)) false))) false)) :named a204))
+
+(check-sat)
+;(get-proof)

diff --git a/test/regress/regress0/ho/match-middle.smt2 b/test/regress/regress0/ho/match-middle.smt2
new file mode 100644 (file)
index 0000000..0485f9a
--- /dev/null
+++ b/test/regress/regress0/ho/match-middle.smt2
@@ -0,0 +1,20 @@
+; COMMAND-LINE: --uf-ho
+; EXPECT: unsat
+(set-logic UFLIA)
+(set-info :status unsat)
+(declare-fun f (Int Int Int) Int)
+(declare-fun h (Int Int Int) Int)
+(declare-fun g (Int Int) Int)
+(declare-fun a () Int)
+(declare-fun b () Int)
+(declare-fun c () Int)
+(declare-fun d () Int)
+
+(assert (or (= (f a) g) (= (h a) g)))
+
+(assert (= (f a b d) c))
+(assert (= (h a b d) c))
+
+(assert (forall ((x Int) (y Int)) (not (= (g x y) c))))
+
+(check-sat)

diff --git a/test/regress/regress1/ho/NUM638^1.smt2 b/test/regress/regress1/ho/NUM638^1.smt2
new file mode 100644 (file)
index 0000000..bee17b2
--- /dev/null
+++ b/test/regress/regress1/ho/NUM638^1.smt2
@@ -0,0 +1,17 @@
+; COMMAND-LINE: --uf-ho --finite-model-find
+; EXPECT: unsat
+
+(set-option :incremental false)
+(set-logic ALL)
+(declare-sort $$unsorted 0)
+(declare-sort nat 0)
+(declare-fun x () nat)
+(declare-fun n_1 () nat)
+(assert (not (= x n_1)))
+(declare-fun suc (nat) nat)
+(declare-fun some ((-> nat Bool)) Bool)
+(assert (forall ((Xx nat) (Xy nat)) (=> (= (suc Xx) (suc Xy)) (= Xx Xy)) ))
+(assert (forall ((Xx nat)) (=> (not (= Xx n_1)) (some (lambda ((Xu nat)) (= Xx (suc Xu))))) ))
+(assert (not (not (=> (forall ((Xx_0 nat) (Xy nat)) (=> (= x (suc Xx_0)) (=> (= x (suc Xy)) (= Xx_0 Xy))) ) (not (some (lambda ((Xu nat)) (= x (suc Xu)))))))))
+(meta-info :filename "NUM638^1")
+(check-sat-assuming ( (not false) ))

diff --git a/test/regress/regress1/ho/NUM925^1.p b/test/regress/regress1/ho/NUM925^1.p
new file mode 100644 (file)
index 0000000..d2977dd
--- /dev/null
+++ b/test/regress/regress1/ho/NUM925^1.p
@@ -0,0 +1,638 @@
+% COMMAND-LINE:  --uf-ho
+% EXPECT: % SZS status Theorem for NUM925^1
+
+%------------------------------------------------------------------------------
+% File     : NUM925^1 : TPTP v7.2.0. Released v5.3.0.
+% Domain   : Number Theory
+% Problem  : Sum of two squares line 192, 100 axioms selected
+% Version  : Especial.
+% English  :
+
+% Refs     : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
+%          : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
+% Source   : [Bla11]
+% Names    : s2s_100_thf_l192 [Bla11]
+
+% Status   : Theorem
+% Rating   : 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0
+% Syntax   : Number of formulae    :  128 (   0 unit;  21 type;   0 defn)
+%            Number of atoms       :  868 ( 105 equality; 251 variable)
+%            Maximal formula depth :   11 (   5 average)
+%            Number of connectives :  571 (  20   ~;   4   |;   7   &; 495   @)
+%                                         (  36 <=>;   9  =>;   0  <=;   0 <~>)
+%                                         (   0  ~|;   0  ~&)
+%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
+%            Number of symbols     :   23 (  21   :;   0   =)
+%            Number of variables   :  118 (   0 sgn; 118   !;   0   ?;   0   ^)
+%                                         ( 118   :;   0  !>;   0  ?*)
+%                                         (   0  @-;   0  @+)
+% SPC      : TH0_THM_EQU_NAR
+
+% Comments : This file was generated by Isabelle (most likely Sledgehammer)
+%            2011-08-09 19:10:38
+%------------------------------------------------------------------------------
+%----Should-be-implicit typings (2)
+thf(ty_ty_tc__Int__Oint,type,(
+    int: $tType )).
+
+thf(ty_ty_tc__Nat__Onat,type,(
+    nat: $tType )).
+
+%----Explicit typings (19)
+thf(sy_c_Groups_Oone__class_Oone_000tc__Int__Oint,type,(
+    one_one_int: int )).
+
+thf(sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat,type,(
+    one_one_nat: nat )).
+
+thf(sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint,type,(
+    plus_plus_int: int > int > int )).
+
+thf(sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat,type,(
+    plus_plus_nat: nat > nat > nat )).
+
+thf(sy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint,type,(
+    zero_zero_int: int )).
+
+thf(sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat,type,(
+    zero_zero_nat: nat )).
+
+thf(sy_c_Int_OBit0,type,(
+    bit0: int > int )).
+
+thf(sy_c_Int_OBit1,type,(
+    bit1: int > int )).
+
+thf(sy_c_Int_OPls,type,(
+    pls: int )).
+
+thf(sy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint,type,(
+    number_number_of_int: int > int )).
+
+thf(sy_c_Int_Onumber__class_Onumber__of_000tc__Nat__Onat,type,(
+    number_number_of_nat: int > nat )).
+
+thf(sy_c_Nat_Osemiring__1__class_Oof__nat_000tc__Int__Oint,type,(
+    semiri1621563631at_int: nat > int )).
+
+thf(sy_c_Nat_Osemiring__1__class_Oof__nat_000tc__Nat__Onat,type,(
+    semiri984289939at_nat: nat > nat )).
+
+thf(sy_c_Orderings_Oord__class_Oless_000tc__Int__Oint,type,(
+    ord_less_int: int > int > $o )).
+
+thf(sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat,type,(
+    ord_less_nat: nat > nat > $o )).
+
+thf(sy_c_Power_Opower__class_Opower_000tc__Int__Oint,type,(
+    power_power_int: int > nat > int )).
+
+thf(sy_c_Power_Opower__class_Opower_000tc__Nat__Onat,type,(
+    power_power_nat: nat > nat > nat )).
+
+thf(sy_v_n____,type,(
+    n: nat )).
+
+thf(sy_v_t____,type,(
+    t: int )).
+
+%----Relevant facts (106)
+thf(fact_0_n1pos,axiom,
+    ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) )).
+
+thf(fact_1_t1,axiom,
+    ( ord_less_int @ one_one_int @ t )).
+
+thf(fact_2_sum__power2__eq__zero__iff,axiom,(
+    ! [X_3: int,Y_3: int] :
+      ( ( ( plus_plus_int @ ( power_power_int @ X_3 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_3 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
+        = zero_zero_int )
+    <=> ( ( X_3 = zero_zero_int )
+        & ( Y_3 = zero_zero_int ) ) ) )).
+
+thf(fact_3_one__power2,axiom,
+    ( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
+    = one_one_int )).
+
+thf(fact_4_one__power2,axiom,
+    ( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
+    = one_one_nat )).
+
+thf(fact_5_zero__power2,axiom,
+    ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
+    = zero_zero_int )).
+
+thf(fact_6_zero__power2,axiom,
+    ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
+    = zero_zero_nat )).
+
+thf(fact_7_zero__eq__power2,axiom,(
+    ! [A_7: int] :
+      ( ( ( power_power_int @ A_7 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
+        = zero_zero_int )
+    <=> ( A_7 = zero_zero_int ) ) )).
+
+thf(fact_8_add__special_I2_J,axiom,(
+    ! [W_7: int] :
+      ( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ W_7 ) )
+      = ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ W_7 ) ) ) )).
+
+thf(fact_9_add__special_I3_J,axiom,(
+    ! [V_5: int] :
+      ( ( plus_plus_int @ ( number_number_of_int @ V_5 ) @ one_one_int )
+      = ( number_number_of_int @ ( plus_plus_int @ V_5 @ ( bit1 @ pls ) ) ) ) )).
+
+thf(fact_10_one__add__one__is__two,axiom,
+    ( ( plus_plus_int @ one_one_int @ one_one_int )
+    = ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )).
+
+thf(fact_11_semiring__one__add__one__is__two,axiom,
+    ( ( plus_plus_int @ one_one_int @ one_one_int )
+    = ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )).
+
+thf(fact_12_semiring__one__add__one__is__two,axiom,
+    ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
+    = ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )).
+
+thf(fact_13_quartic__square__square,axiom,(
+    ! [X_3: int] :
+      ( ( power_power_int @ ( power_power_int @ X_3 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
+      = ( power_power_int @ X_3 @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )).
+
+thf(fact_14_power__0__left__number__of,axiom,(
+    ! [W_6: int] :
+      ( ( ( ( number_number_of_nat @ W_6 )
+          = zero_zero_nat )
+       => ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_6 ) )
+          = one_one_int ) )
+      & ( ( ( number_number_of_nat @ W_6 )
+         != zero_zero_nat )
+       => ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_6 ) )
+          = zero_zero_int ) ) ) )).
+
+thf(fact_15_power__0__left__number__of,axiom,(
+    ! [W_6: int] :
+      ( ( ( ( number_number_of_nat @ W_6 )
+          = zero_zero_nat )
+       => ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_6 ) )
+          = one_one_nat ) )
+      & ( ( ( number_number_of_nat @ W_6 )
+         != zero_zero_nat )
+       => ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_6 ) )
+          = zero_zero_nat ) ) ) )).
+
+thf(fact_16_semiring__norm_I110_J,axiom,
+    ( one_one_int
+    = ( number_number_of_int @ ( bit1 @ pls ) ) )).
+
+thf(fact_17_numeral__1__eq__1,axiom,
+    ( ( number_number_of_int @ ( bit1 @ pls ) )
+    = one_one_int )).
+
+thf(fact_18_n0,axiom,
+    ( ord_less_nat @ zero_zero_nat @ n )).
+
+thf(fact_19_zless__linear,axiom,(
+    ! [X_3: int,Y_3: int] :
+      ( ( ord_less_int @ X_3 @ Y_3 )
+      | ( X_3 = Y_3 )
+      | ( ord_less_int @ Y_3 @ X_3 ) ) )).
+
+thf(fact_20_less__number__of__int__code,axiom,(
+    ! [K: int,L: int] :
+      ( ( ord_less_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
+    <=> ( ord_less_int @ K @ L ) ) )).
+
+thf(fact_21_plus__numeral__code_I9_J,axiom,(
+    ! [V_3: int,W_4: int] :
+      ( ( plus_plus_int @ ( number_number_of_int @ V_3 ) @ ( number_number_of_int @ W_4 ) )
+      = ( number_number_of_int @ ( plus_plus_int @ V_3 @ W_4 ) ) ) )).
+
+thf(fact_22_less__number__of,axiom,(
+    ! [X_6: int,Y_5: int] :
+      ( ( ord_less_int @ ( number_number_of_int @ X_6 ) @ ( number_number_of_int @ Y_5 ) )
+    <=> ( ord_less_int @ X_6 @ Y_5 ) ) )).
+
+thf(fact_23_zero__is__num__zero,axiom,
+    ( zero_zero_int
+    = ( number_number_of_int @ pls ) )).
+
+thf(fact_24_zpower__int,axiom,(
+    ! [M: nat,N_1: nat] :
+      ( ( power_power_int @ ( semiri1621563631at_int @ M ) @ N_1 )
+      = ( semiri1621563631at_int @ ( power_power_nat @ M @ N_1 ) ) ) )).
+
+thf(fact_25_int__power,axiom,(
+    ! [M: nat,N_1: nat] :
+      ( ( semiri1621563631at_int @ ( power_power_nat @ M @ N_1 ) )
+      = ( power_power_int @ ( semiri1621563631at_int @ M ) @ N_1 ) ) )).
+
+thf(fact_26_zadd__int__left,axiom,(
+    ! [M: nat,N_1: nat,Z: int] :
+      ( ( plus_plus_int @ ( semiri1621563631at_int @ M ) @ ( plus_plus_int @ ( semiri1621563631at_int @ N_1 ) @ Z ) )
+      = ( plus_plus_int @ ( semiri1621563631at_int @ ( plus_plus_nat @ M @ N_1 ) ) @ Z ) ) )).
+
+thf(fact_27_zadd__int,axiom,(
+    ! [M: nat,N_1: nat] :
+      ( ( plus_plus_int @ ( semiri1621563631at_int @ M ) @ ( semiri1621563631at_int @ N_1 ) )
+      = ( semiri1621563631at_int @ ( plus_plus_nat @ M @ N_1 ) ) ) )).
+
+thf(fact_28_int__1,axiom,
+    ( ( semiri1621563631at_int @ one_one_nat )
+    = one_one_int )).
+
+thf(fact_29_nat__number__of__Pls,axiom,
+    ( ( number_number_of_nat @ pls )
+    = zero_zero_nat )).
+
+thf(fact_30_semiring__norm_I113_J,axiom,
+    ( zero_zero_nat
+    = ( number_number_of_nat @ pls ) )).
+
+thf(fact_31_int__eq__0__conv,axiom,(
+    ! [N_1: nat] :
+      ( ( ( semiri1621563631at_int @ N_1 )
+        = zero_zero_int )
+    <=> ( N_1 = zero_zero_nat ) ) )).
+
+thf(fact_32_int__0,axiom,
+    ( ( semiri1621563631at_int @ zero_zero_nat )
+    = zero_zero_int )).
+
+thf(fact_33_nat__1__add__1,axiom,
+    ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
+    = ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )).
+
+thf(fact_34_less__int__code_I16_J,axiom,(
+    ! [K1: int,K2: int] :
+      ( ( ord_less_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
+    <=> ( ord_less_int @ K1 @ K2 ) ) )).
+
+thf(fact_35_rel__simps_I17_J,axiom,(
+    ! [K: int,L: int] :
+      ( ( ord_less_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
+    <=> ( ord_less_int @ K @ L ) ) )).
+
+thf(fact_36_rel__simps_I2_J,axiom,(
+    ~ ( ord_less_int @ pls @ pls ) )).
+
+thf(fact_37_less__int__code_I13_J,axiom,(
+    ! [K1: int,K2: int] :
+      ( ( ord_less_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
+    <=> ( ord_less_int @ K1 @ K2 ) ) )).
+
+thf(fact_38_rel__simps_I14_J,axiom,(
+    ! [K: int,L: int] :
+      ( ( ord_less_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
+    <=> ( ord_less_int @ K @ L ) ) )).
+
+thf(fact_39_zadd__strict__right__mono,axiom,(
+    ! [K: int,I: int,J: int] :
+      ( ( ord_less_int @ I @ J )
+     => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ K ) ) ) )).
+
+thf(fact_40_add__nat__number__of,axiom,(
+    ! [V_4: int,V_3: int] :
+      ( ( ( ord_less_int @ V_3 @ pls )
+       => ( ( plus_plus_nat @ ( number_number_of_nat @ V_3 ) @ ( number_number_of_nat @ V_4 ) )
+          = ( number_number_of_nat @ V_4 ) ) )
+      & ( ~ ( ord_less_int @ V_3 @ pls )
+       => ( ( ( ord_less_int @ V_4 @ pls )
+           => ( ( plus_plus_nat @ ( number_number_of_nat @ V_3 ) @ ( number_number_of_nat @ V_4 ) )
+              = ( number_number_of_nat @ V_3 ) ) )
+          & ( ~ ( ord_less_int @ V_4 @ pls )
+           => ( ( plus_plus_nat @ ( number_number_of_nat @ V_3 ) @ ( number_number_of_nat @ V_4 ) )
+              = ( number_number_of_nat @ ( plus_plus_int @ V_3 @ V_4 ) ) ) ) ) ) ) )).
+
+thf(fact_41_one__is__num__one,axiom,
+    ( one_one_int
+    = ( number_number_of_int @ ( bit1 @ pls ) ) )).
+
+thf(fact_42_nat__numeral__1__eq__1,axiom,
+    ( ( number_number_of_nat @ ( bit1 @ pls ) )
+    = one_one_nat )).
+
+thf(fact_43_Numeral1__eq1__nat,axiom,
+    ( one_one_nat
+    = ( number_number_of_nat @ ( bit1 @ pls ) ) )).
+
+thf(fact_44_eq__number__of,axiom,(
+    ! [X_5: int,Y_4: int] :
+      ( ( ( number_number_of_int @ X_5 )
+        = ( number_number_of_int @ Y_4 ) )
+    <=> ( X_5 = Y_4 ) ) )).
+
+thf(fact_45_number__of__reorient,axiom,(
+    ! [W_5: int,X_4: nat] :
+      ( ( ( number_number_of_nat @ W_5 )
+        = X_4 )
+    <=> ( X_4
+        = ( number_number_of_nat @ W_5 ) ) ) )).
+
+thf(fact_46_number__of__reorient,axiom,(
+    ! [W_5: int,X_4: int] :
+      ( ( ( number_number_of_int @ W_5 )
+        = X_4 )
+    <=> ( X_4
+        = ( number_number_of_int @ W_5 ) ) ) )).
+
+thf(fact_47_rel__simps_I51_J,axiom,(
+    ! [K: int,L: int] :
+      ( ( ( bit1 @ K )
+        = ( bit1 @ L ) )
+    <=> ( K = L ) ) )).
+
+thf(fact_48_rel__simps_I48_J,axiom,(
+    ! [K: int,L: int] :
+      ( ( ( bit0 @ K )
+        = ( bit0 @ L ) )
+    <=> ( K = L ) ) )).
+
+thf(fact_49_even__less__0__iff,axiom,(
+    ! [A_6: int] :
+      ( ( ord_less_int @ ( plus_plus_int @ A_6 @ A_6 ) @ zero_zero_int )
+    <=> ( ord_less_int @ A_6 @ zero_zero_int ) ) )).
+
+thf(fact_50_zadd__assoc,axiom,(
+    ! [Z1: int,Z2: int,Z3: int] :
+      ( ( plus_plus_int @ ( plus_plus_int @ Z1 @ Z2 ) @ Z3 )
+      = ( plus_plus_int @ Z1 @ ( plus_plus_int @ Z2 @ Z3 ) ) ) )).
+
+thf(fact_51_zadd__left__commute,axiom,(
+    ! [X_3: int,Y_3: int,Z: int] :
+      ( ( plus_plus_int @ X_3 @ ( plus_plus_int @ Y_3 @ Z ) )
+      = ( plus_plus_int @ Y_3 @ ( plus_plus_int @ X_3 @ Z ) ) ) )).
+
+thf(fact_52_zadd__commute,axiom,(
+    ! [Z: int,W_4: int] :
+      ( ( plus_plus_int @ Z @ W_4 )
+      = ( plus_plus_int @ W_4 @ Z ) ) )).
+
+thf(fact_53_int__int__eq,axiom,(
+    ! [M: nat,N_1: nat] :
+      ( ( ( semiri1621563631at_int @ M )
+        = ( semiri1621563631at_int @ N_1 ) )
+    <=> ( M = N_1 ) ) )).
+
+thf(fact_54_less__special_I3_J,axiom,(
+    ! [X_2: int] :
+      ( ( ord_less_int @ ( number_number_of_int @ X_2 ) @ zero_zero_int )
+    <=> ( ord_less_int @ X_2 @ pls ) ) )).
+
+thf(fact_55_less__special_I1_J,axiom,(
+    ! [Y_2: int] :
+      ( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ Y_2 ) )
+    <=> ( ord_less_int @ pls @ Y_2 ) ) )).
+
+thf(fact_56_rel__simps_I12_J,axiom,(
+    ! [K: int] :
+      ( ( ord_less_int @ ( bit1 @ K ) @ pls )
+    <=> ( ord_less_int @ K @ pls ) ) )).
+
+thf(fact_57_less__int__code_I15_J,axiom,(
+    ! [K1: int,K2: int] :
+      ( ( ord_less_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
+    <=> ( ord_less_int @ K1 @ K2 ) ) )).
+
+thf(fact_58_rel__simps_I16_J,axiom,(
+    ! [K: int,L: int] :
+      ( ( ord_less_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
+    <=> ( ord_less_int @ K @ L ) ) )).
+
+thf(fact_59_rel__simps_I10_J,axiom,(
+    ! [K: int] :
+      ( ( ord_less_int @ ( bit0 @ K ) @ pls )
+    <=> ( ord_less_int @ K @ pls ) ) )).
+
+thf(fact_60_rel__simps_I4_J,axiom,(
+    ! [K: int] :
+      ( ( ord_less_int @ pls @ ( bit0 @ K ) )
+    <=> ( ord_less_int @ pls @ K ) ) )).
+
+thf(fact_61_bin__less__0__simps_I4_J,axiom,(
+    ! [W_4: int] :
+      ( ( ord_less_int @ ( bit1 @ W_4 ) @ zero_zero_int )
+    <=> ( ord_less_int @ W_4 @ zero_zero_int ) ) )).
+
+thf(fact_62_bin__less__0__simps_I1_J,axiom,(
+    ~ ( ord_less_int @ pls @ zero_zero_int ) )).
+
+thf(fact_63_bin__less__0__simps_I3_J,axiom,(
+    ! [W_4: int] :
+      ( ( ord_less_int @ ( bit0 @ W_4 ) @ zero_zero_int )
+    <=> ( ord_less_int @ W_4 @ zero_zero_int ) ) )).
+
+thf(fact_64_int__0__less__1,axiom,
+    ( ord_less_int @ zero_zero_int @ one_one_int )).
+
+thf(fact_65_zless__add1__eq,axiom,(
+    ! [W_4: int,Z: int] :
+      ( ( ord_less_int @ W_4 @ ( plus_plus_int @ Z @ one_one_int ) )
+    <=> ( ( ord_less_int @ W_4 @ Z )
+        | ( W_4 = Z ) ) ) )).
+
+thf(fact_66_int__less__0__conv,axiom,(
+    ! [K: nat] :
+      ~ ( ord_less_int @ ( semiri1621563631at_int @ K ) @ zero_zero_int ) )).
+
+thf(fact_67_less__special_I4_J,axiom,(
+    ! [X_1: int] :
+      ( ( ord_less_int @ ( number_number_of_int @ X_1 ) @ one_one_int )
+    <=> ( ord_less_int @ X_1 @ ( bit1 @ pls ) ) ) )).
+
+thf(fact_68_less__special_I2_J,axiom,(
+    ! [Y_1: int] :
+      ( ( ord_less_int @ one_one_int @ ( number_number_of_int @ Y_1 ) )
+    <=> ( ord_less_int @ ( bit1 @ pls ) @ Y_1 ) ) )).
+
+thf(fact_69_odd__less__0,axiom,(
+    ! [Z: int] :
+      ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
+    <=> ( ord_less_int @ Z @ zero_zero_int ) ) )).
+
+thf(fact_70_double__eq__0__iff,axiom,(
+    ! [A_5: int] :
+      ( ( ( plus_plus_int @ A_5 @ A_5 )
+        = zero_zero_int )
+    <=> ( A_5 = zero_zero_int ) ) )).
+
+thf(fact_71_rel__simps_I46_J,axiom,(
+    ! [K: int] :
+      ( ( bit1 @ K )
+     != pls ) )).
+
+thf(fact_72_rel__simps_I39_J,axiom,(
+    ! [L: int] :
+      ( pls
+     != ( bit1 @ L ) ) )).
+
+thf(fact_73_rel__simps_I50_J,axiom,(
+    ! [K: int,L: int] :
+      ( ( bit1 @ K )
+     != ( bit0 @ L ) ) )).
+
+thf(fact_74_rel__simps_I49_J,axiom,(
+    ! [K: int,L: int] :
+      ( ( bit0 @ K )
+     != ( bit1 @ L ) ) )).
+
+thf(fact_75_rel__simps_I44_J,axiom,(
+    ! [K: int] :
+      ( ( ( bit0 @ K )
+        = pls )
+    <=> ( K = pls ) ) )).
+
+thf(fact_76_rel__simps_I38_J,axiom,(
+    ! [L: int] :
+      ( ( pls
+        = ( bit0 @ L ) )
+    <=> ( pls = L ) ) )).
+
+thf(fact_77_Bit0__Pls,axiom,
+    ( ( bit0 @ pls )
+    = pls )).
+
+thf(fact_78_Pls__def,axiom,(
+    pls = zero_zero_int )).
+
+thf(fact_79_int__0__neq__1,axiom,(
+    zero_zero_int != one_one_int )).
+
+thf(fact_80_add__Pls__right,axiom,(
+    ! [K: int] :
+      ( ( plus_plus_int @ K @ pls )
+      = K ) )).
+
+thf(fact_81_add__Pls,axiom,(
+    ! [K: int] :
+      ( ( plus_plus_int @ pls @ K )
+      = K ) )).
+
+thf(fact_82_add__Bit0__Bit0,axiom,(
+    ! [K: int,L: int] :
+      ( ( plus_plus_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
+      = ( bit0 @ ( plus_plus_int @ K @ L ) ) ) )).
+
+thf(fact_83_Bit0__def,axiom,(
+    ! [K: int] :
+      ( ( bit0 @ K )
+      = ( plus_plus_int @ K @ K ) ) )).
+
+thf(fact_84_zadd__0__right,axiom,(
+    ! [Z: int] :
+      ( ( plus_plus_int @ Z @ zero_zero_int )
+      = Z ) )).
+
+thf(fact_85_zadd__0,axiom,(
+    ! [Z: int] :
+      ( ( plus_plus_int @ zero_zero_int @ Z )
+      = Z ) )).
+
+thf(fact_86_semiring__numeral__0__eq__0,axiom,
+    ( ( number_number_of_int @ pls )
+    = zero_zero_int )).
+
+thf(fact_87_semiring__numeral__0__eq__0,axiom,
+    ( ( number_number_of_nat @ pls )
+    = zero_zero_nat )).
+
+thf(fact_88_number__of__Pls,axiom,
+    ( ( number_number_of_int @ pls )
+    = zero_zero_int )).
+
+thf(fact_89_semiring__norm_I112_J,axiom,
+    ( zero_zero_int
+    = ( number_number_of_int @ pls ) )).
+
+thf(fact_90_add__numeral__0,axiom,(
+    ! [A_4: int] :
+      ( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A_4 )
+      = A_4 ) )).
+
+thf(fact_91_add__numeral__0__right,axiom,(
+    ! [A_3: int] :
+      ( ( plus_plus_int @ A_3 @ ( number_number_of_int @ pls ) )
+      = A_3 ) )).
+
+thf(fact_92_power__eq__0__iff__number__of,axiom,(
+    ! [A_2: int,W_3: int] :
+      ( ( ( power_power_int @ A_2 @ ( number_number_of_nat @ W_3 ) )
+        = zero_zero_int )
+    <=> ( ( A_2 = zero_zero_int )
+        & ( ( number_number_of_nat @ W_3 )
+         != zero_zero_nat ) ) ) )).
+
+thf(fact_93_power__eq__0__iff__number__of,axiom,(
+    ! [A_2: nat,W_3: int] :
+      ( ( ( power_power_nat @ A_2 @ ( number_number_of_nat @ W_3 ) )
+        = zero_zero_nat )
+    <=> ( ( A_2 = zero_zero_nat )
+        & ( ( number_number_of_nat @ W_3 )
+         != zero_zero_nat ) ) ) )).
+
+thf(fact_94_add__number__of__left,axiom,(
+    ! [V_2: int,W_2: int,Z_1: int] :
+      ( ( plus_plus_int @ ( number_number_of_int @ V_2 ) @ ( plus_plus_int @ ( number_number_of_int @ W_2 ) @ Z_1 ) )
+      = ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ V_2 @ W_2 ) ) @ Z_1 ) ) )).
+
+thf(fact_95_add__number__of__eq,axiom,(
+    ! [V_1: int,W_1: int] :
+      ( ( plus_plus_int @ ( number_number_of_int @ V_1 ) @ ( number_number_of_int @ W_1 ) )
+      = ( number_number_of_int @ ( plus_plus_int @ V_1 @ W_1 ) ) ) )).
+
+thf(fact_96_number__of__add,axiom,(
+    ! [V: int,W: int] :
+      ( ( number_number_of_int @ ( plus_plus_int @ V @ W ) )
+      = ( plus_plus_int @ ( number_number_of_int @ V ) @ ( number_number_of_int @ W ) ) ) )).
+
+thf(fact_97_add__Bit1__Bit0,axiom,(
+    ! [K: int,L: int] :
+      ( ( plus_plus_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
+      = ( bit1 @ ( plus_plus_int @ K @ L ) ) ) )).
+
+thf(fact_98_add__Bit0__Bit1,axiom,(
+    ! [K: int,L: int] :
+      ( ( plus_plus_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
+      = ( bit1 @ ( plus_plus_int @ K @ L ) ) ) )).
+
+thf(fact_99_Bit1__def,axiom,(
+    ! [K: int] :
+      ( ( bit1 @ K )
+      = ( plus_plus_int @ ( plus_plus_int @ one_one_int @ K ) @ K ) ) )).
+
+thf(fact_100_odd__nonzero,axiom,(
+    ! [Z: int] :
+      ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
+     != zero_zero_int ) )).
+
+thf(fact_101_number__of__int,axiom,(
+    ! [N: nat] :
+      ( ( number_number_of_nat @ ( semiri1621563631at_int @ N ) )
+      = ( semiri984289939at_nat @ N ) ) )).
+
+thf(fact_102_number__of__int,axiom,(
+    ! [N: nat] :
+      ( ( number_number_of_int @ ( semiri1621563631at_int @ N ) )
+      = ( semiri1621563631at_int @ N ) ) )).
+
+thf(fact_103_zero__less__power2,axiom,(
+    ! [A_1: int] :
+      ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
+    <=> ( A_1 != zero_zero_int ) ) )).
+
+thf(fact_104_power2__less__0,axiom,(
+    ! [A: int] :
+      ~ ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ) )).
+
+thf(fact_105_sum__power2__gt__zero__iff,axiom,(
+    ! [X: int,Y: int] :
+      ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
+    <=> ( ( X != zero_zero_int )
+        | ( Y != zero_zero_int ) ) ) )).
+
+%----Conjectures (1)
+thf(conj_0,conjecture,(
+    ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
+ != zero_zero_int )).
+
+%------------------------------------------------------------------------------

diff --git a/test/regress/regress1/ho/SYO056^1.p b/test/regress/regress1/ho/SYO056^1.p
new file mode 100644 (file)
index 0000000..a8a6baf
--- /dev/null
+++ b/test/regress/regress1/ho/SYO056^1.p
@@ -0,0 +1,100 @@
+% COMMAND-LINE:  --uf-ho --finite-model-find
+% EXPECT: % SZS status CounterSatisfiable for SYO056^1
+
+%------------------------------------------------------------------------------
+% File     : SYO056^1 : TPTP v7.2.0. Released v4.0.0.
+% Domain   : Logic Calculi (Quantified multimodal logic)
+% Problem  : Simple textbook example 13
+% Version  : [Ben09] axioms.
+% English  :
+
+% Refs     : [Gol92] Goldblatt (1992), Logics of Time and Computation
+%          : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
+% Source   : [Ben09]
+% Names    : ex13.p [Ben09]
+
+% Status   : CounterSatisfiable
+% Rating   : 0.25 v7.2.0, 0.33 v6.4.0, 0.00 v6.3.0, 0.33 v5.4.0, 0.00 v5.0.0, 0.67 v4.1.0, 0.50 v4.0.0
+% Syntax   : Number of formulae    :   64 (   0 unit;  32 type;  31 defn)
+%            Number of atoms       :  238 (  36 equality; 137 variable)
+%            Maximal formula depth :   12 (   6 average)
+%            Number of connectives :  138 (   4   ~;   4   |;   8   &; 114   @)
+%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
+%                                         (   0  ~|;   0  ~&)
+%            Number of type conns  :  172 ( 172   >;   0   *;   0   +;   0  <<)
+%            Number of symbols     :   36 (  32   :;   0   =)
+%            Number of variables   :   87 (   3 sgn;  30   !;   6   ?;  51   ^)
+%                                         (  87   :;   0  !>;   0  ?*)
+%                                         (   0  @-;   0  @+)
+% SPC      : TH0_CSA_EQU_NAR
+
+% Comments :
+%------------------------------------------------------------------------------
+%----Include embedding of quantified multimodal logic in simple type theory
+%% include('Axioms/LCL013^0.ax').
+%------------------------------------------------------------------------------
+thf(mvalid_type,type,(
+    mvalid: ( $i > $o ) > $o )).
+
+thf(mvalid,definition,
+    ( mvalid
+    = ( ^ [Phi: $i > $o] :
+        ! [W: $i] :
+          ( Phi @ W ) ) )).
+
+
+thf(mforall_prop_type,type,(
+    mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o )).
+
+thf(mforall_prop,definition,
+    ( mforall_prop
+    = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
+        ! [P: $i > $o] :
+          ( Phi @ P @ W ) ) )).
+
+thf(mnot_type,type,(
+    mnot: ( $i > $o ) > $i > $o )).
+
+thf(mnot,definition,
+    ( mnot
+    = ( ^ [Phi: $i > $o,W: $i] :
+          ~ ( Phi @ W ) ) )).
+
+thf(mor_type,type,(
+    mor: ( $i > $o ) > ( $i > $o ) > $i > $o )).
+
+thf(mor,definition,
+    ( mor
+    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
+          ( ( Phi @ W )
+          | ( Psi @ W ) ) ) )).
+
+thf(mimplies_type,type,(
+    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o )).
+
+thf(mimplies,definition,
+    ( mimplies
+    = ( ^ [Phi: $i > $o,Psi: $i > $o] :
+          ( mor @ ( mnot @ Phi ) @ Psi ) ) )).
+
+thf(mbox_type,type,(
+    mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o )).
+
+thf(mbox,definition,
+    ( mbox
+    = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
+        ! [V: $i] :
+          ( ~ ( R @ W @ V )
+          | ( Phi @ V ) ) ) )).
+
+
+thf(conj,conjecture,(
+    ! [R: $i > $i > $o] :
+      ( mvalid
+      @ ( mforall_prop
+        @ ^ [A: $i > $o] :
+            ( mforall_prop
+            @ ^ [B: $i > $o] :
+                ( mimplies @ ( mbox @ R @ ( mor @ A @ B ) ) @ ( mor @ ( mbox @ R @ A ) @ ( mbox @ R @ B ) ) ) ) ) ) )).
+
+%------------------------------------------------------------------------------

diff --git a/test/regress/regress1/ho/auth0068.smt2 b/test/regress/regress1/ho/auth0068.smt2
deleted file mode 100644 (file)
index eb0bb5d..0000000
--- a/test/regress/regress1/ho/auth0068.smt2
+++ /dev/null
@@ -1,491 +0,0 @@
-; COMMAND-LINE: --uf-ho
-; EXPECT: unsat
-(set-logic ALL)
-(set-info :status unsat)
-(declare-sort Msg$ 0)
-(declare-sort Nat$ 0)
-(declare-sort Agent$ 0)
-(declare-sort Event$ 0)
-(declare-sort Msg_set$ 0)
-(declare-sort Msg_list$ 0)
-(declare-sort Agent_set$ 0)
-(declare-sort Event_set$ 0)
-(declare-sort Agent_list$ 0)
-(declare-sort Event_list$ 0)
-(declare-sort Event_option$ 0)
-(declare-sort Msg_list_set$ 0)
-(declare-sort Agent_list_set$ 0)
-(declare-sort Event_list_set$ 0)
-(declare-sort Event_list_list$ 0)
-(declare-fun p$ () (-> Event$ Bool))
-(declare-fun uu$ ((-> Msg$ Bool) (-> Msg$ Bool) Msg$) Bool)
-(declare-fun bad$ () Agent_set$)
-(declare-fun nil$ () Event_list$)
-(declare-fun set$ (Event_list$) Event_set$)
-(declare-fun spy$ () Agent$)
-(declare-fun uua$ (Event_set$ (-> Event$ Bool) Event$) Bool)
-(declare-fun uub$ (Agent_set$ (-> Agent$ Bool) Agent$) Bool)
-(declare-fun uuc$ (Msg_set$ (-> Msg$ Bool) Msg$) Bool)
-(declare-fun uud$ (Event_set$ Event$) Bool)
-(declare-fun uue$ (Agent_set$ Agent$) Bool)
-(declare-fun uuf$ (Msg_set$ Msg$) Bool)
-(declare-fun uug$ (Event$ Event_list$) Bool)
-(declare-fun uuh$ (Event$ Event_list$) Bool)
-(declare-fun uui$ ((-> Event$ Bool) Event$ Event$) Bool)
-(declare-fun uuj$ (Event_list_set$ Event_list$ Event$) Bool)
-(declare-fun uuk$ (Msg$ (-> Msg$ Bool) Msg$) Bool)
-(declare-fun uul$ (Msg$ Msg_set$ Msg$) Bool)
-(declare-fun uum$ (Event$ Event_set$ Event$) Bool)
-(declare-fun uun$ (Agent$ Agent_set$ Agent$) Bool)
-(declare-fun uuo$ (Event_list$ Agent$ Agent$ Msg$) Msg_set$)
-(declare-fun uup$ (Event_list$ Agent$ Msg$) Msg_set$)
-(declare-fun uuq$ (Event_list$ Agent$ Msg$) Msg_set$)
-(declare-fun uur$ (Agent$ Event_list$ Agent$ Agent$ Msg$) Msg_set$)
-(declare-fun uus$ (Agent$ Event_list$ Agent$ Msg$) Msg_set$)
-(declare-fun bind$ (Event_list$ (-> Event$ Event_list$)) Event_list$)
-(declare-fun cons$ (Event$ Event_list$) Event_list$)
-(declare-fun gets$ (Agent$ Msg$) Event$)
-(declare-fun maps$ ((-> Event$ Event_list$)) (-> Event_list$ Event_list$))
-(declare-fun nil$a () Event_list_list$)
-(declare-fun nil$b () Msg_list$)
-(declare-fun nil$c () Agent_list$)
-(declare-fun null$ (Event_list$) Bool)
-(declare-fun says$ (Agent$ Agent$ Msg$) Event$)
-(declare-fun set$a (Msg_list$) Msg_set$)
-(declare-fun set$b (Agent_list$) Agent_set$)
-(declare-fun succ$ (Event_list_set$ Event_list$) Event_set$)
-(declare-fun cons$a (Event_list$ Event_list_list$) Event_list_list$)
-(declare-fun cons$b (Msg$ Msg_list$) Msg_list$)
-(declare-fun cons$c (Agent$ Agent_list$) Agent_list$)
-(declare-fun knows$ (Agent$ Event_list$) Msg_set$)
-(declare-fun notes$ (Agent$ Msg$) Event$)
-(declare-fun succ$a (Msg_list_set$ Msg_list$) Msg_set$)
-(declare-fun succ$b (Agent_list_set$ Agent_list$) Agent_set$)
-(declare-fun append$ (Event_list$ Event_list$) Event_list$)
-(declare-fun insert$ (Msg$ Msg_set$) Msg_set$)
-(declare-fun member$ (Agent$ Agent_set$) Bool)
-(declare-fun splice$ (Event_list$) (-> Event_list$ Event_list$))
-(declare-fun append$a (Msg_list$ Msg_list$) Msg_list$)
-(declare-fun append$b (Agent_list$ Agent_list$) Agent_list$)
-(declare-fun collect$ ((-> Msg$ Bool)) Msg_set$)
-(declare-fun insert$a (Event$) (-> Event_list$ Event_list$))
-(declare-fun insert$b (Event$ Event_set$) Event_set$)
-(declare-fun insert$c (Agent$ Agent_set$) Agent_set$)
-(declare-fun insert$d (Msg$ Msg_list$) Msg_list$)
-(declare-fun insert$e (Agent$ Agent_list$) Agent_list$)
-(declare-fun less_eq$ (Msg_set$ Msg_set$) Bool)
-(declare-fun list_ex$ ((-> Event$ Bool)) (-> Event_list$ Bool))
-(declare-fun member$a (Msg$ Msg_set$) Bool)
-(declare-fun member$b (Event$ Event_set$) Bool)
-(declare-fun member$c (Event_list$ Event_list_set$) Bool)
-(declare-fun member$d (Event_list$ Event$) Bool)
-(declare-fun member$e (Msg_list$ Msg_list_set$) Bool)
-(declare-fun member$f (Agent_list$ Agent_list_set$) Bool)
-(declare-fun member$g (Msg_list$ Msg$) Bool)
-(declare-fun member$h (Agent_list$ Agent$) Bool)
-(declare-fun rotate1$ (Event_list$) Event_list$)
-(declare-fun subseqs$ (Event_list$) Event_list_list$)
-(declare-fun antimono$ ((-> Msg_set$ Msg_set$)) Bool)
-(declare-fun collect$a ((-> Event$ Bool)) Event_set$)
-(declare-fun collect$b ((-> Agent$ Bool)) Agent_set$)
-(declare-fun greatest$ ((-> Msg_set$ Bool)) Msg_set$)
-(declare-fun less_eq$a (Event_set$ Event_set$) Bool)
-(declare-fun less_eq$b (Agent_set$ Agent_set$) Bool)
-(declare-fun less_eq$c ((-> Event$ Bool) (-> Event$ Bool)) Bool)
-(declare-fun less_eq$d ((-> Agent$ Bool) (-> Agent$ Bool)) Bool)
-(declare-fun less_eq$e ((-> Msg$ Bool) (-> Msg$ Bool)) Bool)
-(declare-fun less_eq$f ((-> Bool Msg_set$) (-> Bool Msg_set$)) Bool)
-(declare-fun list_all$ ((-> Event$ Bool) Event_list$) Bool)
-(declare-fun list_ex$a ((-> Msg$ Bool) Msg_list$) Bool)
-(declare-fun list_ex$b ((-> Agent$ Bool) Agent_list$) Bool)
-(declare-fun list_ex1$ ((-> Event$ Bool)) (-> Event_list$ Bool))
-(declare-fun case_list$ (Bool (-> Event$ (-> Event_list$ Bool)) Event_list$) Bool)
-(declare-fun initState$ (Agent$) Msg_set$)
-(declare-fun list_all$a ((-> Msg$ Bool) Msg_list$) Bool)
-(declare-fun list_all$b ((-> Agent$ Bool) Agent_list$) Bool)
-(declare-fun list_ex1$a ((-> Msg$ Bool) Msg_list$) Bool)
-(declare-fun list_ex1$b ((-> Agent$ Bool) Agent_list$) Bool)
-(declare-fun takeWhile$ ((-> Event$ Bool) Event_list$) Event_list$)
-(declare-fun case_event$ ((-> Agent$ (-> Agent$ (-> Msg$ Msg_set$))) (-> Agent$ (-> Msg$ Msg_set$)) (-> Agent$ (-> Msg$ Msg_set$)) Event$) Msg_set$)
-(declare-fun gen_length$ (Nat$) (-> Event_list$ Nat$))
-(declare-fun map_filter$ ((-> Event$ Event_option$)) (-> Event_list$ Event_list$))
-(declare-fun takeWhile$a ((-> Msg$ Bool) Msg_list$) Msg_list$)
-(declare-fun takeWhile$b ((-> Agent$ Bool) Agent_list$) Agent_list$)
-(declare-fun product_lists$ (Event_list_list$) Event_list_list$)
-(assert (! (forall ((?v0 Agent_set$) (?v1 Agent$)) (! (= (uue$ ?v0 ?v1) (member$ ?v1 ?v0)) :pattern ((uue$ ?v0 ?v1)))) :named a0))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg$)) (! (= (uuf$ ?v0 ?v1) (member$a ?v1 ?v0)) :pattern ((uuf$ ?v0 ?v1)))) :named a1))
-(assert (! (forall ((?v0 Event_set$) (?v1 Event$)) (! (= (uud$ ?v0 ?v1) (member$b ?v1 ?v0)) :pattern ((uud$ ?v0 ?v1)))) :named a2))
-(assert (! (forall ((?v0 Event_list$) (?v1 Agent$) (?v2 Msg$)) (! (= (uuq$ ?v0 ?v1 ?v2) (ite (member$ ?v1 bad$) (insert$ ?v2 (knows$ spy$ ?v0)) (knows$ spy$ ?v0))) :pattern ((uuq$ ?v0 ?v1 ?v2)))) :named a3))
-(assert (! (forall ((?v0 Event_list_set$) (?v1 Event_list$) (?v2 Event$)) (! (= (uuj$ ?v0 ?v1 ?v2) (member$c (append$ ?v1 (cons$ ?v2 nil$)) ?v0)) :pattern ((uuj$ ?v0 ?v1 ?v2)))) :named a4))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent$)) (! (= (uun$ ?v0 ?v1 ?v2) (or (= ?v2 ?v0) (member$ ?v2 ?v1))) :pattern ((uun$ ?v0 ?v1 ?v2)))) :named a5))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg$)) (! (= (uul$ ?v0 ?v1 ?v2) (or (= ?v2 ?v0) (member$a ?v2 ?v1))) :pattern ((uul$ ?v0 ?v1 ?v2)))) :named a6))
-(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event$)) (! (= (uum$ ?v0 ?v1 ?v2) (or (= ?v2 ?v0) (member$b ?v2 ?v1))) :pattern ((uum$ ?v0 ?v1 ?v2)))) :named a7))
-(assert (! (forall ((?v0 Agent_set$) (?v1 (-> Agent$ Bool)) (?v2 Agent$)) (! (= (uub$ ?v0 ?v1 ?v2) (and (member$ ?v2 ?v0) (?v1 ?v2))) :pattern ((uub$ ?v0 ?v1 ?v2)))) :named a8))
-(assert (! (forall ((?v0 Msg_set$) (?v1 (-> Msg$ Bool)) (?v2 Msg$)) (! (= (uuc$ ?v0 ?v1 ?v2) (and (member$a ?v2 ?v0) (?v1 ?v2))) :pattern ((uuc$ ?v0 ?v1 ?v2)))) :named a9))
-(assert (! (forall ((?v0 Event_set$) (?v1 (-> Event$ Bool)) (?v2 Event$)) (! (= (uua$ ?v0 ?v1 ?v2) (and (member$b ?v2 ?v0) (?v1 ?v2))) :pattern ((uua$ ?v0 ?v1 ?v2)))) :named a10))
-(assert (! (forall ((?v0 (-> Msg$ Bool)) (?v1 (-> Msg$ Bool)) (?v2 Msg$)) (! (= (uu$ ?v0 ?v1 ?v2) (and (?v0 ?v2) (?v1 ?v2))) :pattern ((uu$ ?v0 ?v1 ?v2)))) :named a11))
-(assert (! (forall ((?v0 Msg$) (?v1 (-> Msg$ Bool)) (?v2 Msg$)) (! (= (uuk$ ?v0 ?v1 ?v2) (=> (not (= ?v2 ?v0)) (?v1 ?v2))) :pattern ((uuk$ ?v0 ?v1 ?v2)))) :named a12))
-(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event$) (?v2 Event$)) (! (= (uui$ ?v0 ?v1 ?v2) (or (not (?v0 ?v2)) (= ?v1 ?v2))) :pattern ((uui$ ?v0 ?v1 ?v2)))) :named a13))
-(assert (! (forall ((?v0 Event_list$) (?v1 Agent$) (?v2 Msg$)) (! (= (uup$ ?v0 ?v1 ?v2) (knows$ spy$ ?v0)) :pattern ((uup$ ?v0 ?v1 ?v2)))) :named a14))
-(assert (! (forall ((?v0 Agent$) (?v1 Event_list$) (?v2 Agent$) (?v3 Msg$)) (! (= (uus$ ?v0 ?v1 ?v2 ?v3) (ite (= ?v2 ?v0) (insert$ ?v3 (knows$ ?v0 ?v1)) (knows$ ?v0 ?v1))) :pattern ((uus$ ?v0 ?v1 ?v2 ?v3)))) :named a15))
-(assert (! (forall ((?v0 Event_list$) (?v1 Agent$) (?v2 Agent$) (?v3 Msg$)) (! (= (uuo$ ?v0 ?v1 ?v2 ?v3) (insert$ ?v3 (knows$ spy$ ?v0))) :pattern ((uuo$ ?v0 ?v1 ?v2 ?v3)))) :named a16))
-(assert (! (forall ((?v0 Agent$) (?v1 Event_list$) (?v2 Agent$) (?v3 Agent$) (?v4 Msg$)) (! (= (uur$ ?v0 ?v1 ?v2 ?v3 ?v4) (ite (= ?v2 ?v0) (insert$ ?v4 (knows$ ?v0 ?v1)) (knows$ ?v0 ?v1))) :pattern ((uur$ ?v0 ?v1 ?v2 ?v3 ?v4)))) :named a17))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (! (= (uug$ ?v0 ?v1) false) :pattern ((uug$ ?v0 ?v1)))) :named a18))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (! (= (uuh$ ?v0 ?v1) true) :pattern ((uuh$ ?v0 ?v1)))) :named a19))
-(assert (! (not (less_eq$ (knows$ spy$ (takeWhile$ p$ nil$)) (knows$ spy$ nil$))) :named a20))
-(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event_list$)) (= (takeWhile$ ?v0 (takeWhile$ ?v0 ?v1)) (takeWhile$ ?v0 ?v1))) :named a21))
-(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$)) (=> (forall ((?v2 Event$)) (=> (member$b ?v2 ?v0) (member$b ?v2 ?v1))) (less_eq$a ?v0 ?v1))) :named a22))
-(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$)) (=> (forall ((?v2 Agent$)) (=> (member$ ?v2 ?v0) (member$ ?v2 ?v1))) (less_eq$b ?v0 ?v1))) :named a23))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (=> (forall ((?v2 Msg$)) (=> (member$a ?v2 ?v0) (member$a ?v2 ?v1))) (less_eq$ ?v0 ?v1))) :named a24))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v0)) (= ?v0 ?v1))) :named a25))
-(assert (! (forall ((?v0 Msg_set$)) (less_eq$ ?v0 ?v0)) :named a26))
-(assert (! (forall ((?v0 (-> Event$ Bool))) (! (= (takeWhile$ ?v0 nil$) nil$) :pattern ((takeWhile$ ?v0)))) :named a27))
-(assert (! (forall ((?v0 Msg_set$) (?v1 (-> Msg$ Bool)) (?v2 (-> Msg$ Bool))) (= (less_eq$ ?v0 (collect$ (uu$ ?v1 ?v2))) (and (less_eq$ ?v0 (collect$ ?v1)) (less_eq$ ?v0 (collect$ ?v2))))) :named a28))
-(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event_set$) (?v3 (-> Event$ Bool))) (=> (and (member$b ?v0 ?v1) (less_eq$a ?v1 (collect$a (uua$ ?v2 ?v3)))) (?v3 ?v0))) :named a29))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent_set$) (?v3 (-> Agent$ Bool))) (=> (and (member$ ?v0 ?v1) (less_eq$b ?v1 (collect$b (uub$ ?v2 ?v3)))) (?v3 ?v0))) :named a30))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg_set$) (?v3 (-> Msg$ Bool))) (=> (and (member$a ?v0 ?v1) (less_eq$ ?v1 (collect$ (uuc$ ?v2 ?v3)))) (?v3 ?v0))) :named a31))
-(assert (! (forall ((?v0 Event_set$) (?v1 (-> Event$ Bool))) (less_eq$a (collect$a (uua$ ?v0 ?v1)) ?v0)) :named a32))
-(assert (! (forall ((?v0 Agent_set$) (?v1 (-> Agent$ Bool))) (less_eq$b (collect$b (uub$ ?v0 ?v1)) ?v0)) :named a33))
-(assert (! (forall ((?v0 Msg_set$) (?v1 (-> Msg$ Bool))) (less_eq$ (collect$ (uuc$ ?v0 ?v1)) ?v0)) :named a34))
-(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$) (?v2 (-> Event$ Bool)) (?v3 (-> Event$ Bool))) (=> (and (less_eq$a ?v0 ?v1) (forall ((?v4 Event$)) (=> (and (member$b ?v4 ?v0) (?v2 ?v4)) (?v3 ?v4)))) (less_eq$a (collect$a (uua$ ?v0 ?v2)) (collect$a (uua$ ?v1 ?v3))))) :named a35))
-(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$) (?v2 (-> Agent$ Bool)) (?v3 (-> Agent$ Bool))) (=> (and (less_eq$b ?v0 ?v1) (forall ((?v4 Agent$)) (=> (and (member$ ?v4 ?v0) (?v2 ?v4)) (?v3 ?v4)))) (less_eq$b (collect$b (uub$ ?v0 ?v2)) (collect$b (uub$ ?v1 ?v3))))) :named a36))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 (-> Msg$ Bool)) (?v3 (-> Msg$ Bool))) (=> (and (less_eq$ ?v0 ?v1) (forall ((?v4 Msg$)) (=> (and (member$a ?v4 ?v0) (?v2 ?v4)) (?v3 ?v4)))) (less_eq$ (collect$ (uuc$ ?v0 ?v2)) (collect$ (uuc$ ?v1 ?v3))))) :named a37))
-(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$) (?v2 (-> Event$ Bool))) (=> (less_eq$a ?v0 ?v1) (= (less_eq$a ?v0 (collect$a (uua$ ?v1 ?v2))) (forall ((?v3 Event$)) (=> (member$b ?v3 ?v0) (?v2 ?v3)))))) :named a38))
-(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$) (?v2 (-> Agent$ Bool))) (=> (less_eq$b ?v0 ?v1) (= (less_eq$b ?v0 (collect$b (uub$ ?v1 ?v2))) (forall ((?v3 Agent$)) (=> (member$ ?v3 ?v0) (?v2 ?v3)))))) :named a39))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 (-> Msg$ Bool))) (=> (less_eq$ ?v0 ?v1) (= (less_eq$ ?v0 (collect$ (uuc$ ?v1 ?v2))) (forall ((?v3 Msg$)) (=> (member$a ?v3 ?v0) (?v2 ?v3)))))) :named a40))
-(assert (! (forall ((?v0 Event_list$)) (=> (and (=> (= ?v0 nil$) false) (=> (not (= ?v0 nil$)) false)) false)) :named a41))
-(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$) (?v2 Event$)) (=> (and (less_eq$a ?v0 ?v1) (member$b ?v2 ?v0)) (member$b ?v2 ?v1))) :named a42))
-(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$) (?v2 Agent$)) (=> (and (less_eq$b ?v0 ?v1) (member$ ?v2 ?v0)) (member$ ?v2 ?v1))) :named a43))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg$)) (=> (and (less_eq$ ?v0 ?v1) (member$a ?v2 ?v0)) (member$a ?v2 ?v1))) :named a44))
-(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$)) (= (less_eq$a ?v0 ?v1) (less_eq$c (uud$ ?v0) (uud$ ?v1)))) :named a45))
-(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$)) (= (less_eq$b ?v0 ?v1) (less_eq$d (uue$ ?v0) (uue$ ?v1)))) :named a46))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (= (less_eq$ ?v0 ?v1) (less_eq$e (uuf$ ?v0) (uuf$ ?v1)))) :named a47))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v0)) (= ?v1 ?v0))) :named a48))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v2 ?v0)) (less_eq$ ?v2 ?v1))) :named a49))
-(assert (! (forall ((?v0 Msg_set$)) (less_eq$ ?v0 ?v0)) :named a50))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2))) :named a51))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v0)) (= ?v0 ?v1))) :named a52))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (= ?v1 ?v2)) (less_eq$ ?v0 ?v2))) :named a53))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (= ?v0 ?v1) (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2))) :named a54))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (! (=> (less_eq$ ?v0 ?v1) (= (less_eq$ ?v1 ?v0) (= ?v1 ?v0))) :pattern ((less_eq$ ?v1 ?v0)))) :named a55))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2))) :named a56))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (=> (= ?v0 ?v1) (less_eq$ ?v0 ?v1))) :named a57))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v0)) (= ?v0 ?v1))) :named a58))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (= (= ?v0 ?v1) (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v0)))) :named a59))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 (-> Msg_set$ Msg_set$)) (?v3 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (and (= (?v2 ?v1) ?v3) (forall ((?v4 Msg_set$) (?v5 Msg_set$)) (=> (less_eq$ ?v4 ?v5) (less_eq$ (?v2 ?v4) (?v2 ?v5)))))) (less_eq$ (?v2 ?v0) ?v3))) :named a60))
-(assert (! (forall ((?v0 Msg_set$) (?v1 (-> Msg_set$ Msg_set$)) (?v2 Msg_set$) (?v3 Msg_set$)) (=> (and (= ?v0 (?v1 ?v2)) (and (less_eq$ ?v2 ?v3) (forall ((?v4 Msg_set$) (?v5 Msg_set$)) (=> (less_eq$ ?v4 ?v5) (less_eq$ (?v1 ?v4) (?v1 ?v5)))))) (less_eq$ ?v0 (?v1 ?v3)))) :named a61))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 (-> Msg_set$ Msg_set$)) (?v3 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (and (less_eq$ (?v2 ?v1) ?v3) (forall ((?v4 Msg_set$) (?v5 Msg_set$)) (=> (less_eq$ ?v4 ?v5) (less_eq$ (?v2 ?v4) (?v2 ?v5)))))) (less_eq$ (?v2 ?v0) ?v3))) :named a62))
-(assert (! (forall ((?v0 Msg_set$) (?v1 (-> Msg_set$ Msg_set$)) (?v2 Msg_set$) (?v3 Msg_set$)) (=> (and (less_eq$ ?v0 (?v1 ?v2)) (and (less_eq$ ?v2 ?v3) (forall ((?v4 Msg_set$) (?v5 Msg_set$)) (=> (less_eq$ ?v4 ?v5) (less_eq$ (?v1 ?v4) (?v1 ?v5)))))) (less_eq$ ?v0 (?v1 ?v3)))) :named a63))
-(assert (! (forall ((?v0 (-> Msg$ Bool)) (?v1 (-> Msg$ Bool))) (= (less_eq$ (collect$ ?v0) (collect$ ?v1)) (forall ((?v2 Msg$)) (=> (?v0 ?v2) (?v1 ?v2))))) :named a64))
-(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$) (?v2 Event$)) (=> (and (less_eq$a ?v0 ?v1) (not (member$b ?v2 ?v1))) (not (member$b ?v2 ?v0)))) :named a65))
-(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$) (?v2 Agent$)) (=> (and (less_eq$b ?v0 ?v1) (not (member$ ?v2 ?v1))) (not (member$ ?v2 ?v0)))) :named a66))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg$)) (=> (and (less_eq$ ?v0 ?v1) (not (member$a ?v2 ?v1))) (not (member$a ?v2 ?v0)))) :named a67))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (= (= ?v0 ?v1) (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v0)))) :named a68))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2))) :named a69))
-(assert (! (forall ((?v0 (-> Msg$ Bool)) (?v1 (-> Msg$ Bool))) (=> (forall ((?v2 Msg$)) (=> (?v0 ?v2) (?v1 ?v2))) (less_eq$ (collect$ ?v0) (collect$ ?v1)))) :named a70))
-(assert (! (forall ((?v0 Msg_set$)) (less_eq$ ?v0 ?v0)) :named a71))
-(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event_set$)) (=> (and (member$b ?v0 ?v1) (less_eq$a ?v1 ?v2)) (member$b ?v0 ?v2))) :named a72))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent_set$)) (=> (and (member$ ?v0 ?v1) (less_eq$b ?v1 ?v2)) (member$ ?v0 ?v2))) :named a73))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (member$a ?v0 ?v1) (less_eq$ ?v1 ?v2)) (member$a ?v0 ?v2))) :named a74))
-(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$)) (= (less_eq$a ?v0 ?v1) (forall ((?v2 Event$)) (=> (member$b ?v2 ?v0) (member$b ?v2 ?v1))))) :named a75))
-(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$)) (= (less_eq$b ?v0 ?v1) (forall ((?v2 Agent$)) (=> (member$ ?v2 ?v0) (member$ ?v2 ?v1))))) :named a76))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (= (less_eq$ ?v0 ?v1) (forall ((?v2 Msg$)) (=> (member$a ?v2 ?v0) (member$a ?v2 ?v1))))) :named a77))
-(assert (! (forall ((?v0 Msg$) (?v1 (-> Msg$ Bool))) (= (member$a ?v0 (collect$ ?v1)) (?v1 ?v0))) :named a78))
-(assert (! (forall ((?v0 Event$) (?v1 (-> Event$ Bool))) (= (member$b ?v0 (collect$a ?v1)) (?v1 ?v0))) :named a79))
-(assert (! (forall ((?v0 Agent$) (?v1 (-> Agent$ Bool))) (= (member$ ?v0 (collect$b ?v1)) (?v1 ?v0))) :named a80))
-(assert (! (forall ((?v0 Msg_set$)) (= (collect$ (uuf$ ?v0)) ?v0)) :named a81))
-(assert (! (forall ((?v0 Event_set$)) (= (collect$a (uud$ ?v0)) ?v0)) :named a82))
-(assert (! (forall ((?v0 Agent_set$)) (= (collect$b (uue$ ?v0)) ?v0)) :named a83))
-(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event_set$)) (=> (and (member$b ?v0 ?v1) (less_eq$a ?v1 ?v2)) (member$b ?v0 ?v2))) :named a84))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent_set$)) (=> (and (member$ ?v0 ?v1) (less_eq$b ?v1 ?v2)) (member$ ?v0 ?v2))) :named a85))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (member$a ?v0 ?v1) (less_eq$ ?v1 ?v2)) (member$a ?v0 ?v2))) :named a86))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (=> (= ?v0 ?v1) (less_eq$ ?v1 ?v0))) :named a87))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (=> (= ?v0 ?v1) (less_eq$ ?v0 ?v1))) :named a88))
-(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$)) (= (less_eq$a ?v0 ?v1) (forall ((?v2 Event$)) (=> (member$b ?v2 ?v0) (member$b ?v2 ?v1))))) :named a89))
-(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$)) (= (less_eq$b ?v0 ?v1) (forall ((?v2 Agent$)) (=> (member$ ?v2 ?v0) (member$ ?v2 ?v1))))) :named a90))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (= (less_eq$ ?v0 ?v1) (forall ((?v2 Msg$)) (=> (member$a ?v2 ?v0) (member$a ?v2 ?v1))))) :named a91))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (=> (and (= ?v0 ?v1) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v0)) false)) false)) :named a92))
-(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$) (?v2 Event$)) (=> (and (less_eq$a ?v0 ?v1) (and (=> (not (member$b ?v2 ?v0)) false) (=> (member$b ?v2 ?v1) false))) false)) :named a93))
-(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$) (?v2 Agent$)) (=> (and (less_eq$b ?v0 ?v1) (and (=> (not (member$ ?v2 ?v0)) false) (=> (member$ ?v2 ?v1) false))) false)) :named a94))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg$)) (=> (and (less_eq$ ?v0 ?v1) (and (=> (not (member$a ?v2 ?v0)) false) (=> (member$a ?v2 ?v1) false))) false)) :named a95))
-(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$) (?v2 Event$)) (=> (and (less_eq$a ?v0 ?v1) (member$b ?v2 ?v0)) (member$b ?v2 ?v1))) :named a96))
-(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$) (?v2 Agent$)) (=> (and (less_eq$b ?v0 ?v1) (member$ ?v2 ?v0)) (member$ ?v2 ?v1))) :named a97))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg$)) (=> (and (less_eq$ ?v0 ?v1) (member$a ?v2 ?v0)) (member$a ?v2 ?v1))) :named a98))
-(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$) (?v2 Event$)) (=> (and (less_eq$a ?v0 ?v1) (member$b ?v2 ?v0)) (member$b ?v2 ?v1))) :named a99))
-(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$) (?v2 Agent$)) (=> (and (less_eq$b ?v0 ?v1) (member$ ?v2 ?v0)) (member$ ?v2 ?v1))) :named a100))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg$)) (=> (and (less_eq$ ?v0 ?v1) (member$a ?v2 ?v0)) (member$a ?v2 ?v1))) :named a101))
-(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$)) (= (less_eq$c (uud$ ?v0) (uud$ ?v1)) (less_eq$a ?v0 ?v1))) :named a102))
-(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$)) (= (less_eq$d (uue$ ?v0) (uue$ ?v1)) (less_eq$b ?v0 ?v1))) :named a103))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (= (less_eq$e (uuf$ ?v0) (uuf$ ?v1)) (less_eq$ ?v0 ?v1))) :named a104))
-(assert (! (forall ((?v0 (-> Event$ Bool))) (! (= (list_ex1$ ?v0 nil$) false) :pattern ((list_ex1$ ?v0)))) :named a105))
-(assert (! (forall ((?v0 (-> Event$ Event_list$))) (! (= (bind$ nil$ ?v0) nil$) :pattern ((bind$ nil$ ?v0)))) :named a106))
-(assert (! (forall ((?v0 (-> Msg_set$ Bool)) (?v1 Msg_set$)) (=> (and (?v0 ?v1) (forall ((?v2 Msg_set$)) (=> (?v0 ?v2) (less_eq$ ?v2 ?v1)))) (= (greatest$ ?v0) ?v1))) :named a107))
-(assert (! (forall ((?v0 (-> Msg_set$ Bool)) (?v1 Msg_set$) (?v2 (-> Msg_set$ Bool))) (=> (and (?v0 ?v1) (and (forall ((?v3 Msg_set$)) (=> (?v0 ?v3) (less_eq$ ?v3 ?v1))) (forall ((?v3 Msg_set$)) (=> (and (?v0 ?v3) (forall ((?v4 Msg_set$)) (=> (?v0 ?v4) (less_eq$ ?v4 ?v3)))) (?v2 ?v3))))) (?v2 (greatest$ ?v0)))) :named a108))
-(assert (! (forall ((?v0 Event$)) (! (= (member$d nil$ ?v0) false) :pattern ((member$d nil$ ?v0)))) :named a109))
-(assert (! (forall ((?v0 (-> Bool Msg_set$)) (?v1 (-> Bool Msg_set$))) (! (= (less_eq$f ?v0 ?v1) (and (less_eq$ (?v0 false) (?v1 false)) (less_eq$ (?v0 true) (?v1 true)))) :pattern ((less_eq$f ?v0 ?v1)))) :named a110))
-(assert (! (forall ((?v0 Nat$)) (! (= (gen_length$ ?v0 nil$) ?v0) :pattern ((gen_length$ ?v0)))) :named a111))
-(assert (! (forall ((?v0 (-> Event$ Event_list$))) (! (= (maps$ ?v0 nil$) nil$) :pattern ((maps$ ?v0)))) :named a112))
-(assert (! (forall ((?v0 Event_list$)) (= (= ?v0 nil$) (null$ ?v0))) :named a113))
-(assert (! (= (null$ nil$) true) :named a114))
-(assert (! (forall ((?v0 Event_list$)) (! (= (splice$ ?v0 nil$) ?v0) :pattern ((splice$ ?v0)))) :named a115))
-(assert (! (forall ((?v0 Event_list$)) (= (= (rotate1$ ?v0) nil$) (= ?v0 nil$))) :named a116))
-(assert (! (forall ((?v0 (-> Event$ Event_option$))) (! (= (map_filter$ ?v0 nil$) nil$) :pattern ((map_filter$ ?v0)))) :named a117))
-(assert (! (forall ((?v0 (-> Msg_set$ Msg_set$)) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (antimono$ ?v0) (less_eq$ ?v1 ?v2)) (less_eq$ (?v0 ?v2) (?v0 ?v1)))) :named a118))
-(assert (! (= (rotate1$ nil$) nil$) :named a119))
-(assert (! (forall ((?v0 Event_list$)) (! (= (splice$ nil$ ?v0) ?v0) :pattern ((splice$ nil$ ?v0)))) :named a120))
-(assert (! (forall ((?v0 (-> Msg_set$ Msg_set$))) (= (antimono$ ?v0) (forall ((?v1 Msg_set$) (?v2 Msg_set$)) (=> (less_eq$ ?v1 ?v2) (less_eq$ (?v0 ?v2) (?v0 ?v1)))))) :named a121))
-(assert (! (forall ((?v0 (-> Msg_set$ Msg_set$))) (=> (forall ((?v1 Msg_set$) (?v2 Msg_set$)) (=> (less_eq$ ?v1 ?v2) (less_eq$ (?v0 ?v2) (?v0 ?v1)))) (antimono$ ?v0))) :named a122))
-(assert (! (forall ((?v0 (-> Msg_set$ Msg_set$)) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (antimono$ ?v0) (and (less_eq$ ?v1 ?v2) (=> (less_eq$ (?v0 ?v2) (?v0 ?v1)) false))) false)) :named a123))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 Event_list$)) (=> (and (= (splice$ ?v0 ?v1) ?v2) (and (forall ((?v3 Event_list$)) (=> (and (= ?v0 nil$) (and (= ?v1 ?v3) (= ?v2 ?v3))) false)) (and (forall ((?v3 Event$) (?v4 Event_list$)) (=> (and (= ?v0 (cons$ ?v3 ?v4)) (and (= ?v1 nil$) (= ?v2 (cons$ ?v3 ?v4)))) false)) (forall ((?v3 Event$) (?v4 Event_list$) (?v5 Event$) (?v6 Event_list$)) (=> (and (= ?v0 (cons$ ?v3 ?v4)) (and (= ?v1 (cons$ ?v5 ?v6)) (= ?v2 (cons$ ?v3 (cons$ ?v5 (splice$ ?v4 ?v6)))))) false))))) false)) :named a124))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (! (= (splice$ (cons$ ?v0 ?v1) nil$) (cons$ ?v0 ?v1)) :pattern ((cons$ ?v0 ?v1)))) :named a125))
-(assert (! (forall ((?v0 (-> Event$ Bool))) (! (= (list_ex$ ?v0 nil$) false) :pattern ((list_ex$ ?v0)))) :named a126))
-(assert (! (forall ((?v0 Event_list$)) (= (= ?v0 nil$) (case_list$ true uug$ ?v0))) :named a127))
-(assert (! (forall ((?v0 Event_list$)) (= (not (= ?v0 nil$)) (case_list$ false uuh$ ?v0))) :named a128))
-(assert (! (forall ((?v0 Agent$)) (! (= (knows$ ?v0 nil$) (initState$ ?v0)) :pattern ((knows$ ?v0)))) :named a129))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 Event$) (?v3 Event_list$)) (= (= (cons$ ?v0 ?v1) (cons$ ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3)))) :named a130))
-(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event$) (?v2 Event_list$)) (! (= (list_ex$ ?v0 (cons$ ?v1 ?v2)) (or (?v0 ?v1) (list_ex$ ?v0 ?v2))) :pattern ((list_ex$ ?v0 (cons$ ?v1 ?v2))))) :named a131))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (not (= (cons$ ?v0 ?v1) ?v1))) :named a132))
-(assert (! (forall ((?v0 Event_list_list$)) (=> (and (=> (= ?v0 nil$a) false) (and (forall ((?v1 Event_list_list$)) (=> (= ?v0 (cons$a nil$ ?v1)) false)) (forall ((?v1 Event$) (?v2 Event_list$) (?v3 Event_list_list$)) (=> (= ?v0 (cons$a (cons$ ?v1 ?v2) ?v3)) false)))) false)) :named a133))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (not (= nil$ (cons$ ?v0 ?v1)))) :named a134))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event$) (?v2 Event_list$)) (=> (= ?v0 (cons$ ?v1 ?v2)) (not (= ?v0 nil$)))) :named a135))
-(assert (! (forall ((?v0 Event_list$)) (=> (and (=> (= ?v0 nil$) false) (forall ((?v1 Event$) (?v2 Event_list$)) (=> (= ?v0 (cons$ ?v1 ?v2)) false))) false)) :named a136))
-(assert (! (forall ((?v0 Event_list$)) (= (not (= ?v0 nil$)) (exists ((?v1 Event$) (?v2 Event_list$)) (= ?v0 (cons$ ?v1 ?v2))))) :named a137))
-(assert (! (forall ((?v0 (-> Event_list$ (-> Event_list$ Bool))) (?v1 Event_list$) (?v2 Event_list$)) (=> (and (?v0 nil$ nil$) (and (forall ((?v3 Event$) (?v4 Event_list$)) (?v0 (cons$ ?v3 ?v4) nil$)) (and (forall ((?v3 Event$) (?v4 Event_list$)) (?v0 nil$ (cons$ ?v3 ?v4))) (forall ((?v3 Event$) (?v4 Event_list$) (?v5 Event$) (?v6 Event_list$)) (=> (?v0 ?v4 ?v6) (?v0 (cons$ ?v3 ?v4) (cons$ ?v5 ?v6))))))) (?v0 ?v1 ?v2))) :named a138))
-(assert (! (forall ((?v0 Event_list$)) (=> (and (=> (= ?v0 nil$) false) (and (forall ((?v1 Event$)) (=> (= ?v0 (cons$ ?v1 nil$)) false)) (forall ((?v1 Event$) (?v2 Event$) (?v3 Event_list$)) (=> (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3))) false)))) false)) :named a139))
-(assert (! (forall ((?v0 (-> Event_list$ Bool)) (?v1 Event_list$)) (=> (and (?v0 nil$) (and (forall ((?v2 Event$)) (?v0 (cons$ ?v2 nil$))) (forall ((?v2 Event$) (?v3 Event$) (?v4 Event_list$)) (=> (?v0 (cons$ ?v3 ?v4)) (?v0 (cons$ ?v2 (cons$ ?v3 ?v4))))))) (?v0 ?v1))) :named a140))
-(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event_list$ Bool))) (=> (and (not (= ?v0 nil$)) (and (forall ((?v2 Event$)) (?v1 (cons$ ?v2 nil$))) (forall ((?v2 Event$) (?v3 Event_list$)) (=> (and (not (= ?v3 nil$)) (?v1 ?v3)) (?v1 (cons$ ?v2 ?v3)))))) (?v1 ?v0))) :named a141))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 Event$) (?v3 Event_list$)) (! (= (splice$ (cons$ ?v0 ?v1) (cons$ ?v2 ?v3)) (cons$ ?v0 (cons$ ?v2 (splice$ ?v1 ?v3)))) :pattern ((splice$ (cons$ ?v0 ?v1) (cons$ ?v2 ?v3))))) :named a142))
-(assert (! (forall ((?v0 Agent$) (?v1 Event_list$) (?v2 Event$)) (less_eq$ (knows$ ?v0 ?v1) (knows$ ?v0 (cons$ ?v2 ?v1)))) :named a143))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (! (= (null$ (cons$ ?v0 ?v1)) false) :pattern ((cons$ ?v0 ?v1)))) :named a144))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 Event$)) (! (= (member$d (cons$ ?v0 ?v1) ?v2) (or (= ?v0 ?v2) (member$d ?v1 ?v2))) :pattern ((member$d (cons$ ?v0 ?v1) ?v2)))) :named a145))
-(assert (! (forall ((?v0 Agent$) (?v1 Event_list$)) (less_eq$ (initState$ ?v0) (knows$ ?v0 ?v1))) :named a146))
-(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event$) (?v2 Event_list$)) (! (= (takeWhile$ ?v0 (cons$ ?v1 ?v2)) (ite (?v0 ?v1) (cons$ ?v1 (takeWhile$ ?v0 ?v2)) nil$)) :pattern ((takeWhile$ ?v0 (cons$ ?v1 ?v2))))) :named a147))
-(assert (! (forall ((?v0 Event_list$) (?v1 Agent$) (?v2 Msg$)) (less_eq$ (knows$ spy$ ?v0) (knows$ spy$ (cons$ (gets$ ?v1 ?v2) ?v0)))) :named a148))
-(assert (! (forall ((?v0 Event$)) (! (= (insert$a ?v0 nil$) (cons$ ?v0 nil$)) :pattern ((insert$a ?v0)))) :named a149))
-(assert (! (forall ((?v0 Agent$) (?v1 Msg$) (?v2 Event_list$)) (! (= (knows$ spy$ (cons$ (gets$ ?v0 ?v1) ?v2)) (knows$ spy$ ?v2)) :pattern ((cons$ (gets$ ?v0 ?v1) ?v2)))) :named a150))
-(assert (! (forall ((?v0 Event_list$) (?v1 Agent$) (?v2 Msg$)) (less_eq$ (knows$ spy$ ?v0) (knows$ spy$ (cons$ (notes$ ?v1 ?v2) ?v0)))) :named a151))
-(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event$) (?v2 Event_list$)) (= (list_ex1$ ?v0 (cons$ ?v1 ?v2)) (ite (?v0 ?v1) (list_all$ (uui$ ?v0 ?v1) ?v2) (list_ex1$ ?v0 ?v2)))) :named a152))
-(assert (! (forall ((?v0 Agent$) (?v1 Msg$) (?v2 Agent$) (?v3 Msg$)) (= (= (notes$ ?v0 ?v1) (notes$ ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3)))) :named a153))
-(assert (! (forall ((?v0 Agent$) (?v1 Msg$) (?v2 Agent$) (?v3 Msg$)) (= (= (gets$ ?v0 ?v1) (gets$ ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3)))) :named a154))
-(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event$) (?v2 Event_list$)) (! (= (list_all$ ?v0 (cons$ ?v1 ?v2)) (and (?v0 ?v1) (list_all$ ?v0 ?v2))) :pattern ((list_all$ ?v0 (cons$ ?v1 ?v2))))) :named a155))
-(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event$) (?v2 Event_list$)) (! (= (list_all$ ?v0 (cons$ ?v1 ?v2)) (and (?v0 ?v1) (list_all$ ?v0 ?v2))) :pattern ((list_all$ ?v0 (cons$ ?v1 ?v2))))) :named a156))
-(assert (! (forall ((?v0 (-> Event$ Bool))) (! (= (list_all$ ?v0 nil$) true) :pattern ((list_all$ ?v0)))) :named a157))
-(assert (! (forall ((?v0 Agent$) (?v1 Msg$) (?v2 Agent$) (?v3 Msg$)) (not (= (gets$ ?v0 ?v1) (notes$ ?v2 ?v3)))) :named a158))
-(assert (! (forall ((?v0 (-> Event$ Bool))) (list_all$ ?v0 nil$)) :named a159))
-(assert (! (forall ((?v0 Agent$) (?v1 Event_list$) (?v2 Agent$) (?v3 Msg$)) (less_eq$ (knows$ ?v0 ?v1) (knows$ ?v0 (cons$ (notes$ ?v2 ?v3) ?v1)))) :named a160))
-(assert (! (forall ((?v0 Agent$) (?v1 Event_list$) (?v2 Agent$) (?v3 Msg$)) (less_eq$ (knows$ ?v0 ?v1) (knows$ ?v0 (cons$ (gets$ ?v2 ?v3) ?v1)))) :named a161))
-(assert (! (= (product_lists$ nil$a) (cons$a nil$ nil$a)) :named a162))
-(assert (! (forall ((?v0 Event_list$) (?v1 Agent$) (?v2 Msg$)) (= (knows$ spy$ (append$ ?v0 (cons$ (gets$ ?v1 ?v2) nil$))) (knows$ spy$ ?v0))) :named a163))
-(assert (! (= (subseqs$ nil$) (cons$a nil$ nil$a)) :named a164))
-(assert (! (forall ((?v0 Event_list$) (?v1 Agent$) (?v2 Agent$) (?v3 Msg$)) (less_eq$ (knows$ spy$ ?v0) (knows$ spy$ (cons$ (says$ ?v1 ?v2 ?v3) ?v0)))) :named a165))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 Event_list$)) (= (append$ (append$ ?v0 ?v1) ?v2) (append$ ?v0 (append$ ?v1 ?v2)))) :named a166))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 Event_list$)) (= (append$ (append$ ?v0 ?v1) ?v2) (append$ ?v0 (append$ ?v1 ?v2)))) :named a167))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 Event_list$)) (= (= (append$ ?v0 ?v1) (append$ ?v2 ?v1)) (= ?v0 ?v2))) :named a168))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 Event_list$)) (= (= (append$ ?v0 ?v1) (append$ ?v0 ?v2)) (= ?v1 ?v2))) :named a169))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent$) (?v2 Msg$) (?v3 Agent$) (?v4 Agent$) (?v5 Msg$)) (= (= (says$ ?v0 ?v1 ?v2) (says$ ?v3 ?v4 ?v5)) (and (= ?v0 ?v3) (and (= ?v1 ?v4) (= ?v2 ?v5))))) :named a170))
-(assert (! (forall ((?v0 Event_list$)) (! (= (append$ ?v0 nil$) ?v0) :pattern ((append$ ?v0)))) :named a171))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$)) (= (= (append$ ?v0 ?v1) ?v0) (= ?v1 nil$))) :named a172))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$)) (= (= ?v0 (append$ ?v0 ?v1)) (= ?v1 nil$))) :named a173))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$)) (= (= (append$ ?v0 ?v1) ?v1) (= ?v0 nil$))) :named a174))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$)) (= (= ?v0 (append$ ?v1 ?v0)) (= ?v1 nil$))) :named a175))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$)) (= (= nil$ (append$ ?v0 ?v1)) (and (= ?v0 nil$) (= ?v1 nil$)))) :named a176))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$)) (= (= (append$ ?v0 ?v1) nil$) (and (= ?v0 nil$) (= ?v1 nil$)))) :named a177))
-(assert (! (forall ((?v0 Event_list$)) (! (= (append$ ?v0 nil$) ?v0) :pattern ((append$ ?v0)))) :named a178))
-(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event_list$) (?v2 Event_list$)) (= (list_all$ ?v0 (append$ ?v1 ?v2)) (and (list_all$ ?v0 ?v1) (list_all$ ?v0 ?v2)))) :named a179))
-(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event_list$) (?v2 Event_list$)) (= (list_ex$ ?v0 (append$ ?v1 ?v2)) (or (list_ex$ ?v0 ?v1) (list_ex$ ?v0 ?v2)))) :named a180))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event$) (?v2 Event_list$) (?v3 Event$)) (= (= (append$ ?v0 (cons$ ?v1 nil$)) (append$ ?v2 (cons$ ?v3 nil$))) (and (= ?v0 ?v2) (= ?v1 ?v3)))) :named a181))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 (-> Event$ Event_list$))) (! (= (bind$ (cons$ ?v0 ?v1) ?v2) (append$ (?v2 ?v0) (bind$ ?v1 ?v2))) :pattern ((bind$ (cons$ ?v0 ?v1) ?v2)))) :named a182))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 Event_list$)) (! (= (append$ (cons$ ?v0 ?v1) ?v2) (cons$ ?v0 (append$ ?v1 ?v2))) :pattern ((append$ (cons$ ?v0 ?v1) ?v2)))) :named a183))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 Event_list$) (?v3 Event_list$) (?v4 Event_list$)) (=> (and (= (cons$ ?v0 ?v1) ?v2) (= ?v3 (append$ ?v1 ?v4))) (= (cons$ ?v0 ?v3) (append$ ?v2 ?v4)))) :named a184))
-(assert (! (forall ((?v0 Event_list$)) (! (= (append$ nil$ ?v0) ?v0) :pattern ((append$ nil$ ?v0)))) :named a185))
-(assert (! (forall ((?v0 Event_list$)) (! (= (append$ nil$ ?v0) ?v0) :pattern ((append$ nil$ ?v0)))) :named a186))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$)) (=> (= ?v0 ?v1) (= ?v0 (append$ nil$ ?v1)))) :named a187))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 Event_list$) (?v3 Event_list$) (?v4 Event_list$)) (=> (and (= (append$ ?v0 ?v1) ?v2) (= ?v3 (append$ ?v1 ?v4))) (= (append$ ?v0 ?v3) (append$ ?v2 ?v4)))) :named a188))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 Event_list$) (?v3 Event_list$)) (= (= (append$ ?v0 ?v1) (append$ ?v2 ?v3)) (exists ((?v4 Event_list$)) (or (and (= ?v0 (append$ ?v2 ?v4)) (= (append$ ?v4 ?v1) ?v3)) (and (= (append$ ?v0 ?v4) ?v2) (= ?v1 (append$ ?v4 ?v3))))))) :named a189))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent$) (?v2 Msg$) (?v3 Agent$) (?v4 Msg$)) (not (= (says$ ?v0 ?v1 ?v2) (notes$ ?v3 ?v4)))) :named a190))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent$) (?v2 Msg$) (?v3 Agent$) (?v4 Msg$)) (not (= (says$ ?v0 ?v1 ?v2) (gets$ ?v3 ?v4)))) :named a191))
-(assert (! (forall ((?v0 (-> Event_list$ Bool)) (?v1 Event_list$)) (=> (and (?v0 nil$) (forall ((?v2 Event$) (?v3 Event_list$)) (=> (?v0 ?v3) (?v0 (append$ ?v3 (cons$ ?v2 nil$)))))) (?v0 ?v1))) :named a192))
-(assert (! (forall ((?v0 Event_list$)) (=> (and (=> (= ?v0 nil$) false) (forall ((?v1 Event_list$) (?v2 Event$)) (=> (= ?v0 (append$ ?v1 (cons$ ?v2 nil$))) false))) false)) :named a193))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 Event_list$) (?v3 Event_list$)) (= (= (cons$ ?v0 ?v1) (append$ ?v2 ?v3)) (or (and (= ?v2 nil$) (= (cons$ ?v0 ?v1) ?v3)) (exists ((?v4 Event_list$)) (and (= (cons$ ?v0 ?v4) ?v2) (= ?v1 (append$ ?v4 ?v3))))))) :named a194))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 Event$) (?v3 Event_list$)) (= (= (append$ ?v0 ?v1) (cons$ ?v2 ?v3)) (or (and (= ?v0 nil$) (= ?v1 (cons$ ?v2 ?v3))) (exists ((?v4 Event_list$)) (and (= ?v0 (cons$ ?v2 ?v4)) (= (append$ ?v4 ?v1) ?v3)))))) :named a195))
-(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event_list$ Bool))) (=> (and (not (= ?v0 nil$)) (and (forall ((?v2 Event$)) (?v1 (cons$ ?v2 nil$))) (forall ((?v2 Event$) (?v3 Event_list$)) (=> (and (not (= ?v3 nil$)) (?v1 ?v3)) (?v1 (append$ ?v3 (cons$ ?v2 nil$))))))) (?v1 ?v0))) :named a196))
-(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event$) (?v2 Event_list$) (?v3 Event_list$)) (=> (not (?v0 ?v1)) (= (takeWhile$ ?v0 (append$ ?v2 (cons$ ?v1 ?v3))) (takeWhile$ ?v0 ?v2)))) :named a197))
-(assert (! (forall ((?v0 Event$)) (=> (and (forall ((?v1 Agent$) (?v2 Agent$) (?v3 Msg$)) (=> (= ?v0 (says$ ?v1 ?v2 ?v3)) false)) (and (forall ((?v1 Agent$) (?v2 Msg$)) (=> (= ?v0 (gets$ ?v1 ?v2)) false)) (forall ((?v1 Agent$) (?v2 Msg$)) (=> (= ?v0 (notes$ ?v1 ?v2)) false)))) false)) :named a198))
-(assert (! (forall ((?v0 (-> Event$ Event_list$)) (?v1 Event$) (?v2 Event_list$)) (! (= (maps$ ?v0 (cons$ ?v1 ?v2)) (append$ (?v0 ?v1) (maps$ ?v0 ?v2))) :pattern ((maps$ ?v0 (cons$ ?v1 ?v2))))) :named a199))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (= (rotate1$ (cons$ ?v0 ?v1)) (append$ ?v1 (cons$ ?v0 nil$)))) :named a200))
-(assert (! (forall ((?v0 Agent$) (?v1 Event_list$) (?v2 Agent$) (?v3 Agent$) (?v4 Msg$)) (less_eq$ (knows$ ?v0 ?v1) (knows$ ?v0 (cons$ (says$ ?v2 ?v3 ?v4) ?v1)))) :named a201))
-(assert (! (forall ((?v0 Event_list_set$) (?v1 Event_list$)) (= (succ$ ?v0 ?v1) (collect$a (uuj$ ?v0 ?v1)))) :named a202))
-(assert (! (forall ((?v0 Event_list$) (?v1 Agent$) (?v2 Agent$) (?v3 Msg$)) (= (knows$ spy$ (append$ ?v0 (cons$ (says$ ?v1 ?v2 ?v3) nil$))) (insert$ ?v3 (knows$ spy$ ?v0)))) :named a203))
-(assert (! (forall ((?v0 Msg$) (?v1 Agent$) (?v2 Event_list$)) (=> (and (member$a ?v0 (knows$ ?v1 ?v2)) (not (= ?v1 spy$))) (exists ((?v3 Agent$)) (or (member$b (says$ ?v1 ?v3 ?v0) (set$ ?v2)) (or (member$b (gets$ ?v1 ?v0) (set$ ?v2)) (or (member$b (notes$ ?v1 ?v0) (set$ ?v2)) (member$a ?v0 (initState$ ?v1)))))))) :named a204))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_list_set$) (?v2 Msg_list$)) (=> (member$a ?v0 (succ$a ?v1 ?v2)) (member$e (append$a ?v2 (cons$b ?v0 nil$b)) ?v1))) :named a205))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_list_set$) (?v2 Agent_list$)) (=> (member$ ?v0 (succ$b ?v1 ?v2)) (member$f (append$b ?v2 (cons$c ?v0 nil$c)) ?v1))) :named a206))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list_set$) (?v2 Event_list$)) (=> (member$b ?v0 (succ$ ?v1 ?v2)) (member$c (append$ ?v2 (cons$ ?v0 nil$)) ?v1))) :named a207))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$)) (= (insert$ ?v0 (insert$ ?v0 ?v1)) (insert$ ?v0 ?v1))) :named a208))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg$) (?v2 Msg_set$)) (= (member$a ?v0 (insert$ ?v1 ?v2)) (or (= ?v0 ?v1) (member$a ?v0 ?v2)))) :named a209))
-(assert (! (forall ((?v0 Event$) (?v1 Event$) (?v2 Event_set$)) (= (member$b ?v0 (insert$b ?v1 ?v2)) (or (= ?v0 ?v1) (member$b ?v0 ?v2)))) :named a210))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent$) (?v2 Agent_set$)) (= (member$ ?v0 (insert$c ?v1 ?v2)) (or (= ?v0 ?v1) (member$ ?v0 ?v2)))) :named a211))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg$)) (=> (=> (not (member$a ?v0 ?v1)) (= ?v0 ?v2)) (member$a ?v0 (insert$ ?v2 ?v1)))) :named a212))
-(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event$)) (=> (=> (not (member$b ?v0 ?v1)) (= ?v0 ?v2)) (member$b ?v0 (insert$b ?v2 ?v1)))) :named a213))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent$)) (=> (=> (not (member$ ?v0 ?v1)) (= ?v0 ?v2)) (member$ ?v0 (insert$c ?v2 ?v1)))) :named a214))
-(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event_set$)) (= (less_eq$a (insert$b ?v0 ?v1) ?v2) (and (member$b ?v0 ?v2) (less_eq$a ?v1 ?v2)))) :named a215))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent_set$)) (= (less_eq$b (insert$c ?v0 ?v1) ?v2) (and (member$ ?v0 ?v2) (less_eq$b ?v1 ?v2)))) :named a216))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg_set$)) (= (less_eq$ (insert$ ?v0 ?v1) ?v2) (and (member$a ?v0 ?v2) (less_eq$ ?v1 ?v2)))) :named a217))
-(assert (! (forall ((?v0 (-> Msg$ Bool)) (?v1 Msg_list$)) (= (= (takeWhile$a ?v0 ?v1) ?v1) (forall ((?v2 Msg$)) (=> (member$a ?v2 (set$a ?v1)) (?v0 ?v2))))) :named a218))
-(assert (! (forall ((?v0 (-> Agent$ Bool)) (?v1 Agent_list$)) (= (= (takeWhile$b ?v0 ?v1) ?v1) (forall ((?v2 Agent$)) (=> (member$ ?v2 (set$b ?v1)) (?v0 ?v2))))) :named a219))
-(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event_list$)) (= (= (takeWhile$ ?v0 ?v1) ?v1) (forall ((?v2 Event$)) (=> (member$b ?v2 (set$ ?v1)) (?v0 ?v2))))) :named a220))
-(assert (! (forall ((?v0 Event_list$)) (= (set$ (rotate1$ ?v0)) (set$ ?v0))) :named a221))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (! (=> (member$a ?v0 (set$a ?v1)) (= (insert$d ?v0 ?v1) ?v1)) :pattern ((insert$d ?v0 ?v1)))) :named a222))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (! (=> (member$ ?v0 (set$b ?v1)) (= (insert$e ?v0 ?v1) ?v1)) :pattern ((insert$e ?v0 ?v1)))) :named a223))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (! (=> (member$b ?v0 (set$ ?v1)) (= (insert$a ?v0 ?v1) ?v1)) :pattern ((insert$a ?v0 ?v1)))) :named a224))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (! (= (set$a (cons$b ?v0 ?v1)) (insert$ ?v0 (set$a ?v1))) :pattern ((cons$b ?v0 ?v1)))) :named a225))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (! (= (set$ (cons$ ?v0 ?v1)) (insert$b ?v0 (set$ ?v1))) :pattern ((cons$ ?v0 ?v1)))) :named a226))
-(assert (! (forall ((?v0 Msg_list$) (?v1 (-> Msg$ Bool)) (?v2 Msg_list$)) (=> (forall ((?v3 Msg$)) (=> (member$a ?v3 (set$a ?v0)) (?v1 ?v3))) (= (takeWhile$a ?v1 (append$a ?v0 ?v2)) (append$a ?v0 (takeWhile$a ?v1 ?v2))))) :named a227))
-(assert (! (forall ((?v0 Agent_list$) (?v1 (-> Agent$ Bool)) (?v2 Agent_list$)) (=> (forall ((?v3 Agent$)) (=> (member$ ?v3 (set$b ?v0)) (?v1 ?v3))) (= (takeWhile$b ?v1 (append$b ?v0 ?v2)) (append$b ?v0 (takeWhile$b ?v1 ?v2))))) :named a228))
-(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event$ Bool)) (?v2 Event_list$)) (=> (forall ((?v3 Event$)) (=> (member$b ?v3 (set$ ?v0)) (?v1 ?v3))) (= (takeWhile$ ?v1 (append$ ?v0 ?v2)) (append$ ?v0 (takeWhile$ ?v1 ?v2))))) :named a229))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$) (?v2 (-> Msg$ Bool)) (?v3 Msg_list$)) (=> (and (member$a ?v0 (set$a ?v1)) (not (?v2 ?v0))) (= (takeWhile$a ?v2 (append$a ?v1 ?v3)) (takeWhile$a ?v2 ?v1)))) :named a230))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$) (?v2 (-> Agent$ Bool)) (?v3 Agent_list$)) (=> (and (member$ ?v0 (set$b ?v1)) (not (?v2 ?v0))) (= (takeWhile$b ?v2 (append$b ?v1 ?v3)) (takeWhile$b ?v2 ?v1)))) :named a231))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 (-> Event$ Bool)) (?v3 Event_list$)) (=> (and (member$b ?v0 (set$ ?v1)) (not (?v2 ?v0))) (= (takeWhile$ ?v2 (append$ ?v1 ?v3)) (takeWhile$ ?v2 ?v1)))) :named a232))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (= (set$a (insert$d ?v0 ?v1)) (insert$ ?v0 (set$a ?v1)))) :named a233))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (= (set$ (insert$a ?v0 ?v1)) (insert$b ?v0 (set$ ?v1)))) :named a234))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (! (=> (not (member$a ?v0 (set$a ?v1))) (= (insert$d ?v0 ?v1) (cons$b ?v0 ?v1))) :pattern ((insert$d ?v0 ?v1)))) :named a235))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (! (=> (not (member$ ?v0 (set$b ?v1))) (= (insert$e ?v0 ?v1) (cons$c ?v0 ?v1))) :pattern ((insert$e ?v0 ?v1)))) :named a236))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (! (=> (not (member$b ?v0 (set$ ?v1))) (= (insert$a ?v0 ?v1) (cons$ ?v0 ?v1))) :pattern ((insert$a ?v0 ?v1)))) :named a237))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent$) (?v2 Msg$) (?v3 Event_list$)) (! (= (knows$ spy$ (cons$ (says$ ?v0 ?v1 ?v2) ?v3)) (insert$ ?v2 (knows$ spy$ ?v3))) :pattern ((cons$ (says$ ?v0 ?v1 ?v2) ?v3)))) :named a238))
-(assert (! (forall ((?v0 Agent_list$) (?v1 Agent_set$)) (= (less_eq$b (set$b ?v0) ?v1) (forall ((?v2 Agent$)) (=> (member$ ?v2 (set$b ?v0)) (member$ ?v2 ?v1))))) :named a239))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_set$)) (= (less_eq$a (set$ ?v0) ?v1) (forall ((?v2 Event$)) (=> (member$b ?v2 (set$ ?v0)) (member$b ?v2 ?v1))))) :named a240))
-(assert (! (forall ((?v0 Msg_list$) (?v1 Msg_set$)) (= (less_eq$ (set$a ?v0) ?v1) (forall ((?v2 Msg$)) (=> (member$a ?v2 (set$a ?v0)) (member$a ?v2 ?v1))))) :named a241))
-(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event_set$)) (=> (and (member$b ?v0 ?v1) (less_eq$a ?v2 ?v1)) (less_eq$a (insert$b ?v0 ?v2) ?v1))) :named a242))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent_set$)) (=> (and (member$ ?v0 ?v1) (less_eq$b ?v2 ?v1)) (less_eq$b (insert$c ?v0 ?v2) ?v1))) :named a243))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (member$a ?v0 ?v1) (less_eq$ ?v2 ?v1)) (less_eq$ (insert$ ?v0 ?v2) ?v1))) :named a244))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg$)) (=> (less_eq$ ?v0 ?v1) (less_eq$ ?v0 (insert$ ?v2 ?v1)))) :named a245))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg$)) (less_eq$ ?v0 (insert$ ?v1 ?v0))) :named a246))
-(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event_set$)) (=> (not (member$b ?v0 ?v1)) (= (less_eq$a ?v1 (insert$b ?v0 ?v2)) (less_eq$a ?v1 ?v2)))) :named a247))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent_set$)) (=> (not (member$ ?v0 ?v1)) (= (less_eq$b ?v1 (insert$c ?v0 ?v2)) (less_eq$b ?v1 ?v2)))) :named a248))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (not (member$a ?v0 ?v1)) (= (less_eq$ ?v1 (insert$ ?v0 ?v2)) (less_eq$ ?v1 ?v2)))) :named a249))
-(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg$)) (=> (less_eq$ ?v0 ?v1) (less_eq$ (insert$ ?v2 ?v0) (insert$ ?v2 ?v1)))) :named a250))
-(assert (! (forall ((?v0 Msg_list$) (?v1 Msg_list$) (?v2 (-> Msg$ Bool)) (?v3 (-> Msg$ Bool))) (=> (and (= ?v0 ?v1) (forall ((?v4 Msg$)) (=> (member$a ?v4 (set$a ?v1)) (= (?v2 ?v4) (?v3 ?v4))))) (= (list_ex$a ?v2 ?v0) (list_ex$a ?v3 ?v1)))) :named a251))
-(assert (! (forall ((?v0 Agent_list$) (?v1 Agent_list$) (?v2 (-> Agent$ Bool)) (?v3 (-> Agent$ Bool))) (=> (and (= ?v0 ?v1) (forall ((?v4 Agent$)) (=> (member$ ?v4 (set$b ?v1)) (= (?v2 ?v4) (?v3 ?v4))))) (= (list_ex$b ?v2 ?v0) (list_ex$b ?v3 ?v1)))) :named a252))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 (-> Event$ Bool)) (?v3 (-> Event$ Bool))) (=> (and (= ?v0 ?v1) (forall ((?v4 Event$)) (=> (member$b ?v4 (set$ ?v1)) (= (?v2 ?v4) (?v3 ?v4))))) (= (list_ex$ ?v2 ?v0) (list_ex$ ?v3 ?v1)))) :named a253))
-(assert (! (forall ((?v0 Msg$) (?v1 (-> Msg$ Bool))) (= (insert$ ?v0 (collect$ ?v1)) (collect$ (uuk$ ?v0 ?v1)))) :named a254))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$)) (= (insert$ ?v0 ?v1) (collect$ (uul$ ?v0 ?v1)))) :named a255))
-(assert (! (forall ((?v0 Event$) (?v1 Event_set$)) (= (insert$b ?v0 ?v1) (collect$a (uum$ ?v0 ?v1)))) :named a256))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$)) (= (insert$c ?v0 ?v1) (collect$b (uun$ ?v0 ?v1)))) :named a257))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$)) (=> (member$a ?v0 ?v1) (exists ((?v2 Msg_set$)) (and (= ?v1 (insert$ ?v0 ?v2)) (not (member$a ?v0 ?v2)))))) :named a258))
-(assert (! (forall ((?v0 Event$) (?v1 Event_set$)) (=> (member$b ?v0 ?v1) (exists ((?v2 Event_set$)) (and (= ?v1 (insert$b ?v0 ?v2)) (not (member$b ?v0 ?v2)))))) :named a259))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$)) (=> (member$ ?v0 ?v1) (exists ((?v2 Agent_set$)) (and (= ?v1 (insert$c ?v0 ?v2)) (not (member$ ?v0 ?v2)))))) :named a260))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg$) (?v2 Msg_set$)) (= (insert$ ?v0 (insert$ ?v1 ?v2)) (insert$ ?v1 (insert$ ?v0 ?v2)))) :named a261))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg$) (?v3 Msg_set$)) (=> (and (not (member$a ?v0 ?v1)) (not (member$a ?v2 ?v3))) (= (= (insert$ ?v0 ?v1) (insert$ ?v2 ?v3)) (ite (= ?v0 ?v2) (= ?v1 ?v3) (exists ((?v4 Msg_set$)) (and (= ?v1 (insert$ ?v2 ?v4)) (and (not (member$a ?v2 ?v4)) (and (= ?v3 (insert$ ?v0 ?v4)) (not (member$a ?v0 ?v4)))))))))) :named a262))
-(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event$) (?v3 Event_set$)) (=> (and (not (member$b ?v0 ?v1)) (not (member$b ?v2 ?v3))) (= (= (insert$b ?v0 ?v1) (insert$b ?v2 ?v3)) (ite (= ?v0 ?v2) (= ?v1 ?v3) (exists ((?v4 Event_set$)) (and (= ?v1 (insert$b ?v2 ?v4)) (and (not (member$b ?v2 ?v4)) (and (= ?v3 (insert$b ?v0 ?v4)) (not (member$b ?v0 ?v4)))))))))) :named a263))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent$) (?v3 Agent_set$)) (=> (and (not (member$ ?v0 ?v1)) (not (member$ ?v2 ?v3))) (= (= (insert$c ?v0 ?v1) (insert$c ?v2 ?v3)) (ite (= ?v0 ?v2) (= ?v1 ?v3) (exists ((?v4 Agent_set$)) (and (= ?v1 (insert$c ?v2 ?v4)) (and (not (member$ ?v2 ?v4)) (and (= ?v3 (insert$c ?v0 ?v4)) (not (member$ ?v0 ?v4)))))))))) :named a264))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$)) (! (=> (member$a ?v0 ?v1) (= (insert$ ?v0 ?v1) ?v1)) :pattern ((insert$ ?v0 ?v1)))) :named a265))
-(assert (! (forall ((?v0 Event$) (?v1 Event_set$)) (! (=> (member$b ?v0 ?v1) (= (insert$b ?v0 ?v1) ?v1)) :pattern ((insert$b ?v0 ?v1)))) :named a266))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$)) (! (=> (member$ ?v0 ?v1) (= (insert$c ?v0 ?v1) ?v1)) :pattern ((insert$c ?v0 ?v1)))) :named a267))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (not (member$a ?v0 ?v1)) (not (member$a ?v0 ?v2))) (= (= (insert$ ?v0 ?v1) (insert$ ?v0 ?v2)) (= ?v1 ?v2)))) :named a268))
-(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event_set$)) (=> (and (not (member$b ?v0 ?v1)) (not (member$b ?v0 ?v2))) (= (= (insert$b ?v0 ?v1) (insert$b ?v0 ?v2)) (= ?v1 ?v2)))) :named a269))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent_set$)) (=> (and (not (member$ ?v0 ?v1)) (not (member$ ?v0 ?v2))) (= (= (insert$c ?v0 ?v1) (insert$c ?v0 ?v2)) (= ?v1 ?v2)))) :named a270))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$)) (=> (and (member$a ?v0 ?v1) (forall ((?v2 Msg_set$)) (=> (and (= ?v1 (insert$ ?v0 ?v2)) (not (member$a ?v0 ?v2))) false))) false)) :named a271))
-(assert (! (forall ((?v0 Event$) (?v1 Event_set$)) (=> (and (member$b ?v0 ?v1) (forall ((?v2 Event_set$)) (=> (and (= ?v1 (insert$b ?v0 ?v2)) (not (member$b ?v0 ?v2))) false))) false)) :named a272))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$)) (=> (and (member$ ?v0 ?v1) (forall ((?v2 Agent_set$)) (=> (and (= ?v1 (insert$c ?v0 ?v2)) (not (member$ ?v0 ?v2))) false))) false)) :named a273))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg$)) (=> (member$a ?v0 ?v1) (member$a ?v0 (insert$ ?v2 ?v1)))) :named a274))
-(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event$)) (=> (member$b ?v0 ?v1) (member$b ?v0 (insert$b ?v2 ?v1)))) :named a275))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent$)) (=> (member$ ?v0 ?v1) (member$ ?v0 (insert$c ?v2 ?v1)))) :named a276))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$)) (member$a ?v0 (insert$ ?v0 ?v1))) :named a277))
-(assert (! (forall ((?v0 Event$) (?v1 Event_set$)) (member$b ?v0 (insert$b ?v0 ?v1))) :named a278))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$)) (member$ ?v0 (insert$c ?v0 ?v1))) :named a279))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg$) (?v2 Msg_set$)) (=> (and (member$a ?v0 (insert$ ?v1 ?v2)) (and (=> (= ?v0 ?v1) false) (=> (member$a ?v0 ?v2) false))) false)) :named a280))
-(assert (! (forall ((?v0 Event$) (?v1 Event$) (?v2 Event_set$)) (=> (and (member$b ?v0 (insert$b ?v1 ?v2)) (and (=> (= ?v0 ?v1) false) (=> (member$b ?v0 ?v2) false))) false)) :named a281))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent$) (?v2 Agent_set$)) (=> (and (member$ ?v0 (insert$c ?v1 ?v2)) (and (=> (= ?v0 ?v1) false) (=> (member$ ?v0 ?v2) false))) false)) :named a282))
-(assert (! (forall ((?v0 Msg$) (?v1 (-> Msg$ Bool)) (?v2 Msg_list$)) (=> (member$a ?v0 (set$a (takeWhile$a ?v1 ?v2))) (and (member$a ?v0 (set$a ?v2)) (?v1 ?v0)))) :named a283))
-(assert (! (forall ((?v0 Agent$) (?v1 (-> Agent$ Bool)) (?v2 Agent_list$)) (=> (member$ ?v0 (set$b (takeWhile$b ?v1 ?v2))) (and (member$ ?v0 (set$b ?v2)) (?v1 ?v0)))) :named a284))
-(assert (! (forall ((?v0 Event$) (?v1 (-> Event$ Bool)) (?v2 Event_list$)) (=> (member$b ?v0 (set$ (takeWhile$ ?v1 ?v2))) (and (member$b ?v0 (set$ ?v2)) (?v1 ?v0)))) :named a285))
-(assert (! (forall ((?v0 Msg_list$) (?v1 Msg_list$) (?v2 (-> Msg$ Bool)) (?v3 (-> Msg$ Bool))) (=> (and (= ?v0 ?v1) (forall ((?v4 Msg$)) (=> (member$a ?v4 (set$a ?v0)) (= (?v2 ?v4) (?v3 ?v4))))) (= (takeWhile$a ?v2 ?v0) (takeWhile$a ?v3 ?v1)))) :named a286))
-(assert (! (forall ((?v0 Agent_list$) (?v1 Agent_list$) (?v2 (-> Agent$ Bool)) (?v3 (-> Agent$ Bool))) (=> (and (= ?v0 ?v1) (forall ((?v4 Agent$)) (=> (member$ ?v4 (set$b ?v0)) (= (?v2 ?v4) (?v3 ?v4))))) (= (takeWhile$b ?v2 ?v0) (takeWhile$b ?v3 ?v1)))) :named a287))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 (-> Event$ Bool)) (?v3 (-> Event$ Bool))) (=> (and (= ?v0 ?v1) (forall ((?v4 Event$)) (=> (member$b ?v4 (set$ ?v0)) (= (?v2 ?v4) (?v3 ?v4))))) (= (takeWhile$ ?v2 ?v0) (takeWhile$ ?v3 ?v1)))) :named a288))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$) (?v2 Msg$)) (=> (member$a ?v0 (set$a ?v1)) (member$a ?v0 (set$a (cons$b ?v2 ?v1))))) :named a289))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$) (?v2 Agent$)) (=> (member$ ?v0 (set$b ?v1)) (member$ ?v0 (set$b (cons$c ?v2 ?v1))))) :named a290))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 Event$)) (=> (member$b ?v0 (set$ ?v1)) (member$b ?v0 (set$ (cons$ ?v2 ?v1))))) :named a291))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (member$a ?v0 (set$a (cons$b ?v0 ?v1)))) :named a292))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (member$ ?v0 (set$b (cons$c ?v0 ?v1)))) :named a293))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (member$b ?v0 (set$ (cons$ ?v0 ?v1)))) :named a294))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg$) (?v2 Msg_list$)) (=> (member$a ?v0 (set$a (cons$b ?v1 ?v2))) (or (= ?v0 ?v1) (member$a ?v0 (set$a ?v2))))) :named a295))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent$) (?v2 Agent_list$)) (=> (member$ ?v0 (set$b (cons$c ?v1 ?v2))) (or (= ?v0 ?v1) (member$ ?v0 (set$b ?v2))))) :named a296))
-(assert (! (forall ((?v0 Event$) (?v1 Event$) (?v2 Event_list$)) (=> (member$b ?v0 (set$ (cons$ ?v1 ?v2))) (or (= ?v0 ?v1) (member$b ?v0 (set$ ?v2))))) :named a297))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (=> (and (member$a ?v0 (set$a ?v1)) (and (forall ((?v2 Msg_list$)) (=> (= ?v1 (cons$b ?v0 ?v2)) false)) (forall ((?v2 Msg$) (?v3 Msg_list$)) (=> (and (= ?v1 (cons$b ?v2 ?v3)) (member$a ?v0 (set$a ?v3))) false)))) false)) :named a298))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (=> (and (member$ ?v0 (set$b ?v1)) (and (forall ((?v2 Agent_list$)) (=> (= ?v1 (cons$c ?v0 ?v2)) false)) (forall ((?v2 Agent$) (?v3 Agent_list$)) (=> (and (= ?v1 (cons$c ?v2 ?v3)) (member$ ?v0 (set$b ?v3))) false)))) false)) :named a299))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (=> (and (member$b ?v0 (set$ ?v1)) (and (forall ((?v2 Event_list$)) (=> (= ?v1 (cons$ ?v0 ?v2)) false)) (forall ((?v2 Event$) (?v3 Event_list$)) (=> (and (= ?v1 (cons$ ?v2 ?v3)) (member$b ?v0 (set$ ?v3))) false)))) false)) :named a300))
-(assert (! (forall ((?v0 Msg_list$) (?v1 Msg_list$) (?v2 (-> Msg$ Bool)) (?v3 (-> Msg$ Bool))) (=> (and (= ?v0 ?v1) (forall ((?v4 Msg$)) (=> (member$a ?v4 (set$a ?v1)) (= (?v2 ?v4) (?v3 ?v4))))) (= (list_all$a ?v2 ?v0) (list_all$a ?v3 ?v1)))) :named a301))
-(assert (! (forall ((?v0 Agent_list$) (?v1 Agent_list$) (?v2 (-> Agent$ Bool)) (?v3 (-> Agent$ Bool))) (=> (and (= ?v0 ?v1) (forall ((?v4 Agent$)) (=> (member$ ?v4 (set$b ?v1)) (= (?v2 ?v4) (?v3 ?v4))))) (= (list_all$b ?v2 ?v0) (list_all$b ?v3 ?v1)))) :named a302))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 (-> Event$ Bool)) (?v3 (-> Event$ Bool))) (=> (and (= ?v0 ?v1) (forall ((?v4 Event$)) (=> (member$b ?v4 (set$ ?v1)) (= (?v2 ?v4) (?v3 ?v4))))) (= (list_all$ ?v2 ?v0) (list_all$ ?v3 ?v1)))) :named a303))
-(assert (! (forall ((?v0 (-> Msg$ Bool)) (?v1 Msg_list$) (?v2 (-> Msg$ Bool))) (=> (and (list_all$a ?v0 ?v1) (forall ((?v3 Msg$)) (=> (and (member$a ?v3 (set$a ?v1)) (?v0 ?v3)) (?v2 ?v3)))) (list_all$a ?v2 ?v1))) :named a304))
-(assert (! (forall ((?v0 (-> Agent$ Bool)) (?v1 Agent_list$) (?v2 (-> Agent$ Bool))) (=> (and (list_all$b ?v0 ?v1) (forall ((?v3 Agent$)) (=> (and (member$ ?v3 (set$b ?v1)) (?v0 ?v3)) (?v2 ?v3)))) (list_all$b ?v2 ?v1))) :named a305))
-(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event_list$) (?v2 (-> Event$ Bool))) (=> (and (list_all$ ?v0 ?v1) (forall ((?v3 Event$)) (=> (and (member$b ?v3 (set$ ?v1)) (?v0 ?v3)) (?v2 ?v3)))) (list_all$ ?v2 ?v1))) :named a306))
-(assert (! (forall ((?v0 (-> Msg$ Bool)) (?v1 Msg_list$)) (= (list_ex1$a ?v0 ?v1) (exists ((?v2 Msg$)) (and (and (member$a ?v2 (set$a ?v1)) (?v0 ?v2)) (forall ((?v3 Msg$)) (=> (and (member$a ?v3 (set$a ?v1)) (?v0 ?v3)) (= ?v3 ?v2))))))) :named a307))
-(assert (! (forall ((?v0 (-> Agent$ Bool)) (?v1 Agent_list$)) (= (list_ex1$b ?v0 ?v1) (exists ((?v2 Agent$)) (and (and (member$ ?v2 (set$b ?v1)) (?v0 ?v2)) (forall ((?v3 Agent$)) (=> (and (member$ ?v3 (set$b ?v1)) (?v0 ?v3)) (= ?v3 ?v2))))))) :named a308))
-(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event_list$)) (= (list_ex1$ ?v0 ?v1) (exists ((?v2 Event$)) (and (and (member$b ?v2 (set$ ?v1)) (?v0 ?v2)) (forall ((?v3 Event$)) (=> (and (member$b ?v3 (set$ ?v1)) (?v0 ?v3)) (= ?v3 ?v2))))))) :named a309))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (= (member$a ?v0 (set$a ?v1)) (member$g ?v1 ?v0))) :named a310))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (= (member$ ?v0 (set$b ?v1)) (member$h ?v1 ?v0))) :named a311))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (= (member$b ?v0 (set$ ?v1)) (member$d ?v1 ?v0))) :named a312))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event$)) (less_eq$a (set$ ?v0) (set$ (cons$ ?v1 ?v0)))) :named a313))
-(assert (! (forall ((?v0 Msg_list$) (?v1 Msg$)) (less_eq$ (set$a ?v0) (set$a (cons$b ?v1 ?v0)))) :named a314))
-(assert (! (forall ((?v0 Msg_list$) (?v1 (-> Msg$ Bool))) (= (exists ((?v2 Msg$)) (and (member$a ?v2 (set$a ?v0)) (?v1 ?v2))) (exists ((?v2 Msg_list$) (?v3 Msg$) (?v4 Msg_list$)) (and (= ?v0 (append$a ?v2 (cons$b ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Msg$)) (=> (member$a ?v5 (set$a ?v2)) (not (?v1 ?v5))))))))) :named a315))
-(assert (! (forall ((?v0 Agent_list$) (?v1 (-> Agent$ Bool))) (= (exists ((?v2 Agent$)) (and (member$ ?v2 (set$b ?v0)) (?v1 ?v2))) (exists ((?v2 Agent_list$) (?v3 Agent$) (?v4 Agent_list$)) (and (= ?v0 (append$b ?v2 (cons$c ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Agent$)) (=> (member$ ?v5 (set$b ?v2)) (not (?v1 ?v5))))))))) :named a316))
-(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event$ Bool))) (= (exists ((?v2 Event$)) (and (member$b ?v2 (set$ ?v0)) (?v1 ?v2))) (exists ((?v2 Event_list$) (?v3 Event$) (?v4 Event_list$)) (and (= ?v0 (append$ ?v2 (cons$ ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Event$)) (=> (member$b ?v5 (set$ ?v2)) (not (?v1 ?v5))))))))) :named a317))
-(assert (! (forall ((?v0 Msg_list$) (?v1 (-> Msg$ Bool))) (= (exists ((?v2 Msg$)) (and (member$a ?v2 (set$a ?v0)) (?v1 ?v2))) (exists ((?v2 Msg_list$) (?v3 Msg$) (?v4 Msg_list$)) (and (= ?v0 (append$a ?v2 (cons$b ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Msg$)) (=> (member$a ?v5 (set$a ?v4)) (not (?v1 ?v5))))))))) :named a318))
-(assert (! (forall ((?v0 Agent_list$) (?v1 (-> Agent$ Bool))) (= (exists ((?v2 Agent$)) (and (member$ ?v2 (set$b ?v0)) (?v1 ?v2))) (exists ((?v2 Agent_list$) (?v3 Agent$) (?v4 Agent_list$)) (and (= ?v0 (append$b ?v2 (cons$c ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Agent$)) (=> (member$ ?v5 (set$b ?v4)) (not (?v1 ?v5))))))))) :named a319))
-(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event$ Bool))) (= (exists ((?v2 Event$)) (and (member$b ?v2 (set$ ?v0)) (?v1 ?v2))) (exists ((?v2 Event_list$) (?v3 Event$) (?v4 Event_list$)) (and (= ?v0 (append$ ?v2 (cons$ ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Event$)) (=> (member$b ?v5 (set$ ?v4)) (not (?v1 ?v5))))))))) :named a320))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (= (member$a ?v0 (set$a ?v1)) (exists ((?v2 Msg_list$) (?v3 Msg_list$)) (and (= ?v1 (append$a ?v2 (cons$b ?v0 ?v3))) (not (member$a ?v0 (set$a ?v2))))))) :named a321))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (= (member$ ?v0 (set$b ?v1)) (exists ((?v2 Agent_list$) (?v3 Agent_list$)) (and (= ?v1 (append$b ?v2 (cons$c ?v0 ?v3))) (not (member$ ?v0 (set$b ?v2))))))) :named a322))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (= (member$b ?v0 (set$ ?v1)) (exists ((?v2 Event_list$) (?v3 Event_list$)) (and (= ?v1 (append$ ?v2 (cons$ ?v0 ?v3))) (not (member$b ?v0 (set$ ?v2))))))) :named a323))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (= (member$a ?v0 (set$a ?v1)) (exists ((?v2 Msg_list$) (?v3 Msg_list$)) (and (= ?v1 (append$a ?v2 (cons$b ?v0 ?v3))) (not (member$a ?v0 (set$a ?v3))))))) :named a324))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (= (member$ ?v0 (set$b ?v1)) (exists ((?v2 Agent_list$) (?v3 Agent_list$)) (and (= ?v1 (append$b ?v2 (cons$c ?v0 ?v3))) (not (member$ ?v0 (set$b ?v3))))))) :named a325))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (= (member$b ?v0 (set$ ?v1)) (exists ((?v2 Event_list$) (?v3 Event_list$)) (and (= ?v1 (append$ ?v2 (cons$ ?v0 ?v3))) (not (member$b ?v0 (set$ ?v3))))))) :named a326))
-(assert (! (forall ((?v0 Msg_list$) (?v1 (-> Msg$ Bool))) (=> (and (exists ((?v2 Msg$)) (and (member$a ?v2 (set$a ?v0)) (?v1 ?v2))) (forall ((?v2 Msg_list$) (?v3 Msg$) (?v4 Msg_list$)) (=> (and (= ?v0 (append$a ?v2 (cons$b ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Msg$)) (=> (member$a ?v5 (set$a ?v2)) (not (?v1 ?v5)))))) false))) false)) :named a327))
-(assert (! (forall ((?v0 Agent_list$) (?v1 (-> Agent$ Bool))) (=> (and (exists ((?v2 Agent$)) (and (member$ ?v2 (set$b ?v0)) (?v1 ?v2))) (forall ((?v2 Agent_list$) (?v3 Agent$) (?v4 Agent_list$)) (=> (and (= ?v0 (append$b ?v2 (cons$c ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Agent$)) (=> (member$ ?v5 (set$b ?v2)) (not (?v1 ?v5)))))) false))) false)) :named a328))
-(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event$ Bool))) (=> (and (exists ((?v2 Event$)) (and (member$b ?v2 (set$ ?v0)) (?v1 ?v2))) (forall ((?v2 Event_list$) (?v3 Event$) (?v4 Event_list$)) (=> (and (= ?v0 (append$ ?v2 (cons$ ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Event$)) (=> (member$b ?v5 (set$ ?v2)) (not (?v1 ?v5)))))) false))) false)) :named a329))
-(assert (! (forall ((?v0 Msg_list$) (?v1 (-> Msg$ Bool))) (=> (and (exists ((?v2 Msg$)) (and (member$a ?v2 (set$a ?v0)) (?v1 ?v2))) (forall ((?v2 Msg_list$) (?v3 Msg$) (?v4 Msg_list$)) (=> (and (= ?v0 (append$a ?v2 (cons$b ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Msg$)) (=> (member$a ?v5 (set$a ?v4)) (not (?v1 ?v5)))))) false))) false)) :named a330))
-(assert (! (forall ((?v0 Agent_list$) (?v1 (-> Agent$ Bool))) (=> (and (exists ((?v2 Agent$)) (and (member$ ?v2 (set$b ?v0)) (?v1 ?v2))) (forall ((?v2 Agent_list$) (?v3 Agent$) (?v4 Agent_list$)) (=> (and (= ?v0 (append$b ?v2 (cons$c ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Agent$)) (=> (member$ ?v5 (set$b ?v4)) (not (?v1 ?v5)))))) false))) false)) :named a331))
-(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event$ Bool))) (=> (and (exists ((?v2 Event$)) (and (member$b ?v2 (set$ ?v0)) (?v1 ?v2))) (forall ((?v2 Event_list$) (?v3 Event$) (?v4 Event_list$)) (=> (and (= ?v0 (append$ ?v2 (cons$ ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Event$)) (=> (member$b ?v5 (set$ ?v4)) (not (?v1 ?v5)))))) false))) false)) :named a332))
-(assert (! (forall ((?v0 Msg_list$) (?v1 (-> Msg$ Bool))) (=> (exists ((?v2 Msg$)) (and (member$a ?v2 (set$a ?v0)) (?v1 ?v2))) (exists ((?v2 Msg_list$) (?v3 Msg$) (?v4 Msg_list$)) (and (= ?v0 (append$a ?v2 (cons$b ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Msg$)) (=> (member$a ?v5 (set$a ?v2)) (not (?v1 ?v5))))))))) :named a333))
-(assert (! (forall ((?v0 Agent_list$) (?v1 (-> Agent$ Bool))) (=> (exists ((?v2 Agent$)) (and (member$ ?v2 (set$b ?v0)) (?v1 ?v2))) (exists ((?v2 Agent_list$) (?v3 Agent$) (?v4 Agent_list$)) (and (= ?v0 (append$b ?v2 (cons$c ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Agent$)) (=> (member$ ?v5 (set$b ?v2)) (not (?v1 ?v5))))))))) :named a334))
-(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event$ Bool))) (=> (exists ((?v2 Event$)) (and (member$b ?v2 (set$ ?v0)) (?v1 ?v2))) (exists ((?v2 Event_list$) (?v3 Event$) (?v4 Event_list$)) (and (= ?v0 (append$ ?v2 (cons$ ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Event$)) (=> (member$b ?v5 (set$ ?v2)) (not (?v1 ?v5))))))))) :named a335))
-(assert (! (forall ((?v0 Msg_list$) (?v1 (-> Msg$ Bool))) (=> (exists ((?v2 Msg$)) (and (member$a ?v2 (set$a ?v0)) (?v1 ?v2))) (exists ((?v2 Msg_list$) (?v3 Msg$) (?v4 Msg_list$)) (and (= ?v0 (append$a ?v2 (cons$b ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Msg$)) (=> (member$a ?v5 (set$a ?v4)) (not (?v1 ?v5))))))))) :named a336))
-(assert (! (forall ((?v0 Agent_list$) (?v1 (-> Agent$ Bool))) (=> (exists ((?v2 Agent$)) (and (member$ ?v2 (set$b ?v0)) (?v1 ?v2))) (exists ((?v2 Agent_list$) (?v3 Agent$) (?v4 Agent_list$)) (and (= ?v0 (append$b ?v2 (cons$c ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Agent$)) (=> (member$ ?v5 (set$b ?v4)) (not (?v1 ?v5))))))))) :named a337))
-(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event$ Bool))) (=> (exists ((?v2 Event$)) (and (member$b ?v2 (set$ ?v0)) (?v1 ?v2))) (exists ((?v2 Event_list$) (?v3 Event$) (?v4 Event_list$)) (and (= ?v0 (append$ ?v2 (cons$ ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Event$)) (=> (member$b ?v5 (set$ ?v4)) (not (?v1 ?v5))))))))) :named a338))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (= (member$a ?v0 (set$a ?v1)) (exists ((?v2 Msg_list$) (?v3 Msg_list$)) (= ?v1 (append$a ?v2 (cons$b ?v0 ?v3)))))) :named a339))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (= (member$ ?v0 (set$b ?v1)) (exists ((?v2 Agent_list$) (?v3 Agent_list$)) (= ?v1 (append$b ?v2 (cons$c ?v0 ?v3)))))) :named a340))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (= (member$b ?v0 (set$ ?v1)) (exists ((?v2 Event_list$) (?v3 Event_list$)) (= ?v1 (append$ ?v2 (cons$ ?v0 ?v3)))))) :named a341))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$) (?v2 Msg_list$) (?v3 Msg_list$) (?v4 Msg_list$)) (=> (and (not (member$a ?v0 (set$a ?v1))) (not (member$a ?v0 (set$a ?v2)))) (= (= (append$a ?v1 (cons$b ?v0 ?v2)) (append$a ?v3 (cons$b ?v0 ?v4))) (and (= ?v1 ?v3) (= ?v2 ?v4))))) :named a342))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$) (?v2 Agent_list$) (?v3 Agent_list$) (?v4 Agent_list$)) (=> (and (not (member$ ?v0 (set$b ?v1))) (not (member$ ?v0 (set$b ?v2)))) (= (= (append$b ?v1 (cons$c ?v0 ?v2)) (append$b ?v3 (cons$c ?v0 ?v4))) (and (= ?v1 ?v3) (= ?v2 ?v4))))) :named a343))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 Event_list$) (?v3 Event_list$) (?v4 Event_list$)) (=> (and (not (member$b ?v0 (set$ ?v1))) (not (member$b ?v0 (set$ ?v2)))) (= (= (append$ ?v1 (cons$ ?v0 ?v2)) (append$ ?v3 (cons$ ?v0 ?v4))) (and (= ?v1 ?v3) (= ?v2 ?v4))))) :named a344))
-(assert (! (forall ((?v0 Msg_list$) (?v1 (-> Msg$ Bool))) (=> (and (exists ((?v2 Msg$)) (and (member$a ?v2 (set$a ?v0)) (?v1 ?v2))) (forall ((?v2 Msg_list$) (?v3 Msg$) (?v4 Msg_list$)) (=> (and (= ?v0 (append$a ?v2 (cons$b ?v3 ?v4))) (?v1 ?v3)) false))) false)) :named a345))
-(assert (! (forall ((?v0 Agent_list$) (?v1 (-> Agent$ Bool))) (=> (and (exists ((?v2 Agent$)) (and (member$ ?v2 (set$b ?v0)) (?v1 ?v2))) (forall ((?v2 Agent_list$) (?v3 Agent$) (?v4 Agent_list$)) (=> (and (= ?v0 (append$b ?v2 (cons$c ?v3 ?v4))) (?v1 ?v3)) false))) false)) :named a346))
-(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event$ Bool))) (=> (and (exists ((?v2 Event$)) (and (member$b ?v2 (set$ ?v0)) (?v1 ?v2))) (forall ((?v2 Event_list$) (?v3 Event$) (?v4 Event_list$)) (=> (and (= ?v0 (append$ ?v2 (cons$ ?v3 ?v4))) (?v1 ?v3)) false))) false)) :named a347))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (=> (member$a ?v0 (set$a ?v1)) (exists ((?v2 Msg_list$) (?v3 Msg_list$)) (and (= ?v1 (append$a ?v2 (cons$b ?v0 ?v3))) (not (member$a ?v0 (set$a ?v2))))))) :named a348))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (=> (member$ ?v0 (set$b ?v1)) (exists ((?v2 Agent_list$) (?v3 Agent_list$)) (and (= ?v1 (append$b ?v2 (cons$c ?v0 ?v3))) (not (member$ ?v0 (set$b ?v2))))))) :named a349))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (=> (member$b ?v0 (set$ ?v1)) (exists ((?v2 Event_list$) (?v3 Event_list$)) (and (= ?v1 (append$ ?v2 (cons$ ?v0 ?v3))) (not (member$b ?v0 (set$ ?v2))))))) :named a350))
-(assert (! (forall ((?v0 Msg_list$) (?v1 (-> Msg$ Bool))) (=> (exists ((?v2 Msg$)) (and (member$a ?v2 (set$a ?v0)) (?v1 ?v2))) (exists ((?v2 Msg_list$) (?v3 Msg$) (?v4 Msg_list$)) (and (= ?v0 (append$a ?v2 (cons$b ?v3 ?v4))) (?v1 ?v3))))) :named a351))
-(assert (! (forall ((?v0 Agent_list$) (?v1 (-> Agent$ Bool))) (=> (exists ((?v2 Agent$)) (and (member$ ?v2 (set$b ?v0)) (?v1 ?v2))) (exists ((?v2 Agent_list$) (?v3 Agent$) (?v4 Agent_list$)) (and (= ?v0 (append$b ?v2 (cons$c ?v3 ?v4))) (?v1 ?v3))))) :named a352))
-(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event$ Bool))) (=> (exists ((?v2 Event$)) (and (member$b ?v2 (set$ ?v0)) (?v1 ?v2))) (exists ((?v2 Event_list$) (?v3 Event$) (?v4 Event_list$)) (and (= ?v0 (append$ ?v2 (cons$ ?v3 ?v4))) (?v1 ?v3))))) :named a353))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (=> (member$a ?v0 (set$a ?v1)) (exists ((?v2 Msg_list$) (?v3 Msg_list$)) (and (= ?v1 (append$a ?v2 (cons$b ?v0 ?v3))) (not (member$a ?v0 (set$a ?v3))))))) :named a354))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (=> (member$ ?v0 (set$b ?v1)) (exists ((?v2 Agent_list$) (?v3 Agent_list$)) (and (= ?v1 (append$b ?v2 (cons$c ?v0 ?v3))) (not (member$ ?v0 (set$b ?v3))))))) :named a355))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (=> (member$b ?v0 (set$ ?v1)) (exists ((?v2 Event_list$) (?v3 Event_list$)) (and (= ?v1 (append$ ?v2 (cons$ ?v0 ?v3))) (not (member$b ?v0 (set$ ?v3))))))) :named a356))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (=> (member$a ?v0 (set$a ?v1)) (exists ((?v2 Msg_list$) (?v3 Msg_list$)) (= ?v1 (append$a ?v2 (cons$b ?v0 ?v3)))))) :named a357))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (=> (member$ ?v0 (set$b ?v1)) (exists ((?v2 Agent_list$) (?v3 Agent_list$)) (= ?v1 (append$b ?v2 (cons$c ?v0 ?v3)))))) :named a358))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (=> (member$b ?v0 (set$ ?v1)) (exists ((?v2 Event_list$) (?v3 Event_list$)) (= ?v1 (append$ ?v2 (cons$ ?v0 ?v3)))))) :named a359))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent$) (?v2 Msg$) (?v3 Event_list$)) (=> (member$b (says$ ?v0 ?v1 ?v2) (set$ ?v3)) (member$a ?v2 (knows$ ?v0 ?v3)))) :named a360))
-(assert (! (forall ((?v0 Agent$) (?v1 Msg$) (?v2 Event_list$)) (=> (member$b (notes$ ?v0 ?v1) (set$ ?v2)) (member$a ?v1 (knows$ ?v0 ?v2)))) :named a361))
-(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (! (= (insert$d ?v0 ?v1) (ite (member$a ?v0 (set$a ?v1)) ?v1 (cons$b ?v0 ?v1))) :pattern ((insert$d ?v0 ?v1)))) :named a362))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (! (= (insert$e ?v0 ?v1) (ite (member$ ?v0 (set$b ?v1)) ?v1 (cons$c ?v0 ?v1))) :pattern ((insert$e ?v0 ?v1)))) :named a363))
-(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (! (= (insert$a ?v0 ?v1) (ite (member$b ?v0 (set$ ?v1)) ?v1 (cons$ ?v0 ?v1))) :pattern ((insert$a ?v0 ?v1)))) :named a364))
-(assert (! (forall ((?v0 Agent$) (?v1 Agent$) (?v2 Msg$) (?v3 Event_list$)) (=> (member$b (says$ ?v0 ?v1 ?v2) (set$ ?v3)) (member$a ?v2 (knows$ spy$ ?v3)))) :named a365))
-(assert (! (forall ((?v0 Agent$) (?v1 Msg$) (?v2 Event_list$)) (=> (and (not (= ?v0 spy$)) (member$b (gets$ ?v0 ?v1) (set$ ?v2))) (member$a ?v1 (knows$ ?v0 ?v2)))) :named a366))
-(assert (! (forall ((?v0 Msg$) (?v1 Event_list$)) (=> (member$a ?v0 (knows$ spy$ ?v1)) (exists ((?v2 Agent$) (?v3 Agent$)) (or (member$b (says$ ?v2 ?v3 ?v0) (set$ ?v1)) (or (member$b (notes$ ?v2 ?v0) (set$ ?v1)) (member$a ?v0 (initState$ spy$))))))) :named a367))
-(assert (! (forall ((?v0 Msg_list$) (?v1 Msg$) (?v2 Msg_list_set$)) (=> (member$e (append$a ?v0 (cons$b ?v1 nil$b)) ?v2) (member$a ?v1 (succ$a ?v2 ?v0)))) :named a368))
-(assert (! (forall ((?v0 Agent_list$) (?v1 Agent$) (?v2 Agent_list_set$)) (=> (member$f (append$b ?v0 (cons$c ?v1 nil$c)) ?v2) (member$ ?v1 (succ$b ?v2 ?v0)))) :named a369))
-(assert (! (forall ((?v0 Event_list$) (?v1 Event$) (?v2 Event_list_set$)) (=> (member$c (append$ ?v0 (cons$ ?v1 nil$)) ?v2) (member$b ?v1 (succ$ ?v2 ?v0)))) :named a370))
-(assert (! (forall ((?v0 Event_list$) (?v1 Agent$) (?v2 Msg$)) (= (knows$ spy$ (append$ ?v0 (cons$ (notes$ ?v1 ?v2) nil$))) (ite (member$ ?v1 bad$) (insert$ ?v2 (knows$ spy$ ?v0)) (knows$ spy$ ?v0)))) :named a371))
-(assert (! (member$ spy$ bad$) :named a372))
-(assert (! (forall ((?v0 Agent$) (?v1 Msg$) (?v2 Event_list$)) (! (= (knows$ spy$ (cons$ (notes$ ?v0 ?v1) ?v2)) (ite (member$ ?v0 bad$) (insert$ ?v1 (knows$ spy$ ?v2)) (knows$ spy$ ?v2))) :pattern ((cons$ (notes$ ?v0 ?v1) ?v2)))) :named a373))
-(assert (! (forall ((?v0 Agent$) (?v1 Msg$) (?v2 Event_list$)) (=> (and (member$b (notes$ ?v0 ?v1) (set$ ?v2)) (member$ ?v0 bad$)) (member$a ?v1 (knows$ spy$ ?v2)))) :named a374))
-(assert (! (forall ((?v0 Agent$) (?v1 Event$) (?v2 Event_list$)) (= (knows$ ?v0 (cons$ ?v1 ?v2)) (ite (= ?v0 spy$) (case_event$ (uuo$ ?v2) (uup$ ?v2) (uuq$ ?v2) ?v1) (case_event$ (uur$ ?v0 ?v2) (uus$ ?v0 ?v2) (uus$ ?v0 ?v2) ?v1)))) :named a375))
-(check-sat)

diff --git a/test/regress/regress1/ho/bound_var_bug.p b/test/regress/regress1/ho/bound_var_bug.p
new file mode 100644 (file)
index 0000000..0dc946d
--- /dev/null
+++ b/test/regress/regress1/ho/bound_var_bug.p
@@ -0,0 +1,26 @@
+% COMMAND-LINE: --uf-ho
+% EXPECT: % SZS status GaveUp for bound_var_bug
+
+% TIMEFORMAT='%3R'; { time (exec 2>&1; /Users/blanchette/misc/leo --foatp e --atp e="$E_HOME"/eprover --atp epclextract="$E_HOME"/epclextract --proofoutput 1 --timeout 30 /Users/blanchette/hgs/afp_mining/tools/judgment_day_2017/data_afp/leo2-mepo/Call_Arity_SestoftGC_data/prob_308__3244432_1 ) ; }
+% This file was generated by Isabelle (most likely Sledgehammer)
+% 2017-07-27 17:26:12.634
+
+% Could-be-implicit typings (91)
+
+thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Vars__Ovar_Mt__Terms__Oexp_J_J_Mt__Product____Type__Oprod_It__Terms__Oexp_Mt__List__Olist_It__SestoftConf__Ostack____elem_J_J_J, type,
+    produc1516857811k_elem : $tType).
+
+
+thf(ty_n_t__Vars__Ovar, type,
+    var : $tType).
+
+thf(sy_c_Transitive__Closure_Ortranclp_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Vars__Ovar_Mt__Terms__Oexp_J_J_Mt__Product____Type__Oprod_It__Terms__Oexp_Mt__List__Olist_It__SestoftConf__Ostack____elem_J_J_J, type,
+    transi803447880k_elem : (produc1516857811k_elem > produc1516857811k_elem > $o) > produc1516857811k_elem > produc1516857811k_elem > $o).
+
+% Relevant facts (1094)
+
+thf(fact_233_rtranclp__idemp, axiom,
+    ((![R : produc1516857811k_elem > produc1516857811k_elem > $o]: ((transi803447880k_elem @ (transi803447880k_elem @ R)) = (transi803447880k_elem @ R))))). % rtranclp_idemp
+
+thf(fact_293_rtranclp_Osimps, axiom,
+    ((transi803447880k_elem = (^[R4 : produc1516857811k_elem > produc1516857811k_elem > $o]: (^[A12 : produc1516857811k_elem]: (^[A23 : produc1516857811k_elem]: (((?[A5 : produc1516857811k_elem]: (((A12 = A5)) & ((A23 = A5))))) | ((?[A5 : produc1516857811k_elem]: (?[B4 : produc1516857811k_elem]: (?[C5 : produc1516857811k_elem]: (((A12 = A5)) & ((((A23 = C5)) & ((((transi803447880k_elem @ R4 @ A5 @ B4)) & ((R4 @ B4 @ C5)))))))))))))))))). % rtranclp.simps

diff --git a/test/regress/regress1/ho/bug_freeVar_BDD_General_data_270.p b/test/regress/regress1/ho/bug_freeVar_BDD_General_data_270.p
new file mode 100644 (file)
index 0000000..6c35270
--- /dev/null
+++ b/test/regress/regress1/ho/bug_freeVar_BDD_General_data_270.p
@@ -0,0 +1,11 @@
+% COMMAND-LINE: --uf-ho --finite-model-find
+% EXPECT: % SZS status Satisfiable for bug_freeVar_BDD_General_data_270
+
+thf(ty_n_t__Nat__Onat, type,
+    nat : $tType).
+
+thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
+    ord_less_eq_nat : nat > nat > $o).
+
+thf(fact_76_eq__iff, axiom,
+    (((^[Y3 : nat]: (^[Z2 : nat]: (Y3 = Z2))) = (^[X4 : nat]: (^[Y4 : nat]: (((ord_less_eq_nat @ X4 @ Y4)) & ((ord_less_eq_nat @ Y4 @ X4)))))))). % eq_iff

diff --git a/test/regress/regress1/ho/bug_freevar_PHI004^4-delta.smt2 b/test/regress/regress1/ho/bug_freevar_PHI004^4-delta.smt2
new file mode 100644 (file)
index 0000000..9dd95ae
--- /dev/null
+++ b/test/regress/regress1/ho/bug_freevar_PHI004^4-delta.smt2
@@ -0,0 +1,35 @@
+; COMMAND-LINE: --uf-ho --finite-model-find --no-check-models
+; EXPECT: sat
+
+(set-logic ALL)
+(declare-sort $$unsorted 0)
+(declare-sort qML_mu 0)
+(declare-sort qML_i 0)
+(declare-fun scott_G (qML_mu qML_i) Bool)
+(declare-fun scott_P ((-> qML_mu qML_i Bool) qML_i) Bool)
+
+(assert
+  (=
+    scott_G
+    (lambda ((X qML_mu) (__flatten_var_0 qML_i))
+      (forall ((BOUND_VARIABLE_292 (-> qML_mu qML_i Bool)))
+        (or
+          (not (scott_P BOUND_VARIABLE_292 __flatten_var_0))
+          (BOUND_VARIABLE_292 X __flatten_var_0)
+          ) ))))
+
+(assert
+  (forall ((X_1 qML_i))
+    (scott_P
+      (lambda ((X qML_mu) (__flatten_var_0 qML_i))
+        (forall ((BOUND_VARIABLE_292 (-> qML_mu qML_i Bool)))
+          (or
+            (not (scott_P BOUND_VARIABLE_292 __flatten_var_0))
+            (BOUND_VARIABLE_292 X __flatten_var_0)) ))
+      X_1
+      )
+    ))
+
+
+
+(check-sat)
\ No newline at end of file

diff --git a/test/regress/regress1/ho/fta0210.smt2 b/test/regress/regress1/ho/fta0210.smt2
deleted file mode 100644 (file)
index 9f0a39f..0000000
--- a/test/regress/regress1/ho/fta0210.smt2
+++ /dev/null
@@ -1,64 +0,0 @@
-; COMMAND-LINE: --uf-ho
-; EXPECT: unsat
-(set-logic ALL)
-(declare-sort A$ 0)
-(declare-sort Nat$ 0)
-(declare-sort A_poly$ 0)
-(declare-sort Nat_poly$ 0)
-(declare-sort A_poly_poly$ 0)
-(declare-fun p$ () A_poly$)
-(declare-fun uu$ (A_poly$ (-> A_poly$ A_poly$) A_poly$) A_poly$)
-(declare-fun one$ () Nat$)
-(declare-fun suc$ (Nat$) Nat$)
-(declare-fun uua$ (A_poly$) A_poly$)
-(declare-fun uub$ (A$ (-> A$ A$) A$) A$)
-(declare-fun uuc$ (A$) A$)
-(declare-fun uud$ (Nat$ (-> Nat$ Nat$) Nat$) Nat$)
-(declare-fun uue$ (Nat$) Nat$)
-(declare-fun one$a () Nat_poly$)
-(declare-fun one$b () A$)
-(declare-fun one$c () A_poly$)
-(declare-fun plus$ (A_poly$ A_poly$) A_poly$)
-(declare-fun poly$ (A_poly$ A$) A$)
-(declare-fun zero$ () A_poly$)
-(declare-fun pCons$ (A$ A_poly$) A_poly$)
-(declare-fun plus$a (Nat$ Nat$) Nat$)
-(declare-fun plus$b (A$ A$) A$)
-(declare-fun plus$c (Nat_poly$ Nat_poly$) Nat_poly$)
-(declare-fun poly$a (Nat_poly$ Nat$) Nat$)
-(declare-fun poly$b (A_poly_poly$ A_poly$) A_poly$)
-(declare-fun power$ (A$ Nat$) A$)
-(declare-fun psize$ (A_poly$) Nat$)
-(declare-fun times$ (A_poly$ A_poly$) A_poly$)
-(declare-fun zero$a () Nat$)
-(declare-fun zero$b () A$)
-(declare-fun zero$c () Nat_poly$)
-(declare-fun zero$d () A_poly_poly$)
-(declare-fun pCons$a (Nat$ Nat_poly$) Nat_poly$)
-(declare-fun pCons$b (A_poly$ A_poly_poly$) A_poly_poly$)
-(declare-fun power$a (A_poly$ Nat$) A_poly$)
-(declare-fun power$b (Nat_poly$ Nat$) Nat_poly$)
-(declare-fun power$c (Nat$ Nat$) Nat$)
-(declare-fun psize$a (A_poly_poly$) Nat$)
-(declare-fun times$a (Nat$ Nat$) Nat$)
-(declare-fun times$b (A$ A$) A$)
-(declare-fun times$c (Nat_poly$ Nat_poly$) Nat_poly$)
-(declare-fun times$d (A_poly_poly$ A_poly_poly$) A_poly_poly$)
-(declare-fun uminus$ (A_poly$) A_poly$)
-(declare-fun uminus$a (A$) A$)
-(declare-fun constant$ ((-> A$ A$)) Bool)
-(declare-fun pcompose$ (A_poly$ A_poly$) A_poly$)
-(declare-fun pcompose$a (Nat_poly$ Nat_poly$) Nat_poly$)
-(declare-fun pcompose$b (A_poly_poly$ A_poly_poly$) A_poly_poly$)
-(declare-fun poly_shift$ (Nat$ A_poly$) A_poly$)
-(declare-fun fold_coeffs$ ((-> A_poly$ (-> (-> A_poly$ A_poly$) (-> A_poly$ A_poly$))) A_poly_poly$ (-> A_poly$ A_poly$)) (-> A_poly$ A_poly$))
-(declare-fun poly_cutoff$ (Nat$ A_poly$) A_poly$)
-(declare-fun fold_coeffs$a ((-> A$ (-> (-> A$ A$) (-> A$ A$))) A_poly$ (-> A$ A$)) (-> A$ A$))
-(declare-fun fold_coeffs$b ((-> Nat$ (-> (-> Nat$ Nat$) (-> Nat$ Nat$))) Nat_poly$ (-> Nat$ Nat$)) (-> Nat$ Nat$))
-
-(assert (! (forall ((?v0 A$)) (= (poly$ zero$ ?v0) zero$b)) :named a14))
-(assert (! (forall ((?v0 (-> A$ A$))) (= (constant$ ?v0) (forall ((?v1 A$) (?v2 A$)) (= (?v0 ?v1) (?v0 ?v2))))) :named a69))
-(assert (! (not (constant$ (poly$ zero$))) :named a206))
-
-(check-sat)
-;(get-proof)

diff --git a/test/regress/regress1/ho/fta0328.lfho.p b/test/regress/regress1/ho/fta0328.lfho.p
new file mode 100644 (file)
index 0000000..c33b43c
--- /dev/null
+++ b/test/regress/regress1/ho/fta0328.lfho.p
@@ -0,0 +1,200 @@
+% COMMAND-LINE:  --uf-ho --uf-ho --finite-model-find
+% EXPECT: % SZS status CounterSatisfiable for fta0328.lfho
+
+% TIMEFORMAT='%3R'; { time (exec 2>&1; /Users/blanchette/.isabelle/contrib/e-2.0-2/x86_64-darwin/eprover --auto-schedule --tstp-in --tstp-out --silent --cpu-limit=2 --proof-object=1 /Users/blanchette/hgs/matryoshka/papers/2019-TACAS-ehoh/eval/judgment_day/judgment_day_lifting_32/fta/prob_804__4064966_1 ) ; }
+% This file was generated by Isabelle (most likely Sledgehammer)
+% 2018-05-22 19:17:55.732
+
+% Could-be-implicit typings (8)
+thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
+    poly_p1267267526omplex : $tType).
+thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
+    poly_poly_complex : $tType).
+thf(ty_n_t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
+    poly_complex : $tType).
+thf(ty_n_t__Polynomial__Opoly_It__Nat__Onat_J, type,
+    poly_nat : $tType).
+thf(ty_n_t__Complex__Ocomplex, type,
+    complex : $tType).
+thf(ty_n_t__Real__Oreal, type,
+    real : $tType).
+thf(ty_n_t__HOL__Obool, type,
+    bool : $tType).
+thf(ty_n_t__Nat__Onat, type,
+    nat : $tType).
+
+% Explicit typings (28)
+thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__bptywjkimr_Oconstant_001t__Complex__Ocomplex_001t__Complex__Ocomplex, type,
+    fundam769667258omplex : (complex > complex) > $o).
+thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__bptywjkimr_Opsize_001t__Complex__Ocomplex, type,
+    fundam835161864omplex : poly_complex > nat).
+thf(sy_c_Groups_Oplus__class_Oplus_001t__Complex__Ocomplex, type,
+    plus_plus_complex : complex > complex > complex).
+thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat, type,
+    plus_plus_nat : nat > nat > nat).
+thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
+    plus_p1547158847omplex : poly_complex > poly_complex > poly_complex).
+thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
+    plus_p138939463omplex : poly_poly_complex > poly_poly_complex > poly_poly_complex).
+thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
+    zero_zero_complex : complex).
+thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
+    zero_zero_nat : nat).
+thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
+    zero_z1746442943omplex : poly_complex).
+thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
+    zero_zero_poly_nat : poly_nat).
+thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
+    zero_z1040703943omplex : poly_poly_complex).
+thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
+    zero_z1200043727omplex : poly_p1267267526omplex).
+thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
+    ord_less_nat : nat > nat > $o).
+thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
+    ord_less_eq_nat : nat > nat > $o).
+thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
+    ord_less_eq_real : real > real > $o).
+thf(sy_c_Polynomial_Opoly_001t__Complex__Ocomplex, type,
+    poly_complex2 : poly_complex > complex > complex).
+thf(sy_c_Polynomial_Opoly_001t__Nat__Onat, type,
+    poly_nat2 : poly_nat > nat > nat).
+thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
+    poly_poly_complex2 : poly_poly_complex > poly_complex > poly_complex).
+thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
+    poly_p282434315omplex : poly_p1267267526omplex > poly_poly_complex > poly_poly_complex).
+thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex, type,
+    real_V638595069omplex : complex > real).
+thf(sy_c_fFalse, type,
+    fFalse : bool).
+thf(sy_c_fTrue, type,
+    fTrue : bool).
+thf(sy_c_pp, type,
+    pp : bool > $o).
+thf(sy_v_a____, type,
+    a : complex).
+thf(sy_v_c____, type,
+    c : complex).
+thf(sy_v_p, type,
+    p : poly_complex).
+thf(sy_v_pa____, type,
+    pa : poly_complex).
+thf(sy_v_q____, type,
+    q : poly_complex).
+
+% Relevant facts (53)
+thf(fact_0_kas_I1_J, axiom,
+    ((~ ((a = zero_zero_complex))))). % kas(1)
+thf(fact_1_q_I2_J, axiom,
+    ((![X : complex]: ((poly_complex2 @ q @ X) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X)))))). % q(2)
+thf(fact_2_nc, axiom,
+    ((~ ((fundam769667258omplex @ (poly_complex2 @ p)))))). % nc
+thf(fact_3_False, axiom,
+    ((~ (((poly_complex2 @ pa @ c) = zero_zero_complex))))). % False
+thf(fact_4_less_Oprems, axiom,
+    ((~ ((fundam769667258omplex @ (poly_complex2 @ pa)))))). % less.prems
+thf(fact_5_a00, axiom,
+    ((~ (((poly_complex2 @ q @ zero_zero_complex) = zero_zero_complex))))). % a00
+thf(fact_6_pqc0, axiom,
+    (((poly_complex2 @ pa @ c) = (poly_complex2 @ q @ zero_zero_complex)))). % pqc0
+thf(fact_7_q_I1_J, axiom,
+    (((fundam835161864omplex @ q) = (fundam835161864omplex @ pa)))). % q(1)
+thf(fact_8_poly__0, axiom,
+    ((![X2 : poly_poly_complex]: ((poly_p282434315omplex @ zero_z1200043727omplex @ X2) = zero_z1040703943omplex)))). % poly_0
+thf(fact_9_poly__0, axiom,
+    ((![X2 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X2) = zero_zero_nat)))). % poly_0
+thf(fact_10_poly__0, axiom,
+    ((![X2 : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X2) = zero_z1746442943omplex)))). % poly_0
+thf(fact_11_poly__0, axiom,
+    ((![X2 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X2) = zero_zero_complex)))). % poly_0
+thf(fact_12_poly__all__0__iff__0, axiom,
+    ((![P : poly_p1267267526omplex]: ((![X3 : poly_poly_complex]: ((poly_p282434315omplex @ P @ X3) = zero_z1040703943omplex)) <=> (P = zero_z1200043727omplex))))). % poly_all_0_iff_0
+thf(fact_13_poly__all__0__iff__0, axiom,
+    ((![P : poly_complex]: ((![X3 : complex]: ((poly_complex2 @ P @ X3) = zero_zero_complex)) <=> (P = zero_z1746442943omplex))))). % poly_all_0_iff_0
+thf(fact_14_poly__all__0__iff__0, axiom,
+    ((![P : poly_poly_complex]: ((![X3 : poly_complex]: ((poly_poly_complex2 @ P @ X3) = zero_z1746442943omplex)) <=> (P = zero_z1040703943omplex))))). % poly_all_0_iff_0
+thf(fact_15__092_060open_062_092_060exists_062q_O_Apsize_Aq_A_061_Apsize_Ap_A_092_060and_062_A_I_092_060forall_062x_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_J_092_060close_062, axiom,
+    ((?[Q : poly_complex]: (((fundam835161864omplex @ Q) = (fundam835161864omplex @ pa)) & (![X : complex]: ((poly_complex2 @ Q @ X) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X)))))))). % \<open>\<exists>q. psize q = psize p \<and> (\<forall>x. poly q x = poly p (c + x))\<close>
+thf(fact_16__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062q_O_A_092_060lbrakk_062psize_Aq_A_061_Apsize_Ap_059_A_092_060forall_062x_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
+    ((~ ((![Q : poly_complex]: (((fundam835161864omplex @ Q) = (fundam835161864omplex @ pa)) => (~ ((![X : complex]: ((poly_complex2 @ Q @ X) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X)))))))))))). % \<open>\<And>thesis. (\<And>q. \<lbrakk>psize q = psize p; \<forall>x. poly q x = poly p (c + x)\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
+thf(fact_17__092_060open_062constant_A_Ipoly_Aq_J_A_092_060Longrightarrow_062_AFalse_092_060close_062, axiom,
+    ((~ ((fundam769667258omplex @ (poly_complex2 @ q)))))). % \<open>constant (poly q) \<Longrightarrow> False\<close>
+thf(fact_18_qnc, axiom,
+    ((~ ((fundam769667258omplex @ (poly_complex2 @ q)))))). % qnc
+thf(fact_19_poly__eq__poly__eq__iff, axiom,
+    ((![P : poly_poly_complex, Q2 : poly_poly_complex]: (((poly_poly_complex2 @ P) = (poly_poly_complex2 @ Q2)) <=> (P = Q2))))). % poly_eq_poly_eq_iff
+thf(fact_20_poly__eq__poly__eq__iff, axiom,
+    ((![P : poly_complex, Q2 : poly_complex]: (((poly_complex2 @ P) = (poly_complex2 @ Q2)) <=> (P = Q2))))). % poly_eq_poly_eq_iff
+thf(fact_21_c, axiom,
+    ((![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ pa @ c)) @ (real_V638595069omplex @ (poly_complex2 @ pa @ W)))))). % c
+thf(fact_22_zero__reorient, axiom,
+    ((![X2 : poly_poly_complex]: ((zero_z1040703943omplex = X2) <=> (X2 = zero_z1040703943omplex))))). % zero_reorient
+thf(fact_23_zero__reorient, axiom,
+    ((![X2 : nat]: ((zero_zero_nat = X2) <=> (X2 = zero_zero_nat))))). % zero_reorient
+thf(fact_24_zero__reorient, axiom,
+    ((![X2 : complex]: ((zero_zero_complex = X2) <=> (X2 = zero_zero_complex))))). % zero_reorient
+thf(fact_25_zero__reorient, axiom,
+    ((![X2 : poly_complex]: ((zero_z1746442943omplex = X2) <=> (X2 = zero_z1746442943omplex))))). % zero_reorient
+thf(fact_26_cq0, axiom,
+    ((![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ q @ zero_zero_complex)) @ (real_V638595069omplex @ (poly_complex2 @ pa @ W)))))). % cq0
+thf(fact_27_less_Ohyps, axiom,
+    ((![P : poly_complex]: ((ord_less_nat @ (fundam835161864omplex @ P) @ (fundam835161864omplex @ pa)) => ((~ ((fundam769667258omplex @ (poly_complex2 @ P)))) => (?[Z : complex]: ((poly_complex2 @ P @ Z) = zero_zero_complex))))))). % less.hyps
+thf(fact_28_add__left__cancel, axiom,
+    ((![A : poly_complex, B : poly_complex, C : poly_complex]: (((plus_p1547158847omplex @ A @ B) = (plus_p1547158847omplex @ A @ C)) <=> (B = C))))). % add_left_cancel
+thf(fact_29_add__left__cancel, axiom,
+    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) <=> (B = C))))). % add_left_cancel
+thf(fact_30_add__right__cancel, axiom,
+    ((![B : poly_complex, A : poly_complex, C : poly_complex]: (((plus_p1547158847omplex @ B @ A) = (plus_p1547158847omplex @ C @ A)) <=> (B = C))))). % add_right_cancel
+thf(fact_31_add__right__cancel, axiom,
+    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) <=> (B = C))))). % add_right_cancel
+thf(fact_32__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062c_O_A_092_060forall_062w_O_Acmod_A_Ipoly_Ap_Ac_J_A_092_060le_062_Acmod_A_Ipoly_Ap_Aw_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
+    ((~ ((![C2 : complex]: (~ ((![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ pa @ C2)) @ (real_V638595069omplex @ (poly_complex2 @ pa @ W))))))))))). % \<open>\<And>thesis. (\<And>c. \<forall>w. cmod (poly p c) \<le> cmod (poly p w) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
+thf(fact_33_le__zero__eq, axiom,
+    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) <=> (N = zero_zero_nat))))). % le_zero_eq
+thf(fact_34_not__gr__zero, axiom,
+    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) <=> (N = zero_zero_nat))))). % not_gr_zero
+thf(fact_35_zero__eq__add__iff__both__eq__0, axiom,
+    ((![X2 : nat, Y : nat]: ((zero_zero_nat = (plus_plus_nat @ X2 @ Y)) <=> ((X2 = zero_zero_nat) & (Y = zero_zero_nat)))))). % zero_eq_add_iff_both_eq_0
+thf(fact_36_add__eq__0__iff__both__eq__0, axiom,
+    ((![X2 : nat, Y : nat]: (((plus_plus_nat @ X2 @ Y) = zero_zero_nat) <=> ((X2 = zero_zero_nat) & (Y = zero_zero_nat)))))). % add_eq_0_iff_both_eq_0
+thf(fact_37_add__cancel__right__right, axiom,
+    ((![A : poly_poly_complex, B : poly_poly_complex]: ((A = (plus_p138939463omplex @ A @ B)) <=> (B = zero_z1040703943omplex))))). % add_cancel_right_right
+thf(fact_38_add__cancel__right__right, axiom,
+    ((![A : nat, B : nat]: ((A = (plus_plus_nat @ A @ B)) <=> (B = zero_zero_nat))))). % add_cancel_right_right
+thf(fact_39_add__cancel__right__right, axiom,
+    ((![A : complex, B : complex]: ((A = (plus_plus_complex @ A @ B)) <=> (B = zero_zero_complex))))). % add_cancel_right_right
+thf(fact_40_add__cancel__right__right, axiom,
+    ((![A : poly_complex, B : poly_complex]: ((A = (plus_p1547158847omplex @ A @ B)) <=> (B = zero_z1746442943omplex))))). % add_cancel_right_right
+thf(fact_41_add__cancel__right__left, axiom,
+    ((![A : poly_poly_complex, B : poly_poly_complex]: ((A = (plus_p138939463omplex @ B @ A)) <=> (B = zero_z1040703943omplex))))). % add_cancel_right_left
+thf(fact_42_add__cancel__right__left, axiom,
+    ((![A : nat, B : nat]: ((A = (plus_plus_nat @ B @ A)) <=> (B = zero_zero_nat))))). % add_cancel_right_left
+thf(fact_43_add__cancel__right__left, axiom,
+    ((![A : complex, B : complex]: ((A = (plus_plus_complex @ B @ A)) <=> (B = zero_zero_complex))))). % add_cancel_right_left
+thf(fact_44_add__cancel__right__left, axiom,
+    ((![A : poly_complex, B : poly_complex]: ((A = (plus_p1547158847omplex @ B @ A)) <=> (B = zero_z1746442943omplex))))). % add_cancel_right_left
+thf(fact_45_add__cancel__left__right, axiom,
+    ((![A : poly_poly_complex, B : poly_poly_complex]: (((plus_p138939463omplex @ A @ B) = A) <=> (B = zero_z1040703943omplex))))). % add_cancel_left_right
+thf(fact_46_add__cancel__left__right, axiom,
+    ((![A : nat, B : nat]: (((plus_plus_nat @ A @ B) = A) <=> (B = zero_zero_nat))))). % add_cancel_left_right
+thf(fact_47_add__cancel__left__right, axiom,
+    ((![A : complex, B : complex]: (((plus_plus_complex @ A @ B) = A) <=> (B = zero_zero_complex))))). % add_cancel_left_right
+thf(fact_48_add__cancel__left__right, axiom,
+    ((![A : poly_complex, B : poly_complex]: (((plus_p1547158847omplex @ A @ B) = A) <=> (B = zero_z1746442943omplex))))). % add_cancel_left_right
+thf(fact_49_add__cancel__left__left, axiom,
+    ((![B : poly_poly_complex, A : poly_poly_complex]: (((plus_p138939463omplex @ B @ A) = A) <=> (B = zero_z1040703943omplex))))). % add_cancel_left_left
+thf(fact_50_add__cancel__left__left, axiom,
+    ((![B : nat, A : nat]: (((plus_plus_nat @ B @ A) = A) <=> (B = zero_zero_nat))))). % add_cancel_left_left
+thf(fact_51_add__cancel__left__left, axiom,
+    ((![B : complex, A : complex]: (((plus_plus_complex @ B @ A) = A) <=> (B = zero_zero_complex))))). % add_cancel_left_left
+thf(fact_52_add__cancel__left__left, axiom,
+    ((![B : poly_complex, A : poly_complex]: (((plus_p1547158847omplex @ B @ A) = A) <=> (B = zero_z1746442943omplex))))). % add_cancel_left_left
+
+% Helper facts (2)
+thf(help_pp_2_1_U, axiom,
+    ((pp @ fTrue))).
+thf(help_pp_1_1_U, axiom,
+    ((~ ((pp @ fFalse))))).
+
+% Conjectures (1)
+thf(conj_0, conjecture,
+    ((?[Z2 : complex]: ((poly_complex2 @ pa @ Z2) = zero_zero_complex)))).

diff --git a/test/regress/regress1/ho/fta0409.smt2 b/test/regress/regress1/ho/fta0409.smt2
deleted file mode 100644 (file)
index 51ac5f2..0000000
--- a/test/regress/regress1/ho/fta0409.smt2
+++ /dev/null
@@ -1,427 +0,0 @@
-; COMMAND-LINE: --uf-ho
-; EXPECT: unsat
-(set-logic ALL)
-(set-info :status unsat)
-(declare-sort Nat$ 0)
-(declare-sort Complex$ 0)
-(declare-sort Nat_poly$ 0)
-(declare-sort Complex_poly$ 0)
-(declare-sort Complex_poly_poly$ 0)
-(declare-fun n$ () Nat$)
-(declare-fun q$ () Complex_poly$)
-(declare-fun r$ () Complex_poly$)
-(declare-fun dvd$ (Complex_poly$ Complex_poly$) Bool)
-(declare-fun one$ () Nat$)
-(declare-fun suc$ (Nat$) Nat$)
-(declare-fun dvd$a (Complex$ Complex$) Bool)
-(declare-fun dvd$b (Nat$ Nat$) Bool)
-(declare-fun dvd$c (Complex_poly_poly$ Complex_poly_poly$) Bool)
-(declare-fun dvd$d (Nat_poly$ Nat_poly$) Bool)
-(declare-fun one$a () Complex_poly$)
-(declare-fun one$b () Complex$)
-(declare-fun one$c () Nat_poly$)
-(declare-fun plus$ (Complex$ Complex$) Complex$)
-(declare-fun poly$ (Complex_poly$) (-> Complex$ Complex$))
-(declare-fun zero$ () Complex$)
-(declare-fun coeff$ (Complex_poly_poly$ Nat$) Complex_poly$)
-(declare-fun monom$ (Complex$ Nat$) Complex_poly$)
-(declare-fun order$ (Complex$ Complex_poly$) Nat$)
-(declare-fun pCons$ (Complex$ Complex_poly$) Complex_poly$)
-(declare-fun plus$a (Nat$ Nat$) Nat$)
-(declare-fun plus$b (Nat_poly$ Nat_poly$) Nat_poly$)
-(declare-fun plus$c (Complex_poly$ Complex_poly$) Complex_poly$)
-(declare-fun poly$a (Complex_poly_poly$ Complex_poly$) Complex_poly$)
-(declare-fun poly$b (Nat_poly$ Nat$) Nat$)
-(declare-fun power$ (Complex_poly$ Nat$) Complex_poly$)
-(declare-fun psize$ (Complex_poly$) Nat$)
-(declare-fun times$ (Nat$ Nat$) Nat$)
-(declare-fun zero$a () Nat$)
-(declare-fun zero$b () Complex_poly_poly$)
-(declare-fun zero$c () Complex_poly$)
-(declare-fun zero$d () Nat_poly$)
-(declare-fun coeff$a (Nat_poly$ Nat$) Nat$)
-(declare-fun coeff$b (Complex_poly$ Nat$) Complex$)
-(declare-fun degree$ (Complex_poly_poly$) Nat$)
-(declare-fun monom$a (Complex_poly$ Nat$) Complex_poly_poly$)
-(declare-fun monom$b (Nat$ Nat$) Nat_poly$)
-(declare-fun order$a (Complex_poly$ Complex_poly_poly$) Nat$)
-(declare-fun pCons$a (Complex_poly$ Complex_poly_poly$) Complex_poly_poly$)
-(declare-fun pCons$b (Nat$ Nat_poly$) Nat_poly$)
-(declare-fun power$a (Complex_poly_poly$ Nat$) Complex_poly_poly$)
-(declare-fun power$b (Nat_poly$ Nat$) Nat_poly$)
-(declare-fun power$c (Nat$ Nat$) Nat$)
-(declare-fun power$d (Complex$ Nat$) Complex$)
-(declare-fun degree$a (Nat_poly$) Nat$)
-(declare-fun degree$b (Complex_poly$) Nat$)
-(declare-fun is_zero$ (Complex_poly$) Bool)
-(declare-fun less_eq$ (Nat$ Nat$) Bool)
-(declare-fun of_bool$ (Bool) Complex$)
-(declare-fun constant$ ((-> Complex$ Complex$)) Bool)
-(declare-fun of_bool$a (Bool) Complex_poly$)
-(declare-fun of_bool$b (Bool) Nat$)
-(declare-fun pcompose$ (Complex_poly$ Complex_poly$) Complex_poly$)
-(declare-fun pcompose$a (Complex_poly_poly$ Complex_poly_poly$) Complex_poly_poly$)
-(declare-fun pcompose$b (Nat_poly$ Nat_poly$) Nat_poly$)
-(declare-fun poly_shift$ (Nat$ Complex_poly$) Complex_poly$)
-(declare-fun offset_poly$ (Complex_poly$ Complex$) Complex_poly$)
-(declare-fun poly_cutoff$ (Nat$ Complex_poly$) Complex_poly$)
-(declare-fun rsquarefree$ (Complex_poly$) Bool)
-(declare-fun offset_poly$a (Nat_poly$ Nat$) Nat_poly$)
-(declare-fun reflect_poly$ (Complex_poly$) Complex_poly$)
-(declare-fun reflect_poly$a (Complex_poly_poly$) Complex_poly_poly$)
-(declare-fun reflect_poly$b (Nat_poly$) Nat_poly$)
-(declare-fun synthetic_div$ (Complex_poly$ Complex$) Complex_poly$)
-(assert (! (not (= (poly$ (power$ q$ n$)) (poly$ r$))) :named a0))
-(assert (! (forall ((?v0 Complex$)) (= (poly$ (power$ q$ n$) ?v0) (poly$ r$ ?v0))) :named a1))
-(assert (! (forall ((?v0 Complex_poly_poly$) (?v1 Nat$) (?v2 Complex_poly$)) (= (poly$a (power$a ?v0 ?v1) ?v2) (power$ (poly$a ?v0 ?v2) ?v1))) :named a2))
-(assert (! (forall ((?v0 Nat_poly$) (?v1 Nat$) (?v2 Nat$)) (= (poly$b (power$b ?v0 ?v1) ?v2) (power$c (poly$b ?v0 ?v2) ?v1))) :named a3))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$) (?v2 Complex$)) (= (poly$ (power$ ?v0 ?v1) ?v2) (power$d (poly$ ?v0 ?v2) ?v1))) :named a4))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (= (poly$ ?v0) (poly$ ?v1)) (= ?v0 ?v1))) :named a5))
-(assert (! (forall ((?v0 Complex_poly$)) (=> (not (constant$ (poly$ ?v0))) (exists ((?v1 Complex$)) (= (poly$ ?v0 ?v1) zero$)))) :named a6))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$)) (= (reflect_poly$ (power$ ?v0 ?v1)) (power$ (reflect_poly$ ?v0) ?v1))) :named a7))
-(assert (! (forall ((?v0 Complex_poly_poly$) (?v1 Nat$)) (= (coeff$ (power$a ?v0 ?v1) zero$a) (power$ (coeff$ ?v0 zero$a) ?v1))) :named a8))
-(assert (! (forall ((?v0 Nat_poly$) (?v1 Nat$)) (= (coeff$a (power$b ?v0 ?v1) zero$a) (power$c (coeff$a ?v0 zero$a) ?v1))) :named a9))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$)) (= (coeff$b (power$ ?v0 ?v1) zero$a) (power$d (coeff$b ?v0 zero$a) ?v1))) :named a10))
-(assert (! (forall ((?v0 (-> Complex$ Complex$))) (= (constant$ ?v0) (forall ((?v1 Complex$) (?v2 Complex$)) (= (?v0 ?v1) (?v0 ?v2))))) :named a11))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$)) (exists ((?v2 Complex_poly$)) (and (= (psize$ ?v2) (psize$ ?v0)) (forall ((?v3 Complex$)) (= (poly$ ?v2 ?v3) (poly$ ?v0 (plus$ ?v1 ?v3))))))) :named a12))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$) (?v2 Complex$)) (= (poly$ (offset_poly$ ?v0 ?v1) ?v2) (poly$ ?v0 (plus$ ?v1 ?v2)))) :named a13))
-(assert (! (forall ((?v0 Nat_poly$) (?v1 Nat$) (?v2 Nat$)) (= (poly$b (offset_poly$a ?v0 ?v1) ?v2) (poly$b ?v0 (plus$a ?v1 ?v2)))) :named a14))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$) (?v2 Complex$)) (= (poly$ (pcompose$ ?v0 ?v1) ?v2) (poly$ ?v0 (poly$ ?v1 ?v2)))) :named a15))
-(assert (! (forall ((?v0 Complex_poly$)) (= (power$ ?v0 one$) ?v0)) :named a16))
-(assert (! (forall ((?v0 Nat$)) (= (power$c ?v0 one$) ?v0)) :named a17))
-(assert (! (forall ((?v0 Nat$)) (= (power$ one$a ?v0) one$a)) :named a18))
-(assert (! (forall ((?v0 Nat$)) (= (power$c one$ ?v0) one$)) :named a19))
-(assert (! (forall ((?v0 Complex_poly_poly$) (?v1 Nat$)) (= (coeff$ (power$a ?v0 ?v1) (degree$ (power$a ?v0 ?v1))) (power$ (coeff$ ?v0 (degree$ ?v0)) ?v1))) :named a20))
-(assert (! (forall ((?v0 Nat_poly$) (?v1 Nat$)) (= (coeff$a (power$b ?v0 ?v1) (degree$a (power$b ?v0 ?v1))) (power$c (coeff$a ?v0 (degree$a ?v0)) ?v1))) :named a21))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$)) (= (coeff$b (power$ ?v0 ?v1) (degree$b (power$ ?v0 ?v1))) (power$d (coeff$b ?v0 (degree$b ?v0)) ?v1))) :named a22))
-(assert (! (forall ((?v0 Nat$)) (= (coeff$ zero$b ?v0) zero$c)) :named a23))
-(assert (! (forall ((?v0 Nat$)) (= (coeff$a zero$d ?v0) zero$a)) :named a24))
-(assert (! (forall ((?v0 Nat$)) (= (coeff$b zero$c ?v0) zero$)) :named a25))
-(assert (! (forall ((?v0 Nat_poly$) (?v1 Nat_poly$) (?v2 Nat$)) (= (coeff$a (plus$b ?v0 ?v1) ?v2) (plus$a (coeff$a ?v0 ?v2) (coeff$a ?v1 ?v2)))) :named a26))
-(assert (! (forall ((?v0 Complex_poly$)) (= (poly$a zero$b ?v0) zero$c)) :named a27))
-(assert (! (forall ((?v0 Nat$)) (= (poly$b zero$d ?v0) zero$a)) :named a28))
-(assert (! (forall ((?v0 Complex$)) (= (poly$ zero$c ?v0) zero$)) :named a29))
-(assert (! (= (degree$b one$a) zero$a) :named a30))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$) (?v2 Complex$)) (= (poly$ (plus$c ?v0 ?v1) ?v2) (plus$ (poly$ ?v0 ?v2) (poly$ ?v1 ?v2)))) :named a31))
-(assert (! (forall ((?v0 Nat_poly$) (?v1 Nat_poly$) (?v2 Nat$)) (= (poly$b (plus$b ?v0 ?v1) ?v2) (plus$a (poly$b ?v0 ?v2) (poly$b ?v1 ?v2)))) :named a32))
-(assert (! (forall ((?v0 Complex$)) (= (poly$ one$a ?v0) one$b)) :named a33))
-(assert (! (forall ((?v0 Nat$)) (= (poly$b one$c ?v0) one$)) :named a34))
-(assert (! (forall ((?v0 Complex_poly$)) (= (= (coeff$b ?v0 (degree$b ?v0)) zero$) (= ?v0 zero$c))) :named a35))
-(assert (! (forall ((?v0 Complex_poly_poly$)) (= (= (coeff$ ?v0 (degree$ ?v0)) zero$c) (= ?v0 zero$b))) :named a36))
-(assert (! (forall ((?v0 Nat_poly$)) (= (= (coeff$a ?v0 (degree$a ?v0)) zero$a) (= ?v0 zero$d))) :named a37))
-(assert (! (= (coeff$b one$a (degree$b one$a)) one$b) :named a38))
-(assert (! (= (coeff$a one$c (degree$a one$c)) one$) :named a39))
-(assert (! (forall ((?v0 Complex_poly$)) (= (= (poly$ (reflect_poly$ ?v0) zero$) zero$) (= ?v0 zero$c))) :named a40))
-(assert (! (forall ((?v0 Complex_poly_poly$)) (= (= (poly$a (reflect_poly$a ?v0) zero$c) zero$c) (= ?v0 zero$b))) :named a41))
-(assert (! (forall ((?v0 Nat_poly$)) (= (= (poly$b (reflect_poly$b ?v0) zero$a) zero$a) (= ?v0 zero$d))) :named a42))
-(assert (! (forall ((?v0 Complex_poly$)) (=> (not (= (coeff$b ?v0 zero$a) zero$)) (= (reflect_poly$ (reflect_poly$ ?v0)) ?v0))) :named a43))
-(assert (! (forall ((?v0 Complex_poly_poly$)) (=> (not (= (coeff$ ?v0 zero$a) zero$c)) (= (reflect_poly$a (reflect_poly$a ?v0)) ?v0))) :named a44))
-(assert (! (forall ((?v0 Nat_poly$)) (=> (not (= (coeff$a ?v0 zero$a) zero$a)) (= (reflect_poly$b (reflect_poly$b ?v0)) ?v0))) :named a45))
-(assert (! (forall ((?v0 Complex_poly$)) (= (= (coeff$b (reflect_poly$ ?v0) zero$a) zero$) (= ?v0 zero$c))) :named a46))
-(assert (! (forall ((?v0 Complex_poly_poly$)) (= (= (coeff$ (reflect_poly$a ?v0) zero$a) zero$c) (= ?v0 zero$b))) :named a47))
-(assert (! (forall ((?v0 Nat_poly$)) (= (= (coeff$a (reflect_poly$b ?v0) zero$a) zero$a) (= ?v0 zero$d))) :named a48))
-(assert (! (forall ((?v0 Complex_poly$)) (= (coeff$b (reflect_poly$ ?v0) zero$a) (coeff$b ?v0 (degree$b ?v0)))) :named a49))
-(assert (! (forall ((?v0 Complex_poly$)) (=> (not (= (coeff$b ?v0 zero$a) zero$)) (= (degree$b (reflect_poly$ ?v0)) (degree$b ?v0)))) :named a50))
-(assert (! (forall ((?v0 Complex_poly_poly$)) (=> (not (= (coeff$ ?v0 zero$a) zero$c)) (= (degree$ (reflect_poly$a ?v0)) (degree$ ?v0)))) :named a51))
-(assert (! (forall ((?v0 Nat_poly$)) (=> (not (= (coeff$a ?v0 zero$a) zero$a)) (= (degree$a (reflect_poly$b ?v0)) (degree$a ?v0)))) :named a52))
-(assert (! (forall ((?v0 Complex_poly$)) (= (poly$ (reflect_poly$ ?v0) zero$) (coeff$b ?v0 (degree$b ?v0)))) :named a53))
-(assert (! (forall ((?v0 Complex_poly_poly$)) (= (poly$a (reflect_poly$a ?v0) zero$c) (coeff$ ?v0 (degree$ ?v0)))) :named a54))
-(assert (! (forall ((?v0 Nat_poly$)) (= (poly$b (reflect_poly$b ?v0) zero$a) (coeff$a ?v0 (degree$a ?v0)))) :named a55))
-(assert (! (forall ((?v0 Complex_poly$)) (= (poly$ ?v0 zero$) (coeff$b ?v0 zero$a))) :named a56))
-(assert (! (forall ((?v0 Complex_poly_poly$)) (= (poly$a ?v0 zero$c) (coeff$ ?v0 zero$a))) :named a57))
-(assert (! (forall ((?v0 Nat_poly$)) (= (poly$b ?v0 zero$a) (coeff$a ?v0 zero$a))) :named a58))
-(assert (! (forall ((?v0 Nat_poly$) (?v1 Nat_poly$) (?v2 Nat$)) (= (coeff$a (plus$b ?v0 ?v1) ?v2) (plus$a (coeff$a ?v0 ?v2) (coeff$a ?v1 ?v2)))) :named a59))
-(assert (! (forall ((?v0 Complex_poly$)) (= (forall ((?v1 Complex$)) (= (poly$ ?v0 ?v1) zero$)) (= ?v0 zero$c))) :named a60))
-(assert (! (forall ((?v0 Complex_poly_poly$)) (= (forall ((?v1 Complex_poly$)) (= (poly$a ?v0 ?v1) zero$c)) (= ?v0 zero$b))) :named a61))
-(assert (! (forall ((?v0 Nat$)) (= (coeff$ zero$b ?v0) zero$c)) :named a62))
-(assert (! (forall ((?v0 Nat$)) (= (coeff$a zero$d ?v0) zero$a)) :named a63))
-(assert (! (forall ((?v0 Nat$)) (= (coeff$b zero$c ?v0) zero$)) :named a64))
-(assert (! (forall ((?v0 Complex_poly_poly$)) (=> (not (= ?v0 zero$b)) (not (= (coeff$ ?v0 (degree$ ?v0)) zero$c)))) :named a65))
-(assert (! (forall ((?v0 Nat_poly$)) (=> (not (= ?v0 zero$d)) (not (= (coeff$a ?v0 (degree$a ?v0)) zero$a)))) :named a66))
-(assert (! (forall ((?v0 Complex_poly$)) (=> (not (= ?v0 zero$c)) (not (= (coeff$b ?v0 (degree$b ?v0)) zero$)))) :named a67))
-(assert (! (forall ((?v0 Complex_poly$)) (! (= (power$ ?v0 zero$a) one$a) :pattern ((power$ ?v0)))) :named a68))
-(assert (! (forall ((?v0 Nat$)) (! (= (power$c ?v0 zero$a) one$) :pattern ((power$c ?v0)))) :named a69))
-(assert (! (forall ((?v0 Nat$)) (= (power$d zero$ ?v0) (ite (= ?v0 zero$a) one$b zero$))) :named a70))
-(assert (! (forall ((?v0 Nat$)) (= (power$ zero$c ?v0) (ite (= ?v0 zero$a) one$a zero$c))) :named a71))
-(assert (! (forall ((?v0 Nat$)) (= (power$c zero$a ?v0) (ite (= ?v0 zero$a) one$ zero$a))) :named a72))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$)) (= (degree$b (offset_poly$ ?v0 ?v1)) (degree$b ?v0))) :named a73))
-(assert (! (forall ((?v0 Complex_poly$)) (= (constant$ (poly$ ?v0)) (= (degree$b ?v0) zero$a))) :named a74))
-(assert (! (forall ((?v0 Complex$)) (= zero$ (poly$ zero$c ?v0))) :named a75))
-(assert (! (forall ((?v0 Complex_poly$)) (= zero$c (poly$a zero$b ?v0))) :named a76))
-(assert (! (forall ((?v0 Complex_poly$)) (= (exists ((?v1 Complex$)) (and (= (poly$ ?v0 ?v1) zero$) (not (= (poly$ zero$c ?v1) zero$)))) false)) :named a77))
-(assert (! (forall ((?v0 Complex_poly_poly$)) (= (exists ((?v1 Complex_poly$)) (and (= (poly$a ?v0 ?v1) zero$c) (not (= (poly$a zero$b ?v1) zero$c)))) false)) :named a78))
-(assert (! (forall ((?v0 Nat_poly$)) (= (exists ((?v1 Nat$)) (and (= (poly$b ?v0 ?v1) zero$a) (not (= (poly$b zero$d ?v1) zero$a)))) false)) :named a79))
-(assert (! (= (exists ((?v0 Complex_poly$)) (not (= (poly$a zero$b ?v0) zero$c))) false) :named a80))
-(assert (! (= (exists ((?v0 Nat$)) (not (= (poly$b zero$d ?v0) zero$a))) false) :named a81))
-(assert (! (= (exists ((?v0 Complex$)) (not (= (poly$ zero$c ?v0) zero$))) false) :named a82))
-(assert (! (= (exists ((?v0 Complex_poly$)) (= (poly$a zero$b ?v0) zero$c)) true) :named a83))
-(assert (! (= (exists ((?v0 Nat$)) (= (poly$b zero$d ?v0) zero$a)) true) :named a84))
-(assert (! (= (exists ((?v0 Complex$)) (= (poly$ zero$c ?v0) zero$)) true) :named a85))
-(assert (! (forall ((?v0 Complex$) (?v1 Nat$)) (=> (not (= ?v0 zero$)) (not (= (power$d ?v0 ?v1) zero$)))) :named a86))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$)) (=> (not (= ?v0 zero$c)) (not (= (power$ ?v0 ?v1) zero$c)))) :named a87))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (=> (not (= ?v0 zero$a)) (not (= (power$c ?v0 ?v1) zero$a)))) :named a88))
-(assert (! (forall ((?v0 Complex$)) (= (plus$ zero$ ?v0) ?v0)) :named a89))
-(assert (! (forall ((?v0 Complex_poly$)) (= (plus$c zero$c ?v0) ?v0)) :named a90))
-(assert (! (forall ((?v0 Nat$)) (= (plus$a zero$a ?v0) ?v0)) :named a91))
-(assert (! (forall ((?v0 Complex$)) (= (plus$ ?v0 zero$) ?v0)) :named a92))
-(assert (! (forall ((?v0 Complex_poly$)) (= (plus$c ?v0 zero$c) ?v0)) :named a93))
-(assert (! (forall ((?v0 Nat$)) (= (plus$a ?v0 zero$a) ?v0)) :named a94))
-(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (= (= (plus$ ?v0 ?v1) ?v1) (= ?v0 zero$))) :named a95))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (= (plus$c ?v0 ?v1) ?v1) (= ?v0 zero$c))) :named a96))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (plus$a ?v0 ?v1) ?v1) (= ?v0 zero$a))) :named a97))
-(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (= (= (plus$ ?v0 ?v1) ?v0) (= ?v1 zero$))) :named a98))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (= (plus$c ?v0 ?v1) ?v0) (= ?v1 zero$c))) :named a99))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (plus$a ?v0 ?v1) ?v0) (= ?v1 zero$a))) :named a100))
-(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (= (= ?v0 (plus$ ?v1 ?v0)) (= ?v1 zero$))) :named a101))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (= ?v0 (plus$c ?v1 ?v0)) (= ?v1 zero$c))) :named a102))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= ?v0 (plus$a ?v1 ?v0)) (= ?v1 zero$a))) :named a103))
-(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (= (= ?v0 (plus$ ?v0 ?v1)) (= ?v1 zero$))) :named a104))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (= ?v0 (plus$c ?v0 ?v1)) (= ?v1 zero$c))) :named a105))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= ?v0 (plus$a ?v0 ?v1)) (= ?v1 zero$a))) :named a106))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (plus$a ?v0 ?v1) zero$a) (and (= ?v0 zero$a) (= ?v1 zero$a)))) :named a107))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= zero$a (plus$a ?v0 ?v1)) (and (= ?v0 zero$a) (= ?v1 zero$a)))) :named a108))
-(assert (! (forall ((?v0 Complex_poly$)) (! (= (power$ ?v0 zero$a) one$a) :pattern ((power$ ?v0)))) :named a109))
-(assert (! (forall ((?v0 Nat$)) (! (= (power$c ?v0 zero$a) one$) :pattern ((power$c ?v0)))) :named a110))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (= (plus$a ?v0 ?v1) (plus$a ?v2 ?v1)) (= ?v0 ?v2))) :named a111))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (= (plus$a ?v0 ?v1) (plus$a ?v0 ?v2)) (= ?v1 ?v2))) :named a112))
-(assert (! (forall ((?v0 Complex_poly$)) (= (pcompose$ zero$c ?v0) zero$c)) :named a113))
-(assert (! (= (reflect_poly$ zero$c) zero$c) :named a114))
-(assert (! (= (degree$b zero$c) zero$a) :named a115))
-(assert (! (forall ((?v0 Complex_poly$)) (= (= (psize$ ?v0) zero$a) (= ?v0 zero$c))) :named a116))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$)) (= (= (offset_poly$ ?v0 ?v1) zero$c) (= ?v0 zero$c))) :named a117))
-(assert (! (forall ((?v0 Complex$)) (= (offset_poly$ zero$c ?v0) zero$c)) :named a118))
-(assert (! (forall ((?v0 Complex_poly$)) (= (exists ((?v1 Complex$)) (not (= (poly$ ?v0 ?v1) zero$))) (not (= ?v0 zero$c)))) :named a119))
-(assert (! (forall ((?v0 Complex$)) (= (= zero$ ?v0) (= ?v0 zero$))) :named a120))
-(assert (! (forall ((?v0 Complex_poly$)) (= (= zero$c ?v0) (= ?v0 zero$c))) :named a121))
-(assert (! (forall ((?v0 Nat$)) (= (= zero$a ?v0) (= ?v0 zero$a))) :named a122))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (=> (= (plus$a ?v0 ?v1) (plus$a ?v2 ?v1)) (= ?v0 ?v2))) :named a123))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (=> (= (plus$a ?v0 ?v1) (plus$a ?v0 ?v2)) (= ?v1 ?v2))) :named a124))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (plus$a ?v0 (plus$a ?v1 ?v2)) (plus$a ?v1 (plus$a ?v0 ?v2)))) :named a125))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (plus$a ?v0 ?v1) (plus$a ?v1 ?v0))) :named a126))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (plus$a (plus$a ?v0 ?v1) ?v2) (plus$a ?v0 (plus$a ?v1 ?v2)))) :named a127))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$) (?v3 Nat$)) (= (plus$a (plus$a ?v0 ?v1) (plus$a ?v2 ?v3)) (plus$a (plus$a ?v0 ?v2) (plus$a ?v1 ?v3)))) :named a128))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (plus$a (plus$a ?v0 ?v1) ?v2) (plus$a ?v0 (plus$a ?v1 ?v2)))) :named a129))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (plus$a ?v0 (plus$a ?v1 ?v2)) (plus$a ?v1 (plus$a ?v0 ?v2)))) :named a130))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (plus$a (plus$a ?v0 ?v1) ?v2) (plus$a (plus$a ?v0 ?v2) ?v1))) :named a131))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (plus$a ?v0 ?v1) (plus$a ?v1 ?v0))) :named a132))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (plus$a ?v0 (plus$a ?v1 ?v2)) (plus$a (plus$a ?v0 ?v1) ?v2))) :named a133))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$) (?v3 Nat$)) (=> (and (= ?v0 ?v1) (= ?v2 ?v3)) (= (plus$a ?v0 ?v2) (plus$a ?v1 ?v3)))) :named a134))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (plus$a (plus$a ?v0 ?v1) ?v2) (plus$a ?v0 (plus$a ?v1 ?v2)))) :named a135))
-(assert (! (forall ((?v0 Nat$)) (= (= one$ ?v0) (= ?v0 one$))) :named a136))
-(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (= (= ?v0 (plus$ ?v0 ?v1)) (= ?v1 zero$))) :named a137))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (= ?v0 (plus$c ?v0 ?v1)) (= ?v1 zero$c))) :named a138))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= ?v0 (plus$a ?v0 ?v1)) (= ?v1 zero$a))) :named a139))
-(assert (! (forall ((?v0 Complex$)) (= (plus$ zero$ ?v0) ?v0)) :named a140))
-(assert (! (forall ((?v0 Complex_poly$)) (= (plus$c zero$c ?v0) ?v0)) :named a141))
-(assert (! (forall ((?v0 Complex$)) (= (plus$ ?v0 zero$) ?v0)) :named a142))
-(assert (! (forall ((?v0 Complex_poly$)) (= (plus$c ?v0 zero$c) ?v0)) :named a143))
-(assert (! (forall ((?v0 Nat$)) (= (plus$a ?v0 zero$a) ?v0)) :named a144))
-(assert (! (forall ((?v0 Complex$)) (= (plus$ zero$ ?v0) ?v0)) :named a145))
-(assert (! (forall ((?v0 Complex_poly$)) (= (plus$c zero$c ?v0) ?v0)) :named a146))
-(assert (! (forall ((?v0 Nat$)) (= (plus$a zero$a ?v0) ?v0)) :named a147))
-(assert (! (forall ((?v0 Complex$)) (= (plus$ zero$ ?v0) ?v0)) :named a148))
-(assert (! (forall ((?v0 Complex_poly$)) (= (plus$c zero$c ?v0) ?v0)) :named a149))
-(assert (! (forall ((?v0 Nat$)) (= (plus$a zero$a ?v0) ?v0)) :named a150))
-(assert (! (forall ((?v0 Complex$)) (= (plus$ ?v0 zero$) ?v0)) :named a151))
-(assert (! (forall ((?v0 Complex_poly$)) (= (plus$c ?v0 zero$c) ?v0)) :named a152))
-(assert (! (forall ((?v0 Nat$)) (= (plus$a ?v0 zero$a) ?v0)) :named a153))
-(assert (! (forall ((?v0 Complex_poly$)) (= (power$ ?v0 one$) ?v0)) :named a154))
-(assert (! (forall ((?v0 Nat$)) (= (power$c ?v0 one$) ?v0)) :named a155))
-(assert (! (forall ((?v0 Nat$)) (= (poly_cutoff$ ?v0 one$a) (ite (= ?v0 zero$a) zero$c one$a))) :named a156))
-(assert (! (forall ((?v0 Nat$)) (= (plus$a ?v0 zero$a) ?v0)) :named a157))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (plus$a ?v0 ?v1) zero$a) (and (= ?v0 zero$a) (= ?v1 zero$a)))) :named a158))
-(assert (! (forall ((?v0 Nat$)) (= (poly_shift$ ?v0 one$a) (ite (= ?v0 zero$a) one$a zero$c))) :named a159))
-(assert (! (not (= zero$ one$b)) :named a160))
-(assert (! (not (= zero$c one$a)) :named a161))
-(assert (! (not (= zero$a one$)) :named a162))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$)) (= (= (synthetic_div$ ?v0 ?v1) zero$c) (= (degree$b ?v0) zero$a))) :named a163))
-(assert (! (= (of_bool$ false) zero$) :named a164))
-(assert (! (= (of_bool$a false) zero$c) :named a165))
-(assert (! (= (of_bool$b false) zero$a) :named a166))
-(assert (! (= (of_bool$b true) one$) :named a167))
-(assert (! (forall ((?v0 Complex$)) (= (synthetic_div$ zero$c ?v0) zero$c)) :named a168))
-(assert (! (forall ((?v0 Nat$)) (= (poly_shift$ ?v0 zero$c) zero$c)) :named a169))
-(assert (! (forall ((?v0 Nat$)) (= (poly_cutoff$ ?v0 zero$c) zero$c)) :named a170))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (= (plus$a ?v0 ?v1) (plus$a ?v0 ?v2)) (= ?v1 ?v2))) :named a171))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (= (plus$a ?v0 ?v1) (plus$a ?v2 ?v1)) (= ?v0 ?v2))) :named a172))
-(assert (! (forall ((?v0 Bool)) (! (= (of_bool$ ?v0) (ite ?v0 one$b zero$)) :pattern ((of_bool$ ?v0)))) :named a173))
-(assert (! (forall ((?v0 Bool)) (! (= (of_bool$a ?v0) (ite ?v0 one$a zero$c)) :pattern ((of_bool$a ?v0)))) :named a174))
-(assert (! (forall ((?v0 Bool)) (! (= (of_bool$b ?v0) (ite ?v0 one$ zero$a)) :pattern ((of_bool$b ?v0)))) :named a175))
-(assert (! (forall ((?v0 (-> Complex$ Bool)) (?v1 Bool)) (= (?v0 (of_bool$ ?v1)) (and (=> ?v1 (?v0 one$b)) (=> (not ?v1) (?v0 zero$))))) :named a176))
-(assert (! (forall ((?v0 (-> Complex_poly$ Bool)) (?v1 Bool)) (= (?v0 (of_bool$a ?v1)) (and (=> ?v1 (?v0 one$a)) (=> (not ?v1) (?v0 zero$c))))) :named a177))
-(assert (! (forall ((?v0 (-> Nat$ Bool)) (?v1 Bool)) (= (?v0 (of_bool$b ?v1)) (and (=> ?v1 (?v0 one$)) (=> (not ?v1) (?v0 zero$a))))) :named a178))
-(assert (! (forall ((?v0 (-> Complex$ Bool)) (?v1 Bool)) (= (?v0 (of_bool$ ?v1)) (not (or (and ?v1 (not (?v0 one$b))) (and (not ?v1) (not (?v0 zero$))))))) :named a179))
-(assert (! (forall ((?v0 (-> Complex_poly$ Bool)) (?v1 Bool)) (= (?v0 (of_bool$a ?v1)) (not (or (and ?v1 (not (?v0 one$a))) (and (not ?v1) (not (?v0 zero$c))))))) :named a180))
-(assert (! (forall ((?v0 (-> Nat$ Bool)) (?v1 Bool)) (= (?v0 (of_bool$b ?v1)) (not (or (and ?v1 (not (?v0 one$))) (and (not ?v1) (not (?v0 zero$a))))))) :named a181))
-(assert (! (forall ((?v0 Nat$)) (= (plus$a zero$a ?v0) ?v0)) :named a182))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (=> (= (plus$a ?v0 ?v1) ?v0) (= ?v1 zero$a))) :named a183))
-(assert (! (forall ((?v0 Nat$)) (=> (and (=> (= ?v0 zero$a) false) (=> (not (= ?v0 zero$a)) false)) false)) :named a184))
-(assert (! (forall ((?v0 (-> Nat$ (-> Nat$ Bool))) (?v1 Nat$) (?v2 Nat$)) (=> (and (forall ((?v3 Nat$) (?v4 Nat$)) (= (?v0 ?v3 ?v4) (?v0 ?v4 ?v3))) (and (forall ((?v3 Nat$)) (?v0 ?v3 zero$a)) (forall ((?v3 Nat$) (?v4 Nat$)) (=> (?v0 ?v3 ?v4) (?v0 ?v3 (plus$a ?v3 ?v4)))))) (?v0 ?v1 ?v2))) :named a185))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (forall ((?v2 Complex$)) (=> (= (poly$ ?v0 ?v2) zero$) (= (poly$ ?v1 ?v2) zero$))) (or (dvd$ ?v0 (power$ ?v1 (degree$b ?v0))) (and (= ?v0 zero$c) (= ?v1 zero$c))))) :named a186))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$) (?v2 Nat$)) (=> (and (forall ((?v3 Complex$)) (=> (= (poly$ ?v0 ?v3) zero$) (= (poly$ ?v1 ?v3) zero$))) (and (= (degree$b ?v0) ?v2) (not (= ?v2 zero$a)))) (dvd$ ?v0 (power$ ?v1 ?v2)))) :named a187))
-(assert (! (forall ((?v0 Complex_poly$)) (! (= (is_zero$ ?v0) (= ?v0 zero$c)) :pattern ((is_zero$ ?v0)))) :named a188))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$)) (= (= (poly$ ?v0 ?v1) zero$) (or (= ?v0 zero$c) (not (= (order$ ?v1 ?v0) zero$a))))) :named a189))
-(assert (! (forall ((?v0 Complex_poly_poly$) (?v1 Complex_poly$)) (= (= (poly$a ?v0 ?v1) zero$c) (or (= ?v0 zero$b) (not (= (order$a ?v1 ?v0) zero$a))))) :named a190))
-(assert (! (forall ((?v0 Complex$)) (dvd$a ?v0 zero$)) :named a191))
-(assert (! (forall ((?v0 Complex_poly$)) (dvd$ ?v0 zero$c)) :named a192))
-(assert (! (forall ((?v0 Nat$)) (dvd$b ?v0 zero$a)) :named a193))
-(assert (! (forall ((?v0 Complex$)) (= (dvd$a zero$ ?v0) (= ?v0 zero$))) :named a194))
-(assert (! (forall ((?v0 Complex_poly$)) (= (dvd$ zero$c ?v0) (= ?v0 zero$c))) :named a195))
-(assert (! (forall ((?v0 Nat$)) (= (dvd$b zero$a ?v0) (= ?v0 zero$a))) :named a196))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (dvd$ ?v0 (plus$c ?v0 ?v1)) (dvd$ ?v0 ?v1))) :named a197))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (dvd$b ?v0 (plus$a ?v0 ?v1)) (dvd$b ?v0 ?v1))) :named a198))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (dvd$ ?v0 (plus$c ?v1 ?v0)) (dvd$ ?v0 ?v1))) :named a199))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (dvd$b ?v0 (plus$a ?v1 ?v0)) (dvd$b ?v0 ?v1))) :named a200))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (=> (not (= ?v0 zero$a)) (= (dvd$b (power$c ?v1 ?v0) (power$c ?v2 ?v0)) (dvd$b ?v1 ?v2)))) :named a201))
-(assert (! (forall ((?v0 Complex$)) (=> (dvd$a zero$ ?v0) (= ?v0 zero$))) :named a202))
-(assert (! (forall ((?v0 Complex_poly$)) (=> (dvd$ zero$c ?v0) (= ?v0 zero$c))) :named a203))
-(assert (! (forall ((?v0 Nat$)) (=> (dvd$b zero$a ?v0) (= ?v0 zero$a))) :named a204))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$) (?v2 Complex_poly$)) (=> (dvd$ ?v0 ?v1) (= (dvd$ ?v0 (plus$c ?v1 ?v2)) (dvd$ ?v0 ?v2)))) :named a205))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (=> (dvd$b ?v0 ?v1) (= (dvd$b ?v0 (plus$a ?v1 ?v2)) (dvd$b ?v0 ?v2)))) :named a206))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$) (?v2 Complex_poly$)) (=> (dvd$ ?v0 ?v1) (= (dvd$ ?v0 (plus$c ?v2 ?v1)) (dvd$ ?v0 ?v2)))) :named a207))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (=> (dvd$b ?v0 ?v1) (= (dvd$b ?v0 (plus$a ?v2 ?v1)) (dvd$b ?v0 ?v2)))) :named a208))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$) (?v2 Complex_poly$)) (=> (and (dvd$ ?v0 ?v1) (dvd$ ?v0 ?v2)) (dvd$ ?v0 (plus$c ?v1 ?v2)))) :named a209))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (=> (and (dvd$b ?v0 ?v1) (dvd$b ?v0 ?v2)) (dvd$b ?v0 (plus$a ?v1 ?v2)))) :named a210))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (=> (and (dvd$ ?v0 ?v1) (dvd$ ?v1 one$a)) (dvd$ ?v0 one$a))) :named a211))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (=> (and (dvd$b ?v0 ?v1) (dvd$b ?v1 one$)) (dvd$b ?v0 one$))) :named a212))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (=> (dvd$ ?v0 one$a) (dvd$ ?v0 ?v1))) :named a213))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (=> (dvd$b ?v0 one$) (dvd$b ?v0 ?v1))) :named a214))
-(assert (! (forall ((?v0 Complex_poly$)) (dvd$ one$a ?v0)) :named a215))
-(assert (! (forall ((?v0 Nat$)) (dvd$b one$ ?v0)) :named a216))
-(assert (! (forall ((?v0 Complex_poly$)) (dvd$ ?v0 ?v0)) :named a217))
-(assert (! (forall ((?v0 Nat$)) (dvd$b ?v0 ?v0)) :named a218))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$) (?v2 Complex_poly$)) (=> (and (dvd$ ?v0 ?v1) (dvd$ ?v1 ?v2)) (dvd$ ?v0 ?v2))) :named a219))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (=> (and (dvd$b ?v0 ?v1) (dvd$b ?v1 ?v2)) (dvd$b ?v0 ?v2))) :named a220))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$) (?v2 Nat$)) (=> (dvd$ ?v0 ?v1) (dvd$ (power$ ?v0 ?v2) (power$ ?v1 ?v2)))) :named a221))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (=> (dvd$b ?v0 ?v1) (dvd$b (power$c ?v0 ?v2) (power$c ?v1 ?v2)))) :named a222))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (=> (and (dvd$b (power$c ?v0 ?v1) (power$c ?v2 ?v1)) (not (= ?v1 zero$a))) (dvd$b ?v0 ?v2))) :named a223))
-(assert (! (not (dvd$ zero$c one$a)) :named a224))
-(assert (! (not (dvd$b zero$a one$)) :named a225))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$)) (= (dvd$ (power$ ?v0 ?v1) one$a) (or (dvd$ ?v0 one$a) (= ?v1 zero$a)))) :named a226))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (dvd$b (power$c ?v0 ?v1) one$) (or (dvd$b ?v0 one$) (= ?v1 zero$a)))) :named a227))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$)) (! (=> (not (= (poly$ ?v0 ?v1) zero$)) (= (order$ ?v1 ?v0) zero$a)) :pattern ((order$ ?v1 ?v0)))) :named a228))
-(assert (! (forall ((?v0 Complex_poly_poly$) (?v1 Complex_poly$)) (! (=> (not (= (poly$a ?v0 ?v1) zero$c)) (= (order$a ?v1 ?v0) zero$a)) :pattern ((order$a ?v1 ?v0)))) :named a229))
-(assert (! (forall ((?v0 Complex_poly$)) (=> (not (= ?v0 zero$c)) (= (dvd$ ?v0 one$a) (= (degree$b ?v0) zero$a)))) :named a230))
-(assert (! (forall ((?v0 Complex_poly$)) (= (rsquarefree$ ?v0) (and (not (= ?v0 zero$c)) (forall ((?v1 Complex$)) (or (= (order$ ?v1 ?v0) zero$a) (= (order$ ?v1 ?v0) one$)))))) :named a231))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$) (?v2 Complex_poly$)) (=> (not (= ?v0 zero$c)) (= (exists ((?v3 Complex$)) (and (= (poly$ (pCons$ ?v1 ?v0) ?v3) zero$) (not (= (poly$ ?v2 ?v3) zero$)))) (not (dvd$ (pCons$ ?v1 ?v0) (power$ ?v2 (psize$ ?v0))))))) :named a232))
-(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (! (= (dvd$a ?v0 ?v1) (=> (= ?v0 zero$) (= ?v1 zero$))) :pattern ((dvd$a ?v0 ?v1)))) :named a233))
-(assert (! (forall ((?v0 Complex_poly$)) (=> (dvd$ ?v0 one$a) (= (monom$ (coeff$b ?v0 (degree$b ?v0)) zero$a) ?v0))) :named a234))
-(assert (! (forall ((?v0 Nat$)) (= (dvd$b ?v0 one$) (= ?v0 one$))) :named a235))
-(assert (! (forall ((?v0 Complex$) (?v1 Complex_poly$) (?v2 Complex$) (?v3 Complex_poly$)) (= (= (pCons$ ?v0 ?v1) (pCons$ ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3)))) :named a236))
-(assert (! (= (pCons$ zero$ zero$c) zero$c) :named a237))
-(assert (! (= (pCons$a zero$c zero$b) zero$b) :named a238))
-(assert (! (= (pCons$b zero$a zero$d) zero$d) :named a239))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly_poly$)) (= (= (pCons$a ?v0 ?v1) zero$b) (and (= ?v0 zero$c) (= ?v1 zero$b)))) :named a240))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat_poly$)) (= (= (pCons$b ?v0 ?v1) zero$d) (and (= ?v0 zero$a) (= ?v1 zero$d)))) :named a241))
-(assert (! (forall ((?v0 Complex$) (?v1 Complex_poly$)) (= (= (pCons$ ?v0 ?v1) zero$c) (and (= ?v0 zero$) (= ?v1 zero$c)))) :named a242))
-(assert (! (forall ((?v0 Complex$) (?v1 Complex_poly$)) (= (coeff$b (pCons$ ?v0 ?v1) zero$a) ?v0)) :named a243))
-(assert (! (forall ((?v0 Nat$)) (= (monom$ zero$ ?v0) zero$c)) :named a244))
-(assert (! (forall ((?v0 Nat$)) (= (monom$a zero$c ?v0) zero$b)) :named a245))
-(assert (! (forall ((?v0 Nat$)) (= (monom$b zero$a ?v0) zero$d)) :named a246))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$)) (= (= (monom$a ?v0 ?v1) zero$b) (= ?v0 zero$c))) :named a247))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (monom$b ?v0 ?v1) zero$d) (= ?v0 zero$a))) :named a248))
-(assert (! (forall ((?v0 Complex$) (?v1 Nat$)) (= (= (monom$ ?v0 ?v1) zero$c) (= ?v0 zero$))) :named a249))
-(assert (! (forall ((?v0 Complex$) (?v1 Nat$) (?v2 Nat$)) (= (coeff$b (monom$ ?v0 ?v1) ?v2) (ite (= ?v1 ?v2) ?v0 zero$))) :named a250))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$) (?v2 Nat$)) (= (coeff$ (monom$a ?v0 ?v1) ?v2) (ite (= ?v1 ?v2) ?v0 zero$c))) :named a251))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (coeff$a (monom$b ?v0 ?v1) ?v2) (ite (= ?v1 ?v2) ?v0 zero$a))) :named a252))
-(assert (! (forall ((?v0 Complex$) (?v1 Complex_poly$) (?v2 Complex$) (?v3 Complex_poly$)) (= (plus$c (pCons$ ?v0 ?v1) (pCons$ ?v2 ?v3)) (pCons$ (plus$ ?v0 ?v2) (plus$c ?v1 ?v3)))) :named a253))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat_poly$) (?v2 Nat$) (?v3 Nat_poly$)) (= (plus$b (pCons$b ?v0 ?v1) (pCons$b ?v2 ?v3)) (pCons$b (plus$a ?v0 ?v2) (plus$b ?v1 ?v3)))) :named a254))
-(assert (! (forall ((?v0 Complex$) (?v1 Nat$)) (= (coeff$b (monom$ ?v0 ?v1) (degree$b (monom$ ?v0 ?v1))) ?v0)) :named a255))
-(assert (! (forall ((?v0 Complex$) (?v1 Nat$)) (=> (not (= ?v0 zero$)) (= (order$ zero$ (monom$ ?v0 ?v1)) ?v1))) :named a256))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$)) (=> (not (= ?v0 zero$c)) (= (order$a zero$c (monom$a ?v0 ?v1)) ?v1))) :named a257))
-(assert (! (forall ((?v0 Complex$) (?v1 Complex_poly$)) (= (pcompose$ (pCons$ ?v0 zero$c) ?v1) (pCons$ ?v0 zero$c))) :named a258))
-(assert (! (forall ((?v0 Complex$)) (= (reflect_poly$ (pCons$ ?v0 zero$c)) (pCons$ ?v0 zero$c))) :named a259))
-(assert (! (forall ((?v0 Complex$) (?v1 Complex_poly$) (?v2 Complex$)) (= (synthetic_div$ (pCons$ ?v0 ?v1) ?v2) (pCons$ (poly$ ?v1 ?v2) (synthetic_div$ ?v1 ?v2)))) :named a260))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$)) (=> (= ?v0 zero$c) (= (coeff$b (pCons$ ?v1 ?v0) (degree$b (pCons$ ?v1 ?v0))) ?v1))) :named a261))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$)) (=> (not (= ?v0 zero$c)) (= (coeff$b (pCons$ ?v1 ?v0) (degree$b (pCons$ ?v1 ?v0))) (coeff$b ?v0 (degree$b ?v0))))) :named a262))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (dvd$c (pCons$a ?v0 zero$b) (pCons$a ?v1 zero$b)) (dvd$ ?v0 ?v1))) :named a263))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (dvd$d (pCons$b ?v0 zero$d) (pCons$b ?v1 zero$d)) (dvd$b ?v0 ?v1))) :named a264))
-(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (= (dvd$ (pCons$ ?v0 zero$c) (pCons$ ?v1 zero$c)) (dvd$a ?v0 ?v1))) :named a265))
-(assert (! (= (= (pCons$b one$ zero$d) one$c) true) :named a266))
-(assert (! (= (= (pCons$ one$b zero$c) one$a) true) :named a267))
-(assert (! (= (= one$c (pCons$b one$ zero$d)) true) :named a268))
-(assert (! (= (= one$a (pCons$ one$b zero$c)) true) :named a269))
-(assert (! (= (monom$b one$ zero$a) one$c) :named a270))
-(assert (! (forall ((?v0 Complex_poly$)) (= (pcompose$ ?v0 (pCons$ zero$ (pCons$ one$b zero$c))) ?v0)) :named a271))
-(assert (! (forall ((?v0 Complex_poly_poly$)) (= (pcompose$a ?v0 (pCons$a zero$c (pCons$a one$a zero$b))) ?v0)) :named a272))
-(assert (! (forall ((?v0 Nat_poly$)) (= (pcompose$b ?v0 (pCons$b zero$a (pCons$b one$ zero$d))) ?v0)) :named a273))
-(assert (! (forall ((?v0 Nat$)) (=> (dvd$b zero$a ?v0) (= ?v0 zero$a))) :named a274))
-(assert (! (forall ((?v0 Nat$)) (= (not (= ?v0 zero$a)) (and (dvd$b ?v0 zero$a) (not (= ?v0 zero$a))))) :named a275))
-(assert (! (forall ((?v0 Nat$)) (! (= (dvd$b zero$a ?v0) (= ?v0 zero$a)) :pattern ((dvd$b zero$a ?v0)))) :named a276))
-(assert (! (forall ((?v0 Nat$)) (not (and (dvd$b zero$a ?v0) (not (= zero$a ?v0))))) :named a277))
-(assert (! (forall ((?v0 Nat$)) (dvd$b ?v0 zero$a)) :named a278))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$) (?v2 Complex_poly$)) (= (= (monom$a ?v0 ?v1) (pCons$a ?v2 zero$b)) (and (= ?v0 ?v2) (or (= ?v0 zero$c) (= ?v1 zero$a))))) :named a279))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (= (monom$b ?v0 ?v1) (pCons$b ?v2 zero$d)) (and (= ?v0 ?v2) (or (= ?v0 zero$a) (= ?v1 zero$a))))) :named a280))
-(assert (! (forall ((?v0 Complex$) (?v1 Nat$) (?v2 Complex$)) (= (= (monom$ ?v0 ?v1) (pCons$ ?v2 zero$c)) (and (= ?v0 ?v2) (or (= ?v0 zero$) (= ?v1 zero$a))))) :named a281))
-(assert (! (forall ((?v0 Complex_poly$)) (=> (forall ((?v1 Complex$) (?v2 Complex_poly$)) (=> (= ?v0 (pCons$ ?v1 ?v2)) false)) false)) :named a282))
-(assert (! (forall ((?v0 Complex_poly$)) (=> (forall ((?v1 Complex$) (?v2 Complex_poly$)) (=> (= ?v0 (pCons$ ?v1 ?v2)) false)) false)) :named a283))
-(assert (! (forall ((?v0 (-> Complex_poly$ (-> Complex_poly$ Bool))) (?v1 Complex_poly$) (?v2 Complex_poly$)) (=> (and (?v0 zero$c zero$c) (forall ((?v3 Complex$) (?v4 Complex_poly$) (?v5 Complex$) (?v6 Complex_poly$)) (=> (?v0 ?v4 ?v6) (?v0 (pCons$ ?v3 ?v4) (pCons$ ?v5 ?v6))))) (?v0 ?v1 ?v2))) :named a284))
-(assert (! (forall ((?v0 Complex$) (?v1 Nat$) (?v2 Complex$) (?v3 Nat$)) (= (= (monom$ ?v0 ?v1) (monom$ ?v2 ?v3)) (and (= ?v0 ?v2) (or (= ?v0 zero$) (= ?v1 ?v3))))) :named a285))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$) (?v2 Complex_poly$) (?v3 Nat$)) (= (= (monom$a ?v0 ?v1) (monom$a ?v2 ?v3)) (and (= ?v0 ?v2) (or (= ?v0 zero$c) (= ?v1 ?v3))))) :named a286))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$) (?v3 Nat$)) (= (= (monom$b ?v0 ?v1) (monom$b ?v2 ?v3)) (and (= ?v0 ?v2) (or (= ?v0 zero$a) (= ?v1 ?v3))))) :named a287))
-(assert (! (forall ((?v0 Complex$)) (! (= (monom$ ?v0 zero$a) (pCons$ ?v0 zero$c)) :pattern ((monom$ ?v0)))) :named a288))
-(assert (! (forall ((?v0 (-> Complex_poly_poly$ Bool)) (?v1 Complex_poly_poly$)) (=> (and (?v0 zero$b) (forall ((?v2 Complex_poly$) (?v3 Complex_poly_poly$)) (=> (and (or (not (= ?v2 zero$c)) (not (= ?v3 zero$b))) (?v0 ?v3)) (?v0 (pCons$a ?v2 ?v3))))) (?v0 ?v1))) :named a289))
-(assert (! (forall ((?v0 (-> Nat_poly$ Bool)) (?v1 Nat_poly$)) (=> (and (?v0 zero$d) (forall ((?v2 Nat$) (?v3 Nat_poly$)) (=> (and (or (not (= ?v2 zero$a)) (not (= ?v3 zero$d))) (?v0 ?v3)) (?v0 (pCons$b ?v2 ?v3))))) (?v0 ?v1))) :named a290))
-(assert (! (forall ((?v0 (-> Complex_poly$ Bool)) (?v1 Complex_poly$)) (=> (and (?v0 zero$c) (forall ((?v2 Complex$) (?v3 Complex_poly$)) (=> (and (or (not (= ?v2 zero$)) (not (= ?v3 zero$c))) (?v0 ?v3)) (?v0 (pCons$ ?v2 ?v3))))) (?v0 ?v1))) :named a291))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$)) (=> (= (poly$ ?v0 ?v1) zero$) (= (poly$ (pCons$ zero$ ?v0) ?v1) zero$))) :named a292))
-(assert (! (forall ((?v0 Complex_poly_poly$) (?v1 Complex_poly$)) (=> (= (poly$a ?v0 ?v1) zero$c) (= (poly$a (pCons$a zero$c ?v0) ?v1) zero$c))) :named a293))
-(assert (! (forall ((?v0 Nat_poly$) (?v1 Nat$)) (=> (= (poly$b ?v0 ?v1) zero$a) (= (poly$b (pCons$b zero$a ?v0) ?v1) zero$a))) :named a294))
-(assert (! (forall ((?v0 Complex$) (?v1 Nat$)) (=> (not (= ?v0 zero$)) (= (degree$b (monom$ ?v0 ?v1)) ?v1))) :named a295))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$)) (=> (not (= ?v0 zero$c)) (= (degree$ (monom$a ?v0 ?v1)) ?v1))) :named a296))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (=> (not (= ?v0 zero$a)) (= (degree$a (monom$b ?v0 ?v1)) ?v1))) :named a297))
-(assert (! (forall ((?v0 Complex$) (?v1 Nat$) (?v2 Nat$)) (= (coeff$b (monom$ ?v0 ?v1) ?v2) (ite (= ?v1 ?v2) ?v0 zero$))) :named a298))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$) (?v2 Nat$)) (= (coeff$ (monom$a ?v0 ?v1) ?v2) (ite (= ?v1 ?v2) ?v0 zero$c))) :named a299))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (coeff$a (monom$b ?v0 ?v1) ?v2) (ite (= ?v1 ?v2) ?v0 zero$a))) :named a300))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (=> (dvd$ ?v0 ?v1) (dvd$ ?v0 (pCons$ zero$ ?v1)))) :named a301))
-(assert (! (forall ((?v0 Complex_poly_poly$) (?v1 Complex_poly_poly$)) (=> (dvd$c ?v0 ?v1) (dvd$c ?v0 (pCons$a zero$c ?v1)))) :named a302))
-(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (= (poly$ (pCons$ (poly$ zero$c ?v0) zero$c) ?v1) (poly$ zero$c ?v1))) :named a303))
-(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (= ?v0 (poly$ (pCons$ ?v0 zero$c) ?v1))) :named a304))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (plus$b (monom$b ?v0 ?v1) (monom$b ?v2 ?v1)) (monom$b (plus$a ?v0 ?v2) ?v1))) :named a305))
-(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (= (offset_poly$ (pCons$ ?v0 zero$c) ?v1) (pCons$ ?v0 zero$c))) :named a306))
-(assert (! (forall ((?v0 Complex_poly$)) (= (exists ((?v1 Complex_poly$)) (= (poly$a (pCons$a ?v0 zero$b) ?v1) zero$c)) (= ?v0 zero$c))) :named a307))
-(assert (! (forall ((?v0 Nat$)) (= (exists ((?v1 Nat$)) (= (poly$b (pCons$b ?v0 zero$d) ?v1) zero$a)) (= ?v0 zero$a))) :named a308))
-(assert (! (forall ((?v0 Complex$)) (= (exists ((?v1 Complex$)) (= (poly$ (pCons$ ?v0 zero$c) ?v1) zero$)) (= ?v0 zero$))) :named a309))
-(assert (! (forall ((?v0 Complex_poly$)) (= (exists ((?v1 Complex_poly$)) (not (= (poly$a (pCons$a ?v0 zero$b) ?v1) zero$c))) (not (= ?v0 zero$c)))) :named a310))
-(assert (! (forall ((?v0 Nat$)) (= (exists ((?v1 Nat$)) (not (= (poly$b (pCons$b ?v0 zero$d) ?v1) zero$a))) (not (= ?v0 zero$a)))) :named a311))
-(assert (! (forall ((?v0 Complex$)) (= (exists ((?v1 Complex$)) (not (= (poly$ (pCons$ ?v0 zero$c) ?v1) zero$))) (not (= ?v0 zero$)))) :named a312))
-(assert (! (forall ((?v0 Complex$)) (= (poly$ (pCons$ zero$ zero$c) ?v0) (poly$ zero$c ?v0))) :named a313))
-(assert (! (forall ((?v0 Complex_poly$)) (= (poly$a (pCons$a zero$c zero$b) ?v0) (poly$a zero$b ?v0))) :named a314))
-(assert (! (forall ((?v0 Complex$)) (= (degree$b (pCons$ ?v0 zero$c)) zero$a)) :named a315))
-(assert (! (forall ((?v0 Complex_poly$)) (=> (and (= (degree$b ?v0) zero$a) (forall ((?v1 Complex$)) (=> (= ?v0 (pCons$ ?v1 zero$c)) false))) false)) :named a316))
-(assert (! (= (pCons$b one$ zero$d) one$c) :named a317))
-(assert (! (= (pCons$ one$b zero$c) one$a) :named a318))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (monom$b ?v0 ?v1) one$c) (and (= ?v0 one$) (= ?v1 zero$a)))) :named a319))
-(assert (! (forall ((?v0 Complex$)) (= ?v0 (poly$ (pCons$ zero$ (pCons$ one$b zero$c)) ?v0))) :named a320))
-(assert (! (forall ((?v0 Complex_poly$)) (= ?v0 (poly$a (pCons$a zero$c (pCons$a one$a zero$b)) ?v0))) :named a321))
-(assert (! (forall ((?v0 Complex_poly$)) (=> (not (exists ((?v1 Complex$) (?v2 Complex_poly$)) (and (not (= ?v1 zero$)) (and (= ?v2 zero$c) (= ?v0 (pCons$ ?v1 ?v2)))))) (exists ((?v1 Complex$)) (= (poly$ ?v0 ?v1) zero$)))) :named a322))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$) (?v2 Complex$)) (=> (not (= ?v0 zero$c)) (exists ((?v3 Complex$)) (= (poly$ (pCons$ ?v1 (pCons$ ?v2 ?v0)) ?v3) zero$)))) :named a323))
-(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly_poly$)) (= (dvd$c (pCons$a ?v0 zero$b) ?v1) (forall ((?v2 Nat$)) (dvd$ ?v0 (coeff$ ?v1 ?v2))))) :named a324))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat_poly$)) (= (dvd$d (pCons$b ?v0 zero$d) ?v1) (forall ((?v2 Nat$)) (dvd$b ?v0 (coeff$a ?v1 ?v2))))) :named a325))
-(assert (! (forall ((?v0 Complex$) (?v1 Complex_poly$)) (= (dvd$ (pCons$ ?v0 zero$c) ?v1) (forall ((?v2 Nat$)) (dvd$a ?v0 (coeff$b ?v1 ?v2))))) :named a326))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (degree$a (power$b (pCons$b ?v0 (pCons$b one$ zero$d)) ?v1)) ?v1)) :named a327))
-(assert (! (forall ((?v0 Complex$) (?v1 Nat$)) (= (degree$b (power$ (pCons$ ?v0 (pCons$ one$b zero$c)) ?v1)) ?v1)) :named a328))
-(assert (! (forall ((?v0 Complex_poly$)) (= (pcompose$ ?v0 zero$c) (pCons$ (coeff$b ?v0 zero$a) zero$c))) :named a329))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (coeff$a (power$b (pCons$b ?v0 (pCons$b one$ zero$d)) ?v1) ?v1) one$)) :named a330))
-(assert (! (forall ((?v0 Complex$) (?v1 Nat$)) (= (coeff$b (power$ (pCons$ ?v0 (pCons$ one$b zero$c)) ?v1) ?v1) one$b)) :named a331))
-(assert (! (forall ((?v0 Complex$) (?v1 Complex_poly$)) (= (dvd$ (pCons$ ?v0 ?v1) one$a) (and (= ?v1 zero$c) (not (= ?v0 zero$))))) :named a332))
-(assert (! (forall ((?v0 Complex$)) (=> (not (= ?v0 zero$)) (dvd$ (pCons$ ?v0 zero$c) one$a))) :named a333))
-(assert (! (forall ((?v0 Complex_poly$)) (=> (and (dvd$ ?v0 one$a) (forall ((?v1 Complex$)) (=> (and (= ?v0 (monom$ ?v1 zero$a)) (not (= ?v1 zero$))) false))) false)) :named a334))
-(assert (! (forall ((?v0 Complex$)) (=> (not (= ?v0 zero$)) (dvd$ (monom$ ?v0 zero$a) one$a))) :named a335))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (= (times$ ?v0 ?v1) (times$ ?v2 ?v1)) (or (= ?v0 ?v2) (= ?v1 zero$a)))) :named a336))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (= (times$ ?v0 ?v1) (times$ ?v0 ?v2)) (or (= ?v1 ?v2) (= ?v0 zero$a)))) :named a337))
-(assert (! (forall ((?v0 Nat$)) (! (= (times$ ?v0 zero$a) zero$a) :pattern ((times$ ?v0)))) :named a338))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (times$ ?v0 ?v1) zero$a) (or (= ?v0 zero$a) (= ?v1 zero$a)))) :named a339))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (suc$ ?v0) (suc$ ?v1)) (= ?v0 ?v1))) :named a340))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (suc$ ?v0) (suc$ ?v1)) (= ?v0 ?v1))) :named a341))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (times$ ?v0 ?v1) one$) (and (= ?v0 one$) (= ?v1 one$)))) :named a342))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= one$ (times$ ?v0 ?v1)) (and (= ?v0 one$) (= ?v1 one$)))) :named a343))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (times$ ?v0 ?v1) (suc$ zero$a)) (and (= ?v0 (suc$ zero$a)) (= ?v1 (suc$ zero$a))))) :named a344))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (suc$ zero$a) (times$ ?v0 ?v1)) (and (= ?v0 (suc$ zero$a)) (= ?v1 (suc$ zero$a))))) :named a345))
-(assert (! (forall ((?v0 Nat$)) (! (= (power$c (suc$ zero$a) ?v0) (suc$ zero$a)) :pattern ((power$c (suc$ zero$a) ?v0)))) :named a346))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (power$c ?v0 ?v1) (suc$ zero$a)) (or (= ?v1 zero$a) (= ?v0 (suc$ zero$a))))) :named a347))
-(assert (! (forall ((?v0 Nat$)) (less_eq$ zero$a ?v0)) :named a348))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (less_eq$ (suc$ ?v0) (suc$ ?v1)) (less_eq$ ?v0 ?v1))) :named a349))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (plus$a ?v0 (suc$ ?v1)) (suc$ (plus$a ?v0 ?v1)))) :named a350))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (! (= (times$ ?v0 (suc$ ?v1)) (plus$a ?v0 (times$ ?v0 ?v1))) :pattern ((times$ ?v0 (suc$ ?v1))))) :named a351))
-(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (less_eq$ (plus$a ?v0 ?v1) (plus$a ?v0 ?v2)) (less_eq$ ?v1 ?v2))) :named a352))
-(check-sat)

diff --git a/test/regress/regress1/ho/ho-exponential-model.smt2 b/test/regress/regress1/ho/ho-exponential-model.smt2
deleted file mode 100644 (file)
index 3f00118..0000000
--- a/test/regress/regress1/ho/ho-exponential-model.smt2
+++ /dev/null
@@ -1,40 +0,0 @@
-; COMMAND-LINE: --uf-ho
-; EXPECT: sat
-(set-logic UFLIA)
-(set-info :status sat)
-(declare-fun f1 (Int Int Int Int) Int)
-(declare-fun f2 (Int Int Int) Int)
-(declare-fun f3 (Int Int) Int)
-(declare-fun f4 (Int) Int)
-(declare-fun f5 (Int Int Int) Int)
-(declare-fun f6 (Int Int) Int)
-(declare-fun f7 (Int) Int)
-
-
-(assert (= (f1 0) (f1 1)))
-(assert (= (f1 1) f2))
-
-(assert (= (f2 0) (f2 1)))
-(assert (= (f2 1) f3))
-
-(assert (= (f3 0) (f3 1)))
-(assert (= (f3 1) f4))
-
-(assert (= (f4 0) (f4 1)))
-(assert (= (f4 1) 2))
-
-
-(assert (= (f1 3) (f1 4)))
-(assert (= (f1 4) f5))
-
-(assert (= (f5 3) (f5 4)))
-(assert (= (f5 4) f6))
-
-(assert (= (f6 3) (f6 4)))
-(assert (= (f6 4) f7))
-
-(assert (= (f7 3) (f7 4)))
-(assert (= (f7 4) 5))
-
-; this benchmark has a concise model representation for f1 if we use curried (tree-like) models for UF
-(check-sat)

diff --git a/test/regress/regress1/ho/ho-matching-enum-2.smt2 b/test/regress/regress1/ho/ho-matching-enum-2.smt2
deleted file mode 100644 (file)
index 9581e4c..0000000
--- a/test/regress/regress1/ho/ho-matching-enum-2.smt2
+++ /dev/null
@@ -1,18 +0,0 @@
-; COMMAND-LINE: --uf-ho
-; EXPECT: unsat
-(set-logic ALL)
-(set-info :status unsat)
-
-(declare-sort U 0)
-
-(declare-fun p (Int) Bool)
-(declare-fun q (Int) Bool)
-(declare-fun k (Int Int) Int)
-
-(assert (q (k 0 1)))
-(assert (not (p (k 0 0))))
-
-(assert (forall ((f (-> Int Int Int)) (y Int) (z Int)) (or (p (f y z)) (not (q (f z y))))))
-
-(check-sat)
-(exit)

diff --git a/test/regress/regress1/ho/ho-std-fmf.smt2 b/test/regress/regress1/ho/ho-std-fmf.smt2
deleted file mode 100644 (file)
index 61d82d0..0000000
--- a/test/regress/regress1/ho/ho-std-fmf.smt2
+++ /dev/null
@@ -1,18 +0,0 @@
-; COMMAND-LINE: --uf-ho --finite-model-find
-; EXPECT: sat
-(set-logic UF)
-(set-info :status sat)
-(declare-sort U 0)
-(declare-fun P (U U) Bool)
-(declare-fun Q (U U) Bool)
-(declare-fun R (U U) Bool)
-(declare-fun a () U)
-(declare-fun b () U)
-
-; can solve this using standard MBQI model for P = \ xy true
-(assert (forall ((x U) (y U)) (or (P x y) (Q x y))))
-(assert (forall ((x U) (y U)) (or (P x y) (R x y))))
-
-(assert (not (= a b)))
-(assert (= (Q a) (R b)))
-(check-sat)

diff --git a/test/regress/regress1/ho/hoa0008.smt2 b/test/regress/regress1/ho/hoa0008.smt2
deleted file mode 100644 (file)
index f4833aa..0000000
--- a/test/regress/regress1/ho/hoa0008.smt2
+++ /dev/null
@@ -1,68 +0,0 @@
-; COMMAND-LINE: --uf-ho
-; EXPECT: unsat
-(set-logic ALL)
-(declare-sort A$ 0)
-(declare-sort Com$ 0)
-(declare-sort Loc$ 0)
-(declare-sort Nat$ 0)
-(declare-sort Pname$ 0)
-(declare-sort State$ 0)
-(declare-sort Vname$ 0)
-(declare-sort Literal$ 0)
-(declare-sort Natural$ 0)
-(declare-sort Typerep$ 0)
-(declare-sort A_triple$ 0)
-(declare-sort Com_option$ 0)
-(declare-fun p$ () (-> A$ (-> State$ Bool)))
-(declare-fun q$ () (-> A$ (-> State$ Bool)))
-(declare-fun pn$ () Pname$)
-(declare-fun wt$ (Com$) Bool)
-(declare-fun ass$ (Vname$ (-> State$ Nat$)) Com$)
-(declare-fun suc$ (Nat$) Nat$)
-(declare-fun the$ (Com_option$) Com$)
-(declare-fun body$ (Pname$) Com$)
-(declare-fun call$ (Vname$ Pname$ (-> State$ Nat$)) Com$)
-(declare-fun cond$ ((-> State$ Bool) Com$ Com$) Com$)
-(declare-fun none$ () Com_option$)
-(declare-fun plus$ (Nat$ Nat$) Nat$)
-(declare-fun semi$ (Com$ Com$) Com$)
-(declare-fun size$ (A_triple$) Nat$)
-(declare-fun skip$ () Com$)
-(declare-fun some$ (Com$) Com_option$)
-(declare-fun suc$a (Natural$) Natural$)
-(declare-fun zero$ () Nat$)
-(declare-fun body$a (Pname$) Com_option$)
-(declare-fun evalc$ (Com$ State$ State$) Bool)
-(declare-fun evaln$ (Com$ State$ Nat$ State$) Bool)
-(declare-fun local$ (Loc$ (-> State$ Nat$) Com$) Com$)
-(declare-fun plus$a (Natural$ Natural$) Natural$)
-(declare-fun size$a (Com$) Nat$)
-(declare-fun size$b (Natural$) Nat$)
-(declare-fun size$c (Bool) Nat$)
-(declare-fun size$d (Com_option$) Nat$)
-(declare-fun size$e (Typerep$) Nat$)
-(declare-fun size$f (Literal$) Nat$)
-(declare-fun while$ ((-> State$ Bool) Com$) Com$)
-(declare-fun zero$a () Natural$)
-(declare-fun triple$ ((-> A$ (-> State$ Bool)) Com$ (-> A$ (-> State$ Bool))) A_triple$)
-(declare-fun rec_bool$ (Nat$ Nat$) (-> Bool Nat$))
-(declare-fun size_com$ (Com$) Nat$)
-(declare-fun size_bool$ (Bool) Nat$)
-(declare-fun wT_bodies$ () Bool)
-(declare-fun size_option$ ((-> Com$ Nat$)) (-> Com_option$ Nat$))
-(declare-fun size_triple$ ((-> A$ Nat$) A_triple$) Nat$)
-(declare-fun size_natural$ (Natural$) Nat$)
-(declare-fun triple_valid$ (Nat$ A_triple$) Bool)
-(assert (! (not (triple_valid$ zero$ (triple$ p$ (body$ pn$) q$))) :named a0))
-
-(assert (! (forall ((?v0 Nat$) (?v1 (-> A$ (-> State$ Bool))) (?v2 Com$) (?v3 (-> A$ (-> State$ Bool)))) (= (triple_valid$ ?v0 (triple$ ?v1 ?v2 ?v3)) (forall ((?v4 A$) (?v5 State$)) (=> (?v1 ?v4 ?v5) (forall ((?v6 State$)) (=> (evaln$ ?v2 ?v5 ?v0 ?v6) (?v3 ?v4 ?v6))))))) :named a6))
-
-(assert (! (= (size_bool$ true) zero$) :named a13))
-(assert (! (= size_bool$ (rec_bool$ zero$ zero$)) :named a14))
-
-(assert (! (forall ((?v0 Nat$)) (not (= zero$ (suc$ ?v0)))) :named a37))
-
-(assert (! (forall ((?v0 Pname$) (?v1 State$) (?v2 Nat$) (?v3 State$)) (=> (and (evaln$ (body$ ?v0) ?v1 ?v2 ?v3) (forall ((?v4 Nat$)) (=> (and (= ?v2 (suc$ ?v4)) (evaln$ (the$ (body$a ?v0)) ?v1 ?v4 ?v3)) false))) false)) :named a204))
-
-(check-sat)
-;(get-proof)

diff --git a/test/regress/regress1/ho/match-middle.smt2 b/test/regress/regress1/ho/match-middle.smt2
deleted file mode 100644 (file)
index 0485f9a..0000000
--- a/test/regress/regress1/ho/match-middle.smt2
+++ /dev/null
@@ -1,20 +0,0 @@
-; COMMAND-LINE: --uf-ho
-; EXPECT: unsat
-(set-logic UFLIA)
-(set-info :status unsat)
-(declare-fun f (Int Int Int) Int)
-(declare-fun h (Int Int Int) Int)
-(declare-fun g (Int Int) Int)
-(declare-fun a () Int)
-(declare-fun b () Int)
-(declare-fun c () Int)
-(declare-fun d () Int)
-
-(assert (or (= (f a) g) (= (h a) g)))
-
-(assert (= (f a b d) c))
-(assert (= (h a b d) c))
-
-(assert (forall ((x Int) (y Int)) (not (= (g x y) c))))
-
-(check-sat)

diff --git a/test/regress/regress1/ho/nested_lambdas-AGT034^2.smt2 b/test/regress/regress1/ho/nested_lambdas-AGT034^2.smt2
new file mode 100644 (file)
index 0000000..1670e07
--- /dev/null
+++ b/test/regress/regress1/ho/nested_lambdas-AGT034^2.smt2
@@ -0,0 +1,101 @@
+; COMMAND-LINE: --uf-ho --no-check-unsat-cores --no-check-proofs
+; EXPECT: unsat
+
+(set-logic ALL)
+(declare-sort $$unsorted 0)
+(declare-sort mu 0)
+(declare-fun meq_ind (mu mu $$unsorted) Bool)
+(assert (= meq_ind (lambda ((X mu) (Y mu) (W $$unsorted)) (= X Y))))
+(declare-fun meq_prop ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
+(assert (= meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (X W) (Y W)))))
+(declare-fun mnot ((-> $$unsorted Bool) $$unsorted) Bool)
+(assert (= mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (Phi W)))))
+(declare-fun mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
+(assert (= mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (Phi W) (Psi W)))))
+(declare-fun mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
+(assert (= mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (mnot (mor (mnot Phi) (mnot Psi)) __flatten_var_0))))
+(declare-fun mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
+(assert (= mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (mor (mnot Phi) Psi __flatten_var_0))))
+(declare-fun mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
+(assert (= mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (mor (mnot Psi) Phi __flatten_var_0))))
+(declare-fun mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
+(assert (= mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (mand (mimplies Phi Psi) (mimplies Psi Phi) __flatten_var_0))))
+(declare-fun mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
+(assert (= mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (mnot (mequiv Phi Psi) __flatten_var_0))))
+(declare-fun mforall_ind ((-> mu $$unsorted Bool) $$unsorted) Bool)
+(assert (= mforall_ind (lambda ((Phi (-> mu $$unsorted Bool)) (W $$unsorted)) (forall ((X mu)) (Phi X W) ))))
+(declare-fun mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
+(assert (= mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (Phi P W) ))))
+(declare-fun mexists_ind ((-> mu $$unsorted Bool) $$unsorted) Bool)
+(assert (= mexists_ind (lambda ((Phi (-> mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (mnot (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) (mnot (Phi X) __flatten_var_0))) __flatten_var_0))))
+(declare-fun mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
+(assert (= mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (mnot (mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (mnot (Phi P) __flatten_var_0))) __flatten_var_0))))
+(declare-fun mtrue ($$unsorted) Bool)
+(assert (= mtrue (lambda ((W $$unsorted)) true)))
+(declare-fun mfalse ($$unsorted) Bool)
+(assert (= mfalse (mnot mtrue)))
+(declare-fun mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
+(assert (= mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (R W V)) (Phi V)) ))))
+(declare-fun mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
+(assert (= mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (mnot (mbox R (mnot Phi)) __flatten_var_0))))
+(declare-fun mreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
+(assert (= mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (R S S) ))))
+(declare-fun msymmetric ((-> $$unsorted $$unsorted Bool)) Bool)
+(assert (= msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> (R S T) (R T S)) ))))
+(declare-fun mserial ((-> $$unsorted $$unsorted Bool)) Bool)
+(assert (= mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (R S T) ) ))))
+(declare-fun mtransitive ((-> $$unsorted $$unsorted Bool)) Bool)
+(assert (= mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (R S T) (R T U)) (R S U)) ))))
+(declare-fun meuclidean ((-> $$unsorted $$unsorted Bool)) Bool)
+(assert (= meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (R S T) (R S U)) (R T U)) ))))
+(declare-fun mpartially_functional ((-> $$unsorted $$unsorted Bool)) Bool)
+(assert (= mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (R S T) (R S U)) (= T U)) ))))
+(declare-fun mfunctional ((-> $$unsorted $$unsorted Bool)) Bool)
+(assert (= mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and (R S T) (forall ((U $$unsorted)) (=> (R S U) (= T U)) )) ) ))))
+(declare-fun mweakly_dense ((-> $$unsorted $$unsorted Bool)) Bool)
+(assert (= mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (R S T) (exists ((U $$unsorted)) (and (R S U) (R U T)) )) ))))
+(declare-fun mweakly_connected ((-> $$unsorted $$unsorted Bool)) Bool)
+(assert (= mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (R S T) (R S U)) (or (R T U) (= T U) (R U T))) ))))
+(declare-fun mweakly_directed ((-> $$unsorted $$unsorted Bool)) Bool)
+(assert (= mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> (and (R S T) (R S U)) (exists ((V $$unsorted)) (and (R T V) (R U V)) )) ))))
+(declare-fun mvalid ((-> $$unsorted Bool)) Bool)
+(assert (= mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (Phi W) ))))
+(declare-fun minvalid ((-> $$unsorted Bool)) Bool)
+(assert (= minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (Phi W)) ))))
+(declare-fun msatisfiable ((-> $$unsorted Bool)) Bool)
+(assert (= msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (Phi W) ))))
+(declare-fun mcountersatisfiable ((-> $$unsorted Bool)) Bool)
+(assert (= mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (Phi W)) ))))
+(declare-fun a1 ($$unsorted $$unsorted) Bool)
+(declare-fun a2 ($$unsorted $$unsorted) Bool)
+(declare-fun a3 ($$unsorted $$unsorted) Bool)
+(declare-fun jan () mu)
+(declare-fun piotr () mu)
+(declare-fun cola () mu)
+(declare-fun pepsi () mu)
+(declare-fun beer () mu)
+(declare-fun likes (mu mu $$unsorted) Bool)
+(declare-fun very_much_likes (mu mu $$unsorted) Bool)
+(declare-fun possibly_likes (mu mu $$unsorted) Bool)
+(assert (mvalid (mbox a1 (likes jan cola))))
+(assert (mvalid (mbox a1 (likes piotr pepsi))))
+(assert (mvalid (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) (mbox a1 (mimplies (mdia a1 (likes X pepsi)) (likes X cola)) __flatten_var_0)))))
+(assert (mvalid (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) (mbox a1 (mimplies (mdia a1 (likes X cola)) (likes X pepsi)) __flatten_var_0)))))
+(assert (mvalid (mbox a2 (likes jan pepsi))))
+(assert (mvalid (mbox a1 (likes piotr cola))))
+(assert (mvalid (mbox a1 (likes piotr beer))))
+(assert (mvalid (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) (mbox a2 (mimplies (likes X pepsi) (likes X cola)) __flatten_var_0)))))
+(assert (mvalid (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) (mbox a2 (mimplies (likes X cola) (likes X pepsi)) __flatten_var_0)))))
+(assert (mvalid (mbox a3 (likes jan cola))))
+(assert (mvalid (mdia a3 (likes piotr pepsi))))
+(assert (mvalid (mdia a1 (likes piotr beer))))
+(assert (mvalid (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) (mforall_ind (lambda ((Y mu) (__flatten_var_0 $$unsorted)) (mbox a3 (mimplies (mand (likes X Y) (mand (mbox a1 (likes X Y)) (mbox a2 (likes X Y)))) (very_much_likes X Y)) __flatten_var_0)) __flatten_var_0)))))
+(assert (mvalid (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) (mforall_ind (lambda ((Y mu) (__flatten_var_0 $$unsorted)) (mimplies (mbox a3 (very_much_likes X Y)) (very_much_likes X Y) __flatten_var_0)) __flatten_var_0)))))
+(assert (mvalid (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) (mforall_ind (lambda ((Y mu) (__flatten_var_0 $$unsorted)) (mimplies (mdia a3 (very_much_likes X Y)) (likes X Y) __flatten_var_0)) __flatten_var_0)))))
+(assert (mvalid (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) (mforall_ind (lambda ((Y mu) (__flatten_var_0 $$unsorted)) (mimplies (mdia a1 (likes X Y)) (possibly_likes X Y) __flatten_var_0)) __flatten_var_0)))))
+(assert (mvalid (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) (mforall_ind (lambda ((Y mu) (__flatten_var_0 $$unsorted)) (mimplies (mdia a2 (likes X Y)) (possibly_likes X Y) __flatten_var_0)) __flatten_var_0)))))
+(assert (mvalid (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) (mforall_ind (lambda ((Y mu) (__flatten_var_0 $$unsorted)) (mimplies (mdia a3 (likes X Y)) (possibly_likes X Y) __flatten_var_0)) __flatten_var_0)))))
+(assert (not (mvalid (very_much_likes jan cola))))
+(meta-info :filename "AGT034^2")
+
+(check-sat)
\ No newline at end of file

diff --git a/test/regress/regress1/ho/nested_lambdas-sat-SYO056^1-delta.smt2 b/test/regress/regress1/ho/nested_lambdas-sat-SYO056^1-delta.smt2
new file mode 100644 (file)
index 0000000..9211adf
--- /dev/null
+++ b/test/regress/regress1/ho/nested_lambdas-sat-SYO056^1-delta.smt2
@@ -0,0 +1,50 @@
+; COMMAND-LINE:  --uf-ho --finite-model-find --no-check-models
+; EXPECT: sat
+
+
+(set-logic ALL)
+(declare-sort $$unsorted 0)
+
+(declare-fun mvalid ((-> $$unsorted Bool)) Bool)
+(assert (= mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (Phi W) ))))
+
+(declare-fun mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
+(assert (= mforall_prop
+          (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted))
+            (forall ((P (-> $$unsorted Bool))) (Phi P W) ))))
+
+(declare-fun mnot ((-> $$unsorted Bool) $$unsorted) Bool)
+(assert (= mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (Phi W)))))
+
+(declare-fun mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
+(assert (= mor
+          (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted))
+            (or (Phi W) (Psi W)))))
+
+(declare-fun mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
+(assert (= mimplies
+          (lambda (
+                    (Phi (-> $$unsorted Bool))
+                    (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted))
+            (mor (mnot Phi) Psi __flatten_var_0))))
+
+(declare-fun mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
+(assert (= mbox
+          (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted))
+            (forall ((V $$unsorted)) (or (not (R W V)) (Phi V)) ))))
+
+(assert (not (forall ((R (-> $$unsorted $$unsorted Bool)))
+               (mvalid
+                 (mforall_prop
+                   (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted))
+                     (mforall_prop
+                       (lambda ((B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted))
+                         (mimplies
+                           (mbox R (mor A B))
+                           (mor
+                             (mbox R A)
+                             (mbox R B))
+                           __flatten_var_0))
+                       __flatten_var_0)))) )))
+
+(check-sat)

diff --git a/test/regress/regress1/ho/soundness_fmf_SYO362^5-delta.p b/test/regress/regress1/ho/soundness_fmf_SYO362^5-delta.p
new file mode 100644 (file)
index 0000000..baabd67
--- /dev/null
+++ b/test/regress/regress1/ho/soundness_fmf_SYO362^5-delta.p
@@ -0,0 +1,63 @@
+% COMMAND-LINE:  --uf-ho --finite-model-find
+% EXPECT: % SZS status GaveUp for soundness_fmf_SYO362^5-delta
+
+%------------------------------------------------------------------------------
+% File     : SYO362^5 : TPTP v7.2.0. Released v4.0.0.
+% Domain   : Syntactic
+% Problem  : TPS problem THM631A
+% Version  : Especial.
+% English  : If a set function preserves unions, then it is monotone.
+
+% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
+% Source   : [Bro09]
+% Names    : tps_0419 [Bro09]
+%          : THM631 [TPS]
+%          : THM631A [TPS]
+
+% Status   : Theorem
+% Rating   : 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.50 v5.4.0, 0.60 v5.3.0, 0.80 v4.1.0, 1.00 v4.0.0
+% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
+%            Number of atoms       :   22 (   1 equality;  16 variable)
+%            Maximal formula depth :    9 (   6 average)
+%            Number of connectives :   19 (   0   ~;   2   |;   0   &;  13   @)
+%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
+%                                         (   0  ~|;   0  ~&)
+%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
+%            Number of symbols     :    3 (   1   :;   0   =)
+%            Number of variables   :    8 (   0 sgn;   6   !;   0   ?;   2   ^)
+%                                         (   8   :;   0  !>;   0  ?*)
+%                                         (   0  @-;   0  @+)
+% SPC      : TH0_THM_EQU_NAR
+
+% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
+%            project in the Department of Mathematical Sciences at Carnegie
+%            Mellon University. Distributed under the Creative Commons copyleft
+%            license: http://creativecommons.org/licenses/by-sa/3.0/
+%          : Polymorphic definitions expanded.
+%          :
+%------------------------------------------------------------------------------
+thf(cK,type,(
+    cK: ( $i > $o ) > $i > $o )).
+
+thf(cTHM631A_pme,conjecture,
+    ( ! [X: $i > $o,Y: $i > $o] :
+        ( ( cK
+          @ ^ [Xz: $i] :
+              ( ( X @ Xz )
+              | ( Y @ Xz ) ) )
+        = ( ^ [Xw: $i] :
+              ( ( cK @ X @ Xw )
+              | ( cK @ Y @ Xw ) ) ) )
+   => ! [X: $i > $o,Y: $i > $o] :
+        ( ! [Xx: $i] :
+            ( ( X @ Xx )
+           => ( Y @ Xx ) )
+       => ! [Xx: $i] :
+            ( ( cK @ X @ Xx )
+           => ( cK @ Y @ Xx ) ) ) )).
+
+%------------------------------------------------------------------------------
+
+%% soundness issue (since resolved) was due to wrong lambda
+%% lifting. Free variables in lambda body not being carried out to
+%% quantified formula standing for lambda lifting

diff --git a/test/regress/regress1/ho/store-ax-min.p b/test/regress/regress1/ho/store-ax-min.p
new file mode 100644 (file)
index 0000000..d67eb8d
--- /dev/null
+++ b/test/regress/regress1/ho/store-ax-min.p
@@ -0,0 +1,28 @@
+% COMMAND-LINE: --uf-ho --full-saturate-quant --ho-elim-store-ax
+% COMMAND-LINE: --uf-ho --full-saturate-quant --ho-elim
+% EXPECT: % SZS status Theorem for store-ax-min
+
+thf(a, type, (a: $i)).
+thf(b, type, (b: $i)).
+
+%% thf(blah1, axiom, ( ! [X: $i, Y: $i] : (X = Y))).
+
+thf(blah2, axiom, ( ~ (a = b))).
+
+%% thf(storeax, axiom, (
+%%         ! [F : $i > $i, D : $i, R : $i] :
+%%         (
+%%             ? [G : $i > $i] :
+%%             (
+%%                 ! [X : $i] :
+%%                 (
+%%                     (G @ X) = $ite( X = D, R, F @ X)
+%%                 )
+%%             )
+%%         )
+
+
+%% (~ (X = Y)))
+%% ).
+
+thf(blah, conjecture, ( ? [F : $i > $i, G : $i > $i] : (~ (F = G)))).

diff --git a/test/regress/regress2/ho/SYO362^5.p b/test/regress/regress2/ho/SYO362^5.p
new file mode 100644 (file)
index 0000000..c01d3f2
--- /dev/null
+++ b/test/regress/regress2/ho/SYO362^5.p
@@ -0,0 +1,22 @@
+% COMMAND-LINE: --uf-ho --full-saturate-quant --ho-elim
+% EXPECT: % SZS status Theorem for SYO362^5
+
+thf(cK,type,(
+    cK: ( $i > $o ) > $i > $o )).
+
+thf(cTHM631A_pme,conjecture,
+    ( ! [X: $i > $o,Y: $i > $o] :
+        ( ( cK
+          @ ^ [Xz: $i] :
+              ( ( X @ Xz )
+              | ( Y @ Xz ) ) )
+        = ( ^ [Xw: $i] :
+              ( ( cK @ X @ Xw )
+              | ( cK @ Y @ Xw ) ) ) )
+   => ! [X: $i > $o,Y: $i > $o] :
+        ( ! [Xx: $i] :
+            ( ( X @ Xx )
+           => ( Y @ Xx ) )
+       => ! [Xx: $i] :
+            ( ( cK @ X @ Xx )
+           => ( cK @ Y @ Xx ) ) ) )).

diff --git a/test/regress/regress2/ho/auth0068.smt2 b/test/regress/regress2/ho/auth0068.smt2
new file mode 100644 (file)
index 0000000..eb0bb5d
--- /dev/null
+++ b/test/regress/regress2/ho/auth0068.smt2
@@ -0,0 +1,491 @@
+; COMMAND-LINE: --uf-ho
+; EXPECT: unsat
+(set-logic ALL)
+(set-info :status unsat)
+(declare-sort Msg$ 0)
+(declare-sort Nat$ 0)
+(declare-sort Agent$ 0)
+(declare-sort Event$ 0)
+(declare-sort Msg_set$ 0)
+(declare-sort Msg_list$ 0)
+(declare-sort Agent_set$ 0)
+(declare-sort Event_set$ 0)
+(declare-sort Agent_list$ 0)
+(declare-sort Event_list$ 0)
+(declare-sort Event_option$ 0)
+(declare-sort Msg_list_set$ 0)
+(declare-sort Agent_list_set$ 0)
+(declare-sort Event_list_set$ 0)
+(declare-sort Event_list_list$ 0)
+(declare-fun p$ () (-> Event$ Bool))
+(declare-fun uu$ ((-> Msg$ Bool) (-> Msg$ Bool) Msg$) Bool)
+(declare-fun bad$ () Agent_set$)
+(declare-fun nil$ () Event_list$)
+(declare-fun set$ (Event_list$) Event_set$)
+(declare-fun spy$ () Agent$)
+(declare-fun uua$ (Event_set$ (-> Event$ Bool) Event$) Bool)
+(declare-fun uub$ (Agent_set$ (-> Agent$ Bool) Agent$) Bool)
+(declare-fun uuc$ (Msg_set$ (-> Msg$ Bool) Msg$) Bool)
+(declare-fun uud$ (Event_set$ Event$) Bool)
+(declare-fun uue$ (Agent_set$ Agent$) Bool)
+(declare-fun uuf$ (Msg_set$ Msg$) Bool)
+(declare-fun uug$ (Event$ Event_list$) Bool)
+(declare-fun uuh$ (Event$ Event_list$) Bool)
+(declare-fun uui$ ((-> Event$ Bool) Event$ Event$) Bool)
+(declare-fun uuj$ (Event_list_set$ Event_list$ Event$) Bool)
+(declare-fun uuk$ (Msg$ (-> Msg$ Bool) Msg$) Bool)
+(declare-fun uul$ (Msg$ Msg_set$ Msg$) Bool)
+(declare-fun uum$ (Event$ Event_set$ Event$) Bool)
+(declare-fun uun$ (Agent$ Agent_set$ Agent$) Bool)
+(declare-fun uuo$ (Event_list$ Agent$ Agent$ Msg$) Msg_set$)
+(declare-fun uup$ (Event_list$ Agent$ Msg$) Msg_set$)
+(declare-fun uuq$ (Event_list$ Agent$ Msg$) Msg_set$)
+(declare-fun uur$ (Agent$ Event_list$ Agent$ Agent$ Msg$) Msg_set$)
+(declare-fun uus$ (Agent$ Event_list$ Agent$ Msg$) Msg_set$)
+(declare-fun bind$ (Event_list$ (-> Event$ Event_list$)) Event_list$)
+(declare-fun cons$ (Event$ Event_list$) Event_list$)
+(declare-fun gets$ (Agent$ Msg$) Event$)
+(declare-fun maps$ ((-> Event$ Event_list$)) (-> Event_list$ Event_list$))
+(declare-fun nil$a () Event_list_list$)
+(declare-fun nil$b () Msg_list$)
+(declare-fun nil$c () Agent_list$)
+(declare-fun null$ (Event_list$) Bool)
+(declare-fun says$ (Agent$ Agent$ Msg$) Event$)
+(declare-fun set$a (Msg_list$) Msg_set$)
+(declare-fun set$b (Agent_list$) Agent_set$)
+(declare-fun succ$ (Event_list_set$ Event_list$) Event_set$)
+(declare-fun cons$a (Event_list$ Event_list_list$) Event_list_list$)
+(declare-fun cons$b (Msg$ Msg_list$) Msg_list$)
+(declare-fun cons$c (Agent$ Agent_list$) Agent_list$)
+(declare-fun knows$ (Agent$ Event_list$) Msg_set$)
+(declare-fun notes$ (Agent$ Msg$) Event$)
+(declare-fun succ$a (Msg_list_set$ Msg_list$) Msg_set$)
+(declare-fun succ$b (Agent_list_set$ Agent_list$) Agent_set$)
+(declare-fun append$ (Event_list$ Event_list$) Event_list$)
+(declare-fun insert$ (Msg$ Msg_set$) Msg_set$)
+(declare-fun member$ (Agent$ Agent_set$) Bool)
+(declare-fun splice$ (Event_list$) (-> Event_list$ Event_list$))
+(declare-fun append$a (Msg_list$ Msg_list$) Msg_list$)
+(declare-fun append$b (Agent_list$ Agent_list$) Agent_list$)
+(declare-fun collect$ ((-> Msg$ Bool)) Msg_set$)
+(declare-fun insert$a (Event$) (-> Event_list$ Event_list$))
+(declare-fun insert$b (Event$ Event_set$) Event_set$)
+(declare-fun insert$c (Agent$ Agent_set$) Agent_set$)
+(declare-fun insert$d (Msg$ Msg_list$) Msg_list$)
+(declare-fun insert$e (Agent$ Agent_list$) Agent_list$)
+(declare-fun less_eq$ (Msg_set$ Msg_set$) Bool)
+(declare-fun list_ex$ ((-> Event$ Bool)) (-> Event_list$ Bool))
+(declare-fun member$a (Msg$ Msg_set$) Bool)
+(declare-fun member$b (Event$ Event_set$) Bool)
+(declare-fun member$c (Event_list$ Event_list_set$) Bool)
+(declare-fun member$d (Event_list$ Event$) Bool)
+(declare-fun member$e (Msg_list$ Msg_list_set$) Bool)
+(declare-fun member$f (Agent_list$ Agent_list_set$) Bool)
+(declare-fun member$g (Msg_list$ Msg$) Bool)
+(declare-fun member$h (Agent_list$ Agent$) Bool)
+(declare-fun rotate1$ (Event_list$) Event_list$)
+(declare-fun subseqs$ (Event_list$) Event_list_list$)
+(declare-fun antimono$ ((-> Msg_set$ Msg_set$)) Bool)
+(declare-fun collect$a ((-> Event$ Bool)) Event_set$)
+(declare-fun collect$b ((-> Agent$ Bool)) Agent_set$)
+(declare-fun greatest$ ((-> Msg_set$ Bool)) Msg_set$)
+(declare-fun less_eq$a (Event_set$ Event_set$) Bool)
+(declare-fun less_eq$b (Agent_set$ Agent_set$) Bool)
+(declare-fun less_eq$c ((-> Event$ Bool) (-> Event$ Bool)) Bool)
+(declare-fun less_eq$d ((-> Agent$ Bool) (-> Agent$ Bool)) Bool)
+(declare-fun less_eq$e ((-> Msg$ Bool) (-> Msg$ Bool)) Bool)
+(declare-fun less_eq$f ((-> Bool Msg_set$) (-> Bool Msg_set$)) Bool)
+(declare-fun list_all$ ((-> Event$ Bool) Event_list$) Bool)
+(declare-fun list_ex$a ((-> Msg$ Bool) Msg_list$) Bool)
+(declare-fun list_ex$b ((-> Agent$ Bool) Agent_list$) Bool)
+(declare-fun list_ex1$ ((-> Event$ Bool)) (-> Event_list$ Bool))
+(declare-fun case_list$ (Bool (-> Event$ (-> Event_list$ Bool)) Event_list$) Bool)
+(declare-fun initState$ (Agent$) Msg_set$)
+(declare-fun list_all$a ((-> Msg$ Bool) Msg_list$) Bool)
+(declare-fun list_all$b ((-> Agent$ Bool) Agent_list$) Bool)
+(declare-fun list_ex1$a ((-> Msg$ Bool) Msg_list$) Bool)
+(declare-fun list_ex1$b ((-> Agent$ Bool) Agent_list$) Bool)
+(declare-fun takeWhile$ ((-> Event$ Bool) Event_list$) Event_list$)
+(declare-fun case_event$ ((-> Agent$ (-> Agent$ (-> Msg$ Msg_set$))) (-> Agent$ (-> Msg$ Msg_set$)) (-> Agent$ (-> Msg$ Msg_set$)) Event$) Msg_set$)
+(declare-fun gen_length$ (Nat$) (-> Event_list$ Nat$))
+(declare-fun map_filter$ ((-> Event$ Event_option$)) (-> Event_list$ Event_list$))
+(declare-fun takeWhile$a ((-> Msg$ Bool) Msg_list$) Msg_list$)
+(declare-fun takeWhile$b ((-> Agent$ Bool) Agent_list$) Agent_list$)
+(declare-fun product_lists$ (Event_list_list$) Event_list_list$)
+(assert (! (forall ((?v0 Agent_set$) (?v1 Agent$)) (! (= (uue$ ?v0 ?v1) (member$ ?v1 ?v0)) :pattern ((uue$ ?v0 ?v1)))) :named a0))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg$)) (! (= (uuf$ ?v0 ?v1) (member$a ?v1 ?v0)) :pattern ((uuf$ ?v0 ?v1)))) :named a1))
+(assert (! (forall ((?v0 Event_set$) (?v1 Event$)) (! (= (uud$ ?v0 ?v1) (member$b ?v1 ?v0)) :pattern ((uud$ ?v0 ?v1)))) :named a2))
+(assert (! (forall ((?v0 Event_list$) (?v1 Agent$) (?v2 Msg$)) (! (= (uuq$ ?v0 ?v1 ?v2) (ite (member$ ?v1 bad$) (insert$ ?v2 (knows$ spy$ ?v0)) (knows$ spy$ ?v0))) :pattern ((uuq$ ?v0 ?v1 ?v2)))) :named a3))
+(assert (! (forall ((?v0 Event_list_set$) (?v1 Event_list$) (?v2 Event$)) (! (= (uuj$ ?v0 ?v1 ?v2) (member$c (append$ ?v1 (cons$ ?v2 nil$)) ?v0)) :pattern ((uuj$ ?v0 ?v1 ?v2)))) :named a4))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent$)) (! (= (uun$ ?v0 ?v1 ?v2) (or (= ?v2 ?v0) (member$ ?v2 ?v1))) :pattern ((uun$ ?v0 ?v1 ?v2)))) :named a5))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg$)) (! (= (uul$ ?v0 ?v1 ?v2) (or (= ?v2 ?v0) (member$a ?v2 ?v1))) :pattern ((uul$ ?v0 ?v1 ?v2)))) :named a6))
+(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event$)) (! (= (uum$ ?v0 ?v1 ?v2) (or (= ?v2 ?v0) (member$b ?v2 ?v1))) :pattern ((uum$ ?v0 ?v1 ?v2)))) :named a7))
+(assert (! (forall ((?v0 Agent_set$) (?v1 (-> Agent$ Bool)) (?v2 Agent$)) (! (= (uub$ ?v0 ?v1 ?v2) (and (member$ ?v2 ?v0) (?v1 ?v2))) :pattern ((uub$ ?v0 ?v1 ?v2)))) :named a8))
+(assert (! (forall ((?v0 Msg_set$) (?v1 (-> Msg$ Bool)) (?v2 Msg$)) (! (= (uuc$ ?v0 ?v1 ?v2) (and (member$a ?v2 ?v0) (?v1 ?v2))) :pattern ((uuc$ ?v0 ?v1 ?v2)))) :named a9))
+(assert (! (forall ((?v0 Event_set$) (?v1 (-> Event$ Bool)) (?v2 Event$)) (! (= (uua$ ?v0 ?v1 ?v2) (and (member$b ?v2 ?v0) (?v1 ?v2))) :pattern ((uua$ ?v0 ?v1 ?v2)))) :named a10))
+(assert (! (forall ((?v0 (-> Msg$ Bool)) (?v1 (-> Msg$ Bool)) (?v2 Msg$)) (! (= (uu$ ?v0 ?v1 ?v2) (and (?v0 ?v2) (?v1 ?v2))) :pattern ((uu$ ?v0 ?v1 ?v2)))) :named a11))
+(assert (! (forall ((?v0 Msg$) (?v1 (-> Msg$ Bool)) (?v2 Msg$)) (! (= (uuk$ ?v0 ?v1 ?v2) (=> (not (= ?v2 ?v0)) (?v1 ?v2))) :pattern ((uuk$ ?v0 ?v1 ?v2)))) :named a12))
+(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event$) (?v2 Event$)) (! (= (uui$ ?v0 ?v1 ?v2) (or (not (?v0 ?v2)) (= ?v1 ?v2))) :pattern ((uui$ ?v0 ?v1 ?v2)))) :named a13))
+(assert (! (forall ((?v0 Event_list$) (?v1 Agent$) (?v2 Msg$)) (! (= (uup$ ?v0 ?v1 ?v2) (knows$ spy$ ?v0)) :pattern ((uup$ ?v0 ?v1 ?v2)))) :named a14))
+(assert (! (forall ((?v0 Agent$) (?v1 Event_list$) (?v2 Agent$) (?v3 Msg$)) (! (= (uus$ ?v0 ?v1 ?v2 ?v3) (ite (= ?v2 ?v0) (insert$ ?v3 (knows$ ?v0 ?v1)) (knows$ ?v0 ?v1))) :pattern ((uus$ ?v0 ?v1 ?v2 ?v3)))) :named a15))
+(assert (! (forall ((?v0 Event_list$) (?v1 Agent$) (?v2 Agent$) (?v3 Msg$)) (! (= (uuo$ ?v0 ?v1 ?v2 ?v3) (insert$ ?v3 (knows$ spy$ ?v0))) :pattern ((uuo$ ?v0 ?v1 ?v2 ?v3)))) :named a16))
+(assert (! (forall ((?v0 Agent$) (?v1 Event_list$) (?v2 Agent$) (?v3 Agent$) (?v4 Msg$)) (! (= (uur$ ?v0 ?v1 ?v2 ?v3 ?v4) (ite (= ?v2 ?v0) (insert$ ?v4 (knows$ ?v0 ?v1)) (knows$ ?v0 ?v1))) :pattern ((uur$ ?v0 ?v1 ?v2 ?v3 ?v4)))) :named a17))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (! (= (uug$ ?v0 ?v1) false) :pattern ((uug$ ?v0 ?v1)))) :named a18))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (! (= (uuh$ ?v0 ?v1) true) :pattern ((uuh$ ?v0 ?v1)))) :named a19))
+(assert (! (not (less_eq$ (knows$ spy$ (takeWhile$ p$ nil$)) (knows$ spy$ nil$))) :named a20))
+(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event_list$)) (= (takeWhile$ ?v0 (takeWhile$ ?v0 ?v1)) (takeWhile$ ?v0 ?v1))) :named a21))
+(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$)) (=> (forall ((?v2 Event$)) (=> (member$b ?v2 ?v0) (member$b ?v2 ?v1))) (less_eq$a ?v0 ?v1))) :named a22))
+(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$)) (=> (forall ((?v2 Agent$)) (=> (member$ ?v2 ?v0) (member$ ?v2 ?v1))) (less_eq$b ?v0 ?v1))) :named a23))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (=> (forall ((?v2 Msg$)) (=> (member$a ?v2 ?v0) (member$a ?v2 ?v1))) (less_eq$ ?v0 ?v1))) :named a24))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v0)) (= ?v0 ?v1))) :named a25))
+(assert (! (forall ((?v0 Msg_set$)) (less_eq$ ?v0 ?v0)) :named a26))
+(assert (! (forall ((?v0 (-> Event$ Bool))) (! (= (takeWhile$ ?v0 nil$) nil$) :pattern ((takeWhile$ ?v0)))) :named a27))
+(assert (! (forall ((?v0 Msg_set$) (?v1 (-> Msg$ Bool)) (?v2 (-> Msg$ Bool))) (= (less_eq$ ?v0 (collect$ (uu$ ?v1 ?v2))) (and (less_eq$ ?v0 (collect$ ?v1)) (less_eq$ ?v0 (collect$ ?v2))))) :named a28))
+(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event_set$) (?v3 (-> Event$ Bool))) (=> (and (member$b ?v0 ?v1) (less_eq$a ?v1 (collect$a (uua$ ?v2 ?v3)))) (?v3 ?v0))) :named a29))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent_set$) (?v3 (-> Agent$ Bool))) (=> (and (member$ ?v0 ?v1) (less_eq$b ?v1 (collect$b (uub$ ?v2 ?v3)))) (?v3 ?v0))) :named a30))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg_set$) (?v3 (-> Msg$ Bool))) (=> (and (member$a ?v0 ?v1) (less_eq$ ?v1 (collect$ (uuc$ ?v2 ?v3)))) (?v3 ?v0))) :named a31))
+(assert (! (forall ((?v0 Event_set$) (?v1 (-> Event$ Bool))) (less_eq$a (collect$a (uua$ ?v0 ?v1)) ?v0)) :named a32))
+(assert (! (forall ((?v0 Agent_set$) (?v1 (-> Agent$ Bool))) (less_eq$b (collect$b (uub$ ?v0 ?v1)) ?v0)) :named a33))
+(assert (! (forall ((?v0 Msg_set$) (?v1 (-> Msg$ Bool))) (less_eq$ (collect$ (uuc$ ?v0 ?v1)) ?v0)) :named a34))
+(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$) (?v2 (-> Event$ Bool)) (?v3 (-> Event$ Bool))) (=> (and (less_eq$a ?v0 ?v1) (forall ((?v4 Event$)) (=> (and (member$b ?v4 ?v0) (?v2 ?v4)) (?v3 ?v4)))) (less_eq$a (collect$a (uua$ ?v0 ?v2)) (collect$a (uua$ ?v1 ?v3))))) :named a35))
+(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$) (?v2 (-> Agent$ Bool)) (?v3 (-> Agent$ Bool))) (=> (and (less_eq$b ?v0 ?v1) (forall ((?v4 Agent$)) (=> (and (member$ ?v4 ?v0) (?v2 ?v4)) (?v3 ?v4)))) (less_eq$b (collect$b (uub$ ?v0 ?v2)) (collect$b (uub$ ?v1 ?v3))))) :named a36))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 (-> Msg$ Bool)) (?v3 (-> Msg$ Bool))) (=> (and (less_eq$ ?v0 ?v1) (forall ((?v4 Msg$)) (=> (and (member$a ?v4 ?v0) (?v2 ?v4)) (?v3 ?v4)))) (less_eq$ (collect$ (uuc$ ?v0 ?v2)) (collect$ (uuc$ ?v1 ?v3))))) :named a37))
+(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$) (?v2 (-> Event$ Bool))) (=> (less_eq$a ?v0 ?v1) (= (less_eq$a ?v0 (collect$a (uua$ ?v1 ?v2))) (forall ((?v3 Event$)) (=> (member$b ?v3 ?v0) (?v2 ?v3)))))) :named a38))
+(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$) (?v2 (-> Agent$ Bool))) (=> (less_eq$b ?v0 ?v1) (= (less_eq$b ?v0 (collect$b (uub$ ?v1 ?v2))) (forall ((?v3 Agent$)) (=> (member$ ?v3 ?v0) (?v2 ?v3)))))) :named a39))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 (-> Msg$ Bool))) (=> (less_eq$ ?v0 ?v1) (= (less_eq$ ?v0 (collect$ (uuc$ ?v1 ?v2))) (forall ((?v3 Msg$)) (=> (member$a ?v3 ?v0) (?v2 ?v3)))))) :named a40))
+(assert (! (forall ((?v0 Event_list$)) (=> (and (=> (= ?v0 nil$) false) (=> (not (= ?v0 nil$)) false)) false)) :named a41))
+(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$) (?v2 Event$)) (=> (and (less_eq$a ?v0 ?v1) (member$b ?v2 ?v0)) (member$b ?v2 ?v1))) :named a42))
+(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$) (?v2 Agent$)) (=> (and (less_eq$b ?v0 ?v1) (member$ ?v2 ?v0)) (member$ ?v2 ?v1))) :named a43))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg$)) (=> (and (less_eq$ ?v0 ?v1) (member$a ?v2 ?v0)) (member$a ?v2 ?v1))) :named a44))
+(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$)) (= (less_eq$a ?v0 ?v1) (less_eq$c (uud$ ?v0) (uud$ ?v1)))) :named a45))
+(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$)) (= (less_eq$b ?v0 ?v1) (less_eq$d (uue$ ?v0) (uue$ ?v1)))) :named a46))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (= (less_eq$ ?v0 ?v1) (less_eq$e (uuf$ ?v0) (uuf$ ?v1)))) :named a47))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v0)) (= ?v1 ?v0))) :named a48))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v2 ?v0)) (less_eq$ ?v2 ?v1))) :named a49))
+(assert (! (forall ((?v0 Msg_set$)) (less_eq$ ?v0 ?v0)) :named a50))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2))) :named a51))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v0)) (= ?v0 ?v1))) :named a52))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (= ?v1 ?v2)) (less_eq$ ?v0 ?v2))) :named a53))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (= ?v0 ?v1) (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2))) :named a54))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (! (=> (less_eq$ ?v0 ?v1) (= (less_eq$ ?v1 ?v0) (= ?v1 ?v0))) :pattern ((less_eq$ ?v1 ?v0)))) :named a55))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2))) :named a56))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (=> (= ?v0 ?v1) (less_eq$ ?v0 ?v1))) :named a57))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v0)) (= ?v0 ?v1))) :named a58))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (= (= ?v0 ?v1) (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v0)))) :named a59))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 (-> Msg_set$ Msg_set$)) (?v3 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (and (= (?v2 ?v1) ?v3) (forall ((?v4 Msg_set$) (?v5 Msg_set$)) (=> (less_eq$ ?v4 ?v5) (less_eq$ (?v2 ?v4) (?v2 ?v5)))))) (less_eq$ (?v2 ?v0) ?v3))) :named a60))
+(assert (! (forall ((?v0 Msg_set$) (?v1 (-> Msg_set$ Msg_set$)) (?v2 Msg_set$) (?v3 Msg_set$)) (=> (and (= ?v0 (?v1 ?v2)) (and (less_eq$ ?v2 ?v3) (forall ((?v4 Msg_set$) (?v5 Msg_set$)) (=> (less_eq$ ?v4 ?v5) (less_eq$ (?v1 ?v4) (?v1 ?v5)))))) (less_eq$ ?v0 (?v1 ?v3)))) :named a61))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 (-> Msg_set$ Msg_set$)) (?v3 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (and (less_eq$ (?v2 ?v1) ?v3) (forall ((?v4 Msg_set$) (?v5 Msg_set$)) (=> (less_eq$ ?v4 ?v5) (less_eq$ (?v2 ?v4) (?v2 ?v5)))))) (less_eq$ (?v2 ?v0) ?v3))) :named a62))
+(assert (! (forall ((?v0 Msg_set$) (?v1 (-> Msg_set$ Msg_set$)) (?v2 Msg_set$) (?v3 Msg_set$)) (=> (and (less_eq$ ?v0 (?v1 ?v2)) (and (less_eq$ ?v2 ?v3) (forall ((?v4 Msg_set$) (?v5 Msg_set$)) (=> (less_eq$ ?v4 ?v5) (less_eq$ (?v1 ?v4) (?v1 ?v5)))))) (less_eq$ ?v0 (?v1 ?v3)))) :named a63))
+(assert (! (forall ((?v0 (-> Msg$ Bool)) (?v1 (-> Msg$ Bool))) (= (less_eq$ (collect$ ?v0) (collect$ ?v1)) (forall ((?v2 Msg$)) (=> (?v0 ?v2) (?v1 ?v2))))) :named a64))
+(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$) (?v2 Event$)) (=> (and (less_eq$a ?v0 ?v1) (not (member$b ?v2 ?v1))) (not (member$b ?v2 ?v0)))) :named a65))
+(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$) (?v2 Agent$)) (=> (and (less_eq$b ?v0 ?v1) (not (member$ ?v2 ?v1))) (not (member$ ?v2 ?v0)))) :named a66))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg$)) (=> (and (less_eq$ ?v0 ?v1) (not (member$a ?v2 ?v1))) (not (member$a ?v2 ?v0)))) :named a67))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (= (= ?v0 ?v1) (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v0)))) :named a68))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2))) :named a69))
+(assert (! (forall ((?v0 (-> Msg$ Bool)) (?v1 (-> Msg$ Bool))) (=> (forall ((?v2 Msg$)) (=> (?v0 ?v2) (?v1 ?v2))) (less_eq$ (collect$ ?v0) (collect$ ?v1)))) :named a70))
+(assert (! (forall ((?v0 Msg_set$)) (less_eq$ ?v0 ?v0)) :named a71))
+(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event_set$)) (=> (and (member$b ?v0 ?v1) (less_eq$a ?v1 ?v2)) (member$b ?v0 ?v2))) :named a72))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent_set$)) (=> (and (member$ ?v0 ?v1) (less_eq$b ?v1 ?v2)) (member$ ?v0 ?v2))) :named a73))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (member$a ?v0 ?v1) (less_eq$ ?v1 ?v2)) (member$a ?v0 ?v2))) :named a74))
+(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$)) (= (less_eq$a ?v0 ?v1) (forall ((?v2 Event$)) (=> (member$b ?v2 ?v0) (member$b ?v2 ?v1))))) :named a75))
+(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$)) (= (less_eq$b ?v0 ?v1) (forall ((?v2 Agent$)) (=> (member$ ?v2 ?v0) (member$ ?v2 ?v1))))) :named a76))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (= (less_eq$ ?v0 ?v1) (forall ((?v2 Msg$)) (=> (member$a ?v2 ?v0) (member$a ?v2 ?v1))))) :named a77))
+(assert (! (forall ((?v0 Msg$) (?v1 (-> Msg$ Bool))) (= (member$a ?v0 (collect$ ?v1)) (?v1 ?v0))) :named a78))
+(assert (! (forall ((?v0 Event$) (?v1 (-> Event$ Bool))) (= (member$b ?v0 (collect$a ?v1)) (?v1 ?v0))) :named a79))
+(assert (! (forall ((?v0 Agent$) (?v1 (-> Agent$ Bool))) (= (member$ ?v0 (collect$b ?v1)) (?v1 ?v0))) :named a80))
+(assert (! (forall ((?v0 Msg_set$)) (= (collect$ (uuf$ ?v0)) ?v0)) :named a81))
+(assert (! (forall ((?v0 Event_set$)) (= (collect$a (uud$ ?v0)) ?v0)) :named a82))
+(assert (! (forall ((?v0 Agent_set$)) (= (collect$b (uue$ ?v0)) ?v0)) :named a83))
+(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event_set$)) (=> (and (member$b ?v0 ?v1) (less_eq$a ?v1 ?v2)) (member$b ?v0 ?v2))) :named a84))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent_set$)) (=> (and (member$ ?v0 ?v1) (less_eq$b ?v1 ?v2)) (member$ ?v0 ?v2))) :named a85))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (member$a ?v0 ?v1) (less_eq$ ?v1 ?v2)) (member$a ?v0 ?v2))) :named a86))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (=> (= ?v0 ?v1) (less_eq$ ?v1 ?v0))) :named a87))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (=> (= ?v0 ?v1) (less_eq$ ?v0 ?v1))) :named a88))
+(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$)) (= (less_eq$a ?v0 ?v1) (forall ((?v2 Event$)) (=> (member$b ?v2 ?v0) (member$b ?v2 ?v1))))) :named a89))
+(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$)) (= (less_eq$b ?v0 ?v1) (forall ((?v2 Agent$)) (=> (member$ ?v2 ?v0) (member$ ?v2 ?v1))))) :named a90))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (= (less_eq$ ?v0 ?v1) (forall ((?v2 Msg$)) (=> (member$a ?v2 ?v0) (member$a ?v2 ?v1))))) :named a91))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (=> (and (= ?v0 ?v1) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v0)) false)) false)) :named a92))
+(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$) (?v2 Event$)) (=> (and (less_eq$a ?v0 ?v1) (and (=> (not (member$b ?v2 ?v0)) false) (=> (member$b ?v2 ?v1) false))) false)) :named a93))
+(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$) (?v2 Agent$)) (=> (and (less_eq$b ?v0 ?v1) (and (=> (not (member$ ?v2 ?v0)) false) (=> (member$ ?v2 ?v1) false))) false)) :named a94))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg$)) (=> (and (less_eq$ ?v0 ?v1) (and (=> (not (member$a ?v2 ?v0)) false) (=> (member$a ?v2 ?v1) false))) false)) :named a95))
+(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$) (?v2 Event$)) (=> (and (less_eq$a ?v0 ?v1) (member$b ?v2 ?v0)) (member$b ?v2 ?v1))) :named a96))
+(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$) (?v2 Agent$)) (=> (and (less_eq$b ?v0 ?v1) (member$ ?v2 ?v0)) (member$ ?v2 ?v1))) :named a97))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg$)) (=> (and (less_eq$ ?v0 ?v1) (member$a ?v2 ?v0)) (member$a ?v2 ?v1))) :named a98))
+(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$) (?v2 Event$)) (=> (and (less_eq$a ?v0 ?v1) (member$b ?v2 ?v0)) (member$b ?v2 ?v1))) :named a99))
+(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$) (?v2 Agent$)) (=> (and (less_eq$b ?v0 ?v1) (member$ ?v2 ?v0)) (member$ ?v2 ?v1))) :named a100))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg$)) (=> (and (less_eq$ ?v0 ?v1) (member$a ?v2 ?v0)) (member$a ?v2 ?v1))) :named a101))
+(assert (! (forall ((?v0 Event_set$) (?v1 Event_set$)) (= (less_eq$c (uud$ ?v0) (uud$ ?v1)) (less_eq$a ?v0 ?v1))) :named a102))
+(assert (! (forall ((?v0 Agent_set$) (?v1 Agent_set$)) (= (less_eq$d (uue$ ?v0) (uue$ ?v1)) (less_eq$b ?v0 ?v1))) :named a103))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$)) (= (less_eq$e (uuf$ ?v0) (uuf$ ?v1)) (less_eq$ ?v0 ?v1))) :named a104))
+(assert (! (forall ((?v0 (-> Event$ Bool))) (! (= (list_ex1$ ?v0 nil$) false) :pattern ((list_ex1$ ?v0)))) :named a105))
+(assert (! (forall ((?v0 (-> Event$ Event_list$))) (! (= (bind$ nil$ ?v0) nil$) :pattern ((bind$ nil$ ?v0)))) :named a106))
+(assert (! (forall ((?v0 (-> Msg_set$ Bool)) (?v1 Msg_set$)) (=> (and (?v0 ?v1) (forall ((?v2 Msg_set$)) (=> (?v0 ?v2) (less_eq$ ?v2 ?v1)))) (= (greatest$ ?v0) ?v1))) :named a107))
+(assert (! (forall ((?v0 (-> Msg_set$ Bool)) (?v1 Msg_set$) (?v2 (-> Msg_set$ Bool))) (=> (and (?v0 ?v1) (and (forall ((?v3 Msg_set$)) (=> (?v0 ?v3) (less_eq$ ?v3 ?v1))) (forall ((?v3 Msg_set$)) (=> (and (?v0 ?v3) (forall ((?v4 Msg_set$)) (=> (?v0 ?v4) (less_eq$ ?v4 ?v3)))) (?v2 ?v3))))) (?v2 (greatest$ ?v0)))) :named a108))
+(assert (! (forall ((?v0 Event$)) (! (= (member$d nil$ ?v0) false) :pattern ((member$d nil$ ?v0)))) :named a109))
+(assert (! (forall ((?v0 (-> Bool Msg_set$)) (?v1 (-> Bool Msg_set$))) (! (= (less_eq$f ?v0 ?v1) (and (less_eq$ (?v0 false) (?v1 false)) (less_eq$ (?v0 true) (?v1 true)))) :pattern ((less_eq$f ?v0 ?v1)))) :named a110))
+(assert (! (forall ((?v0 Nat$)) (! (= (gen_length$ ?v0 nil$) ?v0) :pattern ((gen_length$ ?v0)))) :named a111))
+(assert (! (forall ((?v0 (-> Event$ Event_list$))) (! (= (maps$ ?v0 nil$) nil$) :pattern ((maps$ ?v0)))) :named a112))
+(assert (! (forall ((?v0 Event_list$)) (= (= ?v0 nil$) (null$ ?v0))) :named a113))
+(assert (! (= (null$ nil$) true) :named a114))
+(assert (! (forall ((?v0 Event_list$)) (! (= (splice$ ?v0 nil$) ?v0) :pattern ((splice$ ?v0)))) :named a115))
+(assert (! (forall ((?v0 Event_list$)) (= (= (rotate1$ ?v0) nil$) (= ?v0 nil$))) :named a116))
+(assert (! (forall ((?v0 (-> Event$ Event_option$))) (! (= (map_filter$ ?v0 nil$) nil$) :pattern ((map_filter$ ?v0)))) :named a117))
+(assert (! (forall ((?v0 (-> Msg_set$ Msg_set$)) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (antimono$ ?v0) (less_eq$ ?v1 ?v2)) (less_eq$ (?v0 ?v2) (?v0 ?v1)))) :named a118))
+(assert (! (= (rotate1$ nil$) nil$) :named a119))
+(assert (! (forall ((?v0 Event_list$)) (! (= (splice$ nil$ ?v0) ?v0) :pattern ((splice$ nil$ ?v0)))) :named a120))
+(assert (! (forall ((?v0 (-> Msg_set$ Msg_set$))) (= (antimono$ ?v0) (forall ((?v1 Msg_set$) (?v2 Msg_set$)) (=> (less_eq$ ?v1 ?v2) (less_eq$ (?v0 ?v2) (?v0 ?v1)))))) :named a121))
+(assert (! (forall ((?v0 (-> Msg_set$ Msg_set$))) (=> (forall ((?v1 Msg_set$) (?v2 Msg_set$)) (=> (less_eq$ ?v1 ?v2) (less_eq$ (?v0 ?v2) (?v0 ?v1)))) (antimono$ ?v0))) :named a122))
+(assert (! (forall ((?v0 (-> Msg_set$ Msg_set$)) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (antimono$ ?v0) (and (less_eq$ ?v1 ?v2) (=> (less_eq$ (?v0 ?v2) (?v0 ?v1)) false))) false)) :named a123))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 Event_list$)) (=> (and (= (splice$ ?v0 ?v1) ?v2) (and (forall ((?v3 Event_list$)) (=> (and (= ?v0 nil$) (and (= ?v1 ?v3) (= ?v2 ?v3))) false)) (and (forall ((?v3 Event$) (?v4 Event_list$)) (=> (and (= ?v0 (cons$ ?v3 ?v4)) (and (= ?v1 nil$) (= ?v2 (cons$ ?v3 ?v4)))) false)) (forall ((?v3 Event$) (?v4 Event_list$) (?v5 Event$) (?v6 Event_list$)) (=> (and (= ?v0 (cons$ ?v3 ?v4)) (and (= ?v1 (cons$ ?v5 ?v6)) (= ?v2 (cons$ ?v3 (cons$ ?v5 (splice$ ?v4 ?v6)))))) false))))) false)) :named a124))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (! (= (splice$ (cons$ ?v0 ?v1) nil$) (cons$ ?v0 ?v1)) :pattern ((cons$ ?v0 ?v1)))) :named a125))
+(assert (! (forall ((?v0 (-> Event$ Bool))) (! (= (list_ex$ ?v0 nil$) false) :pattern ((list_ex$ ?v0)))) :named a126))
+(assert (! (forall ((?v0 Event_list$)) (= (= ?v0 nil$) (case_list$ true uug$ ?v0))) :named a127))
+(assert (! (forall ((?v0 Event_list$)) (= (not (= ?v0 nil$)) (case_list$ false uuh$ ?v0))) :named a128))
+(assert (! (forall ((?v0 Agent$)) (! (= (knows$ ?v0 nil$) (initState$ ?v0)) :pattern ((knows$ ?v0)))) :named a129))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 Event$) (?v3 Event_list$)) (= (= (cons$ ?v0 ?v1) (cons$ ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3)))) :named a130))
+(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event$) (?v2 Event_list$)) (! (= (list_ex$ ?v0 (cons$ ?v1 ?v2)) (or (?v0 ?v1) (list_ex$ ?v0 ?v2))) :pattern ((list_ex$ ?v0 (cons$ ?v1 ?v2))))) :named a131))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (not (= (cons$ ?v0 ?v1) ?v1))) :named a132))
+(assert (! (forall ((?v0 Event_list_list$)) (=> (and (=> (= ?v0 nil$a) false) (and (forall ((?v1 Event_list_list$)) (=> (= ?v0 (cons$a nil$ ?v1)) false)) (forall ((?v1 Event$) (?v2 Event_list$) (?v3 Event_list_list$)) (=> (= ?v0 (cons$a (cons$ ?v1 ?v2) ?v3)) false)))) false)) :named a133))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (not (= nil$ (cons$ ?v0 ?v1)))) :named a134))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event$) (?v2 Event_list$)) (=> (= ?v0 (cons$ ?v1 ?v2)) (not (= ?v0 nil$)))) :named a135))
+(assert (! (forall ((?v0 Event_list$)) (=> (and (=> (= ?v0 nil$) false) (forall ((?v1 Event$) (?v2 Event_list$)) (=> (= ?v0 (cons$ ?v1 ?v2)) false))) false)) :named a136))
+(assert (! (forall ((?v0 Event_list$)) (= (not (= ?v0 nil$)) (exists ((?v1 Event$) (?v2 Event_list$)) (= ?v0 (cons$ ?v1 ?v2))))) :named a137))
+(assert (! (forall ((?v0 (-> Event_list$ (-> Event_list$ Bool))) (?v1 Event_list$) (?v2 Event_list$)) (=> (and (?v0 nil$ nil$) (and (forall ((?v3 Event$) (?v4 Event_list$)) (?v0 (cons$ ?v3 ?v4) nil$)) (and (forall ((?v3 Event$) (?v4 Event_list$)) (?v0 nil$ (cons$ ?v3 ?v4))) (forall ((?v3 Event$) (?v4 Event_list$) (?v5 Event$) (?v6 Event_list$)) (=> (?v0 ?v4 ?v6) (?v0 (cons$ ?v3 ?v4) (cons$ ?v5 ?v6))))))) (?v0 ?v1 ?v2))) :named a138))
+(assert (! (forall ((?v0 Event_list$)) (=> (and (=> (= ?v0 nil$) false) (and (forall ((?v1 Event$)) (=> (= ?v0 (cons$ ?v1 nil$)) false)) (forall ((?v1 Event$) (?v2 Event$) (?v3 Event_list$)) (=> (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3))) false)))) false)) :named a139))
+(assert (! (forall ((?v0 (-> Event_list$ Bool)) (?v1 Event_list$)) (=> (and (?v0 nil$) (and (forall ((?v2 Event$)) (?v0 (cons$ ?v2 nil$))) (forall ((?v2 Event$) (?v3 Event$) (?v4 Event_list$)) (=> (?v0 (cons$ ?v3 ?v4)) (?v0 (cons$ ?v2 (cons$ ?v3 ?v4))))))) (?v0 ?v1))) :named a140))
+(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event_list$ Bool))) (=> (and (not (= ?v0 nil$)) (and (forall ((?v2 Event$)) (?v1 (cons$ ?v2 nil$))) (forall ((?v2 Event$) (?v3 Event_list$)) (=> (and (not (= ?v3 nil$)) (?v1 ?v3)) (?v1 (cons$ ?v2 ?v3)))))) (?v1 ?v0))) :named a141))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 Event$) (?v3 Event_list$)) (! (= (splice$ (cons$ ?v0 ?v1) (cons$ ?v2 ?v3)) (cons$ ?v0 (cons$ ?v2 (splice$ ?v1 ?v3)))) :pattern ((splice$ (cons$ ?v0 ?v1) (cons$ ?v2 ?v3))))) :named a142))
+(assert (! (forall ((?v0 Agent$) (?v1 Event_list$) (?v2 Event$)) (less_eq$ (knows$ ?v0 ?v1) (knows$ ?v0 (cons$ ?v2 ?v1)))) :named a143))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (! (= (null$ (cons$ ?v0 ?v1)) false) :pattern ((cons$ ?v0 ?v1)))) :named a144))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 Event$)) (! (= (member$d (cons$ ?v0 ?v1) ?v2) (or (= ?v0 ?v2) (member$d ?v1 ?v2))) :pattern ((member$d (cons$ ?v0 ?v1) ?v2)))) :named a145))
+(assert (! (forall ((?v0 Agent$) (?v1 Event_list$)) (less_eq$ (initState$ ?v0) (knows$ ?v0 ?v1))) :named a146))
+(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event$) (?v2 Event_list$)) (! (= (takeWhile$ ?v0 (cons$ ?v1 ?v2)) (ite (?v0 ?v1) (cons$ ?v1 (takeWhile$ ?v0 ?v2)) nil$)) :pattern ((takeWhile$ ?v0 (cons$ ?v1 ?v2))))) :named a147))
+(assert (! (forall ((?v0 Event_list$) (?v1 Agent$) (?v2 Msg$)) (less_eq$ (knows$ spy$ ?v0) (knows$ spy$ (cons$ (gets$ ?v1 ?v2) ?v0)))) :named a148))
+(assert (! (forall ((?v0 Event$)) (! (= (insert$a ?v0 nil$) (cons$ ?v0 nil$)) :pattern ((insert$a ?v0)))) :named a149))
+(assert (! (forall ((?v0 Agent$) (?v1 Msg$) (?v2 Event_list$)) (! (= (knows$ spy$ (cons$ (gets$ ?v0 ?v1) ?v2)) (knows$ spy$ ?v2)) :pattern ((cons$ (gets$ ?v0 ?v1) ?v2)))) :named a150))
+(assert (! (forall ((?v0 Event_list$) (?v1 Agent$) (?v2 Msg$)) (less_eq$ (knows$ spy$ ?v0) (knows$ spy$ (cons$ (notes$ ?v1 ?v2) ?v0)))) :named a151))
+(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event$) (?v2 Event_list$)) (= (list_ex1$ ?v0 (cons$ ?v1 ?v2)) (ite (?v0 ?v1) (list_all$ (uui$ ?v0 ?v1) ?v2) (list_ex1$ ?v0 ?v2)))) :named a152))
+(assert (! (forall ((?v0 Agent$) (?v1 Msg$) (?v2 Agent$) (?v3 Msg$)) (= (= (notes$ ?v0 ?v1) (notes$ ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3)))) :named a153))
+(assert (! (forall ((?v0 Agent$) (?v1 Msg$) (?v2 Agent$) (?v3 Msg$)) (= (= (gets$ ?v0 ?v1) (gets$ ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3)))) :named a154))
+(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event$) (?v2 Event_list$)) (! (= (list_all$ ?v0 (cons$ ?v1 ?v2)) (and (?v0 ?v1) (list_all$ ?v0 ?v2))) :pattern ((list_all$ ?v0 (cons$ ?v1 ?v2))))) :named a155))
+(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event$) (?v2 Event_list$)) (! (= (list_all$ ?v0 (cons$ ?v1 ?v2)) (and (?v0 ?v1) (list_all$ ?v0 ?v2))) :pattern ((list_all$ ?v0 (cons$ ?v1 ?v2))))) :named a156))
+(assert (! (forall ((?v0 (-> Event$ Bool))) (! (= (list_all$ ?v0 nil$) true) :pattern ((list_all$ ?v0)))) :named a157))
+(assert (! (forall ((?v0 Agent$) (?v1 Msg$) (?v2 Agent$) (?v3 Msg$)) (not (= (gets$ ?v0 ?v1) (notes$ ?v2 ?v3)))) :named a158))
+(assert (! (forall ((?v0 (-> Event$ Bool))) (list_all$ ?v0 nil$)) :named a159))
+(assert (! (forall ((?v0 Agent$) (?v1 Event_list$) (?v2 Agent$) (?v3 Msg$)) (less_eq$ (knows$ ?v0 ?v1) (knows$ ?v0 (cons$ (notes$ ?v2 ?v3) ?v1)))) :named a160))
+(assert (! (forall ((?v0 Agent$) (?v1 Event_list$) (?v2 Agent$) (?v3 Msg$)) (less_eq$ (knows$ ?v0 ?v1) (knows$ ?v0 (cons$ (gets$ ?v2 ?v3) ?v1)))) :named a161))
+(assert (! (= (product_lists$ nil$a) (cons$a nil$ nil$a)) :named a162))
+(assert (! (forall ((?v0 Event_list$) (?v1 Agent$) (?v2 Msg$)) (= (knows$ spy$ (append$ ?v0 (cons$ (gets$ ?v1 ?v2) nil$))) (knows$ spy$ ?v0))) :named a163))
+(assert (! (= (subseqs$ nil$) (cons$a nil$ nil$a)) :named a164))
+(assert (! (forall ((?v0 Event_list$) (?v1 Agent$) (?v2 Agent$) (?v3 Msg$)) (less_eq$ (knows$ spy$ ?v0) (knows$ spy$ (cons$ (says$ ?v1 ?v2 ?v3) ?v0)))) :named a165))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 Event_list$)) (= (append$ (append$ ?v0 ?v1) ?v2) (append$ ?v0 (append$ ?v1 ?v2)))) :named a166))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 Event_list$)) (= (append$ (append$ ?v0 ?v1) ?v2) (append$ ?v0 (append$ ?v1 ?v2)))) :named a167))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 Event_list$)) (= (= (append$ ?v0 ?v1) (append$ ?v2 ?v1)) (= ?v0 ?v2))) :named a168))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 Event_list$)) (= (= (append$ ?v0 ?v1) (append$ ?v0 ?v2)) (= ?v1 ?v2))) :named a169))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent$) (?v2 Msg$) (?v3 Agent$) (?v4 Agent$) (?v5 Msg$)) (= (= (says$ ?v0 ?v1 ?v2) (says$ ?v3 ?v4 ?v5)) (and (= ?v0 ?v3) (and (= ?v1 ?v4) (= ?v2 ?v5))))) :named a170))
+(assert (! (forall ((?v0 Event_list$)) (! (= (append$ ?v0 nil$) ?v0) :pattern ((append$ ?v0)))) :named a171))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$)) (= (= (append$ ?v0 ?v1) ?v0) (= ?v1 nil$))) :named a172))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$)) (= (= ?v0 (append$ ?v0 ?v1)) (= ?v1 nil$))) :named a173))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$)) (= (= (append$ ?v0 ?v1) ?v1) (= ?v0 nil$))) :named a174))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$)) (= (= ?v0 (append$ ?v1 ?v0)) (= ?v1 nil$))) :named a175))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$)) (= (= nil$ (append$ ?v0 ?v1)) (and (= ?v0 nil$) (= ?v1 nil$)))) :named a176))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$)) (= (= (append$ ?v0 ?v1) nil$) (and (= ?v0 nil$) (= ?v1 nil$)))) :named a177))
+(assert (! (forall ((?v0 Event_list$)) (! (= (append$ ?v0 nil$) ?v0) :pattern ((append$ ?v0)))) :named a178))
+(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event_list$) (?v2 Event_list$)) (= (list_all$ ?v0 (append$ ?v1 ?v2)) (and (list_all$ ?v0 ?v1) (list_all$ ?v0 ?v2)))) :named a179))
+(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event_list$) (?v2 Event_list$)) (= (list_ex$ ?v0 (append$ ?v1 ?v2)) (or (list_ex$ ?v0 ?v1) (list_ex$ ?v0 ?v2)))) :named a180))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event$) (?v2 Event_list$) (?v3 Event$)) (= (= (append$ ?v0 (cons$ ?v1 nil$)) (append$ ?v2 (cons$ ?v3 nil$))) (and (= ?v0 ?v2) (= ?v1 ?v3)))) :named a181))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 (-> Event$ Event_list$))) (! (= (bind$ (cons$ ?v0 ?v1) ?v2) (append$ (?v2 ?v0) (bind$ ?v1 ?v2))) :pattern ((bind$ (cons$ ?v0 ?v1) ?v2)))) :named a182))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 Event_list$)) (! (= (append$ (cons$ ?v0 ?v1) ?v2) (cons$ ?v0 (append$ ?v1 ?v2))) :pattern ((append$ (cons$ ?v0 ?v1) ?v2)))) :named a183))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 Event_list$) (?v3 Event_list$) (?v4 Event_list$)) (=> (and (= (cons$ ?v0 ?v1) ?v2) (= ?v3 (append$ ?v1 ?v4))) (= (cons$ ?v0 ?v3) (append$ ?v2 ?v4)))) :named a184))
+(assert (! (forall ((?v0 Event_list$)) (! (= (append$ nil$ ?v0) ?v0) :pattern ((append$ nil$ ?v0)))) :named a185))
+(assert (! (forall ((?v0 Event_list$)) (! (= (append$ nil$ ?v0) ?v0) :pattern ((append$ nil$ ?v0)))) :named a186))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$)) (=> (= ?v0 ?v1) (= ?v0 (append$ nil$ ?v1)))) :named a187))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 Event_list$) (?v3 Event_list$) (?v4 Event_list$)) (=> (and (= (append$ ?v0 ?v1) ?v2) (= ?v3 (append$ ?v1 ?v4))) (= (append$ ?v0 ?v3) (append$ ?v2 ?v4)))) :named a188))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 Event_list$) (?v3 Event_list$)) (= (= (append$ ?v0 ?v1) (append$ ?v2 ?v3)) (exists ((?v4 Event_list$)) (or (and (= ?v0 (append$ ?v2 ?v4)) (= (append$ ?v4 ?v1) ?v3)) (and (= (append$ ?v0 ?v4) ?v2) (= ?v1 (append$ ?v4 ?v3))))))) :named a189))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent$) (?v2 Msg$) (?v3 Agent$) (?v4 Msg$)) (not (= (says$ ?v0 ?v1 ?v2) (notes$ ?v3 ?v4)))) :named a190))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent$) (?v2 Msg$) (?v3 Agent$) (?v4 Msg$)) (not (= (says$ ?v0 ?v1 ?v2) (gets$ ?v3 ?v4)))) :named a191))
+(assert (! (forall ((?v0 (-> Event_list$ Bool)) (?v1 Event_list$)) (=> (and (?v0 nil$) (forall ((?v2 Event$) (?v3 Event_list$)) (=> (?v0 ?v3) (?v0 (append$ ?v3 (cons$ ?v2 nil$)))))) (?v0 ?v1))) :named a192))
+(assert (! (forall ((?v0 Event_list$)) (=> (and (=> (= ?v0 nil$) false) (forall ((?v1 Event_list$) (?v2 Event$)) (=> (= ?v0 (append$ ?v1 (cons$ ?v2 nil$))) false))) false)) :named a193))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 Event_list$) (?v3 Event_list$)) (= (= (cons$ ?v0 ?v1) (append$ ?v2 ?v3)) (or (and (= ?v2 nil$) (= (cons$ ?v0 ?v1) ?v3)) (exists ((?v4 Event_list$)) (and (= (cons$ ?v0 ?v4) ?v2) (= ?v1 (append$ ?v4 ?v3))))))) :named a194))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 Event$) (?v3 Event_list$)) (= (= (append$ ?v0 ?v1) (cons$ ?v2 ?v3)) (or (and (= ?v0 nil$) (= ?v1 (cons$ ?v2 ?v3))) (exists ((?v4 Event_list$)) (and (= ?v0 (cons$ ?v2 ?v4)) (= (append$ ?v4 ?v1) ?v3)))))) :named a195))
+(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event_list$ Bool))) (=> (and (not (= ?v0 nil$)) (and (forall ((?v2 Event$)) (?v1 (cons$ ?v2 nil$))) (forall ((?v2 Event$) (?v3 Event_list$)) (=> (and (not (= ?v3 nil$)) (?v1 ?v3)) (?v1 (append$ ?v3 (cons$ ?v2 nil$))))))) (?v1 ?v0))) :named a196))
+(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event$) (?v2 Event_list$) (?v3 Event_list$)) (=> (not (?v0 ?v1)) (= (takeWhile$ ?v0 (append$ ?v2 (cons$ ?v1 ?v3))) (takeWhile$ ?v0 ?v2)))) :named a197))
+(assert (! (forall ((?v0 Event$)) (=> (and (forall ((?v1 Agent$) (?v2 Agent$) (?v3 Msg$)) (=> (= ?v0 (says$ ?v1 ?v2 ?v3)) false)) (and (forall ((?v1 Agent$) (?v2 Msg$)) (=> (= ?v0 (gets$ ?v1 ?v2)) false)) (forall ((?v1 Agent$) (?v2 Msg$)) (=> (= ?v0 (notes$ ?v1 ?v2)) false)))) false)) :named a198))
+(assert (! (forall ((?v0 (-> Event$ Event_list$)) (?v1 Event$) (?v2 Event_list$)) (! (= (maps$ ?v0 (cons$ ?v1 ?v2)) (append$ (?v0 ?v1) (maps$ ?v0 ?v2))) :pattern ((maps$ ?v0 (cons$ ?v1 ?v2))))) :named a199))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (= (rotate1$ (cons$ ?v0 ?v1)) (append$ ?v1 (cons$ ?v0 nil$)))) :named a200))
+(assert (! (forall ((?v0 Agent$) (?v1 Event_list$) (?v2 Agent$) (?v3 Agent$) (?v4 Msg$)) (less_eq$ (knows$ ?v0 ?v1) (knows$ ?v0 (cons$ (says$ ?v2 ?v3 ?v4) ?v1)))) :named a201))
+(assert (! (forall ((?v0 Event_list_set$) (?v1 Event_list$)) (= (succ$ ?v0 ?v1) (collect$a (uuj$ ?v0 ?v1)))) :named a202))
+(assert (! (forall ((?v0 Event_list$) (?v1 Agent$) (?v2 Agent$) (?v3 Msg$)) (= (knows$ spy$ (append$ ?v0 (cons$ (says$ ?v1 ?v2 ?v3) nil$))) (insert$ ?v3 (knows$ spy$ ?v0)))) :named a203))
+(assert (! (forall ((?v0 Msg$) (?v1 Agent$) (?v2 Event_list$)) (=> (and (member$a ?v0 (knows$ ?v1 ?v2)) (not (= ?v1 spy$))) (exists ((?v3 Agent$)) (or (member$b (says$ ?v1 ?v3 ?v0) (set$ ?v2)) (or (member$b (gets$ ?v1 ?v0) (set$ ?v2)) (or (member$b (notes$ ?v1 ?v0) (set$ ?v2)) (member$a ?v0 (initState$ ?v1)))))))) :named a204))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_list_set$) (?v2 Msg_list$)) (=> (member$a ?v0 (succ$a ?v1 ?v2)) (member$e (append$a ?v2 (cons$b ?v0 nil$b)) ?v1))) :named a205))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_list_set$) (?v2 Agent_list$)) (=> (member$ ?v0 (succ$b ?v1 ?v2)) (member$f (append$b ?v2 (cons$c ?v0 nil$c)) ?v1))) :named a206))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list_set$) (?v2 Event_list$)) (=> (member$b ?v0 (succ$ ?v1 ?v2)) (member$c (append$ ?v2 (cons$ ?v0 nil$)) ?v1))) :named a207))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$)) (= (insert$ ?v0 (insert$ ?v0 ?v1)) (insert$ ?v0 ?v1))) :named a208))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg$) (?v2 Msg_set$)) (= (member$a ?v0 (insert$ ?v1 ?v2)) (or (= ?v0 ?v1) (member$a ?v0 ?v2)))) :named a209))
+(assert (! (forall ((?v0 Event$) (?v1 Event$) (?v2 Event_set$)) (= (member$b ?v0 (insert$b ?v1 ?v2)) (or (= ?v0 ?v1) (member$b ?v0 ?v2)))) :named a210))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent$) (?v2 Agent_set$)) (= (member$ ?v0 (insert$c ?v1 ?v2)) (or (= ?v0 ?v1) (member$ ?v0 ?v2)))) :named a211))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg$)) (=> (=> (not (member$a ?v0 ?v1)) (= ?v0 ?v2)) (member$a ?v0 (insert$ ?v2 ?v1)))) :named a212))
+(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event$)) (=> (=> (not (member$b ?v0 ?v1)) (= ?v0 ?v2)) (member$b ?v0 (insert$b ?v2 ?v1)))) :named a213))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent$)) (=> (=> (not (member$ ?v0 ?v1)) (= ?v0 ?v2)) (member$ ?v0 (insert$c ?v2 ?v1)))) :named a214))
+(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event_set$)) (= (less_eq$a (insert$b ?v0 ?v1) ?v2) (and (member$b ?v0 ?v2) (less_eq$a ?v1 ?v2)))) :named a215))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent_set$)) (= (less_eq$b (insert$c ?v0 ?v1) ?v2) (and (member$ ?v0 ?v2) (less_eq$b ?v1 ?v2)))) :named a216))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg_set$)) (= (less_eq$ (insert$ ?v0 ?v1) ?v2) (and (member$a ?v0 ?v2) (less_eq$ ?v1 ?v2)))) :named a217))
+(assert (! (forall ((?v0 (-> Msg$ Bool)) (?v1 Msg_list$)) (= (= (takeWhile$a ?v0 ?v1) ?v1) (forall ((?v2 Msg$)) (=> (member$a ?v2 (set$a ?v1)) (?v0 ?v2))))) :named a218))
+(assert (! (forall ((?v0 (-> Agent$ Bool)) (?v1 Agent_list$)) (= (= (takeWhile$b ?v0 ?v1) ?v1) (forall ((?v2 Agent$)) (=> (member$ ?v2 (set$b ?v1)) (?v0 ?v2))))) :named a219))
+(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event_list$)) (= (= (takeWhile$ ?v0 ?v1) ?v1) (forall ((?v2 Event$)) (=> (member$b ?v2 (set$ ?v1)) (?v0 ?v2))))) :named a220))
+(assert (! (forall ((?v0 Event_list$)) (= (set$ (rotate1$ ?v0)) (set$ ?v0))) :named a221))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (! (=> (member$a ?v0 (set$a ?v1)) (= (insert$d ?v0 ?v1) ?v1)) :pattern ((insert$d ?v0 ?v1)))) :named a222))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (! (=> (member$ ?v0 (set$b ?v1)) (= (insert$e ?v0 ?v1) ?v1)) :pattern ((insert$e ?v0 ?v1)))) :named a223))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (! (=> (member$b ?v0 (set$ ?v1)) (= (insert$a ?v0 ?v1) ?v1)) :pattern ((insert$a ?v0 ?v1)))) :named a224))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (! (= (set$a (cons$b ?v0 ?v1)) (insert$ ?v0 (set$a ?v1))) :pattern ((cons$b ?v0 ?v1)))) :named a225))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (! (= (set$ (cons$ ?v0 ?v1)) (insert$b ?v0 (set$ ?v1))) :pattern ((cons$ ?v0 ?v1)))) :named a226))
+(assert (! (forall ((?v0 Msg_list$) (?v1 (-> Msg$ Bool)) (?v2 Msg_list$)) (=> (forall ((?v3 Msg$)) (=> (member$a ?v3 (set$a ?v0)) (?v1 ?v3))) (= (takeWhile$a ?v1 (append$a ?v0 ?v2)) (append$a ?v0 (takeWhile$a ?v1 ?v2))))) :named a227))
+(assert (! (forall ((?v0 Agent_list$) (?v1 (-> Agent$ Bool)) (?v2 Agent_list$)) (=> (forall ((?v3 Agent$)) (=> (member$ ?v3 (set$b ?v0)) (?v1 ?v3))) (= (takeWhile$b ?v1 (append$b ?v0 ?v2)) (append$b ?v0 (takeWhile$b ?v1 ?v2))))) :named a228))
+(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event$ Bool)) (?v2 Event_list$)) (=> (forall ((?v3 Event$)) (=> (member$b ?v3 (set$ ?v0)) (?v1 ?v3))) (= (takeWhile$ ?v1 (append$ ?v0 ?v2)) (append$ ?v0 (takeWhile$ ?v1 ?v2))))) :named a229))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$) (?v2 (-> Msg$ Bool)) (?v3 Msg_list$)) (=> (and (member$a ?v0 (set$a ?v1)) (not (?v2 ?v0))) (= (takeWhile$a ?v2 (append$a ?v1 ?v3)) (takeWhile$a ?v2 ?v1)))) :named a230))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$) (?v2 (-> Agent$ Bool)) (?v3 Agent_list$)) (=> (and (member$ ?v0 (set$b ?v1)) (not (?v2 ?v0))) (= (takeWhile$b ?v2 (append$b ?v1 ?v3)) (takeWhile$b ?v2 ?v1)))) :named a231))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 (-> Event$ Bool)) (?v3 Event_list$)) (=> (and (member$b ?v0 (set$ ?v1)) (not (?v2 ?v0))) (= (takeWhile$ ?v2 (append$ ?v1 ?v3)) (takeWhile$ ?v2 ?v1)))) :named a232))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (= (set$a (insert$d ?v0 ?v1)) (insert$ ?v0 (set$a ?v1)))) :named a233))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (= (set$ (insert$a ?v0 ?v1)) (insert$b ?v0 (set$ ?v1)))) :named a234))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (! (=> (not (member$a ?v0 (set$a ?v1))) (= (insert$d ?v0 ?v1) (cons$b ?v0 ?v1))) :pattern ((insert$d ?v0 ?v1)))) :named a235))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (! (=> (not (member$ ?v0 (set$b ?v1))) (= (insert$e ?v0 ?v1) (cons$c ?v0 ?v1))) :pattern ((insert$e ?v0 ?v1)))) :named a236))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (! (=> (not (member$b ?v0 (set$ ?v1))) (= (insert$a ?v0 ?v1) (cons$ ?v0 ?v1))) :pattern ((insert$a ?v0 ?v1)))) :named a237))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent$) (?v2 Msg$) (?v3 Event_list$)) (! (= (knows$ spy$ (cons$ (says$ ?v0 ?v1 ?v2) ?v3)) (insert$ ?v2 (knows$ spy$ ?v3))) :pattern ((cons$ (says$ ?v0 ?v1 ?v2) ?v3)))) :named a238))
+(assert (! (forall ((?v0 Agent_list$) (?v1 Agent_set$)) (= (less_eq$b (set$b ?v0) ?v1) (forall ((?v2 Agent$)) (=> (member$ ?v2 (set$b ?v0)) (member$ ?v2 ?v1))))) :named a239))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_set$)) (= (less_eq$a (set$ ?v0) ?v1) (forall ((?v2 Event$)) (=> (member$b ?v2 (set$ ?v0)) (member$b ?v2 ?v1))))) :named a240))
+(assert (! (forall ((?v0 Msg_list$) (?v1 Msg_set$)) (= (less_eq$ (set$a ?v0) ?v1) (forall ((?v2 Msg$)) (=> (member$a ?v2 (set$a ?v0)) (member$a ?v2 ?v1))))) :named a241))
+(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event_set$)) (=> (and (member$b ?v0 ?v1) (less_eq$a ?v2 ?v1)) (less_eq$a (insert$b ?v0 ?v2) ?v1))) :named a242))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent_set$)) (=> (and (member$ ?v0 ?v1) (less_eq$b ?v2 ?v1)) (less_eq$b (insert$c ?v0 ?v2) ?v1))) :named a243))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (member$a ?v0 ?v1) (less_eq$ ?v2 ?v1)) (less_eq$ (insert$ ?v0 ?v2) ?v1))) :named a244))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg$)) (=> (less_eq$ ?v0 ?v1) (less_eq$ ?v0 (insert$ ?v2 ?v1)))) :named a245))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg$)) (less_eq$ ?v0 (insert$ ?v1 ?v0))) :named a246))
+(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event_set$)) (=> (not (member$b ?v0 ?v1)) (= (less_eq$a ?v1 (insert$b ?v0 ?v2)) (less_eq$a ?v1 ?v2)))) :named a247))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent_set$)) (=> (not (member$ ?v0 ?v1)) (= (less_eq$b ?v1 (insert$c ?v0 ?v2)) (less_eq$b ?v1 ?v2)))) :named a248))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (not (member$a ?v0 ?v1)) (= (less_eq$ ?v1 (insert$ ?v0 ?v2)) (less_eq$ ?v1 ?v2)))) :named a249))
+(assert (! (forall ((?v0 Msg_set$) (?v1 Msg_set$) (?v2 Msg$)) (=> (less_eq$ ?v0 ?v1) (less_eq$ (insert$ ?v2 ?v0) (insert$ ?v2 ?v1)))) :named a250))
+(assert (! (forall ((?v0 Msg_list$) (?v1 Msg_list$) (?v2 (-> Msg$ Bool)) (?v3 (-> Msg$ Bool))) (=> (and (= ?v0 ?v1) (forall ((?v4 Msg$)) (=> (member$a ?v4 (set$a ?v1)) (= (?v2 ?v4) (?v3 ?v4))))) (= (list_ex$a ?v2 ?v0) (list_ex$a ?v3 ?v1)))) :named a251))
+(assert (! (forall ((?v0 Agent_list$) (?v1 Agent_list$) (?v2 (-> Agent$ Bool)) (?v3 (-> Agent$ Bool))) (=> (and (= ?v0 ?v1) (forall ((?v4 Agent$)) (=> (member$ ?v4 (set$b ?v1)) (= (?v2 ?v4) (?v3 ?v4))))) (= (list_ex$b ?v2 ?v0) (list_ex$b ?v3 ?v1)))) :named a252))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 (-> Event$ Bool)) (?v3 (-> Event$ Bool))) (=> (and (= ?v0 ?v1) (forall ((?v4 Event$)) (=> (member$b ?v4 (set$ ?v1)) (= (?v2 ?v4) (?v3 ?v4))))) (= (list_ex$ ?v2 ?v0) (list_ex$ ?v3 ?v1)))) :named a253))
+(assert (! (forall ((?v0 Msg$) (?v1 (-> Msg$ Bool))) (= (insert$ ?v0 (collect$ ?v1)) (collect$ (uuk$ ?v0 ?v1)))) :named a254))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$)) (= (insert$ ?v0 ?v1) (collect$ (uul$ ?v0 ?v1)))) :named a255))
+(assert (! (forall ((?v0 Event$) (?v1 Event_set$)) (= (insert$b ?v0 ?v1) (collect$a (uum$ ?v0 ?v1)))) :named a256))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$)) (= (insert$c ?v0 ?v1) (collect$b (uun$ ?v0 ?v1)))) :named a257))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$)) (=> (member$a ?v0 ?v1) (exists ((?v2 Msg_set$)) (and (= ?v1 (insert$ ?v0 ?v2)) (not (member$a ?v0 ?v2)))))) :named a258))
+(assert (! (forall ((?v0 Event$) (?v1 Event_set$)) (=> (member$b ?v0 ?v1) (exists ((?v2 Event_set$)) (and (= ?v1 (insert$b ?v0 ?v2)) (not (member$b ?v0 ?v2)))))) :named a259))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$)) (=> (member$ ?v0 ?v1) (exists ((?v2 Agent_set$)) (and (= ?v1 (insert$c ?v0 ?v2)) (not (member$ ?v0 ?v2)))))) :named a260))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg$) (?v2 Msg_set$)) (= (insert$ ?v0 (insert$ ?v1 ?v2)) (insert$ ?v1 (insert$ ?v0 ?v2)))) :named a261))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg$) (?v3 Msg_set$)) (=> (and (not (member$a ?v0 ?v1)) (not (member$a ?v2 ?v3))) (= (= (insert$ ?v0 ?v1) (insert$ ?v2 ?v3)) (ite (= ?v0 ?v2) (= ?v1 ?v3) (exists ((?v4 Msg_set$)) (and (= ?v1 (insert$ ?v2 ?v4)) (and (not (member$a ?v2 ?v4)) (and (= ?v3 (insert$ ?v0 ?v4)) (not (member$a ?v0 ?v4)))))))))) :named a262))
+(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event$) (?v3 Event_set$)) (=> (and (not (member$b ?v0 ?v1)) (not (member$b ?v2 ?v3))) (= (= (insert$b ?v0 ?v1) (insert$b ?v2 ?v3)) (ite (= ?v0 ?v2) (= ?v1 ?v3) (exists ((?v4 Event_set$)) (and (= ?v1 (insert$b ?v2 ?v4)) (and (not (member$b ?v2 ?v4)) (and (= ?v3 (insert$b ?v0 ?v4)) (not (member$b ?v0 ?v4)))))))))) :named a263))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent$) (?v3 Agent_set$)) (=> (and (not (member$ ?v0 ?v1)) (not (member$ ?v2 ?v3))) (= (= (insert$c ?v0 ?v1) (insert$c ?v2 ?v3)) (ite (= ?v0 ?v2) (= ?v1 ?v3) (exists ((?v4 Agent_set$)) (and (= ?v1 (insert$c ?v2 ?v4)) (and (not (member$ ?v2 ?v4)) (and (= ?v3 (insert$c ?v0 ?v4)) (not (member$ ?v0 ?v4)))))))))) :named a264))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$)) (! (=> (member$a ?v0 ?v1) (= (insert$ ?v0 ?v1) ?v1)) :pattern ((insert$ ?v0 ?v1)))) :named a265))
+(assert (! (forall ((?v0 Event$) (?v1 Event_set$)) (! (=> (member$b ?v0 ?v1) (= (insert$b ?v0 ?v1) ?v1)) :pattern ((insert$b ?v0 ?v1)))) :named a266))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$)) (! (=> (member$ ?v0 ?v1) (= (insert$c ?v0 ?v1) ?v1)) :pattern ((insert$c ?v0 ?v1)))) :named a267))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg_set$)) (=> (and (not (member$a ?v0 ?v1)) (not (member$a ?v0 ?v2))) (= (= (insert$ ?v0 ?v1) (insert$ ?v0 ?v2)) (= ?v1 ?v2)))) :named a268))
+(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event_set$)) (=> (and (not (member$b ?v0 ?v1)) (not (member$b ?v0 ?v2))) (= (= (insert$b ?v0 ?v1) (insert$b ?v0 ?v2)) (= ?v1 ?v2)))) :named a269))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent_set$)) (=> (and (not (member$ ?v0 ?v1)) (not (member$ ?v0 ?v2))) (= (= (insert$c ?v0 ?v1) (insert$c ?v0 ?v2)) (= ?v1 ?v2)))) :named a270))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$)) (=> (and (member$a ?v0 ?v1) (forall ((?v2 Msg_set$)) (=> (and (= ?v1 (insert$ ?v0 ?v2)) (not (member$a ?v0 ?v2))) false))) false)) :named a271))
+(assert (! (forall ((?v0 Event$) (?v1 Event_set$)) (=> (and (member$b ?v0 ?v1) (forall ((?v2 Event_set$)) (=> (and (= ?v1 (insert$b ?v0 ?v2)) (not (member$b ?v0 ?v2))) false))) false)) :named a272))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$)) (=> (and (member$ ?v0 ?v1) (forall ((?v2 Agent_set$)) (=> (and (= ?v1 (insert$c ?v0 ?v2)) (not (member$ ?v0 ?v2))) false))) false)) :named a273))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$) (?v2 Msg$)) (=> (member$a ?v0 ?v1) (member$a ?v0 (insert$ ?v2 ?v1)))) :named a274))
+(assert (! (forall ((?v0 Event$) (?v1 Event_set$) (?v2 Event$)) (=> (member$b ?v0 ?v1) (member$b ?v0 (insert$b ?v2 ?v1)))) :named a275))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$) (?v2 Agent$)) (=> (member$ ?v0 ?v1) (member$ ?v0 (insert$c ?v2 ?v1)))) :named a276))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_set$)) (member$a ?v0 (insert$ ?v0 ?v1))) :named a277))
+(assert (! (forall ((?v0 Event$) (?v1 Event_set$)) (member$b ?v0 (insert$b ?v0 ?v1))) :named a278))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_set$)) (member$ ?v0 (insert$c ?v0 ?v1))) :named a279))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg$) (?v2 Msg_set$)) (=> (and (member$a ?v0 (insert$ ?v1 ?v2)) (and (=> (= ?v0 ?v1) false) (=> (member$a ?v0 ?v2) false))) false)) :named a280))
+(assert (! (forall ((?v0 Event$) (?v1 Event$) (?v2 Event_set$)) (=> (and (member$b ?v0 (insert$b ?v1 ?v2)) (and (=> (= ?v0 ?v1) false) (=> (member$b ?v0 ?v2) false))) false)) :named a281))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent$) (?v2 Agent_set$)) (=> (and (member$ ?v0 (insert$c ?v1 ?v2)) (and (=> (= ?v0 ?v1) false) (=> (member$ ?v0 ?v2) false))) false)) :named a282))
+(assert (! (forall ((?v0 Msg$) (?v1 (-> Msg$ Bool)) (?v2 Msg_list$)) (=> (member$a ?v0 (set$a (takeWhile$a ?v1 ?v2))) (and (member$a ?v0 (set$a ?v2)) (?v1 ?v0)))) :named a283))
+(assert (! (forall ((?v0 Agent$) (?v1 (-> Agent$ Bool)) (?v2 Agent_list$)) (=> (member$ ?v0 (set$b (takeWhile$b ?v1 ?v2))) (and (member$ ?v0 (set$b ?v2)) (?v1 ?v0)))) :named a284))
+(assert (! (forall ((?v0 Event$) (?v1 (-> Event$ Bool)) (?v2 Event_list$)) (=> (member$b ?v0 (set$ (takeWhile$ ?v1 ?v2))) (and (member$b ?v0 (set$ ?v2)) (?v1 ?v0)))) :named a285))
+(assert (! (forall ((?v0 Msg_list$) (?v1 Msg_list$) (?v2 (-> Msg$ Bool)) (?v3 (-> Msg$ Bool))) (=> (and (= ?v0 ?v1) (forall ((?v4 Msg$)) (=> (member$a ?v4 (set$a ?v0)) (= (?v2 ?v4) (?v3 ?v4))))) (= (takeWhile$a ?v2 ?v0) (takeWhile$a ?v3 ?v1)))) :named a286))
+(assert (! (forall ((?v0 Agent_list$) (?v1 Agent_list$) (?v2 (-> Agent$ Bool)) (?v3 (-> Agent$ Bool))) (=> (and (= ?v0 ?v1) (forall ((?v4 Agent$)) (=> (member$ ?v4 (set$b ?v0)) (= (?v2 ?v4) (?v3 ?v4))))) (= (takeWhile$b ?v2 ?v0) (takeWhile$b ?v3 ?v1)))) :named a287))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 (-> Event$ Bool)) (?v3 (-> Event$ Bool))) (=> (and (= ?v0 ?v1) (forall ((?v4 Event$)) (=> (member$b ?v4 (set$ ?v0)) (= (?v2 ?v4) (?v3 ?v4))))) (= (takeWhile$ ?v2 ?v0) (takeWhile$ ?v3 ?v1)))) :named a288))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$) (?v2 Msg$)) (=> (member$a ?v0 (set$a ?v1)) (member$a ?v0 (set$a (cons$b ?v2 ?v1))))) :named a289))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$) (?v2 Agent$)) (=> (member$ ?v0 (set$b ?v1)) (member$ ?v0 (set$b (cons$c ?v2 ?v1))))) :named a290))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 Event$)) (=> (member$b ?v0 (set$ ?v1)) (member$b ?v0 (set$ (cons$ ?v2 ?v1))))) :named a291))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (member$a ?v0 (set$a (cons$b ?v0 ?v1)))) :named a292))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (member$ ?v0 (set$b (cons$c ?v0 ?v1)))) :named a293))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (member$b ?v0 (set$ (cons$ ?v0 ?v1)))) :named a294))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg$) (?v2 Msg_list$)) (=> (member$a ?v0 (set$a (cons$b ?v1 ?v2))) (or (= ?v0 ?v1) (member$a ?v0 (set$a ?v2))))) :named a295))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent$) (?v2 Agent_list$)) (=> (member$ ?v0 (set$b (cons$c ?v1 ?v2))) (or (= ?v0 ?v1) (member$ ?v0 (set$b ?v2))))) :named a296))
+(assert (! (forall ((?v0 Event$) (?v1 Event$) (?v2 Event_list$)) (=> (member$b ?v0 (set$ (cons$ ?v1 ?v2))) (or (= ?v0 ?v1) (member$b ?v0 (set$ ?v2))))) :named a297))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (=> (and (member$a ?v0 (set$a ?v1)) (and (forall ((?v2 Msg_list$)) (=> (= ?v1 (cons$b ?v0 ?v2)) false)) (forall ((?v2 Msg$) (?v3 Msg_list$)) (=> (and (= ?v1 (cons$b ?v2 ?v3)) (member$a ?v0 (set$a ?v3))) false)))) false)) :named a298))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (=> (and (member$ ?v0 (set$b ?v1)) (and (forall ((?v2 Agent_list$)) (=> (= ?v1 (cons$c ?v0 ?v2)) false)) (forall ((?v2 Agent$) (?v3 Agent_list$)) (=> (and (= ?v1 (cons$c ?v2 ?v3)) (member$ ?v0 (set$b ?v3))) false)))) false)) :named a299))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (=> (and (member$b ?v0 (set$ ?v1)) (and (forall ((?v2 Event_list$)) (=> (= ?v1 (cons$ ?v0 ?v2)) false)) (forall ((?v2 Event$) (?v3 Event_list$)) (=> (and (= ?v1 (cons$ ?v2 ?v3)) (member$b ?v0 (set$ ?v3))) false)))) false)) :named a300))
+(assert (! (forall ((?v0 Msg_list$) (?v1 Msg_list$) (?v2 (-> Msg$ Bool)) (?v3 (-> Msg$ Bool))) (=> (and (= ?v0 ?v1) (forall ((?v4 Msg$)) (=> (member$a ?v4 (set$a ?v1)) (= (?v2 ?v4) (?v3 ?v4))))) (= (list_all$a ?v2 ?v0) (list_all$a ?v3 ?v1)))) :named a301))
+(assert (! (forall ((?v0 Agent_list$) (?v1 Agent_list$) (?v2 (-> Agent$ Bool)) (?v3 (-> Agent$ Bool))) (=> (and (= ?v0 ?v1) (forall ((?v4 Agent$)) (=> (member$ ?v4 (set$b ?v1)) (= (?v2 ?v4) (?v3 ?v4))))) (= (list_all$b ?v2 ?v0) (list_all$b ?v3 ?v1)))) :named a302))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event_list$) (?v2 (-> Event$ Bool)) (?v3 (-> Event$ Bool))) (=> (and (= ?v0 ?v1) (forall ((?v4 Event$)) (=> (member$b ?v4 (set$ ?v1)) (= (?v2 ?v4) (?v3 ?v4))))) (= (list_all$ ?v2 ?v0) (list_all$ ?v3 ?v1)))) :named a303))
+(assert (! (forall ((?v0 (-> Msg$ Bool)) (?v1 Msg_list$) (?v2 (-> Msg$ Bool))) (=> (and (list_all$a ?v0 ?v1) (forall ((?v3 Msg$)) (=> (and (member$a ?v3 (set$a ?v1)) (?v0 ?v3)) (?v2 ?v3)))) (list_all$a ?v2 ?v1))) :named a304))
+(assert (! (forall ((?v0 (-> Agent$ Bool)) (?v1 Agent_list$) (?v2 (-> Agent$ Bool))) (=> (and (list_all$b ?v0 ?v1) (forall ((?v3 Agent$)) (=> (and (member$ ?v3 (set$b ?v1)) (?v0 ?v3)) (?v2 ?v3)))) (list_all$b ?v2 ?v1))) :named a305))
+(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event_list$) (?v2 (-> Event$ Bool))) (=> (and (list_all$ ?v0 ?v1) (forall ((?v3 Event$)) (=> (and (member$b ?v3 (set$ ?v1)) (?v0 ?v3)) (?v2 ?v3)))) (list_all$ ?v2 ?v1))) :named a306))
+(assert (! (forall ((?v0 (-> Msg$ Bool)) (?v1 Msg_list$)) (= (list_ex1$a ?v0 ?v1) (exists ((?v2 Msg$)) (and (and (member$a ?v2 (set$a ?v1)) (?v0 ?v2)) (forall ((?v3 Msg$)) (=> (and (member$a ?v3 (set$a ?v1)) (?v0 ?v3)) (= ?v3 ?v2))))))) :named a307))
+(assert (! (forall ((?v0 (-> Agent$ Bool)) (?v1 Agent_list$)) (= (list_ex1$b ?v0 ?v1) (exists ((?v2 Agent$)) (and (and (member$ ?v2 (set$b ?v1)) (?v0 ?v2)) (forall ((?v3 Agent$)) (=> (and (member$ ?v3 (set$b ?v1)) (?v0 ?v3)) (= ?v3 ?v2))))))) :named a308))
+(assert (! (forall ((?v0 (-> Event$ Bool)) (?v1 Event_list$)) (= (list_ex1$ ?v0 ?v1) (exists ((?v2 Event$)) (and (and (member$b ?v2 (set$ ?v1)) (?v0 ?v2)) (forall ((?v3 Event$)) (=> (and (member$b ?v3 (set$ ?v1)) (?v0 ?v3)) (= ?v3 ?v2))))))) :named a309))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (= (member$a ?v0 (set$a ?v1)) (member$g ?v1 ?v0))) :named a310))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (= (member$ ?v0 (set$b ?v1)) (member$h ?v1 ?v0))) :named a311))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (= (member$b ?v0 (set$ ?v1)) (member$d ?v1 ?v0))) :named a312))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event$)) (less_eq$a (set$ ?v0) (set$ (cons$ ?v1 ?v0)))) :named a313))
+(assert (! (forall ((?v0 Msg_list$) (?v1 Msg$)) (less_eq$ (set$a ?v0) (set$a (cons$b ?v1 ?v0)))) :named a314))
+(assert (! (forall ((?v0 Msg_list$) (?v1 (-> Msg$ Bool))) (= (exists ((?v2 Msg$)) (and (member$a ?v2 (set$a ?v0)) (?v1 ?v2))) (exists ((?v2 Msg_list$) (?v3 Msg$) (?v4 Msg_list$)) (and (= ?v0 (append$a ?v2 (cons$b ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Msg$)) (=> (member$a ?v5 (set$a ?v2)) (not (?v1 ?v5))))))))) :named a315))
+(assert (! (forall ((?v0 Agent_list$) (?v1 (-> Agent$ Bool))) (= (exists ((?v2 Agent$)) (and (member$ ?v2 (set$b ?v0)) (?v1 ?v2))) (exists ((?v2 Agent_list$) (?v3 Agent$) (?v4 Agent_list$)) (and (= ?v0 (append$b ?v2 (cons$c ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Agent$)) (=> (member$ ?v5 (set$b ?v2)) (not (?v1 ?v5))))))))) :named a316))
+(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event$ Bool))) (= (exists ((?v2 Event$)) (and (member$b ?v2 (set$ ?v0)) (?v1 ?v2))) (exists ((?v2 Event_list$) (?v3 Event$) (?v4 Event_list$)) (and (= ?v0 (append$ ?v2 (cons$ ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Event$)) (=> (member$b ?v5 (set$ ?v2)) (not (?v1 ?v5))))))))) :named a317))
+(assert (! (forall ((?v0 Msg_list$) (?v1 (-> Msg$ Bool))) (= (exists ((?v2 Msg$)) (and (member$a ?v2 (set$a ?v0)) (?v1 ?v2))) (exists ((?v2 Msg_list$) (?v3 Msg$) (?v4 Msg_list$)) (and (= ?v0 (append$a ?v2 (cons$b ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Msg$)) (=> (member$a ?v5 (set$a ?v4)) (not (?v1 ?v5))))))))) :named a318))
+(assert (! (forall ((?v0 Agent_list$) (?v1 (-> Agent$ Bool))) (= (exists ((?v2 Agent$)) (and (member$ ?v2 (set$b ?v0)) (?v1 ?v2))) (exists ((?v2 Agent_list$) (?v3 Agent$) (?v4 Agent_list$)) (and (= ?v0 (append$b ?v2 (cons$c ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Agent$)) (=> (member$ ?v5 (set$b ?v4)) (not (?v1 ?v5))))))))) :named a319))
+(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event$ Bool))) (= (exists ((?v2 Event$)) (and (member$b ?v2 (set$ ?v0)) (?v1 ?v2))) (exists ((?v2 Event_list$) (?v3 Event$) (?v4 Event_list$)) (and (= ?v0 (append$ ?v2 (cons$ ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Event$)) (=> (member$b ?v5 (set$ ?v4)) (not (?v1 ?v5))))))))) :named a320))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (= (member$a ?v0 (set$a ?v1)) (exists ((?v2 Msg_list$) (?v3 Msg_list$)) (and (= ?v1 (append$a ?v2 (cons$b ?v0 ?v3))) (not (member$a ?v0 (set$a ?v2))))))) :named a321))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (= (member$ ?v0 (set$b ?v1)) (exists ((?v2 Agent_list$) (?v3 Agent_list$)) (and (= ?v1 (append$b ?v2 (cons$c ?v0 ?v3))) (not (member$ ?v0 (set$b ?v2))))))) :named a322))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (= (member$b ?v0 (set$ ?v1)) (exists ((?v2 Event_list$) (?v3 Event_list$)) (and (= ?v1 (append$ ?v2 (cons$ ?v0 ?v3))) (not (member$b ?v0 (set$ ?v2))))))) :named a323))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (= (member$a ?v0 (set$a ?v1)) (exists ((?v2 Msg_list$) (?v3 Msg_list$)) (and (= ?v1 (append$a ?v2 (cons$b ?v0 ?v3))) (not (member$a ?v0 (set$a ?v3))))))) :named a324))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (= (member$ ?v0 (set$b ?v1)) (exists ((?v2 Agent_list$) (?v3 Agent_list$)) (and (= ?v1 (append$b ?v2 (cons$c ?v0 ?v3))) (not (member$ ?v0 (set$b ?v3))))))) :named a325))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (= (member$b ?v0 (set$ ?v1)) (exists ((?v2 Event_list$) (?v3 Event_list$)) (and (= ?v1 (append$ ?v2 (cons$ ?v0 ?v3))) (not (member$b ?v0 (set$ ?v3))))))) :named a326))
+(assert (! (forall ((?v0 Msg_list$) (?v1 (-> Msg$ Bool))) (=> (and (exists ((?v2 Msg$)) (and (member$a ?v2 (set$a ?v0)) (?v1 ?v2))) (forall ((?v2 Msg_list$) (?v3 Msg$) (?v4 Msg_list$)) (=> (and (= ?v0 (append$a ?v2 (cons$b ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Msg$)) (=> (member$a ?v5 (set$a ?v2)) (not (?v1 ?v5)))))) false))) false)) :named a327))
+(assert (! (forall ((?v0 Agent_list$) (?v1 (-> Agent$ Bool))) (=> (and (exists ((?v2 Agent$)) (and (member$ ?v2 (set$b ?v0)) (?v1 ?v2))) (forall ((?v2 Agent_list$) (?v3 Agent$) (?v4 Agent_list$)) (=> (and (= ?v0 (append$b ?v2 (cons$c ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Agent$)) (=> (member$ ?v5 (set$b ?v2)) (not (?v1 ?v5)))))) false))) false)) :named a328))
+(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event$ Bool))) (=> (and (exists ((?v2 Event$)) (and (member$b ?v2 (set$ ?v0)) (?v1 ?v2))) (forall ((?v2 Event_list$) (?v3 Event$) (?v4 Event_list$)) (=> (and (= ?v0 (append$ ?v2 (cons$ ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Event$)) (=> (member$b ?v5 (set$ ?v2)) (not (?v1 ?v5)))))) false))) false)) :named a329))
+(assert (! (forall ((?v0 Msg_list$) (?v1 (-> Msg$ Bool))) (=> (and (exists ((?v2 Msg$)) (and (member$a ?v2 (set$a ?v0)) (?v1 ?v2))) (forall ((?v2 Msg_list$) (?v3 Msg$) (?v4 Msg_list$)) (=> (and (= ?v0 (append$a ?v2 (cons$b ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Msg$)) (=> (member$a ?v5 (set$a ?v4)) (not (?v1 ?v5)))))) false))) false)) :named a330))
+(assert (! (forall ((?v0 Agent_list$) (?v1 (-> Agent$ Bool))) (=> (and (exists ((?v2 Agent$)) (and (member$ ?v2 (set$b ?v0)) (?v1 ?v2))) (forall ((?v2 Agent_list$) (?v3 Agent$) (?v4 Agent_list$)) (=> (and (= ?v0 (append$b ?v2 (cons$c ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Agent$)) (=> (member$ ?v5 (set$b ?v4)) (not (?v1 ?v5)))))) false))) false)) :named a331))
+(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event$ Bool))) (=> (and (exists ((?v2 Event$)) (and (member$b ?v2 (set$ ?v0)) (?v1 ?v2))) (forall ((?v2 Event_list$) (?v3 Event$) (?v4 Event_list$)) (=> (and (= ?v0 (append$ ?v2 (cons$ ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Event$)) (=> (member$b ?v5 (set$ ?v4)) (not (?v1 ?v5)))))) false))) false)) :named a332))
+(assert (! (forall ((?v0 Msg_list$) (?v1 (-> Msg$ Bool))) (=> (exists ((?v2 Msg$)) (and (member$a ?v2 (set$a ?v0)) (?v1 ?v2))) (exists ((?v2 Msg_list$) (?v3 Msg$) (?v4 Msg_list$)) (and (= ?v0 (append$a ?v2 (cons$b ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Msg$)) (=> (member$a ?v5 (set$a ?v2)) (not (?v1 ?v5))))))))) :named a333))
+(assert (! (forall ((?v0 Agent_list$) (?v1 (-> Agent$ Bool))) (=> (exists ((?v2 Agent$)) (and (member$ ?v2 (set$b ?v0)) (?v1 ?v2))) (exists ((?v2 Agent_list$) (?v3 Agent$) (?v4 Agent_list$)) (and (= ?v0 (append$b ?v2 (cons$c ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Agent$)) (=> (member$ ?v5 (set$b ?v2)) (not (?v1 ?v5))))))))) :named a334))
+(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event$ Bool))) (=> (exists ((?v2 Event$)) (and (member$b ?v2 (set$ ?v0)) (?v1 ?v2))) (exists ((?v2 Event_list$) (?v3 Event$) (?v4 Event_list$)) (and (= ?v0 (append$ ?v2 (cons$ ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Event$)) (=> (member$b ?v5 (set$ ?v2)) (not (?v1 ?v5))))))))) :named a335))
+(assert (! (forall ((?v0 Msg_list$) (?v1 (-> Msg$ Bool))) (=> (exists ((?v2 Msg$)) (and (member$a ?v2 (set$a ?v0)) (?v1 ?v2))) (exists ((?v2 Msg_list$) (?v3 Msg$) (?v4 Msg_list$)) (and (= ?v0 (append$a ?v2 (cons$b ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Msg$)) (=> (member$a ?v5 (set$a ?v4)) (not (?v1 ?v5))))))))) :named a336))
+(assert (! (forall ((?v0 Agent_list$) (?v1 (-> Agent$ Bool))) (=> (exists ((?v2 Agent$)) (and (member$ ?v2 (set$b ?v0)) (?v1 ?v2))) (exists ((?v2 Agent_list$) (?v3 Agent$) (?v4 Agent_list$)) (and (= ?v0 (append$b ?v2 (cons$c ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Agent$)) (=> (member$ ?v5 (set$b ?v4)) (not (?v1 ?v5))))))))) :named a337))
+(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event$ Bool))) (=> (exists ((?v2 Event$)) (and (member$b ?v2 (set$ ?v0)) (?v1 ?v2))) (exists ((?v2 Event_list$) (?v3 Event$) (?v4 Event_list$)) (and (= ?v0 (append$ ?v2 (cons$ ?v3 ?v4))) (and (?v1 ?v3) (forall ((?v5 Event$)) (=> (member$b ?v5 (set$ ?v4)) (not (?v1 ?v5))))))))) :named a338))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (= (member$a ?v0 (set$a ?v1)) (exists ((?v2 Msg_list$) (?v3 Msg_list$)) (= ?v1 (append$a ?v2 (cons$b ?v0 ?v3)))))) :named a339))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (= (member$ ?v0 (set$b ?v1)) (exists ((?v2 Agent_list$) (?v3 Agent_list$)) (= ?v1 (append$b ?v2 (cons$c ?v0 ?v3)))))) :named a340))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (= (member$b ?v0 (set$ ?v1)) (exists ((?v2 Event_list$) (?v3 Event_list$)) (= ?v1 (append$ ?v2 (cons$ ?v0 ?v3)))))) :named a341))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$) (?v2 Msg_list$) (?v3 Msg_list$) (?v4 Msg_list$)) (=> (and (not (member$a ?v0 (set$a ?v1))) (not (member$a ?v0 (set$a ?v2)))) (= (= (append$a ?v1 (cons$b ?v0 ?v2)) (append$a ?v3 (cons$b ?v0 ?v4))) (and (= ?v1 ?v3) (= ?v2 ?v4))))) :named a342))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$) (?v2 Agent_list$) (?v3 Agent_list$) (?v4 Agent_list$)) (=> (and (not (member$ ?v0 (set$b ?v1))) (not (member$ ?v0 (set$b ?v2)))) (= (= (append$b ?v1 (cons$c ?v0 ?v2)) (append$b ?v3 (cons$c ?v0 ?v4))) (and (= ?v1 ?v3) (= ?v2 ?v4))))) :named a343))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$) (?v2 Event_list$) (?v3 Event_list$) (?v4 Event_list$)) (=> (and (not (member$b ?v0 (set$ ?v1))) (not (member$b ?v0 (set$ ?v2)))) (= (= (append$ ?v1 (cons$ ?v0 ?v2)) (append$ ?v3 (cons$ ?v0 ?v4))) (and (= ?v1 ?v3) (= ?v2 ?v4))))) :named a344))
+(assert (! (forall ((?v0 Msg_list$) (?v1 (-> Msg$ Bool))) (=> (and (exists ((?v2 Msg$)) (and (member$a ?v2 (set$a ?v0)) (?v1 ?v2))) (forall ((?v2 Msg_list$) (?v3 Msg$) (?v4 Msg_list$)) (=> (and (= ?v0 (append$a ?v2 (cons$b ?v3 ?v4))) (?v1 ?v3)) false))) false)) :named a345))
+(assert (! (forall ((?v0 Agent_list$) (?v1 (-> Agent$ Bool))) (=> (and (exists ((?v2 Agent$)) (and (member$ ?v2 (set$b ?v0)) (?v1 ?v2))) (forall ((?v2 Agent_list$) (?v3 Agent$) (?v4 Agent_list$)) (=> (and (= ?v0 (append$b ?v2 (cons$c ?v3 ?v4))) (?v1 ?v3)) false))) false)) :named a346))
+(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event$ Bool))) (=> (and (exists ((?v2 Event$)) (and (member$b ?v2 (set$ ?v0)) (?v1 ?v2))) (forall ((?v2 Event_list$) (?v3 Event$) (?v4 Event_list$)) (=> (and (= ?v0 (append$ ?v2 (cons$ ?v3 ?v4))) (?v1 ?v3)) false))) false)) :named a347))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (=> (member$a ?v0 (set$a ?v1)) (exists ((?v2 Msg_list$) (?v3 Msg_list$)) (and (= ?v1 (append$a ?v2 (cons$b ?v0 ?v3))) (not (member$a ?v0 (set$a ?v2))))))) :named a348))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (=> (member$ ?v0 (set$b ?v1)) (exists ((?v2 Agent_list$) (?v3 Agent_list$)) (and (= ?v1 (append$b ?v2 (cons$c ?v0 ?v3))) (not (member$ ?v0 (set$b ?v2))))))) :named a349))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (=> (member$b ?v0 (set$ ?v1)) (exists ((?v2 Event_list$) (?v3 Event_list$)) (and (= ?v1 (append$ ?v2 (cons$ ?v0 ?v3))) (not (member$b ?v0 (set$ ?v2))))))) :named a350))
+(assert (! (forall ((?v0 Msg_list$) (?v1 (-> Msg$ Bool))) (=> (exists ((?v2 Msg$)) (and (member$a ?v2 (set$a ?v0)) (?v1 ?v2))) (exists ((?v2 Msg_list$) (?v3 Msg$) (?v4 Msg_list$)) (and (= ?v0 (append$a ?v2 (cons$b ?v3 ?v4))) (?v1 ?v3))))) :named a351))
+(assert (! (forall ((?v0 Agent_list$) (?v1 (-> Agent$ Bool))) (=> (exists ((?v2 Agent$)) (and (member$ ?v2 (set$b ?v0)) (?v1 ?v2))) (exists ((?v2 Agent_list$) (?v3 Agent$) (?v4 Agent_list$)) (and (= ?v0 (append$b ?v2 (cons$c ?v3 ?v4))) (?v1 ?v3))))) :named a352))
+(assert (! (forall ((?v0 Event_list$) (?v1 (-> Event$ Bool))) (=> (exists ((?v2 Event$)) (and (member$b ?v2 (set$ ?v0)) (?v1 ?v2))) (exists ((?v2 Event_list$) (?v3 Event$) (?v4 Event_list$)) (and (= ?v0 (append$ ?v2 (cons$ ?v3 ?v4))) (?v1 ?v3))))) :named a353))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (=> (member$a ?v0 (set$a ?v1)) (exists ((?v2 Msg_list$) (?v3 Msg_list$)) (and (= ?v1 (append$a ?v2 (cons$b ?v0 ?v3))) (not (member$a ?v0 (set$a ?v3))))))) :named a354))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (=> (member$ ?v0 (set$b ?v1)) (exists ((?v2 Agent_list$) (?v3 Agent_list$)) (and (= ?v1 (append$b ?v2 (cons$c ?v0 ?v3))) (not (member$ ?v0 (set$b ?v3))))))) :named a355))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (=> (member$b ?v0 (set$ ?v1)) (exists ((?v2 Event_list$) (?v3 Event_list$)) (and (= ?v1 (append$ ?v2 (cons$ ?v0 ?v3))) (not (member$b ?v0 (set$ ?v3))))))) :named a356))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (=> (member$a ?v0 (set$a ?v1)) (exists ((?v2 Msg_list$) (?v3 Msg_list$)) (= ?v1 (append$a ?v2 (cons$b ?v0 ?v3)))))) :named a357))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (=> (member$ ?v0 (set$b ?v1)) (exists ((?v2 Agent_list$) (?v3 Agent_list$)) (= ?v1 (append$b ?v2 (cons$c ?v0 ?v3)))))) :named a358))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (=> (member$b ?v0 (set$ ?v1)) (exists ((?v2 Event_list$) (?v3 Event_list$)) (= ?v1 (append$ ?v2 (cons$ ?v0 ?v3)))))) :named a359))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent$) (?v2 Msg$) (?v3 Event_list$)) (=> (member$b (says$ ?v0 ?v1 ?v2) (set$ ?v3)) (member$a ?v2 (knows$ ?v0 ?v3)))) :named a360))
+(assert (! (forall ((?v0 Agent$) (?v1 Msg$) (?v2 Event_list$)) (=> (member$b (notes$ ?v0 ?v1) (set$ ?v2)) (member$a ?v1 (knows$ ?v0 ?v2)))) :named a361))
+(assert (! (forall ((?v0 Msg$) (?v1 Msg_list$)) (! (= (insert$d ?v0 ?v1) (ite (member$a ?v0 (set$a ?v1)) ?v1 (cons$b ?v0 ?v1))) :pattern ((insert$d ?v0 ?v1)))) :named a362))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent_list$)) (! (= (insert$e ?v0 ?v1) (ite (member$ ?v0 (set$b ?v1)) ?v1 (cons$c ?v0 ?v1))) :pattern ((insert$e ?v0 ?v1)))) :named a363))
+(assert (! (forall ((?v0 Event$) (?v1 Event_list$)) (! (= (insert$a ?v0 ?v1) (ite (member$b ?v0 (set$ ?v1)) ?v1 (cons$ ?v0 ?v1))) :pattern ((insert$a ?v0 ?v1)))) :named a364))
+(assert (! (forall ((?v0 Agent$) (?v1 Agent$) (?v2 Msg$) (?v3 Event_list$)) (=> (member$b (says$ ?v0 ?v1 ?v2) (set$ ?v3)) (member$a ?v2 (knows$ spy$ ?v3)))) :named a365))
+(assert (! (forall ((?v0 Agent$) (?v1 Msg$) (?v2 Event_list$)) (=> (and (not (= ?v0 spy$)) (member$b (gets$ ?v0 ?v1) (set$ ?v2))) (member$a ?v1 (knows$ ?v0 ?v2)))) :named a366))
+(assert (! (forall ((?v0 Msg$) (?v1 Event_list$)) (=> (member$a ?v0 (knows$ spy$ ?v1)) (exists ((?v2 Agent$) (?v3 Agent$)) (or (member$b (says$ ?v2 ?v3 ?v0) (set$ ?v1)) (or (member$b (notes$ ?v2 ?v0) (set$ ?v1)) (member$a ?v0 (initState$ spy$))))))) :named a367))
+(assert (! (forall ((?v0 Msg_list$) (?v1 Msg$) (?v2 Msg_list_set$)) (=> (member$e (append$a ?v0 (cons$b ?v1 nil$b)) ?v2) (member$a ?v1 (succ$a ?v2 ?v0)))) :named a368))
+(assert (! (forall ((?v0 Agent_list$) (?v1 Agent$) (?v2 Agent_list_set$)) (=> (member$f (append$b ?v0 (cons$c ?v1 nil$c)) ?v2) (member$ ?v1 (succ$b ?v2 ?v0)))) :named a369))
+(assert (! (forall ((?v0 Event_list$) (?v1 Event$) (?v2 Event_list_set$)) (=> (member$c (append$ ?v0 (cons$ ?v1 nil$)) ?v2) (member$b ?v1 (succ$ ?v2 ?v0)))) :named a370))
+(assert (! (forall ((?v0 Event_list$) (?v1 Agent$) (?v2 Msg$)) (= (knows$ spy$ (append$ ?v0 (cons$ (notes$ ?v1 ?v2) nil$))) (ite (member$ ?v1 bad$) (insert$ ?v2 (knows$ spy$ ?v0)) (knows$ spy$ ?v0)))) :named a371))
+(assert (! (member$ spy$ bad$) :named a372))
+(assert (! (forall ((?v0 Agent$) (?v1 Msg$) (?v2 Event_list$)) (! (= (knows$ spy$ (cons$ (notes$ ?v0 ?v1) ?v2)) (ite (member$ ?v0 bad$) (insert$ ?v1 (knows$ spy$ ?v2)) (knows$ spy$ ?v2))) :pattern ((cons$ (notes$ ?v0 ?v1) ?v2)))) :named a373))
+(assert (! (forall ((?v0 Agent$) (?v1 Msg$) (?v2 Event_list$)) (=> (and (member$b (notes$ ?v0 ?v1) (set$ ?v2)) (member$ ?v0 bad$)) (member$a ?v1 (knows$ spy$ ?v2)))) :named a374))
+(assert (! (forall ((?v0 Agent$) (?v1 Event$) (?v2 Event_list$)) (= (knows$ ?v0 (cons$ ?v1 ?v2)) (ite (= ?v0 spy$) (case_event$ (uuo$ ?v2) (uup$ ?v2) (uuq$ ?v2) ?v1) (case_event$ (uur$ ?v0 ?v2) (uus$ ?v0 ?v2) (uus$ ?v0 ?v2) ?v1)))) :named a375))
+(check-sat)

diff --git a/test/regress/regress2/ho/bug_instfalse_SEU882^5.p b/test/regress/regress2/ho/bug_instfalse_SEU882^5.p
new file mode 100644 (file)
index 0000000..a62a208
--- /dev/null
+++ b/test/regress/regress2/ho/bug_instfalse_SEU882^5.p
@@ -0,0 +1,44 @@
+% COMMAND-LINE:  --uf-ho --full-saturate-quant --ho-elim
+% EXPECT: % SZS status Theorem for bug_instfalse_SEU882^5
+
+%------------------------------------------------------------------------------
+% File     : SEU882^5 : TPTP v7.2.0. Released v4.0.0.
+% Domain   : Set Theory
+% Problem  : TPS problem THM139
+% Version  : Especial.
+% English  : Every object is in the range of some function.
+
+% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
+% Source   : [Bro09]
+% Names    : tps_0037 [Bro09]
+%          : THM139 [TPS]
+
+% Status   : Theorem
+% Rating   : 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
+% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
+%            Number of atoms       :    4 (   1 equality;   3 variable)
+%            Maximal formula depth :    6 (   6 average)
+%            Number of connectives :    1 (   0   ~;   0   |;   0   &;   1   @)
+%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
+%                                         (   0  ~|;   0  ~&)
+%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
+%            Number of symbols     :    1 (   0   :;   0   =)
+%            Number of variables   :    3 (   0 sgn;   1   !;   2   ?;   0   ^)
+%                                         (   3   :;   0  !>;   0  ?*)
+%                                         (   0  @-;   0  @+)
+% SPC      : TH0_THM_EQU_NAR
+
+% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
+%            project in the Department of Mathematical Sciences at Carnegie
+%            Mellon University. Distributed under the Creative Commons copyleft
+%            license: http://creativecommons.org/licenses/by-sa/3.0/
+%          : Polymorphic definitions expanded.
+%          :
+%------------------------------------------------------------------------------
+thf(cTHM139_pme,conjecture,(
+    ! [Xy: $i] :
+    ? [Xf: $i > $i,Xx: $i] :
+      ( ( Xf @ Xx )
+      = Xy ) )).
+
+%------------------------------------------------------------------------------

diff --git a/test/regress/regress2/ho/fta0409.smt2 b/test/regress/regress2/ho/fta0409.smt2
new file mode 100644 (file)
index 0000000..51ac5f2
--- /dev/null
+++ b/test/regress/regress2/ho/fta0409.smt2
@@ -0,0 +1,427 @@
+; COMMAND-LINE: --uf-ho
+; EXPECT: unsat
+(set-logic ALL)
+(set-info :status unsat)
+(declare-sort Nat$ 0)
+(declare-sort Complex$ 0)
+(declare-sort Nat_poly$ 0)
+(declare-sort Complex_poly$ 0)
+(declare-sort Complex_poly_poly$ 0)
+(declare-fun n$ () Nat$)
+(declare-fun q$ () Complex_poly$)
+(declare-fun r$ () Complex_poly$)
+(declare-fun dvd$ (Complex_poly$ Complex_poly$) Bool)
+(declare-fun one$ () Nat$)
+(declare-fun suc$ (Nat$) Nat$)
+(declare-fun dvd$a (Complex$ Complex$) Bool)
+(declare-fun dvd$b (Nat$ Nat$) Bool)
+(declare-fun dvd$c (Complex_poly_poly$ Complex_poly_poly$) Bool)
+(declare-fun dvd$d (Nat_poly$ Nat_poly$) Bool)
+(declare-fun one$a () Complex_poly$)
+(declare-fun one$b () Complex$)
+(declare-fun one$c () Nat_poly$)
+(declare-fun plus$ (Complex$ Complex$) Complex$)
+(declare-fun poly$ (Complex_poly$) (-> Complex$ Complex$))
+(declare-fun zero$ () Complex$)
+(declare-fun coeff$ (Complex_poly_poly$ Nat$) Complex_poly$)
+(declare-fun monom$ (Complex$ Nat$) Complex_poly$)
+(declare-fun order$ (Complex$ Complex_poly$) Nat$)
+(declare-fun pCons$ (Complex$ Complex_poly$) Complex_poly$)
+(declare-fun plus$a (Nat$ Nat$) Nat$)
+(declare-fun plus$b (Nat_poly$ Nat_poly$) Nat_poly$)
+(declare-fun plus$c (Complex_poly$ Complex_poly$) Complex_poly$)
+(declare-fun poly$a (Complex_poly_poly$ Complex_poly$) Complex_poly$)
+(declare-fun poly$b (Nat_poly$ Nat$) Nat$)
+(declare-fun power$ (Complex_poly$ Nat$) Complex_poly$)
+(declare-fun psize$ (Complex_poly$) Nat$)
+(declare-fun times$ (Nat$ Nat$) Nat$)
+(declare-fun zero$a () Nat$)
+(declare-fun zero$b () Complex_poly_poly$)
+(declare-fun zero$c () Complex_poly$)
+(declare-fun zero$d () Nat_poly$)
+(declare-fun coeff$a (Nat_poly$ Nat$) Nat$)
+(declare-fun coeff$b (Complex_poly$ Nat$) Complex$)
+(declare-fun degree$ (Complex_poly_poly$) Nat$)
+(declare-fun monom$a (Complex_poly$ Nat$) Complex_poly_poly$)
+(declare-fun monom$b (Nat$ Nat$) Nat_poly$)
+(declare-fun order$a (Complex_poly$ Complex_poly_poly$) Nat$)
+(declare-fun pCons$a (Complex_poly$ Complex_poly_poly$) Complex_poly_poly$)
+(declare-fun pCons$b (Nat$ Nat_poly$) Nat_poly$)
+(declare-fun power$a (Complex_poly_poly$ Nat$) Complex_poly_poly$)
+(declare-fun power$b (Nat_poly$ Nat$) Nat_poly$)
+(declare-fun power$c (Nat$ Nat$) Nat$)
+(declare-fun power$d (Complex$ Nat$) Complex$)
+(declare-fun degree$a (Nat_poly$) Nat$)
+(declare-fun degree$b (Complex_poly$) Nat$)
+(declare-fun is_zero$ (Complex_poly$) Bool)
+(declare-fun less_eq$ (Nat$ Nat$) Bool)
+(declare-fun of_bool$ (Bool) Complex$)
+(declare-fun constant$ ((-> Complex$ Complex$)) Bool)
+(declare-fun of_bool$a (Bool) Complex_poly$)
+(declare-fun of_bool$b (Bool) Nat$)
+(declare-fun pcompose$ (Complex_poly$ Complex_poly$) Complex_poly$)
+(declare-fun pcompose$a (Complex_poly_poly$ Complex_poly_poly$) Complex_poly_poly$)
+(declare-fun pcompose$b (Nat_poly$ Nat_poly$) Nat_poly$)
+(declare-fun poly_shift$ (Nat$ Complex_poly$) Complex_poly$)
+(declare-fun offset_poly$ (Complex_poly$ Complex$) Complex_poly$)
+(declare-fun poly_cutoff$ (Nat$ Complex_poly$) Complex_poly$)
+(declare-fun rsquarefree$ (Complex_poly$) Bool)
+(declare-fun offset_poly$a (Nat_poly$ Nat$) Nat_poly$)
+(declare-fun reflect_poly$ (Complex_poly$) Complex_poly$)
+(declare-fun reflect_poly$a (Complex_poly_poly$) Complex_poly_poly$)
+(declare-fun reflect_poly$b (Nat_poly$) Nat_poly$)
+(declare-fun synthetic_div$ (Complex_poly$ Complex$) Complex_poly$)
+(assert (! (not (= (poly$ (power$ q$ n$)) (poly$ r$))) :named a0))
+(assert (! (forall ((?v0 Complex$)) (= (poly$ (power$ q$ n$) ?v0) (poly$ r$ ?v0))) :named a1))
+(assert (! (forall ((?v0 Complex_poly_poly$) (?v1 Nat$) (?v2 Complex_poly$)) (= (poly$a (power$a ?v0 ?v1) ?v2) (power$ (poly$a ?v0 ?v2) ?v1))) :named a2))
+(assert (! (forall ((?v0 Nat_poly$) (?v1 Nat$) (?v2 Nat$)) (= (poly$b (power$b ?v0 ?v1) ?v2) (power$c (poly$b ?v0 ?v2) ?v1))) :named a3))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$) (?v2 Complex$)) (= (poly$ (power$ ?v0 ?v1) ?v2) (power$d (poly$ ?v0 ?v2) ?v1))) :named a4))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (= (poly$ ?v0) (poly$ ?v1)) (= ?v0 ?v1))) :named a5))
+(assert (! (forall ((?v0 Complex_poly$)) (=> (not (constant$ (poly$ ?v0))) (exists ((?v1 Complex$)) (= (poly$ ?v0 ?v1) zero$)))) :named a6))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$)) (= (reflect_poly$ (power$ ?v0 ?v1)) (power$ (reflect_poly$ ?v0) ?v1))) :named a7))
+(assert (! (forall ((?v0 Complex_poly_poly$) (?v1 Nat$)) (= (coeff$ (power$a ?v0 ?v1) zero$a) (power$ (coeff$ ?v0 zero$a) ?v1))) :named a8))
+(assert (! (forall ((?v0 Nat_poly$) (?v1 Nat$)) (= (coeff$a (power$b ?v0 ?v1) zero$a) (power$c (coeff$a ?v0 zero$a) ?v1))) :named a9))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$)) (= (coeff$b (power$ ?v0 ?v1) zero$a) (power$d (coeff$b ?v0 zero$a) ?v1))) :named a10))
+(assert (! (forall ((?v0 (-> Complex$ Complex$))) (= (constant$ ?v0) (forall ((?v1 Complex$) (?v2 Complex$)) (= (?v0 ?v1) (?v0 ?v2))))) :named a11))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$)) (exists ((?v2 Complex_poly$)) (and (= (psize$ ?v2) (psize$ ?v0)) (forall ((?v3 Complex$)) (= (poly$ ?v2 ?v3) (poly$ ?v0 (plus$ ?v1 ?v3))))))) :named a12))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$) (?v2 Complex$)) (= (poly$ (offset_poly$ ?v0 ?v1) ?v2) (poly$ ?v0 (plus$ ?v1 ?v2)))) :named a13))
+(assert (! (forall ((?v0 Nat_poly$) (?v1 Nat$) (?v2 Nat$)) (= (poly$b (offset_poly$a ?v0 ?v1) ?v2) (poly$b ?v0 (plus$a ?v1 ?v2)))) :named a14))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$) (?v2 Complex$)) (= (poly$ (pcompose$ ?v0 ?v1) ?v2) (poly$ ?v0 (poly$ ?v1 ?v2)))) :named a15))
+(assert (! (forall ((?v0 Complex_poly$)) (= (power$ ?v0 one$) ?v0)) :named a16))
+(assert (! (forall ((?v0 Nat$)) (= (power$c ?v0 one$) ?v0)) :named a17))
+(assert (! (forall ((?v0 Nat$)) (= (power$ one$a ?v0) one$a)) :named a18))
+(assert (! (forall ((?v0 Nat$)) (= (power$c one$ ?v0) one$)) :named a19))
+(assert (! (forall ((?v0 Complex_poly_poly$) (?v1 Nat$)) (= (coeff$ (power$a ?v0 ?v1) (degree$ (power$a ?v0 ?v1))) (power$ (coeff$ ?v0 (degree$ ?v0)) ?v1))) :named a20))
+(assert (! (forall ((?v0 Nat_poly$) (?v1 Nat$)) (= (coeff$a (power$b ?v0 ?v1) (degree$a (power$b ?v0 ?v1))) (power$c (coeff$a ?v0 (degree$a ?v0)) ?v1))) :named a21))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$)) (= (coeff$b (power$ ?v0 ?v1) (degree$b (power$ ?v0 ?v1))) (power$d (coeff$b ?v0 (degree$b ?v0)) ?v1))) :named a22))
+(assert (! (forall ((?v0 Nat$)) (= (coeff$ zero$b ?v0) zero$c)) :named a23))
+(assert (! (forall ((?v0 Nat$)) (= (coeff$a zero$d ?v0) zero$a)) :named a24))
+(assert (! (forall ((?v0 Nat$)) (= (coeff$b zero$c ?v0) zero$)) :named a25))
+(assert (! (forall ((?v0 Nat_poly$) (?v1 Nat_poly$) (?v2 Nat$)) (= (coeff$a (plus$b ?v0 ?v1) ?v2) (plus$a (coeff$a ?v0 ?v2) (coeff$a ?v1 ?v2)))) :named a26))
+(assert (! (forall ((?v0 Complex_poly$)) (= (poly$a zero$b ?v0) zero$c)) :named a27))
+(assert (! (forall ((?v0 Nat$)) (= (poly$b zero$d ?v0) zero$a)) :named a28))
+(assert (! (forall ((?v0 Complex$)) (= (poly$ zero$c ?v0) zero$)) :named a29))
+(assert (! (= (degree$b one$a) zero$a) :named a30))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$) (?v2 Complex$)) (= (poly$ (plus$c ?v0 ?v1) ?v2) (plus$ (poly$ ?v0 ?v2) (poly$ ?v1 ?v2)))) :named a31))
+(assert (! (forall ((?v0 Nat_poly$) (?v1 Nat_poly$) (?v2 Nat$)) (= (poly$b (plus$b ?v0 ?v1) ?v2) (plus$a (poly$b ?v0 ?v2) (poly$b ?v1 ?v2)))) :named a32))
+(assert (! (forall ((?v0 Complex$)) (= (poly$ one$a ?v0) one$b)) :named a33))
+(assert (! (forall ((?v0 Nat$)) (= (poly$b one$c ?v0) one$)) :named a34))
+(assert (! (forall ((?v0 Complex_poly$)) (= (= (coeff$b ?v0 (degree$b ?v0)) zero$) (= ?v0 zero$c))) :named a35))
+(assert (! (forall ((?v0 Complex_poly_poly$)) (= (= (coeff$ ?v0 (degree$ ?v0)) zero$c) (= ?v0 zero$b))) :named a36))
+(assert (! (forall ((?v0 Nat_poly$)) (= (= (coeff$a ?v0 (degree$a ?v0)) zero$a) (= ?v0 zero$d))) :named a37))
+(assert (! (= (coeff$b one$a (degree$b one$a)) one$b) :named a38))
+(assert (! (= (coeff$a one$c (degree$a one$c)) one$) :named a39))
+(assert (! (forall ((?v0 Complex_poly$)) (= (= (poly$ (reflect_poly$ ?v0) zero$) zero$) (= ?v0 zero$c))) :named a40))
+(assert (! (forall ((?v0 Complex_poly_poly$)) (= (= (poly$a (reflect_poly$a ?v0) zero$c) zero$c) (= ?v0 zero$b))) :named a41))
+(assert (! (forall ((?v0 Nat_poly$)) (= (= (poly$b (reflect_poly$b ?v0) zero$a) zero$a) (= ?v0 zero$d))) :named a42))
+(assert (! (forall ((?v0 Complex_poly$)) (=> (not (= (coeff$b ?v0 zero$a) zero$)) (= (reflect_poly$ (reflect_poly$ ?v0)) ?v0))) :named a43))
+(assert (! (forall ((?v0 Complex_poly_poly$)) (=> (not (= (coeff$ ?v0 zero$a) zero$c)) (= (reflect_poly$a (reflect_poly$a ?v0)) ?v0))) :named a44))
+(assert (! (forall ((?v0 Nat_poly$)) (=> (not (= (coeff$a ?v0 zero$a) zero$a)) (= (reflect_poly$b (reflect_poly$b ?v0)) ?v0))) :named a45))
+(assert (! (forall ((?v0 Complex_poly$)) (= (= (coeff$b (reflect_poly$ ?v0) zero$a) zero$) (= ?v0 zero$c))) :named a46))
+(assert (! (forall ((?v0 Complex_poly_poly$)) (= (= (coeff$ (reflect_poly$a ?v0) zero$a) zero$c) (= ?v0 zero$b))) :named a47))
+(assert (! (forall ((?v0 Nat_poly$)) (= (= (coeff$a (reflect_poly$b ?v0) zero$a) zero$a) (= ?v0 zero$d))) :named a48))
+(assert (! (forall ((?v0 Complex_poly$)) (= (coeff$b (reflect_poly$ ?v0) zero$a) (coeff$b ?v0 (degree$b ?v0)))) :named a49))
+(assert (! (forall ((?v0 Complex_poly$)) (=> (not (= (coeff$b ?v0 zero$a) zero$)) (= (degree$b (reflect_poly$ ?v0)) (degree$b ?v0)))) :named a50))
+(assert (! (forall ((?v0 Complex_poly_poly$)) (=> (not (= (coeff$ ?v0 zero$a) zero$c)) (= (degree$ (reflect_poly$a ?v0)) (degree$ ?v0)))) :named a51))
+(assert (! (forall ((?v0 Nat_poly$)) (=> (not (= (coeff$a ?v0 zero$a) zero$a)) (= (degree$a (reflect_poly$b ?v0)) (degree$a ?v0)))) :named a52))
+(assert (! (forall ((?v0 Complex_poly$)) (= (poly$ (reflect_poly$ ?v0) zero$) (coeff$b ?v0 (degree$b ?v0)))) :named a53))
+(assert (! (forall ((?v0 Complex_poly_poly$)) (= (poly$a (reflect_poly$a ?v0) zero$c) (coeff$ ?v0 (degree$ ?v0)))) :named a54))
+(assert (! (forall ((?v0 Nat_poly$)) (= (poly$b (reflect_poly$b ?v0) zero$a) (coeff$a ?v0 (degree$a ?v0)))) :named a55))
+(assert (! (forall ((?v0 Complex_poly$)) (= (poly$ ?v0 zero$) (coeff$b ?v0 zero$a))) :named a56))
+(assert (! (forall ((?v0 Complex_poly_poly$)) (= (poly$a ?v0 zero$c) (coeff$ ?v0 zero$a))) :named a57))
+(assert (! (forall ((?v0 Nat_poly$)) (= (poly$b ?v0 zero$a) (coeff$a ?v0 zero$a))) :named a58))
+(assert (! (forall ((?v0 Nat_poly$) (?v1 Nat_poly$) (?v2 Nat$)) (= (coeff$a (plus$b ?v0 ?v1) ?v2) (plus$a (coeff$a ?v0 ?v2) (coeff$a ?v1 ?v2)))) :named a59))
+(assert (! (forall ((?v0 Complex_poly$)) (= (forall ((?v1 Complex$)) (= (poly$ ?v0 ?v1) zero$)) (= ?v0 zero$c))) :named a60))
+(assert (! (forall ((?v0 Complex_poly_poly$)) (= (forall ((?v1 Complex_poly$)) (= (poly$a ?v0 ?v1) zero$c)) (= ?v0 zero$b))) :named a61))
+(assert (! (forall ((?v0 Nat$)) (= (coeff$ zero$b ?v0) zero$c)) :named a62))
+(assert (! (forall ((?v0 Nat$)) (= (coeff$a zero$d ?v0) zero$a)) :named a63))
+(assert (! (forall ((?v0 Nat$)) (= (coeff$b zero$c ?v0) zero$)) :named a64))
+(assert (! (forall ((?v0 Complex_poly_poly$)) (=> (not (= ?v0 zero$b)) (not (= (coeff$ ?v0 (degree$ ?v0)) zero$c)))) :named a65))
+(assert (! (forall ((?v0 Nat_poly$)) (=> (not (= ?v0 zero$d)) (not (= (coeff$a ?v0 (degree$a ?v0)) zero$a)))) :named a66))
+(assert (! (forall ((?v0 Complex_poly$)) (=> (not (= ?v0 zero$c)) (not (= (coeff$b ?v0 (degree$b ?v0)) zero$)))) :named a67))
+(assert (! (forall ((?v0 Complex_poly$)) (! (= (power$ ?v0 zero$a) one$a) :pattern ((power$ ?v0)))) :named a68))
+(assert (! (forall ((?v0 Nat$)) (! (= (power$c ?v0 zero$a) one$) :pattern ((power$c ?v0)))) :named a69))
+(assert (! (forall ((?v0 Nat$)) (= (power$d zero$ ?v0) (ite (= ?v0 zero$a) one$b zero$))) :named a70))
+(assert (! (forall ((?v0 Nat$)) (= (power$ zero$c ?v0) (ite (= ?v0 zero$a) one$a zero$c))) :named a71))
+(assert (! (forall ((?v0 Nat$)) (= (power$c zero$a ?v0) (ite (= ?v0 zero$a) one$ zero$a))) :named a72))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$)) (= (degree$b (offset_poly$ ?v0 ?v1)) (degree$b ?v0))) :named a73))
+(assert (! (forall ((?v0 Complex_poly$)) (= (constant$ (poly$ ?v0)) (= (degree$b ?v0) zero$a))) :named a74))
+(assert (! (forall ((?v0 Complex$)) (= zero$ (poly$ zero$c ?v0))) :named a75))
+(assert (! (forall ((?v0 Complex_poly$)) (= zero$c (poly$a zero$b ?v0))) :named a76))
+(assert (! (forall ((?v0 Complex_poly$)) (= (exists ((?v1 Complex$)) (and (= (poly$ ?v0 ?v1) zero$) (not (= (poly$ zero$c ?v1) zero$)))) false)) :named a77))
+(assert (! (forall ((?v0 Complex_poly_poly$)) (= (exists ((?v1 Complex_poly$)) (and (= (poly$a ?v0 ?v1) zero$c) (not (= (poly$a zero$b ?v1) zero$c)))) false)) :named a78))
+(assert (! (forall ((?v0 Nat_poly$)) (= (exists ((?v1 Nat$)) (and (= (poly$b ?v0 ?v1) zero$a) (not (= (poly$b zero$d ?v1) zero$a)))) false)) :named a79))
+(assert (! (= (exists ((?v0 Complex_poly$)) (not (= (poly$a zero$b ?v0) zero$c))) false) :named a80))
+(assert (! (= (exists ((?v0 Nat$)) (not (= (poly$b zero$d ?v0) zero$a))) false) :named a81))
+(assert (! (= (exists ((?v0 Complex$)) (not (= (poly$ zero$c ?v0) zero$))) false) :named a82))
+(assert (! (= (exists ((?v0 Complex_poly$)) (= (poly$a zero$b ?v0) zero$c)) true) :named a83))
+(assert (! (= (exists ((?v0 Nat$)) (= (poly$b zero$d ?v0) zero$a)) true) :named a84))
+(assert (! (= (exists ((?v0 Complex$)) (= (poly$ zero$c ?v0) zero$)) true) :named a85))
+(assert (! (forall ((?v0 Complex$) (?v1 Nat$)) (=> (not (= ?v0 zero$)) (not (= (power$d ?v0 ?v1) zero$)))) :named a86))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$)) (=> (not (= ?v0 zero$c)) (not (= (power$ ?v0 ?v1) zero$c)))) :named a87))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (=> (not (= ?v0 zero$a)) (not (= (power$c ?v0 ?v1) zero$a)))) :named a88))
+(assert (! (forall ((?v0 Complex$)) (= (plus$ zero$ ?v0) ?v0)) :named a89))
+(assert (! (forall ((?v0 Complex_poly$)) (= (plus$c zero$c ?v0) ?v0)) :named a90))
+(assert (! (forall ((?v0 Nat$)) (= (plus$a zero$a ?v0) ?v0)) :named a91))
+(assert (! (forall ((?v0 Complex$)) (= (plus$ ?v0 zero$) ?v0)) :named a92))
+(assert (! (forall ((?v0 Complex_poly$)) (= (plus$c ?v0 zero$c) ?v0)) :named a93))
+(assert (! (forall ((?v0 Nat$)) (= (plus$a ?v0 zero$a) ?v0)) :named a94))
+(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (= (= (plus$ ?v0 ?v1) ?v1) (= ?v0 zero$))) :named a95))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (= (plus$c ?v0 ?v1) ?v1) (= ?v0 zero$c))) :named a96))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (plus$a ?v0 ?v1) ?v1) (= ?v0 zero$a))) :named a97))
+(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (= (= (plus$ ?v0 ?v1) ?v0) (= ?v1 zero$))) :named a98))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (= (plus$c ?v0 ?v1) ?v0) (= ?v1 zero$c))) :named a99))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (plus$a ?v0 ?v1) ?v0) (= ?v1 zero$a))) :named a100))
+(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (= (= ?v0 (plus$ ?v1 ?v0)) (= ?v1 zero$))) :named a101))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (= ?v0 (plus$c ?v1 ?v0)) (= ?v1 zero$c))) :named a102))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= ?v0 (plus$a ?v1 ?v0)) (= ?v1 zero$a))) :named a103))
+(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (= (= ?v0 (plus$ ?v0 ?v1)) (= ?v1 zero$))) :named a104))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (= ?v0 (plus$c ?v0 ?v1)) (= ?v1 zero$c))) :named a105))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= ?v0 (plus$a ?v0 ?v1)) (= ?v1 zero$a))) :named a106))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (plus$a ?v0 ?v1) zero$a) (and (= ?v0 zero$a) (= ?v1 zero$a)))) :named a107))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= zero$a (plus$a ?v0 ?v1)) (and (= ?v0 zero$a) (= ?v1 zero$a)))) :named a108))
+(assert (! (forall ((?v0 Complex_poly$)) (! (= (power$ ?v0 zero$a) one$a) :pattern ((power$ ?v0)))) :named a109))
+(assert (! (forall ((?v0 Nat$)) (! (= (power$c ?v0 zero$a) one$) :pattern ((power$c ?v0)))) :named a110))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (= (plus$a ?v0 ?v1) (plus$a ?v2 ?v1)) (= ?v0 ?v2))) :named a111))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (= (plus$a ?v0 ?v1) (plus$a ?v0 ?v2)) (= ?v1 ?v2))) :named a112))
+(assert (! (forall ((?v0 Complex_poly$)) (= (pcompose$ zero$c ?v0) zero$c)) :named a113))
+(assert (! (= (reflect_poly$ zero$c) zero$c) :named a114))
+(assert (! (= (degree$b zero$c) zero$a) :named a115))
+(assert (! (forall ((?v0 Complex_poly$)) (= (= (psize$ ?v0) zero$a) (= ?v0 zero$c))) :named a116))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$)) (= (= (offset_poly$ ?v0 ?v1) zero$c) (= ?v0 zero$c))) :named a117))
+(assert (! (forall ((?v0 Complex$)) (= (offset_poly$ zero$c ?v0) zero$c)) :named a118))
+(assert (! (forall ((?v0 Complex_poly$)) (= (exists ((?v1 Complex$)) (not (= (poly$ ?v0 ?v1) zero$))) (not (= ?v0 zero$c)))) :named a119))
+(assert (! (forall ((?v0 Complex$)) (= (= zero$ ?v0) (= ?v0 zero$))) :named a120))
+(assert (! (forall ((?v0 Complex_poly$)) (= (= zero$c ?v0) (= ?v0 zero$c))) :named a121))
+(assert (! (forall ((?v0 Nat$)) (= (= zero$a ?v0) (= ?v0 zero$a))) :named a122))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (=> (= (plus$a ?v0 ?v1) (plus$a ?v2 ?v1)) (= ?v0 ?v2))) :named a123))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (=> (= (plus$a ?v0 ?v1) (plus$a ?v0 ?v2)) (= ?v1 ?v2))) :named a124))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (plus$a ?v0 (plus$a ?v1 ?v2)) (plus$a ?v1 (plus$a ?v0 ?v2)))) :named a125))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (plus$a ?v0 ?v1) (plus$a ?v1 ?v0))) :named a126))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (plus$a (plus$a ?v0 ?v1) ?v2) (plus$a ?v0 (plus$a ?v1 ?v2)))) :named a127))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$) (?v3 Nat$)) (= (plus$a (plus$a ?v0 ?v1) (plus$a ?v2 ?v3)) (plus$a (plus$a ?v0 ?v2) (plus$a ?v1 ?v3)))) :named a128))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (plus$a (plus$a ?v0 ?v1) ?v2) (plus$a ?v0 (plus$a ?v1 ?v2)))) :named a129))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (plus$a ?v0 (plus$a ?v1 ?v2)) (plus$a ?v1 (plus$a ?v0 ?v2)))) :named a130))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (plus$a (plus$a ?v0 ?v1) ?v2) (plus$a (plus$a ?v0 ?v2) ?v1))) :named a131))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (plus$a ?v0 ?v1) (plus$a ?v1 ?v0))) :named a132))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (plus$a ?v0 (plus$a ?v1 ?v2)) (plus$a (plus$a ?v0 ?v1) ?v2))) :named a133))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$) (?v3 Nat$)) (=> (and (= ?v0 ?v1) (= ?v2 ?v3)) (= (plus$a ?v0 ?v2) (plus$a ?v1 ?v3)))) :named a134))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (plus$a (plus$a ?v0 ?v1) ?v2) (plus$a ?v0 (plus$a ?v1 ?v2)))) :named a135))
+(assert (! (forall ((?v0 Nat$)) (= (= one$ ?v0) (= ?v0 one$))) :named a136))
+(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (= (= ?v0 (plus$ ?v0 ?v1)) (= ?v1 zero$))) :named a137))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (= ?v0 (plus$c ?v0 ?v1)) (= ?v1 zero$c))) :named a138))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= ?v0 (plus$a ?v0 ?v1)) (= ?v1 zero$a))) :named a139))
+(assert (! (forall ((?v0 Complex$)) (= (plus$ zero$ ?v0) ?v0)) :named a140))
+(assert (! (forall ((?v0 Complex_poly$)) (= (plus$c zero$c ?v0) ?v0)) :named a141))
+(assert (! (forall ((?v0 Complex$)) (= (plus$ ?v0 zero$) ?v0)) :named a142))
+(assert (! (forall ((?v0 Complex_poly$)) (= (plus$c ?v0 zero$c) ?v0)) :named a143))
+(assert (! (forall ((?v0 Nat$)) (= (plus$a ?v0 zero$a) ?v0)) :named a144))
+(assert (! (forall ((?v0 Complex$)) (= (plus$ zero$ ?v0) ?v0)) :named a145))
+(assert (! (forall ((?v0 Complex_poly$)) (= (plus$c zero$c ?v0) ?v0)) :named a146))
+(assert (! (forall ((?v0 Nat$)) (= (plus$a zero$a ?v0) ?v0)) :named a147))
+(assert (! (forall ((?v0 Complex$)) (= (plus$ zero$ ?v0) ?v0)) :named a148))
+(assert (! (forall ((?v0 Complex_poly$)) (= (plus$c zero$c ?v0) ?v0)) :named a149))
+(assert (! (forall ((?v0 Nat$)) (= (plus$a zero$a ?v0) ?v0)) :named a150))
+(assert (! (forall ((?v0 Complex$)) (= (plus$ ?v0 zero$) ?v0)) :named a151))
+(assert (! (forall ((?v0 Complex_poly$)) (= (plus$c ?v0 zero$c) ?v0)) :named a152))
+(assert (! (forall ((?v0 Nat$)) (= (plus$a ?v0 zero$a) ?v0)) :named a153))
+(assert (! (forall ((?v0 Complex_poly$)) (= (power$ ?v0 one$) ?v0)) :named a154))
+(assert (! (forall ((?v0 Nat$)) (= (power$c ?v0 one$) ?v0)) :named a155))
+(assert (! (forall ((?v0 Nat$)) (= (poly_cutoff$ ?v0 one$a) (ite (= ?v0 zero$a) zero$c one$a))) :named a156))
+(assert (! (forall ((?v0 Nat$)) (= (plus$a ?v0 zero$a) ?v0)) :named a157))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (plus$a ?v0 ?v1) zero$a) (and (= ?v0 zero$a) (= ?v1 zero$a)))) :named a158))
+(assert (! (forall ((?v0 Nat$)) (= (poly_shift$ ?v0 one$a) (ite (= ?v0 zero$a) one$a zero$c))) :named a159))
+(assert (! (not (= zero$ one$b)) :named a160))
+(assert (! (not (= zero$c one$a)) :named a161))
+(assert (! (not (= zero$a one$)) :named a162))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$)) (= (= (synthetic_div$ ?v0 ?v1) zero$c) (= (degree$b ?v0) zero$a))) :named a163))
+(assert (! (= (of_bool$ false) zero$) :named a164))
+(assert (! (= (of_bool$a false) zero$c) :named a165))
+(assert (! (= (of_bool$b false) zero$a) :named a166))
+(assert (! (= (of_bool$b true) one$) :named a167))
+(assert (! (forall ((?v0 Complex$)) (= (synthetic_div$ zero$c ?v0) zero$c)) :named a168))
+(assert (! (forall ((?v0 Nat$)) (= (poly_shift$ ?v0 zero$c) zero$c)) :named a169))
+(assert (! (forall ((?v0 Nat$)) (= (poly_cutoff$ ?v0 zero$c) zero$c)) :named a170))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (= (plus$a ?v0 ?v1) (plus$a ?v0 ?v2)) (= ?v1 ?v2))) :named a171))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (= (plus$a ?v0 ?v1) (plus$a ?v2 ?v1)) (= ?v0 ?v2))) :named a172))
+(assert (! (forall ((?v0 Bool)) (! (= (of_bool$ ?v0) (ite ?v0 one$b zero$)) :pattern ((of_bool$ ?v0)))) :named a173))
+(assert (! (forall ((?v0 Bool)) (! (= (of_bool$a ?v0) (ite ?v0 one$a zero$c)) :pattern ((of_bool$a ?v0)))) :named a174))
+(assert (! (forall ((?v0 Bool)) (! (= (of_bool$b ?v0) (ite ?v0 one$ zero$a)) :pattern ((of_bool$b ?v0)))) :named a175))
+(assert (! (forall ((?v0 (-> Complex$ Bool)) (?v1 Bool)) (= (?v0 (of_bool$ ?v1)) (and (=> ?v1 (?v0 one$b)) (=> (not ?v1) (?v0 zero$))))) :named a176))
+(assert (! (forall ((?v0 (-> Complex_poly$ Bool)) (?v1 Bool)) (= (?v0 (of_bool$a ?v1)) (and (=> ?v1 (?v0 one$a)) (=> (not ?v1) (?v0 zero$c))))) :named a177))
+(assert (! (forall ((?v0 (-> Nat$ Bool)) (?v1 Bool)) (= (?v0 (of_bool$b ?v1)) (and (=> ?v1 (?v0 one$)) (=> (not ?v1) (?v0 zero$a))))) :named a178))
+(assert (! (forall ((?v0 (-> Complex$ Bool)) (?v1 Bool)) (= (?v0 (of_bool$ ?v1)) (not (or (and ?v1 (not (?v0 one$b))) (and (not ?v1) (not (?v0 zero$))))))) :named a179))
+(assert (! (forall ((?v0 (-> Complex_poly$ Bool)) (?v1 Bool)) (= (?v0 (of_bool$a ?v1)) (not (or (and ?v1 (not (?v0 one$a))) (and (not ?v1) (not (?v0 zero$c))))))) :named a180))
+(assert (! (forall ((?v0 (-> Nat$ Bool)) (?v1 Bool)) (= (?v0 (of_bool$b ?v1)) (not (or (and ?v1 (not (?v0 one$))) (and (not ?v1) (not (?v0 zero$a))))))) :named a181))
+(assert (! (forall ((?v0 Nat$)) (= (plus$a zero$a ?v0) ?v0)) :named a182))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (=> (= (plus$a ?v0 ?v1) ?v0) (= ?v1 zero$a))) :named a183))
+(assert (! (forall ((?v0 Nat$)) (=> (and (=> (= ?v0 zero$a) false) (=> (not (= ?v0 zero$a)) false)) false)) :named a184))
+(assert (! (forall ((?v0 (-> Nat$ (-> Nat$ Bool))) (?v1 Nat$) (?v2 Nat$)) (=> (and (forall ((?v3 Nat$) (?v4 Nat$)) (= (?v0 ?v3 ?v4) (?v0 ?v4 ?v3))) (and (forall ((?v3 Nat$)) (?v0 ?v3 zero$a)) (forall ((?v3 Nat$) (?v4 Nat$)) (=> (?v0 ?v3 ?v4) (?v0 ?v3 (plus$a ?v3 ?v4)))))) (?v0 ?v1 ?v2))) :named a185))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (forall ((?v2 Complex$)) (=> (= (poly$ ?v0 ?v2) zero$) (= (poly$ ?v1 ?v2) zero$))) (or (dvd$ ?v0 (power$ ?v1 (degree$b ?v0))) (and (= ?v0 zero$c) (= ?v1 zero$c))))) :named a186))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$) (?v2 Nat$)) (=> (and (forall ((?v3 Complex$)) (=> (= (poly$ ?v0 ?v3) zero$) (= (poly$ ?v1 ?v3) zero$))) (and (= (degree$b ?v0) ?v2) (not (= ?v2 zero$a)))) (dvd$ ?v0 (power$ ?v1 ?v2)))) :named a187))
+(assert (! (forall ((?v0 Complex_poly$)) (! (= (is_zero$ ?v0) (= ?v0 zero$c)) :pattern ((is_zero$ ?v0)))) :named a188))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$)) (= (= (poly$ ?v0 ?v1) zero$) (or (= ?v0 zero$c) (not (= (order$ ?v1 ?v0) zero$a))))) :named a189))
+(assert (! (forall ((?v0 Complex_poly_poly$) (?v1 Complex_poly$)) (= (= (poly$a ?v0 ?v1) zero$c) (or (= ?v0 zero$b) (not (= (order$a ?v1 ?v0) zero$a))))) :named a190))
+(assert (! (forall ((?v0 Complex$)) (dvd$a ?v0 zero$)) :named a191))
+(assert (! (forall ((?v0 Complex_poly$)) (dvd$ ?v0 zero$c)) :named a192))
+(assert (! (forall ((?v0 Nat$)) (dvd$b ?v0 zero$a)) :named a193))
+(assert (! (forall ((?v0 Complex$)) (= (dvd$a zero$ ?v0) (= ?v0 zero$))) :named a194))
+(assert (! (forall ((?v0 Complex_poly$)) (= (dvd$ zero$c ?v0) (= ?v0 zero$c))) :named a195))
+(assert (! (forall ((?v0 Nat$)) (= (dvd$b zero$a ?v0) (= ?v0 zero$a))) :named a196))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (dvd$ ?v0 (plus$c ?v0 ?v1)) (dvd$ ?v0 ?v1))) :named a197))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (dvd$b ?v0 (plus$a ?v0 ?v1)) (dvd$b ?v0 ?v1))) :named a198))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (dvd$ ?v0 (plus$c ?v1 ?v0)) (dvd$ ?v0 ?v1))) :named a199))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (dvd$b ?v0 (plus$a ?v1 ?v0)) (dvd$b ?v0 ?v1))) :named a200))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (=> (not (= ?v0 zero$a)) (= (dvd$b (power$c ?v1 ?v0) (power$c ?v2 ?v0)) (dvd$b ?v1 ?v2)))) :named a201))
+(assert (! (forall ((?v0 Complex$)) (=> (dvd$a zero$ ?v0) (= ?v0 zero$))) :named a202))
+(assert (! (forall ((?v0 Complex_poly$)) (=> (dvd$ zero$c ?v0) (= ?v0 zero$c))) :named a203))
+(assert (! (forall ((?v0 Nat$)) (=> (dvd$b zero$a ?v0) (= ?v0 zero$a))) :named a204))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$) (?v2 Complex_poly$)) (=> (dvd$ ?v0 ?v1) (= (dvd$ ?v0 (plus$c ?v1 ?v2)) (dvd$ ?v0 ?v2)))) :named a205))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (=> (dvd$b ?v0 ?v1) (= (dvd$b ?v0 (plus$a ?v1 ?v2)) (dvd$b ?v0 ?v2)))) :named a206))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$) (?v2 Complex_poly$)) (=> (dvd$ ?v0 ?v1) (= (dvd$ ?v0 (plus$c ?v2 ?v1)) (dvd$ ?v0 ?v2)))) :named a207))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (=> (dvd$b ?v0 ?v1) (= (dvd$b ?v0 (plus$a ?v2 ?v1)) (dvd$b ?v0 ?v2)))) :named a208))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$) (?v2 Complex_poly$)) (=> (and (dvd$ ?v0 ?v1) (dvd$ ?v0 ?v2)) (dvd$ ?v0 (plus$c ?v1 ?v2)))) :named a209))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (=> (and (dvd$b ?v0 ?v1) (dvd$b ?v0 ?v2)) (dvd$b ?v0 (plus$a ?v1 ?v2)))) :named a210))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (=> (and (dvd$ ?v0 ?v1) (dvd$ ?v1 one$a)) (dvd$ ?v0 one$a))) :named a211))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (=> (and (dvd$b ?v0 ?v1) (dvd$b ?v1 one$)) (dvd$b ?v0 one$))) :named a212))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (=> (dvd$ ?v0 one$a) (dvd$ ?v0 ?v1))) :named a213))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (=> (dvd$b ?v0 one$) (dvd$b ?v0 ?v1))) :named a214))
+(assert (! (forall ((?v0 Complex_poly$)) (dvd$ one$a ?v0)) :named a215))
+(assert (! (forall ((?v0 Nat$)) (dvd$b one$ ?v0)) :named a216))
+(assert (! (forall ((?v0 Complex_poly$)) (dvd$ ?v0 ?v0)) :named a217))
+(assert (! (forall ((?v0 Nat$)) (dvd$b ?v0 ?v0)) :named a218))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$) (?v2 Complex_poly$)) (=> (and (dvd$ ?v0 ?v1) (dvd$ ?v1 ?v2)) (dvd$ ?v0 ?v2))) :named a219))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (=> (and (dvd$b ?v0 ?v1) (dvd$b ?v1 ?v2)) (dvd$b ?v0 ?v2))) :named a220))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$) (?v2 Nat$)) (=> (dvd$ ?v0 ?v1) (dvd$ (power$ ?v0 ?v2) (power$ ?v1 ?v2)))) :named a221))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (=> (dvd$b ?v0 ?v1) (dvd$b (power$c ?v0 ?v2) (power$c ?v1 ?v2)))) :named a222))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (=> (and (dvd$b (power$c ?v0 ?v1) (power$c ?v2 ?v1)) (not (= ?v1 zero$a))) (dvd$b ?v0 ?v2))) :named a223))
+(assert (! (not (dvd$ zero$c one$a)) :named a224))
+(assert (! (not (dvd$b zero$a one$)) :named a225))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$)) (= (dvd$ (power$ ?v0 ?v1) one$a) (or (dvd$ ?v0 one$a) (= ?v1 zero$a)))) :named a226))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (dvd$b (power$c ?v0 ?v1) one$) (or (dvd$b ?v0 one$) (= ?v1 zero$a)))) :named a227))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$)) (! (=> (not (= (poly$ ?v0 ?v1) zero$)) (= (order$ ?v1 ?v0) zero$a)) :pattern ((order$ ?v1 ?v0)))) :named a228))
+(assert (! (forall ((?v0 Complex_poly_poly$) (?v1 Complex_poly$)) (! (=> (not (= (poly$a ?v0 ?v1) zero$c)) (= (order$a ?v1 ?v0) zero$a)) :pattern ((order$a ?v1 ?v0)))) :named a229))
+(assert (! (forall ((?v0 Complex_poly$)) (=> (not (= ?v0 zero$c)) (= (dvd$ ?v0 one$a) (= (degree$b ?v0) zero$a)))) :named a230))
+(assert (! (forall ((?v0 Complex_poly$)) (= (rsquarefree$ ?v0) (and (not (= ?v0 zero$c)) (forall ((?v1 Complex$)) (or (= (order$ ?v1 ?v0) zero$a) (= (order$ ?v1 ?v0) one$)))))) :named a231))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$) (?v2 Complex_poly$)) (=> (not (= ?v0 zero$c)) (= (exists ((?v3 Complex$)) (and (= (poly$ (pCons$ ?v1 ?v0) ?v3) zero$) (not (= (poly$ ?v2 ?v3) zero$)))) (not (dvd$ (pCons$ ?v1 ?v0) (power$ ?v2 (psize$ ?v0))))))) :named a232))
+(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (! (= (dvd$a ?v0 ?v1) (=> (= ?v0 zero$) (= ?v1 zero$))) :pattern ((dvd$a ?v0 ?v1)))) :named a233))
+(assert (! (forall ((?v0 Complex_poly$)) (=> (dvd$ ?v0 one$a) (= (monom$ (coeff$b ?v0 (degree$b ?v0)) zero$a) ?v0))) :named a234))
+(assert (! (forall ((?v0 Nat$)) (= (dvd$b ?v0 one$) (= ?v0 one$))) :named a235))
+(assert (! (forall ((?v0 Complex$) (?v1 Complex_poly$) (?v2 Complex$) (?v3 Complex_poly$)) (= (= (pCons$ ?v0 ?v1) (pCons$ ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3)))) :named a236))
+(assert (! (= (pCons$ zero$ zero$c) zero$c) :named a237))
+(assert (! (= (pCons$a zero$c zero$b) zero$b) :named a238))
+(assert (! (= (pCons$b zero$a zero$d) zero$d) :named a239))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly_poly$)) (= (= (pCons$a ?v0 ?v1) zero$b) (and (= ?v0 zero$c) (= ?v1 zero$b)))) :named a240))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat_poly$)) (= (= (pCons$b ?v0 ?v1) zero$d) (and (= ?v0 zero$a) (= ?v1 zero$d)))) :named a241))
+(assert (! (forall ((?v0 Complex$) (?v1 Complex_poly$)) (= (= (pCons$ ?v0 ?v1) zero$c) (and (= ?v0 zero$) (= ?v1 zero$c)))) :named a242))
+(assert (! (forall ((?v0 Complex$) (?v1 Complex_poly$)) (= (coeff$b (pCons$ ?v0 ?v1) zero$a) ?v0)) :named a243))
+(assert (! (forall ((?v0 Nat$)) (= (monom$ zero$ ?v0) zero$c)) :named a244))
+(assert (! (forall ((?v0 Nat$)) (= (monom$a zero$c ?v0) zero$b)) :named a245))
+(assert (! (forall ((?v0 Nat$)) (= (monom$b zero$a ?v0) zero$d)) :named a246))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$)) (= (= (monom$a ?v0 ?v1) zero$b) (= ?v0 zero$c))) :named a247))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (monom$b ?v0 ?v1) zero$d) (= ?v0 zero$a))) :named a248))
+(assert (! (forall ((?v0 Complex$) (?v1 Nat$)) (= (= (monom$ ?v0 ?v1) zero$c) (= ?v0 zero$))) :named a249))
+(assert (! (forall ((?v0 Complex$) (?v1 Nat$) (?v2 Nat$)) (= (coeff$b (monom$ ?v0 ?v1) ?v2) (ite (= ?v1 ?v2) ?v0 zero$))) :named a250))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$) (?v2 Nat$)) (= (coeff$ (monom$a ?v0 ?v1) ?v2) (ite (= ?v1 ?v2) ?v0 zero$c))) :named a251))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (coeff$a (monom$b ?v0 ?v1) ?v2) (ite (= ?v1 ?v2) ?v0 zero$a))) :named a252))
+(assert (! (forall ((?v0 Complex$) (?v1 Complex_poly$) (?v2 Complex$) (?v3 Complex_poly$)) (= (plus$c (pCons$ ?v0 ?v1) (pCons$ ?v2 ?v3)) (pCons$ (plus$ ?v0 ?v2) (plus$c ?v1 ?v3)))) :named a253))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat_poly$) (?v2 Nat$) (?v3 Nat_poly$)) (= (plus$b (pCons$b ?v0 ?v1) (pCons$b ?v2 ?v3)) (pCons$b (plus$a ?v0 ?v2) (plus$b ?v1 ?v3)))) :named a254))
+(assert (! (forall ((?v0 Complex$) (?v1 Nat$)) (= (coeff$b (monom$ ?v0 ?v1) (degree$b (monom$ ?v0 ?v1))) ?v0)) :named a255))
+(assert (! (forall ((?v0 Complex$) (?v1 Nat$)) (=> (not (= ?v0 zero$)) (= (order$ zero$ (monom$ ?v0 ?v1)) ?v1))) :named a256))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$)) (=> (not (= ?v0 zero$c)) (= (order$a zero$c (monom$a ?v0 ?v1)) ?v1))) :named a257))
+(assert (! (forall ((?v0 Complex$) (?v1 Complex_poly$)) (= (pcompose$ (pCons$ ?v0 zero$c) ?v1) (pCons$ ?v0 zero$c))) :named a258))
+(assert (! (forall ((?v0 Complex$)) (= (reflect_poly$ (pCons$ ?v0 zero$c)) (pCons$ ?v0 zero$c))) :named a259))
+(assert (! (forall ((?v0 Complex$) (?v1 Complex_poly$) (?v2 Complex$)) (= (synthetic_div$ (pCons$ ?v0 ?v1) ?v2) (pCons$ (poly$ ?v1 ?v2) (synthetic_div$ ?v1 ?v2)))) :named a260))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$)) (=> (= ?v0 zero$c) (= (coeff$b (pCons$ ?v1 ?v0) (degree$b (pCons$ ?v1 ?v0))) ?v1))) :named a261))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$)) (=> (not (= ?v0 zero$c)) (= (coeff$b (pCons$ ?v1 ?v0) (degree$b (pCons$ ?v1 ?v0))) (coeff$b ?v0 (degree$b ?v0))))) :named a262))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (= (dvd$c (pCons$a ?v0 zero$b) (pCons$a ?v1 zero$b)) (dvd$ ?v0 ?v1))) :named a263))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (dvd$d (pCons$b ?v0 zero$d) (pCons$b ?v1 zero$d)) (dvd$b ?v0 ?v1))) :named a264))
+(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (= (dvd$ (pCons$ ?v0 zero$c) (pCons$ ?v1 zero$c)) (dvd$a ?v0 ?v1))) :named a265))
+(assert (! (= (= (pCons$b one$ zero$d) one$c) true) :named a266))
+(assert (! (= (= (pCons$ one$b zero$c) one$a) true) :named a267))
+(assert (! (= (= one$c (pCons$b one$ zero$d)) true) :named a268))
+(assert (! (= (= one$a (pCons$ one$b zero$c)) true) :named a269))
+(assert (! (= (monom$b one$ zero$a) one$c) :named a270))
+(assert (! (forall ((?v0 Complex_poly$)) (= (pcompose$ ?v0 (pCons$ zero$ (pCons$ one$b zero$c))) ?v0)) :named a271))
+(assert (! (forall ((?v0 Complex_poly_poly$)) (= (pcompose$a ?v0 (pCons$a zero$c (pCons$a one$a zero$b))) ?v0)) :named a272))
+(assert (! (forall ((?v0 Nat_poly$)) (= (pcompose$b ?v0 (pCons$b zero$a (pCons$b one$ zero$d))) ?v0)) :named a273))
+(assert (! (forall ((?v0 Nat$)) (=> (dvd$b zero$a ?v0) (= ?v0 zero$a))) :named a274))
+(assert (! (forall ((?v0 Nat$)) (= (not (= ?v0 zero$a)) (and (dvd$b ?v0 zero$a) (not (= ?v0 zero$a))))) :named a275))
+(assert (! (forall ((?v0 Nat$)) (! (= (dvd$b zero$a ?v0) (= ?v0 zero$a)) :pattern ((dvd$b zero$a ?v0)))) :named a276))
+(assert (! (forall ((?v0 Nat$)) (not (and (dvd$b zero$a ?v0) (not (= zero$a ?v0))))) :named a277))
+(assert (! (forall ((?v0 Nat$)) (dvd$b ?v0 zero$a)) :named a278))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$) (?v2 Complex_poly$)) (= (= (monom$a ?v0 ?v1) (pCons$a ?v2 zero$b)) (and (= ?v0 ?v2) (or (= ?v0 zero$c) (= ?v1 zero$a))))) :named a279))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (= (monom$b ?v0 ?v1) (pCons$b ?v2 zero$d)) (and (= ?v0 ?v2) (or (= ?v0 zero$a) (= ?v1 zero$a))))) :named a280))
+(assert (! (forall ((?v0 Complex$) (?v1 Nat$) (?v2 Complex$)) (= (= (monom$ ?v0 ?v1) (pCons$ ?v2 zero$c)) (and (= ?v0 ?v2) (or (= ?v0 zero$) (= ?v1 zero$a))))) :named a281))
+(assert (! (forall ((?v0 Complex_poly$)) (=> (forall ((?v1 Complex$) (?v2 Complex_poly$)) (=> (= ?v0 (pCons$ ?v1 ?v2)) false)) false)) :named a282))
+(assert (! (forall ((?v0 Complex_poly$)) (=> (forall ((?v1 Complex$) (?v2 Complex_poly$)) (=> (= ?v0 (pCons$ ?v1 ?v2)) false)) false)) :named a283))
+(assert (! (forall ((?v0 (-> Complex_poly$ (-> Complex_poly$ Bool))) (?v1 Complex_poly$) (?v2 Complex_poly$)) (=> (and (?v0 zero$c zero$c) (forall ((?v3 Complex$) (?v4 Complex_poly$) (?v5 Complex$) (?v6 Complex_poly$)) (=> (?v0 ?v4 ?v6) (?v0 (pCons$ ?v3 ?v4) (pCons$ ?v5 ?v6))))) (?v0 ?v1 ?v2))) :named a284))
+(assert (! (forall ((?v0 Complex$) (?v1 Nat$) (?v2 Complex$) (?v3 Nat$)) (= (= (monom$ ?v0 ?v1) (monom$ ?v2 ?v3)) (and (= ?v0 ?v2) (or (= ?v0 zero$) (= ?v1 ?v3))))) :named a285))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$) (?v2 Complex_poly$) (?v3 Nat$)) (= (= (monom$a ?v0 ?v1) (monom$a ?v2 ?v3)) (and (= ?v0 ?v2) (or (= ?v0 zero$c) (= ?v1 ?v3))))) :named a286))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$) (?v3 Nat$)) (= (= (monom$b ?v0 ?v1) (monom$b ?v2 ?v3)) (and (= ?v0 ?v2) (or (= ?v0 zero$a) (= ?v1 ?v3))))) :named a287))
+(assert (! (forall ((?v0 Complex$)) (! (= (monom$ ?v0 zero$a) (pCons$ ?v0 zero$c)) :pattern ((monom$ ?v0)))) :named a288))
+(assert (! (forall ((?v0 (-> Complex_poly_poly$ Bool)) (?v1 Complex_poly_poly$)) (=> (and (?v0 zero$b) (forall ((?v2 Complex_poly$) (?v3 Complex_poly_poly$)) (=> (and (or (not (= ?v2 zero$c)) (not (= ?v3 zero$b))) (?v0 ?v3)) (?v0 (pCons$a ?v2 ?v3))))) (?v0 ?v1))) :named a289))
+(assert (! (forall ((?v0 (-> Nat_poly$ Bool)) (?v1 Nat_poly$)) (=> (and (?v0 zero$d) (forall ((?v2 Nat$) (?v3 Nat_poly$)) (=> (and (or (not (= ?v2 zero$a)) (not (= ?v3 zero$d))) (?v0 ?v3)) (?v0 (pCons$b ?v2 ?v3))))) (?v0 ?v1))) :named a290))
+(assert (! (forall ((?v0 (-> Complex_poly$ Bool)) (?v1 Complex_poly$)) (=> (and (?v0 zero$c) (forall ((?v2 Complex$) (?v3 Complex_poly$)) (=> (and (or (not (= ?v2 zero$)) (not (= ?v3 zero$c))) (?v0 ?v3)) (?v0 (pCons$ ?v2 ?v3))))) (?v0 ?v1))) :named a291))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$)) (=> (= (poly$ ?v0 ?v1) zero$) (= (poly$ (pCons$ zero$ ?v0) ?v1) zero$))) :named a292))
+(assert (! (forall ((?v0 Complex_poly_poly$) (?v1 Complex_poly$)) (=> (= (poly$a ?v0 ?v1) zero$c) (= (poly$a (pCons$a zero$c ?v0) ?v1) zero$c))) :named a293))
+(assert (! (forall ((?v0 Nat_poly$) (?v1 Nat$)) (=> (= (poly$b ?v0 ?v1) zero$a) (= (poly$b (pCons$b zero$a ?v0) ?v1) zero$a))) :named a294))
+(assert (! (forall ((?v0 Complex$) (?v1 Nat$)) (=> (not (= ?v0 zero$)) (= (degree$b (monom$ ?v0 ?v1)) ?v1))) :named a295))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$)) (=> (not (= ?v0 zero$c)) (= (degree$ (monom$a ?v0 ?v1)) ?v1))) :named a296))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (=> (not (= ?v0 zero$a)) (= (degree$a (monom$b ?v0 ?v1)) ?v1))) :named a297))
+(assert (! (forall ((?v0 Complex$) (?v1 Nat$) (?v2 Nat$)) (= (coeff$b (monom$ ?v0 ?v1) ?v2) (ite (= ?v1 ?v2) ?v0 zero$))) :named a298))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Nat$) (?v2 Nat$)) (= (coeff$ (monom$a ?v0 ?v1) ?v2) (ite (= ?v1 ?v2) ?v0 zero$c))) :named a299))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (coeff$a (monom$b ?v0 ?v1) ?v2) (ite (= ?v1 ?v2) ?v0 zero$a))) :named a300))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly$)) (=> (dvd$ ?v0 ?v1) (dvd$ ?v0 (pCons$ zero$ ?v1)))) :named a301))
+(assert (! (forall ((?v0 Complex_poly_poly$) (?v1 Complex_poly_poly$)) (=> (dvd$c ?v0 ?v1) (dvd$c ?v0 (pCons$a zero$c ?v1)))) :named a302))
+(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (= (poly$ (pCons$ (poly$ zero$c ?v0) zero$c) ?v1) (poly$ zero$c ?v1))) :named a303))
+(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (= ?v0 (poly$ (pCons$ ?v0 zero$c) ?v1))) :named a304))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (plus$b (monom$b ?v0 ?v1) (monom$b ?v2 ?v1)) (monom$b (plus$a ?v0 ?v2) ?v1))) :named a305))
+(assert (! (forall ((?v0 Complex$) (?v1 Complex$)) (= (offset_poly$ (pCons$ ?v0 zero$c) ?v1) (pCons$ ?v0 zero$c))) :named a306))
+(assert (! (forall ((?v0 Complex_poly$)) (= (exists ((?v1 Complex_poly$)) (= (poly$a (pCons$a ?v0 zero$b) ?v1) zero$c)) (= ?v0 zero$c))) :named a307))
+(assert (! (forall ((?v0 Nat$)) (= (exists ((?v1 Nat$)) (= (poly$b (pCons$b ?v0 zero$d) ?v1) zero$a)) (= ?v0 zero$a))) :named a308))
+(assert (! (forall ((?v0 Complex$)) (= (exists ((?v1 Complex$)) (= (poly$ (pCons$ ?v0 zero$c) ?v1) zero$)) (= ?v0 zero$))) :named a309))
+(assert (! (forall ((?v0 Complex_poly$)) (= (exists ((?v1 Complex_poly$)) (not (= (poly$a (pCons$a ?v0 zero$b) ?v1) zero$c))) (not (= ?v0 zero$c)))) :named a310))
+(assert (! (forall ((?v0 Nat$)) (= (exists ((?v1 Nat$)) (not (= (poly$b (pCons$b ?v0 zero$d) ?v1) zero$a))) (not (= ?v0 zero$a)))) :named a311))
+(assert (! (forall ((?v0 Complex$)) (= (exists ((?v1 Complex$)) (not (= (poly$ (pCons$ ?v0 zero$c) ?v1) zero$))) (not (= ?v0 zero$)))) :named a312))
+(assert (! (forall ((?v0 Complex$)) (= (poly$ (pCons$ zero$ zero$c) ?v0) (poly$ zero$c ?v0))) :named a313))
+(assert (! (forall ((?v0 Complex_poly$)) (= (poly$a (pCons$a zero$c zero$b) ?v0) (poly$a zero$b ?v0))) :named a314))
+(assert (! (forall ((?v0 Complex$)) (= (degree$b (pCons$ ?v0 zero$c)) zero$a)) :named a315))
+(assert (! (forall ((?v0 Complex_poly$)) (=> (and (= (degree$b ?v0) zero$a) (forall ((?v1 Complex$)) (=> (= ?v0 (pCons$ ?v1 zero$c)) false))) false)) :named a316))
+(assert (! (= (pCons$b one$ zero$d) one$c) :named a317))
+(assert (! (= (pCons$ one$b zero$c) one$a) :named a318))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (monom$b ?v0 ?v1) one$c) (and (= ?v0 one$) (= ?v1 zero$a)))) :named a319))
+(assert (! (forall ((?v0 Complex$)) (= ?v0 (poly$ (pCons$ zero$ (pCons$ one$b zero$c)) ?v0))) :named a320))
+(assert (! (forall ((?v0 Complex_poly$)) (= ?v0 (poly$a (pCons$a zero$c (pCons$a one$a zero$b)) ?v0))) :named a321))
+(assert (! (forall ((?v0 Complex_poly$)) (=> (not (exists ((?v1 Complex$) (?v2 Complex_poly$)) (and (not (= ?v1 zero$)) (and (= ?v2 zero$c) (= ?v0 (pCons$ ?v1 ?v2)))))) (exists ((?v1 Complex$)) (= (poly$ ?v0 ?v1) zero$)))) :named a322))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex$) (?v2 Complex$)) (=> (not (= ?v0 zero$c)) (exists ((?v3 Complex$)) (= (poly$ (pCons$ ?v1 (pCons$ ?v2 ?v0)) ?v3) zero$)))) :named a323))
+(assert (! (forall ((?v0 Complex_poly$) (?v1 Complex_poly_poly$)) (= (dvd$c (pCons$a ?v0 zero$b) ?v1) (forall ((?v2 Nat$)) (dvd$ ?v0 (coeff$ ?v1 ?v2))))) :named a324))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat_poly$)) (= (dvd$d (pCons$b ?v0 zero$d) ?v1) (forall ((?v2 Nat$)) (dvd$b ?v0 (coeff$a ?v1 ?v2))))) :named a325))
+(assert (! (forall ((?v0 Complex$) (?v1 Complex_poly$)) (= (dvd$ (pCons$ ?v0 zero$c) ?v1) (forall ((?v2 Nat$)) (dvd$a ?v0 (coeff$b ?v1 ?v2))))) :named a326))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (degree$a (power$b (pCons$b ?v0 (pCons$b one$ zero$d)) ?v1)) ?v1)) :named a327))
+(assert (! (forall ((?v0 Complex$) (?v1 Nat$)) (= (degree$b (power$ (pCons$ ?v0 (pCons$ one$b zero$c)) ?v1)) ?v1)) :named a328))
+(assert (! (forall ((?v0 Complex_poly$)) (= (pcompose$ ?v0 zero$c) (pCons$ (coeff$b ?v0 zero$a) zero$c))) :named a329))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (coeff$a (power$b (pCons$b ?v0 (pCons$b one$ zero$d)) ?v1) ?v1) one$)) :named a330))
+(assert (! (forall ((?v0 Complex$) (?v1 Nat$)) (= (coeff$b (power$ (pCons$ ?v0 (pCons$ one$b zero$c)) ?v1) ?v1) one$b)) :named a331))
+(assert (! (forall ((?v0 Complex$) (?v1 Complex_poly$)) (= (dvd$ (pCons$ ?v0 ?v1) one$a) (and (= ?v1 zero$c) (not (= ?v0 zero$))))) :named a332))
+(assert (! (forall ((?v0 Complex$)) (=> (not (= ?v0 zero$)) (dvd$ (pCons$ ?v0 zero$c) one$a))) :named a333))
+(assert (! (forall ((?v0 Complex_poly$)) (=> (and (dvd$ ?v0 one$a) (forall ((?v1 Complex$)) (=> (and (= ?v0 (monom$ ?v1 zero$a)) (not (= ?v1 zero$))) false))) false)) :named a334))
+(assert (! (forall ((?v0 Complex$)) (=> (not (= ?v0 zero$)) (dvd$ (monom$ ?v0 zero$a) one$a))) :named a335))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (= (times$ ?v0 ?v1) (times$ ?v2 ?v1)) (or (= ?v0 ?v2) (= ?v1 zero$a)))) :named a336))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (= (times$ ?v0 ?v1) (times$ ?v0 ?v2)) (or (= ?v1 ?v2) (= ?v0 zero$a)))) :named a337))
+(assert (! (forall ((?v0 Nat$)) (! (= (times$ ?v0 zero$a) zero$a) :pattern ((times$ ?v0)))) :named a338))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (times$ ?v0 ?v1) zero$a) (or (= ?v0 zero$a) (= ?v1 zero$a)))) :named a339))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (suc$ ?v0) (suc$ ?v1)) (= ?v0 ?v1))) :named a340))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (suc$ ?v0) (suc$ ?v1)) (= ?v0 ?v1))) :named a341))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (times$ ?v0 ?v1) one$) (and (= ?v0 one$) (= ?v1 one$)))) :named a342))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= one$ (times$ ?v0 ?v1)) (and (= ?v0 one$) (= ?v1 one$)))) :named a343))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (times$ ?v0 ?v1) (suc$ zero$a)) (and (= ?v0 (suc$ zero$a)) (= ?v1 (suc$ zero$a))))) :named a344))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (suc$ zero$a) (times$ ?v0 ?v1)) (and (= ?v0 (suc$ zero$a)) (= ?v1 (suc$ zero$a))))) :named a345))
+(assert (! (forall ((?v0 Nat$)) (! (= (power$c (suc$ zero$a) ?v0) (suc$ zero$a)) :pattern ((power$c (suc$ zero$a) ?v0)))) :named a346))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (= (power$c ?v0 ?v1) (suc$ zero$a)) (or (= ?v1 zero$a) (= ?v0 (suc$ zero$a))))) :named a347))
+(assert (! (forall ((?v0 Nat$)) (less_eq$ zero$a ?v0)) :named a348))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (less_eq$ (suc$ ?v0) (suc$ ?v1)) (less_eq$ ?v0 ?v1))) :named a349))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (= (plus$a ?v0 (suc$ ?v1)) (suc$ (plus$a ?v0 ?v1)))) :named a350))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$)) (! (= (times$ ?v0 (suc$ ?v1)) (plus$a ?v0 (times$ ?v0 ?v1))) :pattern ((times$ ?v0 (suc$ ?v1))))) :named a351))
+(assert (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (= (less_eq$ (plus$a ?v0 ?v1) (plus$a ?v0 ?v2)) (less_eq$ ?v1 ?v2))) :named a352))
+(check-sat)

diff --git a/test/regress/regress2/ho/involved_parsing_ALG248^3.p b/test/regress/regress2/ho/involved_parsing_ALG248^3.p
new file mode 100644 (file)
index 0000000..5ad6936
--- /dev/null
+++ b/test/regress/regress2/ho/involved_parsing_ALG248^3.p
@@ -0,0 +1,2126 @@
+% COMMAND-LINE:  --uf-ho
+% EXPECT: % SZS status Theorem for involved_parsing_ALG248^3
+
+%------------------------------------------------------------------------------
+% File     : ALG248^3 : TPTP v7.2.0. Bugfixed v5.2.0.
+% Domain   : Algebra
+% Problem  : Push property lemma 1
+% Version  : [Bro09] axioms : Reduced > Especial.
+% English  :
+
+% Refs     : [DHK95] Dowek et al. (1995), Higher-order Unification via Expl
+%          : [Zha08] Zhang (2008), Using LEO-II to Prove Properties of an E
+%          : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
+%          : [Bro09] Brown (2009), M-Set Models
+% Source   : [Ben09]
+% Names    : pushprop_lem1v2_lthm [Ben09]
+
+% Status   : Theorem
+% Rating   : 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0
+% Syntax   : Number of formulae    :  238 (   1 unit; 124 type; 113 defn)
+%            Number of atoms       : 2372 ( 161 equality; 723 variable)
+%            Maximal formula depth :   39 (   8 average)
+%            Number of connectives : 1942 (   6   ~;   0   |;   4   &; 916   @)
+%                                         (   2 <=>;1014  =>;   0  <=;   0 <~>)
+%                                         (   0  ~|;   0  ~&)
+%            Number of type conns  :  128 ( 128   >;   0   *;   0   +;   0  <<)
+%            Number of symbols     :  126 ( 124   :;   0   =)
+%            Number of variables   :  327 (   3 sgn; 283   !;   5   ?;  39   ^)
+%                                         ( 327   :;   0  !>;   0  ?*)
+%                                         (   0  @-;   0  @+)
+% SPC      : TH0_THM_EQU_NAR
+
+% Comments :
+% Bugfixes : v5.2.0 - Bugfixes in ALG003^0.ax
+%------------------------------------------------------------------------------
+%----Include Untyped Lambda Sigma defs
+%% include('Axioms/ALG003^0.ax').
+%------------------------------------------------------------------------------
+thf(term_type,type,(
+    term: $tType )).
+
+thf(subst_type,type,(
+    subst: $tType )).
+
+thf(one_type,type,(
+    one: term )).
+
+thf(ap_type,type,(
+    ap: term > term > term )).
+
+thf(lam_type,type,(
+    lam: term > term )).
+
+thf(sub_type,type,(
+    sub: term > subst > term )).
+
+thf(id_type,type,(
+    id: subst )).
+
+thf(sh_type,type,(
+    sh: subst )).
+
+thf(push_type,type,(
+    push: term > subst > subst )).
+
+thf(comp_type,type,(
+    comp: subst > subst > subst )).
+
+thf(var_type,type,(
+    var: term > $o )).
+
+thf(pushprop_lem1v2_type,type,(
+    pushprop_lem1v2: $o )).
+
+thf(pushprop_lem1_gthm_type,type,(
+    pushprop_lem1_gthm: $o )).
+
+thf(axmap_type,type,(
+    axmap: $o )).
+
+thf(pushprop_lem0_gthm_type,type,(
+    pushprop_lem0_gthm: $o )).
+
+thf(shinj_type,type,(
+    shinj: $o )).
+
+thf(hoasinduction_lem1v2_type,type,(
+    hoasinduction_lem1v2: $o )).
+
+thf(hoasinduction_lem1v2_gthm_type,type,(
+    hoasinduction_lem1v2_gthm: $o )).
+
+thf(hoasap_type,type,(
+    hoasap: subst > term > subst > term > term )).
+
+thf(induction2lem_type,type,(
+    induction2lem: $o )).
+
+thf(hoasinduction_lem3v2_f_type,type,(
+    hoasinduction_lem3v2_f: $o )).
+
+thf(axvarshift_type,type,(
+    axvarshift: $o )).
+
+thf(hoasapinj2_type,type,(
+    hoasapinj2: $o )).
+
+thf(hoasapnotvar_gthm_type,type,(
+    hoasapnotvar_gthm: $o )).
+
+thf(hoasapinj1_type,type,(
+    hoasapinj1: $o )).
+
+thf(ulamvar1_type,type,(
+    ulamvar1: $o )).
+
+thf(induction2lem_lthm_type,type,(
+    induction2lem_lthm: $o )).
+
+thf(hoasinduction_lem3v2_gthm_type,type,(
+    hoasinduction_lem3v2_gthm: $o )).
+
+thf(apnotvar_type,type,(
+    apnotvar: $o )).
+
+thf(pushprop_lthm_orig_type,type,(
+    pushprop_lthm_orig: $o )).
+
+thf(hoasinduction_lem3v2_f_lthm_type,type,(
+    hoasinduction_lem3v2_f_lthm: $o )).
+
+thf(hoasinduction_lthm_type,type,(
+    hoasinduction_lthm: $o )).
+
+thf(hoasinduction_no_psi_cond_lthm_type,type,(
+    hoasinduction_no_psi_cond_lthm: $o )).
+
+thf(hoaslaminj_type,type,(
+    hoaslaminj: $o )).
+
+thf(hoasinduction_lem3aaa_type,type,(
+    hoasinduction_lem3aaa: $o )).
+
+thf(induction2lem_gthm_type,type,(
+    induction2lem_gthm: $o )).
+
+thf(hoasinduction_lem3aa_lthm_type,type,(
+    hoasinduction_lem3aa_lthm: $o )).
+
+thf(hoasinduction_lem3_type,type,(
+    hoasinduction_lem3: $o )).
+
+thf(hoasinduction_lem2_type,type,(
+    hoasinduction_lem2: $o )).
+
+thf(termmset_lthm_type,type,(
+    termmset_lthm: $o )).
+
+thf(hoasinduction_lem1_type,type,(
+    hoasinduction_lem1: $o )).
+
+thf(hoaslamnotap_lthm_type,type,(
+    hoaslamnotap_lthm: $o )).
+
+thf(pushprop_lem1v2_lthm_type,type,(
+    pushprop_lem1v2_lthm: $o )).
+
+thf(hoasapnotvar_type,type,(
+    hoasapnotvar: $o )).
+
+thf(hoasinduction_lem0_type,type,(
+    hoasinduction_lem0: $o )).
+
+thf(hoasinduction_type,type,(
+    hoasinduction: $o )).
+
+thf(hoasinduction_gthm_type,type,(
+    hoasinduction_gthm: $o )).
+
+thf(axapp_type,type,(
+    axapp: $o )).
+
+thf(hoaslamnotvar_lthm_type,type,(
+    hoaslamnotvar_lthm: $o )).
+
+thf(pushprop_lem3v2_lthm_type,type,(
+    pushprop_lem3v2_lthm: $o )).
+
+thf(hoasinduction_lem3b_lthm_type,type,(
+    hoasinduction_lem3b_lthm: $o )).
+
+thf(ulamvarind_type,type,(
+    ulamvarind: $o )).
+
+thf(induction_type,type,(
+    induction: $o )).
+
+thf(hoasinduction_lem3a_lthm_type,type,(
+    hoasinduction_lem3a_lthm: $o )).
+
+thf(termmset_gthm_type,type,(
+    termmset_gthm: $o )).
+
+thf(hoasinduction_lem3aa_type,type,(
+    hoasinduction_lem3aa: $o )).
+
+thf(pushprop_lem1v2_gthm_type,type,(
+    pushprop_lem1v2_gthm: $o )).
+
+thf(hoaslamnotap_gthm_type,type,(
+    hoaslamnotap_gthm: $o )).
+
+thf(hoaslamnotvar_gthm_type,type,(
+    hoaslamnotvar_gthm: $o )).
+
+thf(hoasinduction_lem3b_gthm_type,type,(
+    hoasinduction_lem3b_gthm: $o )).
+
+thf(pushprop_lem2v2_type,type,(
+    pushprop_lem2v2: $o )).
+
+thf(hoasinduction_lem3a_gthm_type,type,(
+    hoasinduction_lem3a_gthm: $o )).
+
+thf(axclos_type,type,(
+    axclos: $o )).
+
+thf(axassoc_type,type,(
+    axassoc: $o )).
+
+thf(hoasinduction_lem2v2_type,type,(
+    hoasinduction_lem2v2: $o )).
+
+thf(pushprop_lthm_type,type,(
+    pushprop_lthm: $o )).
+
+thf(apinj2_type,type,(
+    apinj2: $o )).
+
+thf(apinj1_type,type,(
+    apinj1: $o )).
+
+thf(hoasapinj2_lthm_type,type,(
+    hoasapinj2_lthm: $o )).
+
+thf(hoasinduction_lem3v2a_type,type,(
+    hoasinduction_lem3v2a: $o )).
+
+thf(hoasapinj1_lthm_type,type,(
+    hoasapinj1_lthm: $o )).
+
+thf(hoaslaminj_lthm_type,type,(
+    hoaslaminj_lthm: $o )).
+
+thf(axvarcons_type,type,(
+    axvarcons: $o )).
+
+thf(hoaslam_type,type,(
+    hoaslam: subst > ( subst > term > term ) > term )).
+
+thf(axscons_type,type,(
+    axscons: $o )).
+
+thf(hoasinduction_lem2v2_gthm_type,type,(
+    hoasinduction_lem2v2_gthm: $o )).
+
+thf(axidr_type,type,(
+    axidr: $o )).
+
+thf(pushprop_lem1_type,type,(
+    pushprop_lem1: $o )).
+
+thf(laminj_type,type,(
+    laminj: $o )).
+
+thf(hoasinduction_lem3_lthm_type,type,(
+    hoasinduction_lem3_lthm: $o )).
+
+thf(pushprop_lem0_type,type,(
+    pushprop_lem0: $o )).
+
+thf(pushprop_gthm_type,type,(
+    pushprop_gthm: $o )).
+
+thf(axabs_type,type,(
+    axabs: $o )).
+
+thf(hoasinduction_lem3v2a_lthm_type,type,(
+    hoasinduction_lem3v2a_lthm: $o )).
+
+thf(hoasinduction_lem2_lthm_type,type,(
+    hoasinduction_lem2_lthm: $o )).
+
+thf(hoasapinj2_gthm_type,type,(
+    hoasapinj2_gthm: $o )).
+
+thf(hoasinduction_p_and_p_prime_type,type,(
+    hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o )).
+
+thf(hoasinduction_lem1_lthm_type,type,(
+    hoasinduction_lem1_lthm: $o )).
+
+thf(lamnotap_type,type,(
+    lamnotap: $o )).
+
+thf(hoasapinj1_gthm_type,type,(
+    hoasapinj1_gthm: $o )).
+
+thf(hoaslamnotvar_type,type,(
+    hoaslamnotvar: $o )).
+
+thf(axidl_type,type,(
+    axidl: $o )).
+
+thf(hoaslaminj_gthm_type,type,(
+    hoaslaminj_gthm: $o )).
+
+thf(induction2_lthm_type,type,(
+    induction2_lthm: $o )).
+
+thf(hoasinduction_lem0_lthm_type,type,(
+    hoasinduction_lem0_lthm: $o )).
+
+thf(substmonoid_lthm_type,type,(
+    substmonoid_lthm: $o )).
+
+thf(pushprop_type,type,(
+    pushprop: $o )).
+
+thf(hoasinduction_lem3_gthm_type,type,(
+    hoasinduction_lem3_gthm: $o )).
+
+thf(hoasinduction_lem2_gthm_type,type,(
+    hoasinduction_lem2_gthm: $o )).
+
+thf(hoasinduction_lem3b_type,type,(
+    hoasinduction_lem3b: $o )).
+
+thf(substmonoid_type,type,(
+    substmonoid: $o )).
+
+thf(lamnotvar_type,type,(
+    lamnotvar: $o )).
+
+thf(hoasinduction_lem3a_type,type,(
+    hoasinduction_lem3a: $o )).
+
+thf(hoasinduction_lem1_gthm_type,type,(
+    hoasinduction_lem1_gthm: $o )).
+
+thf(hoasinduction_no_psi_cond_type,type,(
+    hoasinduction_no_psi_cond: $o )).
+
+thf(induction2_gthm_type,type,(
+    induction2_gthm: $o )).
+
+thf(pushprop_lem2v2_lthm_type,type,(
+    pushprop_lem2v2_lthm: $o )).
+
+thf(hoasvar_type,type,(
+    hoasvar: subst > term > subst > $o )).
+
+thf(hoaslamnotap_type,type,(
+    hoaslamnotap: $o )).
+
+thf(substmonoid_gthm_type,type,(
+    substmonoid_gthm: $o )).
+
+thf(ulamvarsh_type,type,(
+    ulamvarsh: $o )).
+
+thf(induction2_type,type,(
+    induction2: $o )).
+
+thf(pushprop_lem3v2_type,type,(
+    pushprop_lem3v2: $o )).
+
+thf(pushprop_lem2v2_gthm_type,type,(
+    pushprop_lem2v2_gthm: $o )).
+
+thf(pushprop_lem1_lthm_type,type,(
+    pushprop_lem1_lthm: $o )).
+
+thf(hoasinduction_lem3v2_type,type,(
+    hoasinduction_lem3v2: $o )).
+
+thf(axshiftcons_type,type,(
+    axshiftcons: $o )).
+
+thf(termmset_type,type,(
+    termmset: $o )).
+
+thf(pushprop_lem0_lthm_type,type,(
+    pushprop_lem0_lthm: $o )).
+
+thf(hoasapnotvar_lthm_type,type,(
+    hoasapnotvar_lthm: $o )).
+
+thf(hoasinduction_lem3v2_lthm_type,type,(
+    hoasinduction_lem3v2_lthm: $o )).
+
+thf(pushprop_p_and_p_prime_type,type,(
+    pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o )).
+
+thf(axvarid_type,type,(
+    axvarid: $o )).
+
+thf(hoasinduction_lthm_3_type,type,(
+    hoasinduction_lthm_3: $o )).
+
+thf(axapp,definition,
+    ( axapp
+    = ( ! [A: term,B: term,M: subst] :
+          ( ( sub @ ( ap @ A @ B ) @ M )
+          = ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ) ) )).
+
+thf(axvarcons,definition,
+    ( axvarcons
+    = ( ! [A: term,M: subst] :
+          ( ( sub @ one @ ( push @ A @ M ) )
+          = A ) ) )).
+
+thf(axvarid,definition,
+    ( axvarid
+    = ( ! [A: term] :
+          ( ( sub @ A @ id )
+          = A ) ) )).
+
+thf(axabs,definition,
+    ( axabs
+    = ( ! [A: term,M: subst] :
+          ( ( sub @ ( lam @ A ) @ M )
+          = ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) ) )).
+
+thf(axclos,definition,
+    ( axclos
+    = ( ! [A: term,M: subst,N: subst] :
+          ( ( sub @ ( sub @ A @ M ) @ N )
+          = ( sub @ A @ ( comp @ M @ N ) ) ) ) )).
+
+thf(axidl,definition,
+    ( axidl
+    = ( ! [M: subst] :
+          ( ( comp @ id @ M )
+          = M ) ) )).
+
+thf(axshiftcons,definition,
+    ( axshiftcons
+    = ( ! [A: term,M: subst] :
+          ( ( comp @ sh @ ( push @ A @ M ) )
+          = M ) ) )).
+
+thf(axassoc,definition,
+    ( axassoc
+    = ( ! [M: subst,N: subst,K: subst] :
+          ( ( comp @ ( comp @ M @ N ) @ K )
+          = ( comp @ M @ ( comp @ N @ K ) ) ) ) )).
+
+thf(axmap,definition,
+    ( axmap
+    = ( ! [A: term,M: subst,N: subst] :
+          ( ( comp @ ( push @ A @ M ) @ N )
+          = ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ) ) )).
+
+thf(axidr,definition,
+    ( axidr
+    = ( ! [M: subst] :
+          ( ( comp @ M @ id )
+          = M ) ) )).
+
+thf(axvarshift,definition,
+    ( axvarshift
+    = ( ( push @ one @ sh )
+      = id ) )).
+
+thf(axscons,definition,
+    ( axscons
+    = ( ! [M: subst] :
+          ( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
+          = M ) ) )).
+
+thf(ulamvar1,definition,
+    ( ulamvar1
+    = ( var @ one ) )).
+
+thf(ulamvarsh,definition,
+    ( ulamvarsh
+    = ( ! [A: term] :
+          ( ( var @ A )
+         => ( var @ ( sub @ A @ sh ) ) ) ) )).
+
+thf(ulamvarind,definition,
+    ( ulamvarind
+    = ( ! [P: term > $o] :
+          ( ( P @ one )
+         => ( ! [A: term] :
+                ( ( var @ A )
+               => ( ( P @ A )
+                 => ( P @ ( sub @ A @ sh ) ) ) )
+           => ! [A: term] :
+                ( ( var @ A )
+               => ( P @ A ) ) ) ) ) )).
+
+thf(apinj1,definition,
+    ( apinj1
+    = ( ! [A: term,B: term,C: term,D: term] :
+          ( ( ( ap @ A @ C )
+            = ( ap @ B @ D ) )
+         => ( A = B ) ) ) )).
+
+thf(apinj2,definition,
+    ( apinj2
+    = ( ! [A: term,B: term,C: term,D: term] :
+          ( ( ( ap @ A @ C )
+            = ( ap @ B @ D ) )
+         => ( C = D ) ) ) )).
+
+thf(laminj,definition,
+    ( laminj
+    = ( ! [A: term,B: term] :
+          ( ( ( lam @ A )
+            = ( lam @ B ) )
+         => ( A = B ) ) ) )).
+
+thf(shinj,definition,
+    ( shinj
+    = ( ! [A: term,B: term] :
+          ( ( ( sub @ A @ sh )
+            = ( sub @ B @ sh ) )
+         => ( A = B ) ) ) )).
+
+thf(lamnotap,definition,
+    ( lamnotap
+    = ( ! [A: term,B: term,C: term] :
+          ( ( lam @ A )
+         != ( ap @ B @ C ) ) ) )).
+
+thf(apnotvar,definition,
+    ( apnotvar
+    = ( ! [A: term,B: term] :
+          ~ ( var @ ( ap @ A @ B ) ) ) )).
+
+thf(lamnotvar,definition,
+    ( lamnotvar
+    = ( ! [A: term] :
+          ~ ( var @ ( lam @ A ) ) ) )).
+
+thf(induction,definition,
+    ( induction
+    = ( ! [P: term > $o] :
+          ( ! [A: term] :
+              ( ( var @ A )
+             => ( P @ A ) )
+         => ( ! [A: term,B: term] :
+                ( ( P @ A )
+               => ( ( P @ B )
+                 => ( P @ ( ap @ A @ B ) ) ) )
+           => ( ! [A: term] :
+                  ( ( P @ A )
+                 => ( P @ ( lam @ A ) ) )
+             => ! [A: term] :
+                  ( P @ A ) ) ) ) ) )).
+
+thf(pushprop_p_and_p_prime,definition,
+    ( pushprop_p_and_p_prime
+    = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
+        ! [X: term] :
+          ( ( Q @ X )
+        <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) )).
+
+thf(pushprop_lem0,definition,
+    ( pushprop_lem0
+    = ( ! [P: term > $o,A: term,M: subst] :
+        ? [Q: term > $o] :
+          ( pushprop_p_and_p_prime @ A @ M @ P @ Q ) ) )).
+
+thf(pushprop_lem0_gthm,definition,
+    ( pushprop_lem0_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => pushprop_lem0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(pushprop_lem0_lthm,definition,(
+    pushprop_lem0_lthm = pushprop_lem0 )).
+
+thf(pushprop_lem1,definition,
+    ( pushprop_lem1
+    = ( ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
+          ( ( P @ A )
+         => ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) )).
+
+thf(pushprop_lem1_gthm,definition,
+    ( pushprop_lem1_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => pushprop_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(pushprop_lem1_lthm,definition,
+    ( pushprop_lem1_lthm
+    = ( axvarcons
+     => ( axclos
+       => ( axshiftcons
+         => ( ulamvarind
+           => pushprop_lem1 ) ) ) ) )).
+
+thf(pushprop_lem1v2,definition,
+    ( pushprop_lem1v2
+    = ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
+          ( ( P @ A )
+         => ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
+           => ( Q @ one ) ) ) ) )).
+
+thf(pushprop_lem1v2_gthm,definition,
+    ( pushprop_lem1v2_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => pushprop_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(pushprop_lem1v2_lthm,definition,
+    ( pushprop_lem1v2_lthm
+    = ( axvarcons
+     => pushprop_lem1v2 ) )).
+
+thf(pushprop_lem2v2,definition,
+    ( pushprop_lem2v2
+    = ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
+          ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
+         => ( ! [B: term] :
+                ( ( var @ B )
+               => ( P @ ( sub @ B @ M ) ) )
+           => ! [C: term] :
+                ( ( var @ C )
+               => ( ( Q @ C )
+                 => ( Q @ ( sub @ C @ sh ) ) ) ) ) ) ) )).
+
+thf(pushprop_lem2v2_gthm,definition,
+    ( pushprop_lem2v2_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => pushprop_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(pushprop_lem2v2_lthm,definition,
+    ( pushprop_lem2v2_lthm
+    = ( axclos
+     => ( axshiftcons
+       => pushprop_lem2v2 ) ) )).
+
+thf(pushprop_lem3v2,definition,
+    ( pushprop_lem3v2
+    = ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
+          ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
+         => ( ! [B: term] :
+                ( ( var @ B )
+               => ( Q @ B ) )
+           => ! [B: term] :
+                ( ( var @ B )
+               => ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ) )).
+
+thf(pushprop_lem3v2_lthm,definition,(
+    pushprop_lem3v2_lthm = pushprop_lem3v2 )).
+
+thf(pushprop,definition,
+    ( pushprop
+    = ( ! [P: term > $o,A: term,M: subst] :
+          ( ! [B: term] :
+              ( ( var @ B )
+             => ( P @ ( sub @ B @ M ) ) )
+         => ( ( P @ A )
+           => ! [B: term] :
+                ( ( var @ B )
+               => ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ) )).
+
+thf(pushprop_gthm,definition,
+    ( pushprop_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => pushprop ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(pushprop_lthm_orig,definition,
+    ( pushprop_lthm_orig
+    = ( ulamvar1
+     => ( axvarcons
+       => ( axclos
+         => ( axshiftcons
+           => ( ulamvarind
+             => pushprop ) ) ) ) ) )).
+
+thf(pushprop_lthm,definition,
+    ( pushprop_lthm
+    = ( pushprop_lem0
+     => ( ulamvar1
+       => ( axvarcons
+         => ( axclos
+           => ( axshiftcons
+             => ( ulamvarind
+               => pushprop ) ) ) ) ) ) )).
+
+thf(induction2lem,definition,
+    ( induction2lem
+    = ( ! [P: term > $o] :
+          ( ! [A: term,B: term] :
+              ( ( P @ A )
+             => ( ( P @ B )
+               => ( P @ ( ap @ A @ B ) ) ) )
+         => ( ! [A: term] :
+                ( ! [B: term] :
+                    ( ( P @ B )
+                   => ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
+               => ( P @ ( lam @ A ) ) )
+           => ! [A: term,M: subst] :
+                ( ! [B: term] :
+                    ( ( var @ B )
+                   => ( P @ ( sub @ B @ M ) ) )
+               => ( P @ ( sub @ A @ M ) ) ) ) ) ) )).
+
+thf(induction2lem_gthm,definition,
+    ( induction2lem_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => induction2lem ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(induction2lem_lthm,definition,
+    ( induction2lem_lthm
+    = ( axapp
+     => ( axvarcons
+       => ( axabs
+         => ( axclos
+           => ( axshiftcons
+             => ( axassoc
+               => ( axmap
+                 => ( axidr
+                   => ( induction
+                     => ( pushprop
+                       => induction2lem ) ) ) ) ) ) ) ) ) ) )).
+
+thf(induction2,definition,
+    ( induction2
+    = ( ! [P: term > $o] :
+          ( ! [A: term] :
+              ( ( var @ A )
+             => ( P @ A ) )
+         => ( ! [A: term,B: term] :
+                ( ( P @ A )
+               => ( ( P @ B )
+                 => ( P @ ( ap @ A @ B ) ) ) )
+           => ( ! [A: term] :
+                  ( ! [B: term] :
+                      ( ( P @ B )
+                     => ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
+                 => ( P @ ( lam @ A ) ) )
+             => ! [A: term] :
+                  ( P @ A ) ) ) ) ) )).
+
+thf(induction2_gthm,definition,
+    ( induction2_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => induction2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(induction2_lthm,definition,
+    ( induction2_lthm
+    = ( axvarid
+     => ( induction2lem
+       => induction2 ) ) )).
+
+thf(substmonoid,definition,
+    ( substmonoid
+    = ( ! [M: subst,N: subst,K: subst] :
+          ( ( comp @ ( comp @ M @ N ) @ K )
+          = ( comp @ M @ ( comp @ N @ K ) ) )
+      & ! [M: subst] :
+          ( ( comp @ id @ M )
+          = M )
+      & ! [M: subst] :
+          ( ( comp @ M @ id )
+          = M ) ) )).
+
+thf(substmonoid_gthm,definition,
+    ( substmonoid_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => substmonoid ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(substmonoid_lthm,definition,
+    ( substmonoid_lthm
+    = ( axidl
+     => ( axassoc
+       => ( axidr
+         => substmonoid ) ) ) )).
+
+thf(termmset,definition,
+    ( termmset
+    = ( ! [A: term,M: subst,N: subst] :
+          ( ( sub @ ( sub @ A @ M ) @ N )
+          = ( sub @ A @ ( comp @ M @ N ) ) )
+      & ! [A: term] :
+          ( ( sub @ A @ id )
+          = A ) ) )).
+
+thf(termmset_gthm,definition,
+    ( termmset_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => ( substmonoid
+                                                         => termmset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(termmset_lthm,definition,
+    ( termmset_lthm
+    = ( axvarid
+     => ( axclos
+       => termmset ) ) )).
+
+thf(hoasap,definition,
+    ( hoasap
+    = ( ^ [M: subst,A: term,N: subst,B: term] :
+          ( ap @ ( sub @ A @ N ) @ B ) ) )).
+
+thf(hoaslam,definition,
+    ( hoaslam
+    = ( ^ [M: subst,F: subst > term > term] :
+          ( lam @ ( F @ sh @ one ) ) ) )).
+
+thf(hoasvar,definition,
+    ( hoasvar
+    = ( ^ [M: subst,A: term,N: subst] :
+          ( var @ ( sub @ A @ N ) ) ) )).
+
+thf(hoasapinj1,definition,
+    ( hoasapinj1
+    = ( ! [A: term,B: term,C: term,D: term] :
+          ( ( ( hoasap @ id @ A @ id @ C )
+            = ( hoasap @ id @ B @ id @ D ) )
+         => ( A = B ) ) ) )).
+
+thf(hoasapinj1_gthm,definition,
+    ( hoasapinj1_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => ( substmonoid
+                                                         => ( termmset
+                                                           => hoasapinj1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(hoasapinj1_lthm,definition,
+    ( hoasapinj1_lthm
+    = ( axvarid
+     => ( apinj1
+       => hoasapinj1 ) ) )).
+
+thf(hoasapinj2,definition,
+    ( hoasapinj2
+    = ( ! [A: term,B: term,C: term,D: term] :
+          ( ( ( hoasap @ id @ A @ id @ C )
+            = ( hoasap @ id @ B @ id @ D ) )
+         => ( C = D ) ) ) )).
+
+thf(hoasapinj2_gthm,definition,
+    ( hoasapinj2_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => ( substmonoid
+                                                         => ( termmset
+                                                           => ( hoasapinj1
+                                                             => hoasapinj2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(hoasapinj2_lthm,definition,
+    ( hoasapinj2_lthm
+    = ( apinj2
+     => hoasapinj2 ) )).
+
+thf(hoaslaminj,definition,
+    ( hoaslaminj
+    = ( ! [F: subst > term > term] :
+          ( ! [M: subst,A: term,N: subst] :
+              ( ( sub @ ( F @ M @ A ) @ N )
+              = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
+         => ! [G: subst > term > term] :
+              ( ! [M: subst,A: term,N: subst] :
+                  ( ( sub @ ( G @ M @ A ) @ N )
+                  = ( G @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
+             => ( ( ( hoaslam @ id
+                    @ ^ [M: subst,A: term] :
+                        ( F @ M @ A ) )
+                  = ( hoaslam @ id
+                    @ ^ [M: subst,A: term] :
+                        ( G @ M @ A ) ) )
+               => ! [M: subst,A: term] :
+                    ( ( F @ M @ A )
+                    = ( G @ M @ A ) ) ) ) ) ) )).
+
+thf(hoaslaminj_gthm,definition,
+    ( hoaslaminj_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => ( substmonoid
+                                                         => ( termmset
+                                                           => ( hoasapinj1
+                                                             => ( hoasapinj2
+                                                               => hoaslaminj ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(hoaslaminj_lthm,definition,
+    ( hoaslaminj_lthm
+    = ( axvarcons
+     => ( axshiftcons
+       => ( laminj
+         => hoaslaminj ) ) ) )).
+
+thf(hoaslamnotap,definition,
+    ( hoaslamnotap
+    = ( ! [F: subst > term > term] :
+          ( ! [M: subst,A: term,N: subst] :
+              ( ( sub @ ( F @ M @ A ) @ N )
+              = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
+         => ! [A: term,B: term] :
+              ( ( hoaslam @ id
+                @ ^ [M: subst,C: term] :
+                    ( F @ M @ C ) )
+             != ( hoasap @ id @ A @ id @ B ) ) ) ) )).
+
+thf(hoaslamnotap_gthm,definition,
+    ( hoaslamnotap_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => ( substmonoid
+                                                         => ( termmset
+                                                           => ( hoasapinj1
+                                                             => ( hoasapinj2
+                                                               => ( hoaslaminj
+                                                                 => hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(hoaslamnotap_lthm,definition,
+    ( hoaslamnotap_lthm
+    = ( lamnotap
+     => hoaslamnotap ) )).
+
+thf(hoaslamnotvar,definition,
+    ( hoaslamnotvar
+    = ( ! [F: subst > term > term] :
+          ( ! [M: subst,A: term,N: subst] :
+              ( ( sub @ ( F @ M @ A ) @ N )
+              = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
+         => ~ ( hoasvar @ id
+              @ ( hoaslam @ id
+                @ ^ [M: subst,A: term] :
+                    ( F @ M @ A ) )
+              @ id ) ) ) )).
+
+thf(hoaslamnotvar_gthm,definition,
+    ( hoaslamnotvar_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => ( substmonoid
+                                                         => ( termmset
+                                                           => ( hoasapinj1
+                                                             => ( hoasapinj2
+                                                               => ( hoaslaminj
+                                                                 => ( hoaslamnotap
+                                                                   => hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(hoaslamnotvar_lthm,definition,
+    ( hoaslamnotvar_lthm
+    = ( axvarid
+     => ( lamnotvar
+       => hoaslamnotvar ) ) )).
+
+thf(hoasapnotvar,definition,
+    ( hoasapnotvar
+    = ( ! [A: term,B: term] :
+          ~ ( hoasvar @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )).
+
+thf(hoasapnotvar_gthm,definition,
+    ( hoasapnotvar_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => ( substmonoid
+                                                         => ( termmset
+                                                           => ( hoasapinj1
+                                                             => ( hoasapinj2
+                                                               => ( hoaslaminj
+                                                                 => ( hoaslamnotap
+                                                                   => ( hoaslamnotvar
+                                                                     => hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(hoasapnotvar_lthm,definition,
+    ( hoasapnotvar_lthm
+    = ( axvarid
+     => ( apnotvar
+       => hoasapnotvar ) ) )).
+
+thf(hoasinduction_p_and_p_prime,definition,
+    ( hoasinduction_p_and_p_prime
+    = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
+        ! [X: term] :
+          ( ( Q @ X )
+        <=> ( P @ id @ X @ id ) ) ) )).
+
+thf(hoasinduction_lem0,definition,
+    ( hoasinduction_lem0
+    = ( ! [P: subst > term > subst > $o] :
+        ? [Q: term > $o] :
+          ( hoasinduction_p_and_p_prime @ P @ Q ) ) )).
+
+thf(hoasinduction_lem0_lthm,definition,(
+    hoasinduction_lem0_lthm = hoasinduction_lem0 )).
+
+thf(hoasinduction_lem1v2,definition,
+    ( hoasinduction_lem1v2
+    = ( ! [P: subst > term > subst > $o,Q: term > $o] :
+          ( ! [M: subst,A: term,N: subst,K: subst] :
+              ( ( P @ M @ A @ ( comp @ K @ N ) )
+             => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
+         => ( ! [M: subst,A: term,N: subst,K: subst] :
+                ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
+               => ( P @ M @ A @ ( comp @ K @ N ) ) )
+           => ( ! [A: term] :
+                  ( ( hoasvar @ id @ A @ id )
+                 => ( P @ id @ A @ id ) )
+             => ( ( hoasinduction_p_and_p_prime @ P @ Q )
+               => ! [A: term] :
+                    ( ( var @ A )
+                   => ( Q @ A ) ) ) ) ) ) ) )).
+
+thf(hoasinduction_lem1v2_gthm,definition,
+    ( hoasinduction_lem1v2_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => ( substmonoid
+                                                         => ( termmset
+                                                           => ( hoasapinj1
+                                                             => ( hoasapinj2
+                                                               => ( hoaslaminj
+                                                                 => ( hoaslamnotap
+                                                                   => ( hoaslamnotvar
+                                                                     => ( hoasapnotvar
+                                                                       => hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(hoasinduction_lem2v2,definition,
+    ( hoasinduction_lem2v2
+    = ( ! [P: subst > term > subst > $o,Q: term > $o] :
+          ( ! [M: subst,A: term,N: subst,K: subst] :
+              ( ( P @ M @ A @ ( comp @ K @ N ) )
+             => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
+         => ( ! [M: subst,A: term,N: subst,K: subst] :
+                ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
+               => ( P @ M @ A @ ( comp @ K @ N ) ) )
+           => ( ! [A: term,B: term] :
+                  ( ( P @ id @ A @ id )
+                 => ( ( P @ id @ B @ id )
+                   => ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
+             => ( ( hoasinduction_p_and_p_prime @ P @ Q )
+               => ! [A: term,B: term] :
+                    ( ( Q @ A )
+                   => ( ( Q @ B )
+                     => ( Q @ ( ap @ A @ B ) ) ) ) ) ) ) ) ) )).
+
+thf(hoasinduction_lem2v2_gthm,definition,
+    ( hoasinduction_lem2v2_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => ( substmonoid
+                                                         => ( termmset
+                                                           => ( hoasapinj1
+                                                             => ( hoasapinj2
+                                                               => ( hoaslaminj
+                                                                 => ( hoaslamnotap
+                                                                   => ( hoaslamnotvar
+                                                                     => ( hoasapnotvar
+                                                                       => hoasinduction_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(hoasinduction_lem3v2_f,definition,
+    ( hoasinduction_lem3v2_f
+    = ( ! [B: term] :
+        ? [F: subst > term > term] :
+        ! [A: term,M: subst] :
+          ( ( F @ M @ A )
+          = ( sub @ B @ ( push @ A @ M ) ) ) ) )).
+
+thf(hoasinduction_lem3v2_f_lthm,definition,(
+    hoasinduction_lem3v2_f_lthm = hoasinduction_lem3v2_f )).
+
+thf(hoasinduction_lem3v2,definition,
+    ( hoasinduction_lem3v2
+    = ( ! [P: subst > term > subst > $o,Q: term > $o] :
+          ( ! [M: subst,A: term,N: subst,K: subst] :
+              ( ( P @ M @ A @ ( comp @ K @ N ) )
+             => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
+         => ( ! [M: subst,A: term,N: subst,K: subst] :
+                ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
+               => ( P @ M @ A @ ( comp @ K @ N ) ) )
+           => ( ! [F: subst > term > term] :
+                  ( ! [M: subst,A: term,N: subst] :
+                      ( ( sub @ ( F @ M @ A ) @ N )
+                      = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
+                 => ( ! [A: term] :
+                        ( ( P @ id @ A @ id )
+                       => ( P @ id @ ( F @ id @ A ) @ id ) )
+                   => ( P @ id
+                      @ ( hoaslam @ id
+                        @ ^ [M: subst,A: term] :
+                            ( F @ M @ A ) )
+                      @ id ) ) )
+             => ( ( hoasinduction_p_and_p_prime @ P @ Q )
+               => ! [A: term] :
+                    ( ! [B: term] :
+                        ( ( Q @ B )
+                       => ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
+                   => ( Q @ ( lam @ A ) ) ) ) ) ) ) ) )).
+
+thf(hoasinduction_lem3v2_gthm,definition,
+    ( hoasinduction_lem3v2_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => ( substmonoid
+                                                         => ( termmset
+                                                           => ( hoasapinj1
+                                                             => ( hoasapinj2
+                                                               => ( hoaslaminj
+                                                                 => ( hoaslamnotap
+                                                                   => ( hoaslamnotvar
+                                                                     => ( hoasapnotvar
+                                                                       => hoasinduction_lem3v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(hoasinduction_lem3v2_lthm,definition,
+    ( hoasinduction_lem3v2_lthm
+    = ( axvarid
+     => ( axvarshift
+       => ( axclos
+         => ( axmap
+           => hoasinduction_lem3v2 ) ) ) ) )).
+
+thf(hoasinduction_lem3v2a,definition,
+    ( hoasinduction_lem3v2a
+    = ( ! [P: subst > term > subst > $o,Q: term > $o] :
+          ( ! [F: subst > term > term] :
+              ( ! [M: subst,A: term,N: subst] :
+                  ( ( sub @ ( F @ M @ A ) @ N )
+                  = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
+             => ( ! [A: term] :
+                    ( ( P @ id @ A @ id )
+                   => ( P @ id @ ( F @ id @ A ) @ id ) )
+               => ( P @ id
+                  @ ( hoaslam @ id
+                    @ ^ [M: subst,A: term] :
+                        ( F @ M @ A ) )
+                  @ id ) ) )
+         => ( ( hoasinduction_p_and_p_prime @ P @ Q )
+           => ! [A: term] :
+                ( ! [B: term] :
+                    ( ( Q @ B )
+                   => ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
+               => ( Q @ ( lam @ A ) ) ) ) ) ) )).
+
+thf(hoasinduction_lem3v2a_lthm,definition,
+    ( hoasinduction_lem3v2a_lthm
+    = ( hoasinduction_lem3v2_f
+     => ( axvarid
+       => ( axvarshift
+         => ( axclos
+           => ( axmap
+             => hoasinduction_lem3v2a ) ) ) ) ) )).
+
+thf(hoasinduction_lem1,definition,
+    ( hoasinduction_lem1
+    = ( ! [P: subst > term > subst > $o] :
+          ( ! [M: subst,A: term,N: subst,K: subst] :
+              ( ( P @ M @ A @ ( comp @ K @ N ) )
+             => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
+         => ( ! [M: subst,A: term,N: subst,K: subst] :
+                ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
+               => ( P @ M @ A @ ( comp @ K @ N ) ) )
+           => ( ! [A: term] :
+                  ( ( hoasvar @ id @ A @ id )
+                 => ( P @ id @ A @ id ) )
+             => ! [A: term] :
+                  ( ( var @ A )
+                 => ( P @ id @ A @ id ) ) ) ) ) ) )).
+
+thf(hoasinduction_lem1_gthm,definition,
+    ( hoasinduction_lem1_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => ( substmonoid
+                                                         => ( termmset
+                                                           => ( hoasapinj1
+                                                             => ( hoasapinj2
+                                                               => ( hoaslaminj
+                                                                 => ( hoaslamnotap
+                                                                   => ( hoaslamnotvar
+                                                                     => ( hoasapnotvar
+                                                                       => hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(hoasinduction_lem1_lthm,definition,
+    ( hoasinduction_lem1_lthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => ( substmonoid
+                                                         => ( termmset
+                                                           => ( hoasapinj1
+                                                             => ( hoasapinj2
+                                                               => ( hoaslaminj
+                                                                 => ( hoaslamnotap
+                                                                   => ( hoaslamnotvar
+                                                                     => ( hoasapnotvar
+                                                                       => hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(hoasinduction_lem2,definition,
+    ( hoasinduction_lem2
+    = ( ! [P: subst > term > subst > $o] :
+          ( ! [M: subst,A: term,N: subst,K: subst] :
+              ( ( P @ M @ A @ ( comp @ K @ N ) )
+             => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
+         => ( ! [M: subst,A: term,N: subst,K: subst] :
+                ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
+               => ( P @ M @ A @ ( comp @ K @ N ) ) )
+           => ( ! [A: term,B: term] :
+                  ( ( P @ id @ A @ id )
+                 => ( ( P @ id @ B @ id )
+                   => ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
+             => ! [A: term,B: term] :
+                  ( ( P @ id @ A @ id )
+                 => ( ( P @ id @ B @ id )
+                   => ( P @ id @ ( ap @ A @ B ) @ id ) ) ) ) ) ) ) )).
+
+thf(hoasinduction_lem2_gthm,definition,
+    ( hoasinduction_lem2_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => ( substmonoid
+                                                         => ( termmset
+                                                           => ( hoasapinj1
+                                                             => ( hoasapinj2
+                                                               => ( hoaslaminj
+                                                                 => ( hoaslamnotap
+                                                                   => ( hoaslamnotvar
+                                                                     => ( hoasapnotvar
+                                                                       => hoasinduction_lem2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(hoasinduction_lem2_lthm,definition,
+    ( hoasinduction_lem2_lthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => ( substmonoid
+                                                         => ( termmset
+                                                           => ( hoasapinj1
+                                                             => ( hoasapinj2
+                                                               => ( hoaslaminj
+                                                                 => ( hoaslamnotap
+                                                                   => ( hoaslamnotvar
+                                                                     => ( hoasapnotvar
+                                                                       => hoasinduction_lem2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(hoasinduction_lem3aa,definition,
+    ( hoasinduction_lem3aa
+    = ( ! [P: subst > term > subst > $o] :
+          ( ! [F: subst > term > term] :
+              ( ! [M: subst,A: term,N: subst] :
+                  ( ( sub @ ( F @ M @ A ) @ N )
+                  = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
+             => ( ! [A: term] :
+                    ( ( P @ id @ A @ id )
+                   => ( P @ id @ ( F @ id @ A ) @ id ) )
+               => ( P @ id
+                  @ ( hoaslam @ id
+                    @ ^ [M: subst,A: term] :
+                        ( F @ M @ A ) )
+                  @ id ) ) )
+         => ! [A: term] :
+              ( ! [B: term] :
+                  ( ( P @ id @ B @ id )
+                 => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
+             => ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )).
+
+thf(hoasinduction_lem3aa_lthm,definition,
+    ( hoasinduction_lem3aa_lthm
+    = ( axclos
+     => ( axmap
+       => hoasinduction_lem3aa ) ) )).
+
+thf(hoasinduction_lem3aaa,definition,
+    ( hoasinduction_lem3aaa
+    = ( ! [P: subst > term > subst > $o] :
+          ( ! [F: subst > term > term] :
+              ( ? [C: term] :
+                ! [M: subst,A: term,N: subst] :
+                  ( ( ( sub @ ( F @ M @ A ) @ N )
+                    = ( sub @ ( sub @ C @ ( push @ A @ M ) ) @ N ) )
+                  & ( ( sub @ C @ ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) )
+                    = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) )
+             => ( ! [A: term] :
+                    ( ( P @ id @ A @ id )
+                   => ( P @ id @ ( F @ id @ A ) @ id ) )
+               => ( P @ id
+                  @ ( hoaslam @ id
+                    @ ^ [M: subst,A: term] :
+                        ( F @ M @ A ) )
+                  @ id ) ) )
+         => ! [A: term] :
+              ( ! [B: term] :
+                  ( ( P @ id @ B @ id )
+                 => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
+             => ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) )).
+
+thf(hoasinduction_lem3,definition,
+    ( hoasinduction_lem3
+    = ( ! [P: subst > term > subst > $o] :
+          ( ! [M: subst,A: term,N: subst,K: subst] :
+              ( ( P @ M @ A @ ( comp @ K @ N ) )
+             => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
+         => ( ! [M: subst,A: term,N: subst,K: subst] :
+                ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
+               => ( P @ M @ A @ ( comp @ K @ N ) ) )
+           => ( ! [F: subst > term > term] :
+                  ( ! [M: subst,A: term,N: subst] :
+                      ( ( sub @ ( F @ M @ A ) @ N )
+                      = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
+                 => ( ! [A: term] :
+                        ( ( P @ id @ A @ id )
+                       => ( P @ id @ ( F @ id @ A ) @ id ) )
+                   => ( P @ id
+                      @ ( hoaslam @ id
+                        @ ^ [M: subst,A: term] :
+                            ( F @ M @ A ) )
+                      @ id ) ) )
+             => ! [A: term] :
+                  ( ! [B: term] :
+                      ( ( P @ id @ B @ id )
+                     => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
+                 => ( P @ id @ ( lam @ A ) @ id ) ) ) ) ) ) )).
+
+thf(hoasinduction_lem3_gthm,definition,
+    ( hoasinduction_lem3_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => ( substmonoid
+                                                         => ( termmset
+                                                           => ( hoasapinj1
+                                                             => ( hoasapinj2
+                                                               => ( hoaslaminj
+                                                                 => ( hoaslamnotap
+                                                                   => ( hoaslamnotvar
+                                                                     => ( hoasapnotvar
+                                                                       => ( hoasinduction_lem1
+                                                                         => ( hoasinduction_lem2
+                                                                           => hoasinduction_lem3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(hoasinduction_lem3_lthm,definition,
+    ( hoasinduction_lem3_lthm
+    = ( axvarid
+     => ( axvarshift
+       => ( hoasinduction_lem3aa
+         => hoasinduction_lem3 ) ) ) )).
+
+thf(hoasinduction_lem3a,definition,
+    ( hoasinduction_lem3a
+    = ( ! [P: subst > term > subst > $o] :
+          ( ! [F: subst > term > term] :
+              ( ! [M: subst,A: term,N: subst] :
+                  ( ( sub @ ( F @ M @ A ) @ N )
+                  = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
+             => ( ! [A: term] :
+                    ( ( P @ id @ A @ id )
+                   => ( P @ id @ ( F @ id @ A ) @ id ) )
+               => ( P @ id
+                  @ ( hoaslam @ id
+                    @ ^ [M: subst,A: term] :
+                        ( F @ M @ A ) )
+                  @ id ) ) )
+         => ! [A: term] :
+              ( ! [B: term] :
+                  ( ( P @ id @ B @ id )
+                 => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
+             => ( P @ id @ ( lam @ A ) @ id ) ) ) ) )).
+
+thf(hoasinduction_lem3a_gthm,definition,
+    ( hoasinduction_lem3a_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => ( substmonoid
+                                                         => ( termmset
+                                                           => ( hoasapinj1
+                                                             => ( hoasapinj2
+                                                               => ( hoaslaminj
+                                                                 => ( hoaslamnotap
+                                                                   => ( hoaslamnotvar
+                                                                     => ( hoasapnotvar
+                                                                       => ( hoasinduction_lem1
+                                                                         => ( hoasinduction_lem2
+                                                                           => hoasinduction_lem3a ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(hoasinduction_lem3a_lthm,definition,
+    ( hoasinduction_lem3a_lthm
+    = ( axvarid
+     => ( axvarshift
+       => ( hoasinduction_lem3aa
+         => hoasinduction_lem3a ) ) ) )).
+
+thf(hoasinduction_lem3b,definition,
+    ( hoasinduction_lem3b
+    = ( ! [B: term] :
+        ? [F: subst > term > term] :
+          ( ( sub @ B @ ( push @ one @ sh ) )
+          = ( F @ sh @ one ) ) ) )).
+
+thf(hoasinduction_lem3b_gthm,definition,
+    ( hoasinduction_lem3b_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => ( substmonoid
+                                                         => ( termmset
+                                                           => ( hoasapinj1
+                                                             => ( hoasapinj2
+                                                               => ( hoaslaminj
+                                                                 => ( hoaslamnotap
+                                                                   => ( hoaslamnotvar
+                                                                     => ( hoasapnotvar
+                                                                       => ( hoasinduction_lem1
+                                                                         => ( hoasinduction_lem2
+                                                                           => hoasinduction_lem3b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(hoasinduction_lem3b_lthm,definition,(
+    hoasinduction_lem3b_lthm = hoasinduction_lem3b )).
+
+thf(hoasinduction,definition,
+    ( hoasinduction
+    = ( ! [P: subst > term > subst > $o] :
+          ( ! [M: subst,A: term,N: subst,K: subst] :
+              ( ( P @ M @ A @ ( comp @ K @ N ) )
+             => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
+         => ( ! [M: subst,A: term,N: subst,K: subst] :
+                ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
+               => ( P @ M @ A @ ( comp @ K @ N ) ) )
+           => ( ! [A: term] :
+                  ( ( hoasvar @ id @ A @ id )
+                 => ( P @ id @ A @ id ) )
+             => ( ! [A: term,B: term] :
+                    ( ( P @ id @ A @ id )
+                   => ( ( P @ id @ B @ id )
+                     => ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
+               => ( ! [F: subst > term > term] :
+                      ( ! [M: subst,A: term,N: subst] :
+                          ( ( sub @ ( F @ M @ A ) @ N )
+                          = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
+                     => ( ! [A: term] :
+                            ( ( P @ id @ A @ id )
+                           => ( P @ id @ ( F @ id @ A ) @ id ) )
+                       => ( P @ id
+                          @ ( hoaslam @ id
+                            @ ^ [M: subst,A: term] :
+                                ( F @ M @ A ) )
+                          @ id ) ) )
+                 => ! [A: term] :
+                      ( P @ id @ A @ id ) ) ) ) ) ) ) )).
+
+thf(hoasinduction_gthm,definition,
+    ( hoasinduction_gthm
+    = ( axapp
+     => ( axvarcons
+       => ( axvarid
+         => ( axabs
+           => ( axclos
+             => ( axidl
+               => ( axshiftcons
+                 => ( axassoc
+                   => ( axmap
+                     => ( axidr
+                       => ( axvarshift
+                         => ( axscons
+                           => ( ulamvar1
+                             => ( ulamvarsh
+                               => ( ulamvarind
+                                 => ( apinj1
+                                   => ( apinj2
+                                     => ( laminj
+                                       => ( shinj
+                                         => ( lamnotap
+                                           => ( apnotvar
+                                             => ( lamnotvar
+                                               => ( induction
+                                                 => ( pushprop
+                                                   => ( induction2lem
+                                                     => ( induction2
+                                                       => ( substmonoid
+                                                         => ( termmset
+                                                           => ( hoasapinj1
+                                                             => ( hoasapinj2
+                                                               => ( hoaslaminj
+                                                                 => ( hoaslamnotap
+                                                                   => ( hoaslamnotvar
+                                                                     => ( hoasapnotvar
+                                                                       => ( hoasinduction_lem1
+                                                                         => ( hoasinduction_lem2
+                                                                           => ( hoasinduction_lem3
+                                                                             => hoasinduction ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
+
+thf(hoasinduction_lthm,definition,
+    ( hoasinduction_lthm
+    = ( induction2
+     => ( hoasinduction_lem1
+       => ( hoasinduction_lem2
+         => ( hoasinduction_lem3
+           => hoasinduction ) ) ) ) )).
+
+thf(hoasinduction_lthm_3,definition,
+    ( hoasinduction_lthm_3
+    = ( hoasinduction_lem0
+     => ( induction2
+       => ( axvarid
+         => ( hoasinduction_lem3v2a
+           => hoasinduction ) ) ) ) )).
+
+thf(hoasinduction_no_psi_cond,definition,
+    ( hoasinduction_no_psi_cond
+    = ( ! [P: subst > term > subst > $o] :
+          ( ! [A: term,B: term] :
+              ( ( P @ id @ A @ id )
+             => ( ( P @ id @ B @ id )
+               => ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
+         => ( ! [F: subst > term > term] :
+                ( ! [M: subst,A: term,N: subst] :
+                    ( ( sub @ ( F @ M @ A ) @ N )
+                    = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
+               => ( ! [A: term] :
+                      ( ( P @ id @ A @ id )
+                     => ( P @ id @ ( F @ id @ A ) @ id ) )
+                 => ( P @ id
+                    @ ( hoaslam @ id
+                      @ ^ [M: subst,A: term] :
+                          ( F @ M @ A ) )
+                    @ id ) ) )
+           => ! [A: term] :
+                ( P @ id @ A @ id ) ) ) ) )).
+
+thf(hoasinduction_no_psi_cond_lthm,definition,
+    ( hoasinduction_no_psi_cond_lthm
+    = ( hoasinduction_lem0
+     => ( induction2
+       => ( axvarid
+         => ( hoasinduction_lem3v2a
+           => hoasinduction_no_psi_cond ) ) ) ) )).
+
+
+thf(thm,conjecture,(
+    pushprop_lem1v2_lthm )).
+
+%------------------------------------------------------------------------------

diff --git a/test/regress/regress2/ho/partial_app_interpreted_SWW474^2.p b/test/regress/regress2/ho/partial_app_interpreted_SWW474^2.p
new file mode 100644 (file)
index 0000000..b4e9e9b
--- /dev/null
+++ b/test/regress/regress2/ho/partial_app_interpreted_SWW474^2.p
@@ -0,0 +1,5211 @@
+% COMMAND-LINE: --uf-ho --full-saturate-quant --ho-elim --no-check-unsat-cores --no-check-proofs
+% EXPECT: % SZS status Theorem for partial_app_interpreted_SWW474^2
+
+%------------------------------------------------------------------------------
+% File     : SWW474^2 : TPTP v7.2.0. Released v5.3.0.
+% Domain   : Software Verification
+% Problem  : Hoare's Logic with Procedures line 440, 500 axioms selected
+% Version  : Especial.
+% English  :
+
+% Refs     : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
+%          : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
+% Source   : [Bla11]
+% Names    : hoare_500_thf_l440 [Bla11]
+
+% Status   : Theorem
+% Rating   : 0.56 v7.2.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.71 v5.5.0, 0.67 v5.4.0, 0.80 v5.3.0
+% Syntax   : Number of formulae    :  833 (   2 unit; 110 type;   0 defn)
+%            Number of atoms       : 8029 ( 594 equality;4565 variable)
+%            Maximal formula depth :   19 (   8 average)
+%            Number of connectives : 6344 ( 226   ~;  35   |; 108   &;5021   @)
+%                                         ( 116 <=>; 838  =>;   0  <=;   0 <~>)
+%                                         (   0  ~|;   0  ~&)
+%            Number of type conns  : 2404 (2404   >;   0   *;   0   +;   0  <<)
+%            Number of symbols     :  118 ( 110   :;   0   =)
+%            Number of variables   : 2030 (  12 sgn;1851   !;  48   ?; 131   ^)
+%                                         (2030   :;   0  !>;   0  ?*)
+%                                         (   0  @-;   0  @+)
+% SPC      : TH0_THM_EQU_NAR
+
+% Comments : This file was generated by Isabelle (most likely Sledgehammer)
+%            2011-08-09 19:43:11
+%------------------------------------------------------------------------------
+%----Should-be-implicit typings (7)
+thf(ty_ty_tc__Com__Ocom,type,(
+    com: $tType )).
+
+thf(ty_ty_tc__Com__Opname,type,(
+    pname: $tType )).
+
+thf(ty_ty_tc__Com__Ostate,type,(
+    state: $tType )).
+
+thf(ty_ty_tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J,type,(
+    hoare_1167836817_state: $tType )).
+
+thf(ty_ty_tc__Option__Ooption_Itc__Com__Ocom_J,type,(
+    option_com: $tType )).
+
+thf(ty_ty_tc__Option__Ooption_Itc__Com__Opname_J,type,(
+    option_pname: $tType )).
+
+thf(ty_ty_tc__Option__Ooption_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Co,type,(
+    option1574264306_state: $tType )).
+
+%----Explicit typings (103)
+thf(sy_c_Com_OWT,type,(
+    wt: com > $o )).
+
+thf(sy_c_Com_OWT__bodies,type,(
+    wT_bodies: $o )).
+
+thf(sy_c_Com_Obody,type,(
+    body: pname > option_com )).
+
+thf(sy_c_Com_Ocom_OBODY,type,(
+    body_1: pname > com )).
+
+thf(sy_c_Com_Ocom_OSKIP,type,(
+    skip: com )).
+
+thf(sy_c_Com_Ocom_OSemi,type,(
+    semi: com > com > com )).
+
+thf(sy_c_Com_Ocom_OWhile,type,(
+    while: ( state > $o ) > com > com )).
+
+thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,(
+    finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o )).
+
+thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Hoare____Mirabelle____srushsumbx__Ot,type,(
+    finite33115244te_o_o: ( ( ( hoare_1167836817_state > $o ) > $o ) > $o ) > $o )).
+
+thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J,type,(
+    finite297249702name_o: ( ( pname > $o ) > $o ) > $o )).
+
+thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_,type,(
+    finite1380128977tate_o: ( ( hoare_1167836817_state > $o ) > $o ) > $o )).
+
+thf(sy_c_Finite__Set_Ofinite_000tc__Com__Opname,type,(
+    finite_finite_pname: ( pname > $o ) > $o )).
+
+thf(sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__C,type,(
+    finite1084549118_state: ( hoare_1167836817_state > $o ) > $o )).
+
+thf(sy_c_Finite__Set_Ofolding__one_000_062_Itc__Com__Opname_M_Eo_J,type,(
+    finite349908348name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( ( ( pname > $o ) > $o ) > pname > $o ) > $o )).
+
+thf(sy_c_Finite__Set_Ofolding__one_000_062_Itc__Hoare____Mirabelle____srushsumbx__Ot,type,(
+    finite979047547tate_o: ( ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > ( ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o ) > $o )).
+
+thf(sy_c_Finite__Set_Ofolding__one_000tc__Com__Opname,type,(
+    finite1282449217_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o )).
+
+thf(sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____srushsumbx__Otriple_,type,(
+    finite1074406356_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > $o )).
+
+thf(sy_c_Finite__Set_Ofolding__one__idem_000_062_Itc__Com__Opname_M_Eo_J,type,(
+    finite697516351name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( ( ( pname > $o ) > $o ) > pname > $o ) > $o )).
+
+thf(sy_c_Finite__Set_Ofolding__one__idem_000_062_Itc__Hoare____Mirabelle____srushsum,type,(
+    finite671847800tate_o: ( ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > ( ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o ) > $o )).
+
+thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname,type,(
+    finite89670078_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o )).
+
+thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____srushsumbx__Ot,type,(
+    finite806517911_state: ( hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > $o )).
+
+thf(sy_c_Groups_Ominus__class_Ominus_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,(
+    minus_1480864103me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o )).
+
+thf(sy_c_Groups_Ominus__class_Ominus_000_062_I_062_Itc__Hoare____Mirabelle____srushs,type,(
+    minus_1708687022te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o )).
+
+thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Com__Opname_M_Eo_J,type,(
+    minus_minus_pname_o: ( pname > $o ) > ( pname > $o ) > pname > $o )).
+
+thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____srushsumbx__,type,(
+    minus_2107060239tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o )).
+
+thf(sy_c_HOL_OThe_000tc__Com__Opname,type,(
+    the_pname: ( pname > $o ) > pname )).
+
+thf(sy_c_HOL_OThe_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_,type,(
+    the_Ho310147232_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state )).
+
+thf(sy_c_Hoare__Mirabelle__srushsumbx_OMGT,type,(
+    hoare_Mirabelle_MGT: com > hoare_1167836817_state )).
+
+thf(sy_c_Hoare__Mirabelle__srushsumbx_Ohoare__derivs_000tc__Com__Ostate,type,(
+    hoare_123228589_state: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o )).
+
+thf(sy_c_Hoare__Mirabelle__srushsumbx_Ohoare__valids_000tc__Com__Ostate,type,(
+    hoare_529639851_state: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o )).
+
+thf(sy_c_Hoare__Mirabelle__srushsumbx_Ostate__not__singleton,type,(
+    hoare_1201148605gleton: $o )).
+
+thf(sy_c_Hoare__Mirabelle__srushsumbx_Otriple_Otriple_000tc__Com__Ostate,type,(
+    hoare_908217195_state: ( state > state > $o ) > com > ( state > state > $o ) > hoare_1167836817_state )).
+
+thf(sy_c_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J,type,(
+    if_Hoa833675553_state: $o > hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state )).
+
+thf(sy_c_If_000tc__Option__Ooption_Itc__Com__Ocom_J,type,(
+    if_option_com: $o > option_com > option_com > option_com )).
+
+thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Com__Opname_M_Eo_,type,(
+    semila2013987940me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o )).
+
+thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Hoare____Mirabell,type,(
+    semila1758709489te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o )).
+
+thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Com__Opname_M_Eo_J,type,(
+    semila1673364395name_o: ( pname > $o ) > ( pname > $o ) > pname > $o )).
+
+thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Hoare____Mirabelle____s,type,(
+    semila179895820tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o )).
+
+thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Com__Opname_M_Eo_,type,(
+    semila181081674me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o )).
+
+thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Hoare____Mirabell,type,(
+    semila866907787te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o )).
+
+thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Com__Opname_M_Eo_J,type,(
+    semila1780557381name_o: ( pname > $o ) > ( pname > $o ) > pname > $o )).
+
+thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Hoare____Mirabelle____s,type,(
+    semila1172322802tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o )).
+
+thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_Eo,type,(
+    semila10642723_sup_o: $o > $o > $o )).
+
+thf(sy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom,type,(
+    dom_pname_com: ( pname > option_com ) > pname > $o )).
+
+thf(sy_c_Natural_Oevalc,type,(
+    evalc: com > state > state > $o )).
+
+thf(sy_c_Option_Ooption_OSome_000tc__Com__Ocom,type,(
+    some_com: com > option_com )).
+
+thf(sy_c_Option_Ooption_OSome_000tc__Com__Opname,type,(
+    some_pname: pname > option_pname )).
+
+thf(sy_c_Option_Ooption_OSome_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__,type,(
+    some_H1433514562_state: hoare_1167836817_state > option1574264306_state )).
+
+thf(sy_c_Option_Oset_000tc__Com__Ocom,type,(
+    set_com: option_com > com > $o )).
+
+thf(sy_c_Option_Oset_000tc__Com__Opname,type,(
+    set_pname: option_pname > pname > $o )).
+
+thf(sy_c_Option_Oset_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Osta,type,(
+    set_Ho2131684873_state: option1574264306_state > hoare_1167836817_state > $o )).
+
+thf(sy_c_Option_Othe_000tc__Com__Ocom,type,(
+    the_com: option_com > com )).
+
+thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,(
+    bot_bot_pname_o_o: ( pname > $o ) > $o )).
+
+thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____srushsu,type,(
+    bot_bo691907561te_o_o: ( hoare_1167836817_state > $o ) > $o )).
+
+thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Ocom_M_Eo_J,type,(
+    bot_bot_com_o: com > $o )).
+
+thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Opname_M_Eo_J,type,(
+    bot_bot_pname_o: pname > $o )).
+
+thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____srushsumbx__O,type,(
+    bot_bo70021908tate_o: hoare_1167836817_state > $o )).
+
+thf(sy_c_Orderings_Obot__class_Obot_000_Eo,type,(
+    bot_bot_o: $o )).
+
+thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_,type,(
+    ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o )).
+
+thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Hoare____Mirabelle____sr,type,(
+    ord_le741939125te_o_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > $o )).
+
+thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Com__Opname_M_Eo_J,type,(
+    ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o )).
+
+thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Hoare____Mirabelle____srushsum,type,(
+    ord_le827224136tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o )).
+
+thf(sy_c_Orderings_Oord__class_Oless__eq_000_Eo,type,(
+    ord_less_eq_o: $o > $o > $o )).
+
+thf(sy_c_Set_OCollect_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,(
+    collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o )).
+
+thf(sy_c_Set_OCollect_000_062_I_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_I,type,(
+    collec1218656682te_o_o: ( ( ( hoare_1167836817_state > $o ) > $o ) > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > $o )).
+
+thf(sy_c_Set_OCollect_000_062_Itc__Com__Opname_M_Eo_J,type,(
+    collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o )).
+
+thf(sy_c_Set_OCollect_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Co,type,(
+    collec269976083tate_o: ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o )).
+
+thf(sy_c_Set_OCollect_000tc__Com__Opname,type,(
+    collect_pname: ( pname > $o ) > pname > $o )).
+
+thf(sy_c_Set_OCollect_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ost,type,(
+    collec1027672124_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o )).
+
+thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000_062_Itc__Com__Opname_M_Eo_J,type,(
+    image_1085733413name_o: ( ( pname > $o ) > pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o )).
+
+thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Opname,type,(
+    image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o )).
+
+thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Hoare____Mirabelle____sru,type,(
+    image_1381916541_state: ( ( pname > $o ) > hoare_1167836817_state ) > ( ( pname > $o ) > $o ) > hoare_1167836817_state > $o )).
+
+thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com_,type,(
+    image_1488525317tate_o: ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o )).
+
+thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__001,type,(
+    image_980295115_pname: ( ( hoare_1167836817_state > $o ) > pname ) > ( ( hoare_1167836817_state > $o ) > $o ) > pname > $o )).
+
+thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__002,type,(
+    image_635813834_state: ( ( hoare_1167836817_state > $o ) > hoare_1167836817_state ) > ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o )).
+
+thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J,type,(
+    image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o )).
+
+thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Hoare____Mirabelle____srushsumbx,type,(
+    image_475339327tate_o: ( pname > hoare_1167836817_state > $o ) > ( pname > $o ) > ( hoare_1167836817_state > $o ) > $o )).
+
+thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,type,(
+    image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o )).
+
+thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____srushsumbx__Otri,type,(
+    image_575578384_state: ( pname > hoare_1167836817_state ) > ( pname > $o ) > hoare_1167836817_state > $o )).
+
+thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat,type,(
+    image_2066861949name_o: ( hoare_1167836817_state > pname > $o ) > ( hoare_1167836817_state > $o ) > ( pname > $o ) > $o )).
+
+thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat_003,type,(
+    image_1745649338tate_o: ( hoare_1167836817_state > hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o )).
+
+thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat_004,type,(
+    image_8178176_pname: ( hoare_1167836817_state > pname ) > ( hoare_1167836817_state > $o ) > pname > $o )).
+
+thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostat_005,type,(
+    image_31595733_state: ( hoare_1167836817_state > hoare_1167836817_state ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o )).
+
+thf(sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J,type,(
+    insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o )).
+
+thf(sy_c_Set_Oinsert_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com,type,(
+    insert999278200tate_o: ( hoare_1167836817_state > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > ( hoare_1167836817_state > $o ) > $o )).
+
+thf(sy_c_Set_Oinsert_000tc__Com__Ocom,type,(
+    insert_com: com > ( com > $o ) > com > $o )).
+
+thf(sy_c_Set_Oinsert_000tc__Com__Opname,type,(
+    insert_pname: pname > ( pname > $o ) > pname > $o )).
+
+thf(sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Osta,type,(
+    insert2134838167_state: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o )).
+
+thf(sy_c_Set_Othe__elem_000tc__Com__Opname,type,(
+    the_elem_pname: ( pname > $o ) > pname )).
+
+thf(sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__O,type,(
+    the_el323660082_state: ( hoare_1167836817_state > $o ) > hoare_1167836817_state )).
+
+thf(sy_c_fequal_000_062_Itc__Com__Opname_M_Eo_J,type,(
+    fequal_pname_o: ( pname > $o ) > ( pname > $o ) > $o )).
+
+thf(sy_c_fequal_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ost,type,(
+    fequal1486222077tate_o: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > $o )).
+
+thf(sy_c_fequal_000tc__Com__Opname,type,(
+    fequal_pname: pname > pname > $o )).
+
+thf(sy_c_fequal_000tc__Com__Ostate,type,(
+    fequal_state: state > state > $o )).
+
+thf(sy_c_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J,type,(
+    fequal1831255762_state: hoare_1167836817_state > hoare_1167836817_state > $o )).
+
+thf(sy_c_member_000_062_Itc__Com__Opname_M_Eo_J,type,(
+    member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o )).
+
+thf(sy_c_member_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ost,type,(
+    member864234961tate_o: ( hoare_1167836817_state > $o ) > ( ( hoare_1167836817_state > $o ) > $o ) > $o )).
+
+thf(sy_c_member_000tc__Com__Ocom,type,(
+    member_com: com > ( com > $o ) > $o )).
+
+thf(sy_c_member_000tc__Com__Opname,type,(
+    member_pname: pname > ( pname > $o ) > $o )).
+
+thf(sy_c_member_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate_J,type,(
+    member2058392318_state: hoare_1167836817_state > ( hoare_1167836817_state > $o ) > $o )).
+
+thf(sy_v_Fa,type,(
+    fa: hoare_1167836817_state > $o )).
+
+thf(sy_v_pn,type,(
+    pn: pname )).
+
+thf(sy_v_y,type,(
+    y: com )).
+
+%----Relevant facts (699)
+thf(fact_0_empty,axiom,(
+    ! [G_3: hoare_1167836817_state > $o] :
+      ( hoare_123228589_state @ G_3 @ bot_bo70021908tate_o ) )).
+
+thf(fact_1_asm,axiom,(
+    ! [Ts_7: hoare_1167836817_state > $o,G_35: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ Ts_7 @ G_35 )
+     => ( hoare_123228589_state @ G_35 @ Ts_7 ) ) )).
+
+thf(fact_2_weaken,axiom,(
+    ! [Ts_6: hoare_1167836817_state > $o,G_34: hoare_1167836817_state > $o,Ts_5: hoare_1167836817_state > $o] :
+      ( ( hoare_123228589_state @ G_34 @ Ts_5 )
+     => ( ( ord_le827224136tate_o @ Ts_6 @ Ts_5 )
+       => ( hoare_123228589_state @ G_34 @ Ts_6 ) ) ) )).
+
+thf(fact_3_thin,axiom,(
+    ! [G_33: hoare_1167836817_state > $o,G_32: hoare_1167836817_state > $o,Ts_4: hoare_1167836817_state > $o] :
+      ( ( hoare_123228589_state @ G_32 @ Ts_4 )
+     => ( ( ord_le827224136tate_o @ G_32 @ G_33 )
+       => ( hoare_123228589_state @ G_33 @ Ts_4 ) ) ) )).
+
+thf(fact_4_cut,axiom,(
+    ! [G_31: hoare_1167836817_state > $o,G_30: hoare_1167836817_state > $o,Ts_3: hoare_1167836817_state > $o] :
+      ( ( hoare_123228589_state @ G_30 @ Ts_3 )
+     => ( ( hoare_123228589_state @ G_31 @ G_30 )
+       => ( hoare_123228589_state @ G_31 @ Ts_3 ) ) ) )).
+
+thf(fact_5_hoare__derivs_Oinsert,axiom,(
+    ! [Ts_2: hoare_1167836817_state > $o,G_29: hoare_1167836817_state > $o,T_3: hoare_1167836817_state] :
+      ( ( hoare_123228589_state @ G_29 @ ( insert2134838167_state @ T_3 @ bot_bo70021908tate_o ) )
+     => ( ( hoare_123228589_state @ G_29 @ Ts_2 )
+       => ( hoare_123228589_state @ G_29 @ ( insert2134838167_state @ T_3 @ Ts_2 ) ) ) ) )).
+
+thf(fact_6_derivs__insertD,axiom,(
+    ! [G_28: hoare_1167836817_state > $o,T_2: hoare_1167836817_state,Ts_1: hoare_1167836817_state > $o] :
+      ( ( hoare_123228589_state @ G_28 @ ( insert2134838167_state @ T_2 @ Ts_1 ) )
+     => ( ( hoare_123228589_state @ G_28 @ ( insert2134838167_state @ T_2 @ bot_bo70021908tate_o ) )
+        & ( hoare_123228589_state @ G_28 @ Ts_1 ) ) ) )).
+
+thf(fact_7_MGT__BodyN,axiom,(
+    ! [Pn_1: pname,G_3: hoare_1167836817_state > $o] :
+      ( ( hoare_123228589_state @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ Pn_1 ) ) @ G_3 ) @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn_1 ) ) ) @ bot_bo70021908tate_o ) )
+     => ( hoare_123228589_state @ G_3 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ Pn_1 ) ) @ bot_bo70021908tate_o ) ) ) )).
+
+thf(fact_8_finite__Collect__subsets,axiom,(
+    ! [A_201: ( pname > $o ) > $o] :
+      ( ( finite297249702name_o @ A_201 )
+     => ( finite1066544169me_o_o
+        @ ( collect_pname_o_o
+          @ ^ [B_43: ( pname > $o ) > $o] :
+              ( ord_le1205211808me_o_o @ B_43 @ A_201 ) ) ) ) )).
+
+thf(fact_9_finite__Collect__subsets,axiom,(
+    ! [A_201: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( finite1380128977tate_o @ A_201 )
+     => ( finite33115244te_o_o
+        @ ( collec1218656682te_o_o
+          @ ^ [B_43: ( hoare_1167836817_state > $o ) > $o] :
+              ( ord_le741939125te_o_o @ B_43 @ A_201 ) ) ) ) )).
+
+thf(fact_10_finite__Collect__subsets,axiom,(
+    ! [A_201: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ A_201 )
+     => ( finite1380128977tate_o
+        @ ( collec269976083tate_o
+          @ ^ [B_43: hoare_1167836817_state > $o] :
+              ( ord_le827224136tate_o @ B_43 @ A_201 ) ) ) ) )).
+
+thf(fact_11_finite__Collect__subsets,axiom,(
+    ! [A_201: pname > $o] :
+      ( ( finite_finite_pname @ A_201 )
+     => ( finite297249702name_o
+        @ ( collect_pname_o
+          @ ^ [B_43: pname > $o] :
+              ( ord_less_eq_pname_o @ B_43 @ A_201 ) ) ) ) )).
+
+thf(fact_12_finite__imageI,axiom,(
+    ! [H_1: hoare_1167836817_state > pname > $o,F_61: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ F_61 )
+     => ( finite297249702name_o @ ( image_2066861949name_o @ H_1 @ F_61 ) ) ) )).
+
+thf(fact_13_finite__imageI,axiom,(
+    ! [H_1: hoare_1167836817_state > hoare_1167836817_state > $o,F_61: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ F_61 )
+     => ( finite1380128977tate_o @ ( image_1745649338tate_o @ H_1 @ F_61 ) ) ) )).
+
+thf(fact_14_finite__imageI,axiom,(
+    ! [H_1: pname > pname > $o,F_61: pname > $o] :
+      ( ( finite_finite_pname @ F_61 )
+     => ( finite297249702name_o @ ( image_pname_pname_o @ H_1 @ F_61 ) ) ) )).
+
+thf(fact_15_finite__imageI,axiom,(
+    ! [H_1: pname > hoare_1167836817_state > $o,F_61: pname > $o] :
+      ( ( finite_finite_pname @ F_61 )
+     => ( finite1380128977tate_o @ ( image_475339327tate_o @ H_1 @ F_61 ) ) ) )).
+
+thf(fact_16_finite__imageI,axiom,(
+    ! [H_1: ( pname > $o ) > hoare_1167836817_state,F_61: ( pname > $o ) > $o] :
+      ( ( finite297249702name_o @ F_61 )
+     => ( finite1084549118_state @ ( image_1381916541_state @ H_1 @ F_61 ) ) ) )).
+
+thf(fact_17_finite__imageI,axiom,(
+    ! [H_1: ( hoare_1167836817_state > $o ) > hoare_1167836817_state,F_61: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( finite1380128977tate_o @ F_61 )
+     => ( finite1084549118_state @ ( image_635813834_state @ H_1 @ F_61 ) ) ) )).
+
+thf(fact_18_finite__imageI,axiom,(
+    ! [H_1: ( pname > $o ) > pname,F_61: ( pname > $o ) > $o] :
+      ( ( finite297249702name_o @ F_61 )
+     => ( finite_finite_pname @ ( image_pname_o_pname @ H_1 @ F_61 ) ) ) )).
+
+thf(fact_19_finite__imageI,axiom,(
+    ! [H_1: ( hoare_1167836817_state > $o ) > pname,F_61: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( finite1380128977tate_o @ F_61 )
+     => ( finite_finite_pname @ ( image_980295115_pname @ H_1 @ F_61 ) ) ) )).
+
+thf(fact_20_finite__imageI,axiom,(
+    ! [H_1: pname > hoare_1167836817_state,F_61: pname > $o] :
+      ( ( finite_finite_pname @ F_61 )
+     => ( finite1084549118_state @ ( image_575578384_state @ H_1 @ F_61 ) ) ) )).
+
+thf(fact_21_empty__subsetI,axiom,(
+    ! [A_200: pname > $o] :
+      ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_200 ) )).
+
+thf(fact_22_empty__subsetI,axiom,(
+    ! [A_200: hoare_1167836817_state > $o] :
+      ( ord_le827224136tate_o @ bot_bo70021908tate_o @ A_200 ) )).
+
+thf(fact_23_finite_OinsertI,axiom,(
+    ! [A_199: pname > $o,A_198: ( pname > $o ) > $o] :
+      ( ( finite297249702name_o @ A_198 )
+     => ( finite297249702name_o @ ( insert_pname_o @ A_199 @ A_198 ) ) ) )).
+
+thf(fact_24_finite_OinsertI,axiom,(
+    ! [A_199: hoare_1167836817_state > $o,A_198: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( finite1380128977tate_o @ A_198 )
+     => ( finite1380128977tate_o @ ( insert999278200tate_o @ A_199 @ A_198 ) ) ) )).
+
+thf(fact_25_finite_OinsertI,axiom,(
+    ! [A_199: pname,A_198: pname > $o] :
+      ( ( finite_finite_pname @ A_198 )
+     => ( finite_finite_pname @ ( insert_pname @ A_199 @ A_198 ) ) ) )).
+
+thf(fact_26_finite_OinsertI,axiom,(
+    ! [A_199: hoare_1167836817_state,A_198: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ A_198 )
+     => ( finite1084549118_state @ ( insert2134838167_state @ A_199 @ A_198 ) ) ) )).
+
+thf(fact_27_finite_OemptyI,axiom,
+    ( finite297249702name_o @ bot_bot_pname_o_o )).
+
+thf(fact_28_finite_OemptyI,axiom,
+    ( finite1380128977tate_o @ bot_bo691907561te_o_o )).
+
+thf(fact_29_finite_OemptyI,axiom,
+    ( finite1084549118_state @ bot_bo70021908tate_o )).
+
+thf(fact_30_finite_OemptyI,axiom,
+    ( finite_finite_pname @ bot_bot_pname_o )).
+
+thf(fact_31_finite__Collect__conjI,axiom,(
+    ! [Q_24: ( pname > $o ) > $o,P_42: ( pname > $o ) > $o] :
+      ( ( ( finite297249702name_o @ ( collect_pname_o @ P_42 ) )
+        | ( finite297249702name_o @ ( collect_pname_o @ Q_24 ) ) )
+     => ( finite297249702name_o
+        @ ( collect_pname_o
+          @ ^ [X_5: pname > $o] :
+              ( (&) @ ( P_42 @ X_5 ) @ ( Q_24 @ X_5 ) ) ) ) ) )).
+
+thf(fact_32_finite__Collect__conjI,axiom,(
+    ! [Q_24: ( hoare_1167836817_state > $o ) > $o,P_42: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( ( finite1380128977tate_o @ ( collec269976083tate_o @ P_42 ) )
+        | ( finite1380128977tate_o @ ( collec269976083tate_o @ Q_24 ) ) )
+     => ( finite1380128977tate_o
+        @ ( collec269976083tate_o
+          @ ^ [X_5: hoare_1167836817_state > $o] :
+              ( (&) @ ( P_42 @ X_5 ) @ ( Q_24 @ X_5 ) ) ) ) ) )).
+
+thf(fact_33_finite__Collect__conjI,axiom,(
+    ! [Q_24: hoare_1167836817_state > $o,P_42: hoare_1167836817_state > $o] :
+      ( ( ( finite1084549118_state @ ( collec1027672124_state @ P_42 ) )
+        | ( finite1084549118_state @ ( collec1027672124_state @ Q_24 ) ) )
+     => ( finite1084549118_state
+        @ ( collec1027672124_state
+          @ ^ [X_5: hoare_1167836817_state] :
+              ( (&) @ ( P_42 @ X_5 ) @ ( Q_24 @ X_5 ) ) ) ) ) )).
+
+thf(fact_34_finite__Collect__conjI,axiom,(
+    ! [Q_24: pname > $o,P_42: pname > $o] :
+      ( ( ( finite_finite_pname @ ( collect_pname @ P_42 ) )
+        | ( finite_finite_pname @ ( collect_pname @ Q_24 ) ) )
+     => ( finite_finite_pname
+        @ ( collect_pname
+          @ ^ [X_5: pname] :
+              ( (&) @ ( P_42 @ X_5 ) @ ( Q_24 @ X_5 ) ) ) ) ) )).
+
+thf(fact_35_image__constant__conv,axiom,(
+    ! [C_54: pname,A_197: hoare_1167836817_state > $o] :
+      ( ( ( A_197 = bot_bo70021908tate_o )
+       => ( ( image_8178176_pname
+            @ ^ [X_5: hoare_1167836817_state] : C_54
+            @ A_197 )
+          = bot_bot_pname_o ) )
+      & ( ( A_197 != bot_bo70021908tate_o )
+       => ( ( image_8178176_pname
+            @ ^ [X_5: hoare_1167836817_state] : C_54
+            @ A_197 )
+          = ( insert_pname @ C_54 @ bot_bot_pname_o ) ) ) ) )).
+
+thf(fact_36_image__constant__conv,axiom,(
+    ! [C_54: hoare_1167836817_state,A_197: pname > $o] :
+      ( ( ( A_197 = bot_bot_pname_o )
+       => ( ( image_575578384_state
+            @ ^ [X_5: pname] : C_54
+            @ A_197 )
+          = bot_bo70021908tate_o ) )
+      & ( ( A_197 != bot_bot_pname_o )
+       => ( ( image_575578384_state
+            @ ^ [X_5: pname] : C_54
+            @ A_197 )
+          = ( insert2134838167_state @ C_54 @ bot_bo70021908tate_o ) ) ) ) )).
+
+thf(fact_37_image__constant,axiom,(
+    ! [C_53: pname,X_101: hoare_1167836817_state,A_196: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ X_101 @ A_196 )
+     => ( ( image_8178176_pname
+          @ ^ [X_5: hoare_1167836817_state] : C_53
+          @ A_196 )
+        = ( insert_pname @ C_53 @ bot_bot_pname_o ) ) ) )).
+
+thf(fact_38_image__constant,axiom,(
+    ! [C_53: hoare_1167836817_state,X_101: pname,A_196: pname > $o] :
+      ( ( member_pname @ X_101 @ A_196 )
+     => ( ( image_575578384_state
+          @ ^ [X_5: pname] : C_53
+          @ A_196 )
+        = ( insert2134838167_state @ C_53 @ bot_bo70021908tate_o ) ) ) )).
+
+thf(fact_39_insert__dom,axiom,(
+    ! [F_60: pname > option_com,X_100: pname,Y_49: com] :
+      ( ( ( F_60 @ X_100 )
+        = ( some_com @ Y_49 ) )
+     => ( ( insert_pname @ X_100 @ ( dom_pname_com @ F_60 ) )
+        = ( dom_pname_com @ F_60 ) ) ) )).
+
+thf(fact_40_finite__surj,axiom,(
+    ! [B_130: ( pname > $o ) > $o,F_59: hoare_1167836817_state > pname > $o,A_195: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ A_195 )
+     => ( ( ord_le1205211808me_o_o @ B_130 @ ( image_2066861949name_o @ F_59 @ A_195 ) )
+       => ( finite297249702name_o @ B_130 ) ) ) )).
+
+thf(fact_41_finite__surj,axiom,(
+    ! [B_130: ( hoare_1167836817_state > $o ) > $o,F_59: hoare_1167836817_state > hoare_1167836817_state > $o,A_195: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ A_195 )
+     => ( ( ord_le741939125te_o_o @ B_130 @ ( image_1745649338tate_o @ F_59 @ A_195 ) )
+       => ( finite1380128977tate_o @ B_130 ) ) ) )).
+
+thf(fact_42_finite__surj,axiom,(
+    ! [B_130: pname > $o,F_59: hoare_1167836817_state > pname,A_195: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ A_195 )
+     => ( ( ord_less_eq_pname_o @ B_130 @ ( image_8178176_pname @ F_59 @ A_195 ) )
+       => ( finite_finite_pname @ B_130 ) ) ) )).
+
+thf(fact_43_finite__surj,axiom,(
+    ! [B_130: ( pname > $o ) > $o,F_59: pname > pname > $o,A_195: pname > $o] :
+      ( ( finite_finite_pname @ A_195 )
+     => ( ( ord_le1205211808me_o_o @ B_130 @ ( image_pname_pname_o @ F_59 @ A_195 ) )
+       => ( finite297249702name_o @ B_130 ) ) ) )).
+
+thf(fact_44_finite__surj,axiom,(
+    ! [B_130: ( hoare_1167836817_state > $o ) > $o,F_59: pname > hoare_1167836817_state > $o,A_195: pname > $o] :
+      ( ( finite_finite_pname @ A_195 )
+     => ( ( ord_le741939125te_o_o @ B_130 @ ( image_475339327tate_o @ F_59 @ A_195 ) )
+       => ( finite1380128977tate_o @ B_130 ) ) ) )).
+
+thf(fact_45_finite__surj,axiom,(
+    ! [B_130: pname > $o,F_59: pname > pname,A_195: pname > $o] :
+      ( ( finite_finite_pname @ A_195 )
+     => ( ( ord_less_eq_pname_o @ B_130 @ ( image_pname_pname @ F_59 @ A_195 ) )
+       => ( finite_finite_pname @ B_130 ) ) ) )).
+
+thf(fact_46_finite__surj,axiom,(
+    ! [B_130: hoare_1167836817_state > $o,F_59: ( pname > $o ) > hoare_1167836817_state,A_195: ( pname > $o ) > $o] :
+      ( ( finite297249702name_o @ A_195 )
+     => ( ( ord_le827224136tate_o @ B_130 @ ( image_1381916541_state @ F_59 @ A_195 ) )
+       => ( finite1084549118_state @ B_130 ) ) ) )).
+
+thf(fact_47_finite__surj,axiom,(
+    ! [B_130: hoare_1167836817_state > $o,F_59: ( hoare_1167836817_state > $o ) > hoare_1167836817_state,A_195: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( finite1380128977tate_o @ A_195 )
+     => ( ( ord_le827224136tate_o @ B_130 @ ( image_635813834_state @ F_59 @ A_195 ) )
+       => ( finite1084549118_state @ B_130 ) ) ) )).
+
+thf(fact_48_finite__surj,axiom,(
+    ! [B_130: pname > $o,F_59: ( pname > $o ) > pname,A_195: ( pname > $o ) > $o] :
+      ( ( finite297249702name_o @ A_195 )
+     => ( ( ord_less_eq_pname_o @ B_130 @ ( image_pname_o_pname @ F_59 @ A_195 ) )
+       => ( finite_finite_pname @ B_130 ) ) ) )).
+
+thf(fact_49_finite__surj,axiom,(
+    ! [B_130: pname > $o,F_59: ( hoare_1167836817_state > $o ) > pname,A_195: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( finite1380128977tate_o @ A_195 )
+     => ( ( ord_less_eq_pname_o @ B_130 @ ( image_980295115_pname @ F_59 @ A_195 ) )
+       => ( finite_finite_pname @ B_130 ) ) ) )).
+
+thf(fact_50_finite__surj,axiom,(
+    ! [B_130: hoare_1167836817_state > $o,F_59: pname > hoare_1167836817_state,A_195: pname > $o] :
+      ( ( finite_finite_pname @ A_195 )
+     => ( ( ord_le827224136tate_o @ B_130 @ ( image_575578384_state @ F_59 @ A_195 ) )
+       => ( finite1084549118_state @ B_130 ) ) ) )).
+
+thf(fact_51_subset__singletonD,axiom,(
+    ! [A_194: pname > $o,X_99: pname] :
+      ( ( ord_less_eq_pname_o @ A_194 @ ( insert_pname @ X_99 @ bot_bot_pname_o ) )
+     => ( ( A_194 = bot_bot_pname_o )
+        | ( A_194
+          = ( insert_pname @ X_99 @ bot_bot_pname_o ) ) ) ) )).
+
+thf(fact_52_subset__singletonD,axiom,(
+    ! [A_194: hoare_1167836817_state > $o,X_99: hoare_1167836817_state] :
+      ( ( ord_le827224136tate_o @ A_194 @ ( insert2134838167_state @ X_99 @ bot_bo70021908tate_o ) )
+     => ( ( A_194 = bot_bo70021908tate_o )
+        | ( A_194
+          = ( insert2134838167_state @ X_99 @ bot_bo70021908tate_o ) ) ) ) )).
+
+thf(fact_53_MGF,axiom,(
+    ! [C_21: com] :
+      ( hoare_1201148605gleton
+     => ( wT_bodies
+       => ( ( wt @ C_21 )
+         => ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ C_21 ) @ bot_bo70021908tate_o ) ) ) ) ) )).
+
+thf(fact_54_emptyE,axiom,(
+    ! [A_193: pname] :
+      ~ ( member_pname @ A_193 @ bot_bot_pname_o ) )).
+
+thf(fact_55_emptyE,axiom,(
+    ! [A_193: hoare_1167836817_state] :
+      ~ ( member2058392318_state @ A_193 @ bot_bo70021908tate_o ) )).
+
+thf(fact_56_insertCI,axiom,(
+    ! [B_129: pname,A_192: pname,B_128: pname > $o] :
+      ( ( ~ ( member_pname @ A_192 @ B_128 )
+       => ( A_192 = B_129 ) )
+     => ( member_pname @ A_192 @ ( insert_pname @ B_129 @ B_128 ) ) ) )).
+
+thf(fact_57_insertCI,axiom,(
+    ! [B_129: hoare_1167836817_state,A_192: hoare_1167836817_state,B_128: hoare_1167836817_state > $o] :
+      ( ( ~ ( member2058392318_state @ A_192 @ B_128 )
+       => ( A_192 = B_129 ) )
+     => ( member2058392318_state @ A_192 @ ( insert2134838167_state @ B_129 @ B_128 ) ) ) )).
+
+thf(fact_58_insertE,axiom,(
+    ! [A_191: pname,B_127: pname,A_190: pname > $o] :
+      ( ( member_pname @ A_191 @ ( insert_pname @ B_127 @ A_190 ) )
+     => ( ( A_191 != B_127 )
+       => ( member_pname @ A_191 @ A_190 ) ) ) )).
+
+thf(fact_59_insertE,axiom,(
+    ! [A_191: hoare_1167836817_state,B_127: hoare_1167836817_state,A_190: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ A_191 @ ( insert2134838167_state @ B_127 @ A_190 ) )
+     => ( ( A_191 != B_127 )
+       => ( member2058392318_state @ A_191 @ A_190 ) ) ) )).
+
+thf(fact_60_equalityI,axiom,(
+    ! [A_189: pname > $o,B_126: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_189 @ B_126 )
+     => ( ( ord_less_eq_pname_o @ B_126 @ A_189 )
+       => ( A_189 = B_126 ) ) ) )).
+
+thf(fact_61_equalityI,axiom,(
+    ! [A_189: hoare_1167836817_state > $o,B_126: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_189 @ B_126 )
+     => ( ( ord_le827224136tate_o @ B_126 @ A_189 )
+       => ( A_189 = B_126 ) ) ) )).
+
+thf(fact_62_subsetD,axiom,(
+    ! [C_52: pname,A_188: pname > $o,B_125: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_188 @ B_125 )
+     => ( ( member_pname @ C_52 @ A_188 )
+       => ( member_pname @ C_52 @ B_125 ) ) ) )).
+
+thf(fact_63_subsetD,axiom,(
+    ! [C_52: hoare_1167836817_state,A_188: hoare_1167836817_state > $o,B_125: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_188 @ B_125 )
+     => ( ( member2058392318_state @ C_52 @ A_188 )
+       => ( member2058392318_state @ C_52 @ B_125 ) ) ) )).
+
+thf(fact_64_image__eqI,axiom,(
+    ! [A_187: hoare_1167836817_state > $o,B_124: pname,F_58: hoare_1167836817_state > pname,X_98: hoare_1167836817_state] :
+      ( ( B_124
+        = ( F_58 @ X_98 ) )
+     => ( ( member2058392318_state @ X_98 @ A_187 )
+       => ( member_pname @ B_124 @ ( image_8178176_pname @ F_58 @ A_187 ) ) ) ) )).
+
+thf(fact_65_image__eqI,axiom,(
+    ! [A_187: pname > $o,B_124: hoare_1167836817_state,F_58: pname > hoare_1167836817_state,X_98: pname] :
+      ( ( B_124
+        = ( F_58 @ X_98 ) )
+     => ( ( member_pname @ X_98 @ A_187 )
+       => ( member2058392318_state @ B_124 @ ( image_575578384_state @ F_58 @ A_187 ) ) ) ) )).
+
+thf(fact_66_equals0D,axiom,(
+    ! [A_186: pname,A_185: pname > $o] :
+      ( ( A_185 = bot_bot_pname_o )
+     => ~ ( member_pname @ A_186 @ A_185 ) ) )).
+
+thf(fact_67_equals0D,axiom,(
+    ! [A_186: hoare_1167836817_state,A_185: hoare_1167836817_state > $o] :
+      ( ( A_185 = bot_bo70021908tate_o )
+     => ~ ( member2058392318_state @ A_186 @ A_185 ) ) )).
+
+thf(fact_68_Collect__empty__eq,axiom,(
+    ! [P_41: pname > $o] :
+      ( ( ( collect_pname @ P_41 )
+        = bot_bot_pname_o )
+    <=> ! [X_5: pname] :
+          ~ ( P_41 @ X_5 ) ) )).
+
+thf(fact_69_Collect__empty__eq,axiom,(
+    ! [P_41: ( pname > $o ) > $o] :
+      ( ( ( collect_pname_o @ P_41 )
+        = bot_bot_pname_o_o )
+    <=> ! [X_5: pname > $o] :
+          ~ ( P_41 @ X_5 ) ) )).
+
+thf(fact_70_Collect__empty__eq,axiom,(
+    ! [P_41: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( ( collec269976083tate_o @ P_41 )
+        = bot_bo691907561te_o_o )
+    <=> ! [X_5: hoare_1167836817_state > $o] :
+          ~ ( P_41 @ X_5 ) ) )).
+
+thf(fact_71_Collect__empty__eq,axiom,(
+    ! [P_41: hoare_1167836817_state > $o] :
+      ( ( ( collec1027672124_state @ P_41 )
+        = bot_bo70021908tate_o )
+    <=> ! [X_5: hoare_1167836817_state] :
+          ~ ( P_41 @ X_5 ) ) )).
+
+thf(fact_72_empty__iff,axiom,(
+    ! [C_51: pname] :
+      ~ ( member_pname @ C_51 @ bot_bot_pname_o ) )).
+
+thf(fact_73_empty__iff,axiom,(
+    ! [C_51: hoare_1167836817_state] :
+      ~ ( member2058392318_state @ C_51 @ bot_bo70021908tate_o ) )).
+
+thf(fact_74_empty__Collect__eq,axiom,(
+    ! [P_40: pname > $o] :
+      ( ( bot_bot_pname_o
+        = ( collect_pname @ P_40 ) )
+    <=> ! [X_5: pname] :
+          ~ ( P_40 @ X_5 ) ) )).
+
+thf(fact_75_empty__Collect__eq,axiom,(
+    ! [P_40: ( pname > $o ) > $o] :
+      ( ( bot_bot_pname_o_o
+        = ( collect_pname_o @ P_40 ) )
+    <=> ! [X_5: pname > $o] :
+          ~ ( P_40 @ X_5 ) ) )).
+
+thf(fact_76_empty__Collect__eq,axiom,(
+    ! [P_40: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( bot_bo691907561te_o_o
+        = ( collec269976083tate_o @ P_40 ) )
+    <=> ! [X_5: hoare_1167836817_state > $o] :
+          ~ ( P_40 @ X_5 ) ) )).
+
+thf(fact_77_empty__Collect__eq,axiom,(
+    ! [P_40: hoare_1167836817_state > $o] :
+      ( ( bot_bo70021908tate_o
+        = ( collec1027672124_state @ P_40 ) )
+    <=> ! [X_5: hoare_1167836817_state] :
+          ~ ( P_40 @ X_5 ) ) )).
+
+thf(fact_78_ex__in__conv,axiom,(
+    ! [A_184: pname > $o] :
+      ( ? [X_5: pname] :
+          ( member_pname @ X_5 @ A_184 )
+    <=> ( A_184 != bot_bot_pname_o ) ) )).
+
+thf(fact_79_ex__in__conv,axiom,(
+    ! [A_184: hoare_1167836817_state > $o] :
+      ( ? [X_5: hoare_1167836817_state] :
+          ( member2058392318_state @ X_5 @ A_184 )
+    <=> ( A_184 != bot_bo70021908tate_o ) ) )).
+
+thf(fact_80_all__not__in__conv,axiom,(
+    ! [A_183: pname > $o] :
+      ( ! [X_5: pname] :
+          ~ ( member_pname @ X_5 @ A_183 )
+    <=> ( A_183 = bot_bot_pname_o ) ) )).
+
+thf(fact_81_all__not__in__conv,axiom,(
+    ! [A_183: hoare_1167836817_state > $o] :
+      ( ! [X_5: hoare_1167836817_state] :
+          ~ ( member2058392318_state @ X_5 @ A_183 )
+    <=> ( A_183 = bot_bo70021908tate_o ) ) )).
+
+thf(fact_82_empty__def,axiom,
+    ( bot_bot_pname_o
+    = ( collect_pname
+      @ ^ [X_5: pname] : $false ) )).
+
+thf(fact_83_empty__def,axiom,
+    ( bot_bot_pname_o_o
+    = ( collect_pname_o
+      @ ^ [X_5: pname > $o] : $false ) )).
+
+thf(fact_84_empty__def,axiom,
+    ( bot_bo691907561te_o_o
+    = ( collec269976083tate_o
+      @ ^ [X_5: hoare_1167836817_state > $o] : $false ) )).
+
+thf(fact_85_empty__def,axiom,
+    ( bot_bo70021908tate_o
+    = ( collec1027672124_state
+      @ ^ [X_5: hoare_1167836817_state] : $false ) )).
+
+thf(fact_86_insert__absorb,axiom,(
+    ! [A_182: pname,A_181: pname > $o] :
+      ( ( member_pname @ A_182 @ A_181 )
+     => ( ( insert_pname @ A_182 @ A_181 )
+        = A_181 ) ) )).
+
+thf(fact_87_insert__absorb,axiom,(
+    ! [A_182: hoare_1167836817_state,A_181: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ A_182 @ A_181 )
+     => ( ( insert2134838167_state @ A_182 @ A_181 )
+        = A_181 ) ) )).
+
+thf(fact_88_insertI2,axiom,(
+    ! [B_123: pname,A_180: pname,B_122: pname > $o] :
+      ( ( member_pname @ A_180 @ B_122 )
+     => ( member_pname @ A_180 @ ( insert_pname @ B_123 @ B_122 ) ) ) )).
+
+thf(fact_89_insertI2,axiom,(
+    ! [B_123: hoare_1167836817_state,A_180: hoare_1167836817_state,B_122: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ A_180 @ B_122 )
+     => ( member2058392318_state @ A_180 @ ( insert2134838167_state @ B_123 @ B_122 ) ) ) )).
+
+thf(fact_90_insert__ident,axiom,(
+    ! [B_121: pname > $o,X_97: pname,A_179: pname > $o] :
+      ( ~ ( member_pname @ X_97 @ A_179 )
+     => ( ~ ( member_pname @ X_97 @ B_121 )
+       => ( ( ( insert_pname @ X_97 @ A_179 )
+            = ( insert_pname @ X_97 @ B_121 ) )
+        <=> ( A_179 = B_121 ) ) ) ) )).
+
+thf(fact_91_insert__ident,axiom,(
+    ! [B_121: hoare_1167836817_state > $o,X_97: hoare_1167836817_state,A_179: hoare_1167836817_state > $o] :
+      ( ~ ( member2058392318_state @ X_97 @ A_179 )
+     => ( ~ ( member2058392318_state @ X_97 @ B_121 )
+       => ( ( ( insert2134838167_state @ X_97 @ A_179 )
+            = ( insert2134838167_state @ X_97 @ B_121 ) )
+        <=> ( A_179 = B_121 ) ) ) ) )).
+
+thf(fact_92_insert__code,axiom,(
+    ! [Y_48: pname,A_178: pname > $o,X_96: pname] :
+      ( ( insert_pname @ Y_48 @ A_178 @ X_96 )
+    <=> ( ( Y_48 = X_96 )
+        | ( A_178 @ X_96 ) ) ) )).
+
+thf(fact_93_insert__code,axiom,(
+    ! [Y_48: hoare_1167836817_state,A_178: hoare_1167836817_state > $o,X_96: hoare_1167836817_state] :
+      ( ( insert2134838167_state @ Y_48 @ A_178 @ X_96 )
+    <=> ( ( Y_48 = X_96 )
+        | ( A_178 @ X_96 ) ) ) )).
+
+thf(fact_94_insert__iff,axiom,(
+    ! [A_177: pname,B_120: pname,A_176: pname > $o] :
+      ( ( member_pname @ A_177 @ ( insert_pname @ B_120 @ A_176 ) )
+    <=> ( ( A_177 = B_120 )
+        | ( member_pname @ A_177 @ A_176 ) ) ) )).
+
+thf(fact_95_insert__iff,axiom,(
+    ! [A_177: hoare_1167836817_state,B_120: hoare_1167836817_state,A_176: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ A_177 @ ( insert2134838167_state @ B_120 @ A_176 ) )
+    <=> ( ( A_177 = B_120 )
+        | ( member2058392318_state @ A_177 @ A_176 ) ) ) )).
+
+thf(fact_96_insert__commute,axiom,(
+    ! [X_95: pname,Y_47: pname,A_175: pname > $o] :
+      ( ( insert_pname @ X_95 @ ( insert_pname @ Y_47 @ A_175 ) )
+      = ( insert_pname @ Y_47 @ ( insert_pname @ X_95 @ A_175 ) ) ) )).
+
+thf(fact_97_insert__commute,axiom,(
+    ! [X_95: hoare_1167836817_state,Y_47: hoare_1167836817_state,A_175: hoare_1167836817_state > $o] :
+      ( ( insert2134838167_state @ X_95 @ ( insert2134838167_state @ Y_47 @ A_175 ) )
+      = ( insert2134838167_state @ Y_47 @ ( insert2134838167_state @ X_95 @ A_175 ) ) ) )).
+
+thf(fact_98_insert__absorb2,axiom,(
+    ! [X_94: pname,A_174: pname > $o] :
+      ( ( insert_pname @ X_94 @ ( insert_pname @ X_94 @ A_174 ) )
+      = ( insert_pname @ X_94 @ A_174 ) ) )).
+
+thf(fact_99_insert__absorb2,axiom,(
+    ! [X_94: hoare_1167836817_state,A_174: hoare_1167836817_state > $o] :
+      ( ( insert2134838167_state @ X_94 @ ( insert2134838167_state @ X_94 @ A_174 ) )
+      = ( insert2134838167_state @ X_94 @ A_174 ) ) )).
+
+thf(fact_100_insert__Collect,axiom,(
+    ! [A_173: pname,P_39: pname > $o] :
+      ( ( insert_pname @ A_173 @ ( collect_pname @ P_39 ) )
+      = ( collect_pname
+        @ ^ [U_2: pname] :
+            ( (=>) @ ( (~) @ ( U_2 = A_173 ) ) @ ( P_39 @ U_2 ) ) ) ) )).
+
+thf(fact_101_insert__Collect,axiom,(
+    ! [A_173: pname > $o,P_39: ( pname > $o ) > $o] :
+      ( ( insert_pname_o @ A_173 @ ( collect_pname_o @ P_39 ) )
+      = ( collect_pname_o
+        @ ^ [U_2: pname > $o] :
+            ( (=>) @ ( (~) @ ( U_2 = A_173 ) ) @ ( P_39 @ U_2 ) ) ) ) )).
+
+thf(fact_102_insert__Collect,axiom,(
+    ! [A_173: hoare_1167836817_state > $o,P_39: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( insert999278200tate_o @ A_173 @ ( collec269976083tate_o @ P_39 ) )
+      = ( collec269976083tate_o
+        @ ^ [U_2: hoare_1167836817_state > $o] :
+            ( (=>) @ ( (~) @ ( U_2 = A_173 ) ) @ ( P_39 @ U_2 ) ) ) ) )).
+
+thf(fact_103_insert__Collect,axiom,(
+    ! [A_173: hoare_1167836817_state,P_39: hoare_1167836817_state > $o] :
+      ( ( insert2134838167_state @ A_173 @ ( collec1027672124_state @ P_39 ) )
+      = ( collec1027672124_state
+        @ ^ [U_2: hoare_1167836817_state] :
+            ( (=>) @ ( (~) @ ( U_2 = A_173 ) ) @ ( P_39 @ U_2 ) ) ) ) )).
+
+thf(fact_104_insert__compr,axiom,(
+    ! [A_172: pname,B_119: pname > $o] :
+      ( ( insert_pname @ A_172 @ B_119 )
+      = ( collect_pname
+        @ ^ [X_5: pname] :
+            ( (|) @ ( X_5 = A_172 ) @ ( member_pname @ X_5 @ B_119 ) ) ) ) )).
+
+thf(fact_105_insert__compr,axiom,(
+    ! [A_172: pname > $o,B_119: ( pname > $o ) > $o] :
+      ( ( insert_pname_o @ A_172 @ B_119 )
+      = ( collect_pname_o
+        @ ^ [X_5: pname > $o] :
+            ( (|) @ ( X_5 = A_172 ) @ ( member_pname_o @ X_5 @ B_119 ) ) ) ) )).
+
+thf(fact_106_insert__compr,axiom,(
+    ! [A_172: hoare_1167836817_state > $o,B_119: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( insert999278200tate_o @ A_172 @ B_119 )
+      = ( collec269976083tate_o
+        @ ^ [X_5: hoare_1167836817_state > $o] :
+            ( (|) @ ( X_5 = A_172 ) @ ( member864234961tate_o @ X_5 @ B_119 ) ) ) ) )).
+
+thf(fact_107_insert__compr,axiom,(
+    ! [A_172: hoare_1167836817_state,B_119: hoare_1167836817_state > $o] :
+      ( ( insert2134838167_state @ A_172 @ B_119 )
+      = ( collec1027672124_state
+        @ ^ [X_5: hoare_1167836817_state] :
+            ( (|) @ ( X_5 = A_172 ) @ ( member2058392318_state @ X_5 @ B_119 ) ) ) ) )).
+
+thf(fact_108_insertI1,axiom,(
+    ! [A_171: pname,B_118: pname > $o] :
+      ( member_pname @ A_171 @ ( insert_pname @ A_171 @ B_118 ) ) )).
+
+thf(fact_109_insertI1,axiom,(
+    ! [A_171: hoare_1167836817_state,B_118: hoare_1167836817_state > $o] :
+      ( member2058392318_state @ A_171 @ ( insert2134838167_state @ A_171 @ B_118 ) ) )).
+
+thf(fact_110_equalityE,axiom,(
+    ! [A_170: pname > $o,B_117: pname > $o] :
+      ( ( A_170 = B_117 )
+     => ~ ( ( ord_less_eq_pname_o @ A_170 @ B_117 )
+         => ~ ( ord_less_eq_pname_o @ B_117 @ A_170 ) ) ) )).
+
+thf(fact_111_equalityE,axiom,(
+    ! [A_170: hoare_1167836817_state > $o,B_117: hoare_1167836817_state > $o] :
+      ( ( A_170 = B_117 )
+     => ~ ( ( ord_le827224136tate_o @ A_170 @ B_117 )
+         => ~ ( ord_le827224136tate_o @ B_117 @ A_170 ) ) ) )).
+
+thf(fact_112_subset__trans,axiom,(
+    ! [C_50: pname > $o,A_169: pname > $o,B_116: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_169 @ B_116 )
+     => ( ( ord_less_eq_pname_o @ B_116 @ C_50 )
+       => ( ord_less_eq_pname_o @ A_169 @ C_50 ) ) ) )).
+
+thf(fact_113_subset__trans,axiom,(
+    ! [C_50: hoare_1167836817_state > $o,A_169: hoare_1167836817_state > $o,B_116: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_169 @ B_116 )
+     => ( ( ord_le827224136tate_o @ B_116 @ C_50 )
+       => ( ord_le827224136tate_o @ A_169 @ C_50 ) ) ) )).
+
+thf(fact_114_set__mp,axiom,(
+    ! [X_93: pname,A_168: pname > $o,B_115: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_168 @ B_115 )
+     => ( ( member_pname @ X_93 @ A_168 )
+       => ( member_pname @ X_93 @ B_115 ) ) ) )).
+
+thf(fact_115_set__mp,axiom,(
+    ! [X_93: hoare_1167836817_state,A_168: hoare_1167836817_state > $o,B_115: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_168 @ B_115 )
+     => ( ( member2058392318_state @ X_93 @ A_168 )
+       => ( member2058392318_state @ X_93 @ B_115 ) ) ) )).
+
+thf(fact_116_set__rev__mp,axiom,(
+    ! [B_114: pname > $o,X_92: pname,A_167: pname > $o] :
+      ( ( member_pname @ X_92 @ A_167 )
+     => ( ( ord_less_eq_pname_o @ A_167 @ B_114 )
+       => ( member_pname @ X_92 @ B_114 ) ) ) )).
+
+thf(fact_117_set__rev__mp,axiom,(
+    ! [B_114: hoare_1167836817_state > $o,X_92: hoare_1167836817_state,A_167: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ X_92 @ A_167 )
+     => ( ( ord_le827224136tate_o @ A_167 @ B_114 )
+       => ( member2058392318_state @ X_92 @ B_114 ) ) ) )).
+
+thf(fact_118_in__mono,axiom,(
+    ! [X_91: pname,A_166: pname > $o,B_113: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_166 @ B_113 )
+     => ( ( member_pname @ X_91 @ A_166 )
+       => ( member_pname @ X_91 @ B_113 ) ) ) )).
+
+thf(fact_119_in__mono,axiom,(
+    ! [X_91: hoare_1167836817_state,A_166: hoare_1167836817_state > $o,B_113: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_166 @ B_113 )
+     => ( ( member2058392318_state @ X_91 @ A_166 )
+       => ( member2058392318_state @ X_91 @ B_113 ) ) ) )).
+
+thf(fact_120_equalityD2,axiom,(
+    ! [A_165: pname > $o,B_112: pname > $o] :
+      ( ( A_165 = B_112 )
+     => ( ord_less_eq_pname_o @ B_112 @ A_165 ) ) )).
+
+thf(fact_121_equalityD2,axiom,(
+    ! [A_165: hoare_1167836817_state > $o,B_112: hoare_1167836817_state > $o] :
+      ( ( A_165 = B_112 )
+     => ( ord_le827224136tate_o @ B_112 @ A_165 ) ) )).
+
+thf(fact_122_equalityD1,axiom,(
+    ! [A_164: pname > $o,B_111: pname > $o] :
+      ( ( A_164 = B_111 )
+     => ( ord_less_eq_pname_o @ A_164 @ B_111 ) ) )).
+
+thf(fact_123_equalityD1,axiom,(
+    ! [A_164: hoare_1167836817_state > $o,B_111: hoare_1167836817_state > $o] :
+      ( ( A_164 = B_111 )
+     => ( ord_le827224136tate_o @ A_164 @ B_111 ) ) )).
+
+thf(fact_124_set__eq__subset,axiom,(
+    ! [A_163: pname > $o,B_110: pname > $o] :
+      ( ( A_163 = B_110 )
+    <=> ( ( ord_less_eq_pname_o @ A_163 @ B_110 )
+        & ( ord_less_eq_pname_o @ B_110 @ A_163 ) ) ) )).
+
+thf(fact_125_set__eq__subset,axiom,(
+    ! [A_163: hoare_1167836817_state > $o,B_110: hoare_1167836817_state > $o] :
+      ( ( A_163 = B_110 )
+    <=> ( ( ord_le827224136tate_o @ A_163 @ B_110 )
+        & ( ord_le827224136tate_o @ B_110 @ A_163 ) ) ) )).
+
+thf(fact_126_subset__refl,axiom,(
+    ! [A_162: pname > $o] :
+      ( ord_less_eq_pname_o @ A_162 @ A_162 ) )).
+
+thf(fact_127_subset__refl,axiom,(
+    ! [A_162: hoare_1167836817_state > $o] :
+      ( ord_le827224136tate_o @ A_162 @ A_162 ) )).
+
+thf(fact_128_rev__image__eqI,axiom,(
+    ! [B_109: pname,F_57: hoare_1167836817_state > pname,X_90: hoare_1167836817_state,A_161: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ X_90 @ A_161 )
+     => ( ( B_109
+          = ( F_57 @ X_90 ) )
+       => ( member_pname @ B_109 @ ( image_8178176_pname @ F_57 @ A_161 ) ) ) ) )).
+
+thf(fact_129_rev__image__eqI,axiom,(
+    ! [B_109: hoare_1167836817_state,F_57: pname > hoare_1167836817_state,X_90: pname,A_161: pname > $o] :
+      ( ( member_pname @ X_90 @ A_161 )
+     => ( ( B_109
+          = ( F_57 @ X_90 ) )
+       => ( member2058392318_state @ B_109 @ ( image_575578384_state @ F_57 @ A_161 ) ) ) ) )).
+
+thf(fact_130_imageI,axiom,(
+    ! [F_56: hoare_1167836817_state > pname,X_89: hoare_1167836817_state,A_160: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ X_89 @ A_160 )
+     => ( member_pname @ ( F_56 @ X_89 ) @ ( image_8178176_pname @ F_56 @ A_160 ) ) ) )).
+
+thf(fact_131_imageI,axiom,(
+    ! [F_56: pname > hoare_1167836817_state,X_89: pname,A_160: pname > $o] :
+      ( ( member_pname @ X_89 @ A_160 )
+     => ( member2058392318_state @ ( F_56 @ X_89 ) @ ( image_575578384_state @ F_56 @ A_160 ) ) ) )).
+
+thf(fact_132_image__iff,axiom,(
+    ! [Z_21: hoare_1167836817_state,F_55: pname > hoare_1167836817_state,A_159: pname > $o] :
+      ( ( member2058392318_state @ Z_21 @ ( image_575578384_state @ F_55 @ A_159 ) )
+    <=> ? [X_5: pname] :
+          ( ( member_pname @ X_5 @ A_159 )
+          & ( Z_21
+            = ( F_55 @ X_5 ) ) ) ) )).
+
+thf(fact_133_finite__Collect__disjI,axiom,(
+    ! [P_38: ( pname > $o ) > $o,Q_23: ( pname > $o ) > $o] :
+      ( ( finite297249702name_o
+        @ ( collect_pname_o
+          @ ^ [X_5: pname > $o] :
+              ( (|) @ ( P_38 @ X_5 ) @ ( Q_23 @ X_5 ) ) ) )
+    <=> ( ( finite297249702name_o @ ( collect_pname_o @ P_38 ) )
+        & ( finite297249702name_o @ ( collect_pname_o @ Q_23 ) ) ) ) )).
+
+thf(fact_134_finite__Collect__disjI,axiom,(
+    ! [P_38: ( hoare_1167836817_state > $o ) > $o,Q_23: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( finite1380128977tate_o
+        @ ( collec269976083tate_o
+          @ ^ [X_5: hoare_1167836817_state > $o] :
+              ( (|) @ ( P_38 @ X_5 ) @ ( Q_23 @ X_5 ) ) ) )
+    <=> ( ( finite1380128977tate_o @ ( collec269976083tate_o @ P_38 ) )
+        & ( finite1380128977tate_o @ ( collec269976083tate_o @ Q_23 ) ) ) ) )).
+
+thf(fact_135_finite__Collect__disjI,axiom,(
+    ! [P_38: hoare_1167836817_state > $o,Q_23: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state
+        @ ( collec1027672124_state
+          @ ^ [X_5: hoare_1167836817_state] :
+              ( (|) @ ( P_38 @ X_5 ) @ ( Q_23 @ X_5 ) ) ) )
+    <=> ( ( finite1084549118_state @ ( collec1027672124_state @ P_38 ) )
+        & ( finite1084549118_state @ ( collec1027672124_state @ Q_23 ) ) ) ) )).
+
+thf(fact_136_finite__Collect__disjI,axiom,(
+    ! [P_38: pname > $o,Q_23: pname > $o] :
+      ( ( finite_finite_pname
+        @ ( collect_pname
+          @ ^ [X_5: pname] :
+              ( (|) @ ( P_38 @ X_5 ) @ ( Q_23 @ X_5 ) ) ) )
+    <=> ( ( finite_finite_pname @ ( collect_pname @ P_38 ) )
+        & ( finite_finite_pname @ ( collect_pname @ Q_23 ) ) ) ) )).
+
+thf(fact_137_insert__compr__raw,axiom,(
+    ! [X_5: pname,Xa: pname > $o] :
+      ( ( insert_pname @ X_5 @ Xa )
+      = ( collect_pname
+        @ ^ [Y_2: pname] :
+            ( (|) @ ( Y_2 = X_5 ) @ ( member_pname @ Y_2 @ Xa ) ) ) ) )).
+
+thf(fact_138_insert__compr__raw,axiom,(
+    ! [X_5: pname > $o,Xa: ( pname > $o ) > $o] :
+      ( ( insert_pname_o @ X_5 @ Xa )
+      = ( collect_pname_o
+        @ ^ [Y_2: pname > $o] :
+            ( (|) @ ( Y_2 = X_5 ) @ ( member_pname_o @ Y_2 @ Xa ) ) ) ) )).
+
+thf(fact_139_insert__compr__raw,axiom,(
+    ! [X_5: hoare_1167836817_state > $o,Xa: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( insert999278200tate_o @ X_5 @ Xa )
+      = ( collec269976083tate_o
+        @ ^ [Y_2: hoare_1167836817_state > $o] :
+            ( (|) @ ( Y_2 = X_5 ) @ ( member864234961tate_o @ Y_2 @ Xa ) ) ) ) )).
+
+thf(fact_140_insert__compr__raw,axiom,(
+    ! [X_5: hoare_1167836817_state,Xa: hoare_1167836817_state > $o] :
+      ( ( insert2134838167_state @ X_5 @ Xa )
+      = ( collec1027672124_state
+        @ ^ [Y_2: hoare_1167836817_state] :
+            ( (|) @ ( Y_2 = X_5 ) @ ( member2058392318_state @ Y_2 @ Xa ) ) ) ) )).
+
+thf(fact_141_singleton__inject,axiom,(
+    ! [A_158: pname,B_108: pname] :
+      ( ( ( insert_pname @ A_158 @ bot_bot_pname_o )
+        = ( insert_pname @ B_108 @ bot_bot_pname_o ) )
+     => ( A_158 = B_108 ) ) )).
+
+thf(fact_142_singleton__inject,axiom,(
+    ! [A_158: hoare_1167836817_state,B_108: hoare_1167836817_state] :
+      ( ( ( insert2134838167_state @ A_158 @ bot_bo70021908tate_o )
+        = ( insert2134838167_state @ B_108 @ bot_bo70021908tate_o ) )
+     => ( A_158 = B_108 ) ) )).
+
+thf(fact_143_singletonE,axiom,(
+    ! [B_107: pname,A_157: pname] :
+      ( ( member_pname @ B_107 @ ( insert_pname @ A_157 @ bot_bot_pname_o ) )
+     => ( B_107 = A_157 ) ) )).
+
+thf(fact_144_singletonE,axiom,(
+    ! [B_107: hoare_1167836817_state,A_157: hoare_1167836817_state] :
+      ( ( member2058392318_state @ B_107 @ ( insert2134838167_state @ A_157 @ bot_bo70021908tate_o ) )
+     => ( B_107 = A_157 ) ) )).
+
+thf(fact_145_doubleton__eq__iff,axiom,(
+    ! [A_156: pname,B_106: pname,C_49: pname,D_6: pname] :
+      ( ( ( insert_pname @ A_156 @ ( insert_pname @ B_106 @ bot_bot_pname_o ) )
+        = ( insert_pname @ C_49 @ ( insert_pname @ D_6 @ bot_bot_pname_o ) ) )
+    <=> ( ( ( A_156 = C_49 )
+          & ( B_106 = D_6 ) )
+        | ( ( A_156 = D_6 )
+          & ( B_106 = C_49 ) ) ) ) )).
+
+thf(fact_146_doubleton__eq__iff,axiom,(
+    ! [A_156: hoare_1167836817_state,B_106: hoare_1167836817_state,C_49: hoare_1167836817_state,D_6: hoare_1167836817_state] :
+      ( ( ( insert2134838167_state @ A_156 @ ( insert2134838167_state @ B_106 @ bot_bo70021908tate_o ) )
+        = ( insert2134838167_state @ C_49 @ ( insert2134838167_state @ D_6 @ bot_bo70021908tate_o ) ) )
+    <=> ( ( ( A_156 = C_49 )
+          & ( B_106 = D_6 ) )
+        | ( ( A_156 = D_6 )
+          & ( B_106 = C_49 ) ) ) ) )).
+
+thf(fact_147_singleton__iff,axiom,(
+    ! [B_105: pname,A_155: pname] :
+      ( ( member_pname @ B_105 @ ( insert_pname @ A_155 @ bot_bot_pname_o ) )
+    <=> ( B_105 = A_155 ) ) )).
+
+thf(fact_148_singleton__iff,axiom,(
+    ! [B_105: hoare_1167836817_state,A_155: hoare_1167836817_state] :
+      ( ( member2058392318_state @ B_105 @ ( insert2134838167_state @ A_155 @ bot_bo70021908tate_o ) )
+    <=> ( B_105 = A_155 ) ) )).
+
+thf(fact_149_insert__not__empty,axiom,(
+    ! [A_154: pname,A_153: pname > $o] :
+      ( ( insert_pname @ A_154 @ A_153 )
+     != bot_bot_pname_o ) )).
+
+thf(fact_150_insert__not__empty,axiom,(
+    ! [A_154: hoare_1167836817_state,A_153: hoare_1167836817_state > $o] :
+      ( ( insert2134838167_state @ A_154 @ A_153 )
+     != bot_bo70021908tate_o ) )).
+
+thf(fact_151_empty__not__insert,axiom,(
+    ! [A_152: pname,A_151: pname > $o] :
+      ( bot_bot_pname_o
+     != ( insert_pname @ A_152 @ A_151 ) ) )).
+
+thf(fact_152_empty__not__insert,axiom,(
+    ! [A_152: hoare_1167836817_state,A_151: hoare_1167836817_state > $o] :
+      ( bot_bo70021908tate_o
+     != ( insert2134838167_state @ A_152 @ A_151 ) ) )).
+
+thf(fact_153_finite__insert,axiom,(
+    ! [A_150: pname > $o,A_149: ( pname > $o ) > $o] :
+      ( ( finite297249702name_o @ ( insert_pname_o @ A_150 @ A_149 ) )
+    <=> ( finite297249702name_o @ A_149 ) ) )).
+
+thf(fact_154_finite__insert,axiom,(
+    ! [A_150: hoare_1167836817_state > $o,A_149: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( finite1380128977tate_o @ ( insert999278200tate_o @ A_150 @ A_149 ) )
+    <=> ( finite1380128977tate_o @ A_149 ) ) )).
+
+thf(fact_155_finite__insert,axiom,(
+    ! [A_150: pname,A_149: pname > $o] :
+      ( ( finite_finite_pname @ ( insert_pname @ A_150 @ A_149 ) )
+    <=> ( finite_finite_pname @ A_149 ) ) )).
+
+thf(fact_156_finite__insert,axiom,(
+    ! [A_150: hoare_1167836817_state,A_149: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ ( insert2134838167_state @ A_150 @ A_149 ) )
+    <=> ( finite1084549118_state @ A_149 ) ) )).
+
+thf(fact_157_subset__empty,axiom,(
+    ! [A_148: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_148 @ bot_bot_pname_o )
+    <=> ( A_148 = bot_bot_pname_o ) ) )).
+
+thf(fact_158_subset__empty,axiom,(
+    ! [A_148: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_148 @ bot_bo70021908tate_o )
+    <=> ( A_148 = bot_bo70021908tate_o ) ) )).
+
+thf(fact_159_image__is__empty,axiom,(
+    ! [F_54: hoare_1167836817_state > pname,A_147: hoare_1167836817_state > $o] :
+      ( ( ( image_8178176_pname @ F_54 @ A_147 )
+        = bot_bot_pname_o )
+    <=> ( A_147 = bot_bo70021908tate_o ) ) )).
+
+thf(fact_160_image__is__empty,axiom,(
+    ! [F_54: pname > hoare_1167836817_state,A_147: pname > $o] :
+      ( ( ( image_575578384_state @ F_54 @ A_147 )
+        = bot_bo70021908tate_o )
+    <=> ( A_147 = bot_bot_pname_o ) ) )).
+
+thf(fact_161_image__empty,axiom,(
+    ! [F_53: hoare_1167836817_state > pname] :
+      ( ( image_8178176_pname @ F_53 @ bot_bo70021908tate_o )
+      = bot_bot_pname_o ) )).
+
+thf(fact_162_image__empty,axiom,(
+    ! [F_53: pname > hoare_1167836817_state] :
+      ( ( image_575578384_state @ F_53 @ bot_bot_pname_o )
+      = bot_bo70021908tate_o ) )).
+
+thf(fact_163_empty__is__image,axiom,(
+    ! [F_52: hoare_1167836817_state > pname,A_146: hoare_1167836817_state > $o] :
+      ( ( bot_bot_pname_o
+        = ( image_8178176_pname @ F_52 @ A_146 ) )
+    <=> ( A_146 = bot_bo70021908tate_o ) ) )).
+
+thf(fact_164_empty__is__image,axiom,(
+    ! [F_52: pname > hoare_1167836817_state,A_146: pname > $o] :
+      ( ( bot_bo70021908tate_o
+        = ( image_575578384_state @ F_52 @ A_146 ) )
+    <=> ( A_146 = bot_bot_pname_o ) ) )).
+
+thf(fact_165_finite__subset,axiom,(
+    ! [A_145: ( pname > $o ) > $o,B_104: ( pname > $o ) > $o] :
+      ( ( ord_le1205211808me_o_o @ A_145 @ B_104 )
+     => ( ( finite297249702name_o @ B_104 )
+       => ( finite297249702name_o @ A_145 ) ) ) )).
+
+thf(fact_166_finite__subset,axiom,(
+    ! [A_145: ( hoare_1167836817_state > $o ) > $o,B_104: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( ord_le741939125te_o_o @ A_145 @ B_104 )
+     => ( ( finite1380128977tate_o @ B_104 )
+       => ( finite1380128977tate_o @ A_145 ) ) ) )).
+
+thf(fact_167_finite__subset,axiom,(
+    ! [A_145: hoare_1167836817_state > $o,B_104: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_145 @ B_104 )
+     => ( ( finite1084549118_state @ B_104 )
+       => ( finite1084549118_state @ A_145 ) ) ) )).
+
+thf(fact_168_finite__subset,axiom,(
+    ! [A_145: pname > $o,B_104: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_145 @ B_104 )
+     => ( ( finite_finite_pname @ B_104 )
+       => ( finite_finite_pname @ A_145 ) ) ) )).
+
+thf(fact_169_rev__finite__subset,axiom,(
+    ! [A_144: ( pname > $o ) > $o,B_103: ( pname > $o ) > $o] :
+      ( ( finite297249702name_o @ B_103 )
+     => ( ( ord_le1205211808me_o_o @ A_144 @ B_103 )
+       => ( finite297249702name_o @ A_144 ) ) ) )).
+
+thf(fact_170_rev__finite__subset,axiom,(
+    ! [A_144: ( hoare_1167836817_state > $o ) > $o,B_103: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( finite1380128977tate_o @ B_103 )
+     => ( ( ord_le741939125te_o_o @ A_144 @ B_103 )
+       => ( finite1380128977tate_o @ A_144 ) ) ) )).
+
+thf(fact_171_rev__finite__subset,axiom,(
+    ! [A_144: hoare_1167836817_state > $o,B_103: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ B_103 )
+     => ( ( ord_le827224136tate_o @ A_144 @ B_103 )
+       => ( finite1084549118_state @ A_144 ) ) ) )).
+
+thf(fact_172_rev__finite__subset,axiom,(
+    ! [A_144: pname > $o,B_103: pname > $o] :
+      ( ( finite_finite_pname @ B_103 )
+     => ( ( ord_less_eq_pname_o @ A_144 @ B_103 )
+       => ( finite_finite_pname @ A_144 ) ) ) )).
+
+thf(fact_173_insert__mono,axiom,(
+    ! [A_143: pname,C_48: pname > $o,D_5: pname > $o] :
+      ( ( ord_less_eq_pname_o @ C_48 @ D_5 )
+     => ( ord_less_eq_pname_o @ ( insert_pname @ A_143 @ C_48 ) @ ( insert_pname @ A_143 @ D_5 ) ) ) )).
+
+thf(fact_174_insert__mono,axiom,(
+    ! [A_143: hoare_1167836817_state,C_48: hoare_1167836817_state > $o,D_5: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ C_48 @ D_5 )
+     => ( ord_le827224136tate_o @ ( insert2134838167_state @ A_143 @ C_48 ) @ ( insert2134838167_state @ A_143 @ D_5 ) ) ) )).
+
+thf(fact_175_mem__def,axiom,(
+    ! [X_88: pname,A_142: pname > $o] :
+      ( ( member_pname @ X_88 @ A_142 )
+    <=> ( A_142 @ X_88 ) ) )).
+
+thf(fact_176_mem__def,axiom,(
+    ! [X_88: hoare_1167836817_state,A_142: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ X_88 @ A_142 )
+    <=> ( A_142 @ X_88 ) ) )).
+
+thf(fact_177_Collect__def,axiom,(
+    ! [P_37: hoare_1167836817_state > $o] :
+      ( ( collec1027672124_state @ P_37 )
+      = P_37 ) )).
+
+thf(fact_178_Collect__def,axiom,(
+    ! [P_37: pname > $o] :
+      ( ( collect_pname @ P_37 )
+      = P_37 ) )).
+
+thf(fact_179_Collect__def,axiom,(
+    ! [P_37: ( pname > $o ) > $o] :
+      ( ( collect_pname_o @ P_37 )
+      = P_37 ) )).
+
+thf(fact_180_Collect__def,axiom,(
+    ! [P_37: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( collec269976083tate_o @ P_37 )
+      = P_37 ) )).
+
+thf(fact_181_subset__insertI2,axiom,(
+    ! [B_102: pname,A_141: pname > $o,B_101: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_141 @ B_101 )
+     => ( ord_less_eq_pname_o @ A_141 @ ( insert_pname @ B_102 @ B_101 ) ) ) )).
+
+thf(fact_182_subset__insertI2,axiom,(
+    ! [B_102: hoare_1167836817_state,A_141: hoare_1167836817_state > $o,B_101: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_141 @ B_101 )
+     => ( ord_le827224136tate_o @ A_141 @ ( insert2134838167_state @ B_102 @ B_101 ) ) ) )).
+
+thf(fact_183_subset__insert,axiom,(
+    ! [B_100: pname > $o,X_87: pname,A_140: pname > $o] :
+      ( ~ ( member_pname @ X_87 @ A_140 )
+     => ( ( ord_less_eq_pname_o @ A_140 @ ( insert_pname @ X_87 @ B_100 ) )
+      <=> ( ord_less_eq_pname_o @ A_140 @ B_100 ) ) ) )).
+
+thf(fact_184_subset__insert,axiom,(
+    ! [B_100: hoare_1167836817_state > $o,X_87: hoare_1167836817_state,A_140: hoare_1167836817_state > $o] :
+      ( ~ ( member2058392318_state @ X_87 @ A_140 )
+     => ( ( ord_le827224136tate_o @ A_140 @ ( insert2134838167_state @ X_87 @ B_100 ) )
+      <=> ( ord_le827224136tate_o @ A_140 @ B_100 ) ) ) )).
+
+thf(fact_185_insert__subset,axiom,(
+    ! [X_86: pname,A_139: pname > $o,B_99: pname > $o] :
+      ( ( ord_less_eq_pname_o @ ( insert_pname @ X_86 @ A_139 ) @ B_99 )
+    <=> ( ( member_pname @ X_86 @ B_99 )
+        & ( ord_less_eq_pname_o @ A_139 @ B_99 ) ) ) )).
+
+thf(fact_186_insert__subset,axiom,(
+    ! [X_86: hoare_1167836817_state,A_139: hoare_1167836817_state > $o,B_99: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ ( insert2134838167_state @ X_86 @ A_139 ) @ B_99 )
+    <=> ( ( member2058392318_state @ X_86 @ B_99 )
+        & ( ord_le827224136tate_o @ A_139 @ B_99 ) ) ) )).
+
+thf(fact_187_subset__insertI,axiom,(
+    ! [B_98: pname > $o,A_138: pname] :
+      ( ord_less_eq_pname_o @ B_98 @ ( insert_pname @ A_138 @ B_98 ) ) )).
+
+thf(fact_188_subset__insertI,axiom,(
+    ! [B_98: hoare_1167836817_state > $o,A_138: hoare_1167836817_state] :
+      ( ord_le827224136tate_o @ B_98 @ ( insert2134838167_state @ A_138 @ B_98 ) ) )).
+
+thf(fact_189_insert__image,axiom,(
+    ! [F_51: hoare_1167836817_state > pname,X_85: hoare_1167836817_state,A_137: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ X_85 @ A_137 )
+     => ( ( insert_pname @ ( F_51 @ X_85 ) @ ( image_8178176_pname @ F_51 @ A_137 ) )
+        = ( image_8178176_pname @ F_51 @ A_137 ) ) ) )).
+
+thf(fact_190_insert__image,axiom,(
+    ! [F_51: pname > hoare_1167836817_state,X_85: pname,A_137: pname > $o] :
+      ( ( member_pname @ X_85 @ A_137 )
+     => ( ( insert2134838167_state @ ( F_51 @ X_85 ) @ ( image_575578384_state @ F_51 @ A_137 ) )
+        = ( image_575578384_state @ F_51 @ A_137 ) ) ) )).
+
+thf(fact_191_image__insert,axiom,(
+    ! [F_50: hoare_1167836817_state > pname,A_136: hoare_1167836817_state,B_97: hoare_1167836817_state > $o] :
+      ( ( image_8178176_pname @ F_50 @ ( insert2134838167_state @ A_136 @ B_97 ) )
+      = ( insert_pname @ ( F_50 @ A_136 ) @ ( image_8178176_pname @ F_50 @ B_97 ) ) ) )).
+
+thf(fact_192_image__insert,axiom,(
+    ! [F_50: pname > hoare_1167836817_state,A_136: pname,B_97: pname > $o] :
+      ( ( image_575578384_state @ F_50 @ ( insert_pname @ A_136 @ B_97 ) )
+      = ( insert2134838167_state @ ( F_50 @ A_136 ) @ ( image_575578384_state @ F_50 @ B_97 ) ) ) )).
+
+thf(fact_193_image__mono,axiom,(
+    ! [F_49: hoare_1167836817_state > pname,A_135: hoare_1167836817_state > $o,B_96: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_135 @ B_96 )
+     => ( ord_less_eq_pname_o @ ( image_8178176_pname @ F_49 @ A_135 ) @ ( image_8178176_pname @ F_49 @ B_96 ) ) ) )).
+
+thf(fact_194_image__mono,axiom,(
+    ! [F_49: pname > hoare_1167836817_state,A_135: pname > $o,B_96: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_135 @ B_96 )
+     => ( ord_le827224136tate_o @ ( image_575578384_state @ F_49 @ A_135 ) @ ( image_575578384_state @ F_49 @ B_96 ) ) ) )).
+
+thf(fact_195_subset__image__iff,axiom,(
+    ! [B_95: pname > $o,F_48: hoare_1167836817_state > pname,A_134: hoare_1167836817_state > $o] :
+      ( ( ord_less_eq_pname_o @ B_95 @ ( image_8178176_pname @ F_48 @ A_134 ) )
+    <=> ? [AA: hoare_1167836817_state > $o] :
+          ( ( ord_le827224136tate_o @ AA @ A_134 )
+          & ( B_95
+            = ( image_8178176_pname @ F_48 @ AA ) ) ) ) )).
+
+thf(fact_196_subset__image__iff,axiom,(
+    ! [B_95: hoare_1167836817_state > $o,F_48: pname > hoare_1167836817_state,A_134: pname > $o] :
+      ( ( ord_le827224136tate_o @ B_95 @ ( image_575578384_state @ F_48 @ A_134 ) )
+    <=> ? [AA: pname > $o] :
+          ( ( ord_less_eq_pname_o @ AA @ A_134 )
+          & ( B_95
+            = ( image_575578384_state @ F_48 @ AA ) ) ) ) )).
+
+thf(fact_197_domI,axiom,(
+    ! [M_2: pname > option_com,A_133: pname,B_94: com] :
+      ( ( ( M_2 @ A_133 )
+        = ( some_com @ B_94 ) )
+     => ( member_pname @ A_133 @ ( dom_pname_com @ M_2 ) ) ) )).
+
+thf(fact_198_Collect__conv__if,axiom,(
+    ! [P_36: pname > $o,A_132: pname] :
+      ( ( ( P_36 @ A_132 )
+       => ( ( collect_pname
+            @ ^ [X_5: pname] :
+                ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
+          = ( insert_pname @ A_132 @ bot_bot_pname_o ) ) )
+      & ( ~ ( P_36 @ A_132 )
+       => ( ( collect_pname
+            @ ^ [X_5: pname] :
+                ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
+          = bot_bot_pname_o ) ) ) )).
+
+thf(fact_199_Collect__conv__if,axiom,(
+    ! [P_36: ( pname > $o ) > $o,A_132: pname > $o] :
+      ( ( ( P_36 @ A_132 )
+       => ( ( collect_pname_o
+            @ ^ [X_5: pname > $o] :
+                ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
+          = ( insert_pname_o @ A_132 @ bot_bot_pname_o_o ) ) )
+      & ( ~ ( P_36 @ A_132 )
+       => ( ( collect_pname_o
+            @ ^ [X_5: pname > $o] :
+                ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
+          = bot_bot_pname_o_o ) ) ) )).
+
+thf(fact_200_Collect__conv__if,axiom,(
+    ! [P_36: ( hoare_1167836817_state > $o ) > $o,A_132: hoare_1167836817_state > $o] :
+      ( ( ( P_36 @ A_132 )
+       => ( ( collec269976083tate_o
+            @ ^ [X_5: hoare_1167836817_state > $o] :
+                ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
+          = ( insert999278200tate_o @ A_132 @ bot_bo691907561te_o_o ) ) )
+      & ( ~ ( P_36 @ A_132 )
+       => ( ( collec269976083tate_o
+            @ ^ [X_5: hoare_1167836817_state > $o] :
+                ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
+          = bot_bo691907561te_o_o ) ) ) )).
+
+thf(fact_201_Collect__conv__if,axiom,(
+    ! [P_36: hoare_1167836817_state > $o,A_132: hoare_1167836817_state] :
+      ( ( ( P_36 @ A_132 )
+       => ( ( collec1027672124_state
+            @ ^ [X_5: hoare_1167836817_state] :
+                ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
+          = ( insert2134838167_state @ A_132 @ bot_bo70021908tate_o ) ) )
+      & ( ~ ( P_36 @ A_132 )
+       => ( ( collec1027672124_state
+            @ ^ [X_5: hoare_1167836817_state] :
+                ( (&) @ ( X_5 = A_132 ) @ ( P_36 @ X_5 ) ) )
+          = bot_bo70021908tate_o ) ) ) )).
+
+thf(fact_202_Collect__conv__if2,axiom,(
+    ! [P_35: pname > $o,A_131: pname] :
+      ( ( ( P_35 @ A_131 )
+       => ( ( collect_pname
+            @ ^ [X_5: pname] :
+                ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
+          = ( insert_pname @ A_131 @ bot_bot_pname_o ) ) )
+      & ( ~ ( P_35 @ A_131 )
+       => ( ( collect_pname
+            @ ^ [X_5: pname] :
+                ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
+          = bot_bot_pname_o ) ) ) )).
+
+thf(fact_203_Collect__conv__if2,axiom,(
+    ! [P_35: ( pname > $o ) > $o,A_131: pname > $o] :
+      ( ( ( P_35 @ A_131 )
+       => ( ( collect_pname_o
+            @ ^ [X_5: pname > $o] :
+                ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
+          = ( insert_pname_o @ A_131 @ bot_bot_pname_o_o ) ) )
+      & ( ~ ( P_35 @ A_131 )
+       => ( ( collect_pname_o
+            @ ^ [X_5: pname > $o] :
+                ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
+          = bot_bot_pname_o_o ) ) ) )).
+
+thf(fact_204_Collect__conv__if2,axiom,(
+    ! [P_35: ( hoare_1167836817_state > $o ) > $o,A_131: hoare_1167836817_state > $o] :
+      ( ( ( P_35 @ A_131 )
+       => ( ( collec269976083tate_o
+            @ ^ [X_5: hoare_1167836817_state > $o] :
+                ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
+          = ( insert999278200tate_o @ A_131 @ bot_bo691907561te_o_o ) ) )
+      & ( ~ ( P_35 @ A_131 )
+       => ( ( collec269976083tate_o
+            @ ^ [X_5: hoare_1167836817_state > $o] :
+                ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
+          = bot_bo691907561te_o_o ) ) ) )).
+
+thf(fact_205_Collect__conv__if2,axiom,(
+    ! [P_35: hoare_1167836817_state > $o,A_131: hoare_1167836817_state] :
+      ( ( ( P_35 @ A_131 )
+       => ( ( collec1027672124_state
+            @ ^ [X_5: hoare_1167836817_state] :
+                ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
+          = ( insert2134838167_state @ A_131 @ bot_bo70021908tate_o ) ) )
+      & ( ~ ( P_35 @ A_131 )
+       => ( ( collec1027672124_state
+            @ ^ [X_5: hoare_1167836817_state] :
+                ( (&) @ ( A_131 = X_5 ) @ ( P_35 @ X_5 ) ) )
+          = bot_bo70021908tate_o ) ) ) )).
+
+thf(fact_206_singleton__conv,axiom,(
+    ! [A_130: pname] :
+      ( ( collect_pname
+        @ ^ [X_5: pname] : ( X_5 = A_130 ) )
+      = ( insert_pname @ A_130 @ bot_bot_pname_o ) ) )).
+
+thf(fact_207_singleton__conv,axiom,(
+    ! [A_130: pname > $o] :
+      ( ( collect_pname_o
+        @ ^ [X_5: pname > $o] : ( X_5 = A_130 ) )
+      = ( insert_pname_o @ A_130 @ bot_bot_pname_o_o ) ) )).
+
+thf(fact_208_singleton__conv,axiom,(
+    ! [A_130: hoare_1167836817_state > $o] :
+      ( ( collec269976083tate_o
+        @ ^ [X_5: hoare_1167836817_state > $o] : ( X_5 = A_130 ) )
+      = ( insert999278200tate_o @ A_130 @ bot_bo691907561te_o_o ) ) )).
+
+thf(fact_209_singleton__conv,axiom,(
+    ! [A_130: hoare_1167836817_state] :
+      ( ( collec1027672124_state
+        @ ^ [X_5: hoare_1167836817_state] : ( X_5 = A_130 ) )
+      = ( insert2134838167_state @ A_130 @ bot_bo70021908tate_o ) ) )).
+
+thf(fact_210_singleton__conv2,axiom,(
+    ! [A_129: pname] :
+      ( ( collect_pname @ ( fequal_pname @ A_129 ) )
+      = ( insert_pname @ A_129 @ bot_bot_pname_o ) ) )).
+
+thf(fact_211_singleton__conv2,axiom,(
+    ! [A_129: pname > $o] :
+      ( ( collect_pname_o @ ( fequal_pname_o @ A_129 ) )
+      = ( insert_pname_o @ A_129 @ bot_bot_pname_o_o ) ) )).
+
+thf(fact_212_singleton__conv2,axiom,(
+    ! [A_129: hoare_1167836817_state > $o] :
+      ( ( collec269976083tate_o @ ( fequal1486222077tate_o @ A_129 ) )
+      = ( insert999278200tate_o @ A_129 @ bot_bo691907561te_o_o ) ) )).
+
+thf(fact_213_singleton__conv2,axiom,(
+    ! [A_129: hoare_1167836817_state] :
+      ( ( collec1027672124_state @ ( fequal1831255762_state @ A_129 ) )
+      = ( insert2134838167_state @ A_129 @ bot_bo70021908tate_o ) ) )).
+
+thf(fact_214_MGF__lemma1,axiom,(
+    ! [C_21: com,G_3: hoare_1167836817_state > $o] :
+      ( hoare_1201148605gleton
+     => ( ! [X_5: pname] :
+            ( ( member_pname @ X_5 @ ( dom_pname_com @ body ) )
+           => ( hoare_123228589_state @ G_3 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ X_5 ) ) @ bot_bo70021908tate_o ) ) )
+       => ( ( wt @ C_21 )
+         => ( hoare_123228589_state @ G_3 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ C_21 ) @ bot_bo70021908tate_o ) ) ) ) ) )).
+
+thf(fact_215_WT__bodiesD,axiom,(
+    ! [Pn_1: pname,B_42: com] :
+      ( wT_bodies
+     => ( ( ( body @ Pn_1 )
+          = ( some_com @ B_42 ) )
+       => ( wt @ B_42 ) ) ) )).
+
+thf(fact_216_imageE,axiom,(
+    ! [B_93: pname,F_47: hoare_1167836817_state > pname,A_128: hoare_1167836817_state > $o] :
+      ( ( member_pname @ B_93 @ ( image_8178176_pname @ F_47 @ A_128 ) )
+     => ~ ! [X_5: hoare_1167836817_state] :
+            ( ( B_93
+              = ( F_47 @ X_5 ) )
+           => ~ ( member2058392318_state @ X_5 @ A_128 ) ) ) )).
+
+thf(fact_217_imageE,axiom,(
+    ! [B_93: hoare_1167836817_state,F_47: pname > hoare_1167836817_state,A_128: pname > $o] :
+      ( ( member2058392318_state @ B_93 @ ( image_575578384_state @ F_47 @ A_128 ) )
+     => ~ ! [X_5: pname] :
+            ( ( B_93
+              = ( F_47 @ X_5 ) )
+           => ~ ( member_pname @ X_5 @ A_128 ) ) ) )).
+
+thf(fact_218_finite__subset__induct,axiom,(
+    ! [P_34: ( ( pname > $o ) > $o ) > $o,A_127: ( pname > $o ) > $o,F_46: ( pname > $o ) > $o] :
+      ( ( finite297249702name_o @ F_46 )
+     => ( ( ord_le1205211808me_o_o @ F_46 @ A_127 )
+       => ( ( P_34 @ bot_bot_pname_o_o )
+         => ( ! [A_122: pname > $o,F_26: ( pname > $o ) > $o] :
+                ( ( finite297249702name_o @ F_26 )
+               => ( ( member_pname_o @ A_122 @ A_127 )
+                 => ( ~ ( member_pname_o @ A_122 @ F_26 )
+                   => ( ( P_34 @ F_26 )
+                     => ( P_34 @ ( insert_pname_o @ A_122 @ F_26 ) ) ) ) ) )
+           => ( P_34 @ F_46 ) ) ) ) ) )).
+
+thf(fact_219_finite__subset__induct,axiom,(
+    ! [P_34: ( ( hoare_1167836817_state > $o ) > $o ) > $o,A_127: ( hoare_1167836817_state > $o ) > $o,F_46: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( finite1380128977tate_o @ F_46 )
+     => ( ( ord_le741939125te_o_o @ F_46 @ A_127 )
+       => ( ( P_34 @ bot_bo691907561te_o_o )
+         => ( ! [A_122: hoare_1167836817_state > $o,F_26: ( hoare_1167836817_state > $o ) > $o] :
+                ( ( finite1380128977tate_o @ F_26 )
+               => ( ( member864234961tate_o @ A_122 @ A_127 )
+                 => ( ~ ( member864234961tate_o @ A_122 @ F_26 )
+                   => ( ( P_34 @ F_26 )
+                     => ( P_34 @ ( insert999278200tate_o @ A_122 @ F_26 ) ) ) ) ) )
+           => ( P_34 @ F_46 ) ) ) ) ) )).
+
+thf(fact_220_finite__subset__induct,axiom,(
+    ! [P_34: ( pname > $o ) > $o,A_127: pname > $o,F_46: pname > $o] :
+      ( ( finite_finite_pname @ F_46 )
+     => ( ( ord_less_eq_pname_o @ F_46 @ A_127 )
+       => ( ( P_34 @ bot_bot_pname_o )
+         => ( ! [A_122: pname,F_26: pname > $o] :
+                ( ( finite_finite_pname @ F_26 )
+               => ( ( member_pname @ A_122 @ A_127 )
+                 => ( ~ ( member_pname @ A_122 @ F_26 )
+                   => ( ( P_34 @ F_26 )
+                     => ( P_34 @ ( insert_pname @ A_122 @ F_26 ) ) ) ) ) )
+           => ( P_34 @ F_46 ) ) ) ) ) )).
+
+thf(fact_221_finite__subset__induct,axiom,(
+    ! [P_34: ( hoare_1167836817_state > $o ) > $o,A_127: hoare_1167836817_state > $o,F_46: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ F_46 )
+     => ( ( ord_le827224136tate_o @ F_46 @ A_127 )
+       => ( ( P_34 @ bot_bo70021908tate_o )
+         => ( ! [A_122: hoare_1167836817_state,F_26: hoare_1167836817_state > $o] :
+                ( ( finite1084549118_state @ F_26 )
+               => ( ( member2058392318_state @ A_122 @ A_127 )
+                 => ( ~ ( member2058392318_state @ A_122 @ F_26 )
+                   => ( ( P_34 @ F_26 )
+                     => ( P_34 @ ( insert2134838167_state @ A_122 @ F_26 ) ) ) ) ) )
+           => ( P_34 @ F_46 ) ) ) ) ) )).
+
+thf(fact_222_WTs__elim__cases_I7_J,axiom,(
+    ! [P: pname] :
+      ( ( wt @ ( body_1 @ P ) )
+     => ~ ! [Y_2: com] :
+            ( ( body @ P )
+           != ( some_com @ Y_2 ) ) ) )).
+
+thf(fact_223_subsetI,axiom,(
+    ! [B_92: pname > $o,A_126: pname > $o] :
+      ( ! [X_5: pname] :
+          ( ( member_pname @ X_5 @ A_126 )
+         => ( member_pname @ X_5 @ B_92 ) )
+     => ( ord_less_eq_pname_o @ A_126 @ B_92 ) ) )).
+
+thf(fact_224_subsetI,axiom,(
+    ! [B_92: hoare_1167836817_state > $o,A_126: hoare_1167836817_state > $o] :
+      ( ! [X_5: hoare_1167836817_state] :
+          ( ( member2058392318_state @ X_5 @ A_126 )
+         => ( member2058392318_state @ X_5 @ B_92 ) )
+     => ( ord_le827224136tate_o @ A_126 @ B_92 ) ) )).
+
+thf(fact_225_finite__subset__image,axiom,(
+    ! [F_45: ( pname > $o ) > hoare_1167836817_state,A_125: ( pname > $o ) > $o,B_91: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ B_91 )
+     => ( ( ord_le827224136tate_o @ B_91 @ ( image_1381916541_state @ F_45 @ A_125 ) )
+       => ? [C_47: ( pname > $o ) > $o] :
+            ( ( ord_le1205211808me_o_o @ C_47 @ A_125 )
+            & ( finite297249702name_o @ C_47 )
+            & ( B_91
+              = ( image_1381916541_state @ F_45 @ C_47 ) ) ) ) ) )).
+
+thf(fact_226_finite__subset__image,axiom,(
+    ! [F_45: ( hoare_1167836817_state > $o ) > hoare_1167836817_state,A_125: ( hoare_1167836817_state > $o ) > $o,B_91: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ B_91 )
+     => ( ( ord_le827224136tate_o @ B_91 @ ( image_635813834_state @ F_45 @ A_125 ) )
+       => ? [C_47: ( hoare_1167836817_state > $o ) > $o] :
+            ( ( ord_le741939125te_o_o @ C_47 @ A_125 )
+            & ( finite1380128977tate_o @ C_47 )
+            & ( B_91
+              = ( image_635813834_state @ F_45 @ C_47 ) ) ) ) ) )).
+
+thf(fact_227_finite__subset__image,axiom,(
+    ! [F_45: ( pname > $o ) > pname,A_125: ( pname > $o ) > $o,B_91: pname > $o] :
+      ( ( finite_finite_pname @ B_91 )
+     => ( ( ord_less_eq_pname_o @ B_91 @ ( image_pname_o_pname @ F_45 @ A_125 ) )
+       => ? [C_47: ( pname > $o ) > $o] :
+            ( ( ord_le1205211808me_o_o @ C_47 @ A_125 )
+            & ( finite297249702name_o @ C_47 )
+            & ( B_91
+              = ( image_pname_o_pname @ F_45 @ C_47 ) ) ) ) ) )).
+
+thf(fact_228_finite__subset__image,axiom,(
+    ! [F_45: ( hoare_1167836817_state > $o ) > pname,A_125: ( hoare_1167836817_state > $o ) > $o,B_91: pname > $o] :
+      ( ( finite_finite_pname @ B_91 )
+     => ( ( ord_less_eq_pname_o @ B_91 @ ( image_980295115_pname @ F_45 @ A_125 ) )
+       => ? [C_47: ( hoare_1167836817_state > $o ) > $o] :
+            ( ( ord_le741939125te_o_o @ C_47 @ A_125 )
+            & ( finite1380128977tate_o @ C_47 )
+            & ( B_91
+              = ( image_980295115_pname @ F_45 @ C_47 ) ) ) ) ) )).
+
+thf(fact_229_finite__subset__image,axiom,(
+    ! [F_45: hoare_1167836817_state > pname > $o,A_125: hoare_1167836817_state > $o,B_91: ( pname > $o ) > $o] :
+      ( ( finite297249702name_o @ B_91 )
+     => ( ( ord_le1205211808me_o_o @ B_91 @ ( image_2066861949name_o @ F_45 @ A_125 ) )
+       => ? [C_47: hoare_1167836817_state > $o] :
+            ( ( ord_le827224136tate_o @ C_47 @ A_125 )
+            & ( finite1084549118_state @ C_47 )
+            & ( B_91
+              = ( image_2066861949name_o @ F_45 @ C_47 ) ) ) ) ) )).
+
+thf(fact_230_finite__subset__image,axiom,(
+    ! [F_45: hoare_1167836817_state > hoare_1167836817_state > $o,A_125: hoare_1167836817_state > $o,B_91: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( finite1380128977tate_o @ B_91 )
+     => ( ( ord_le741939125te_o_o @ B_91 @ ( image_1745649338tate_o @ F_45 @ A_125 ) )
+       => ? [C_47: hoare_1167836817_state > $o] :
+            ( ( ord_le827224136tate_o @ C_47 @ A_125 )
+            & ( finite1084549118_state @ C_47 )
+            & ( B_91
+              = ( image_1745649338tate_o @ F_45 @ C_47 ) ) ) ) ) )).
+
+thf(fact_231_finite__subset__image,axiom,(
+    ! [F_45: hoare_1167836817_state > pname,A_125: hoare_1167836817_state > $o,B_91: pname > $o] :
+      ( ( finite_finite_pname @ B_91 )
+     => ( ( ord_less_eq_pname_o @ B_91 @ ( image_8178176_pname @ F_45 @ A_125 ) )
+       => ? [C_47: hoare_1167836817_state > $o] :
+            ( ( ord_le827224136tate_o @ C_47 @ A_125 )
+            & ( finite1084549118_state @ C_47 )
+            & ( B_91
+              = ( image_8178176_pname @ F_45 @ C_47 ) ) ) ) ) )).
+
+thf(fact_232_finite__subset__image,axiom,(
+    ! [F_45: pname > pname > $o,A_125: pname > $o,B_91: ( pname > $o ) > $o] :
+      ( ( finite297249702name_o @ B_91 )
+     => ( ( ord_le1205211808me_o_o @ B_91 @ ( image_pname_pname_o @ F_45 @ A_125 ) )
+       => ? [C_47: pname > $o] :
+            ( ( ord_less_eq_pname_o @ C_47 @ A_125 )
+            & ( finite_finite_pname @ C_47 )
+            & ( B_91
+              = ( image_pname_pname_o @ F_45 @ C_47 ) ) ) ) ) )).
+
+thf(fact_233_finite__subset__image,axiom,(
+    ! [F_45: pname > hoare_1167836817_state > $o,A_125: pname > $o,B_91: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( finite1380128977tate_o @ B_91 )
+     => ( ( ord_le741939125te_o_o @ B_91 @ ( image_475339327tate_o @ F_45 @ A_125 ) )
+       => ? [C_47: pname > $o] :
+            ( ( ord_less_eq_pname_o @ C_47 @ A_125 )
+            & ( finite_finite_pname @ C_47 )
+            & ( B_91
+              = ( image_475339327tate_o @ F_45 @ C_47 ) ) ) ) ) )).
+
+thf(fact_234_finite__subset__image,axiom,(
+    ! [F_45: pname > pname,A_125: pname > $o,B_91: pname > $o] :
+      ( ( finite_finite_pname @ B_91 )
+     => ( ( ord_less_eq_pname_o @ B_91 @ ( image_pname_pname @ F_45 @ A_125 ) )
+       => ? [C_47: pname > $o] :
+            ( ( ord_less_eq_pname_o @ C_47 @ A_125 )
+            & ( finite_finite_pname @ C_47 )
+            & ( B_91
+              = ( image_pname_pname @ F_45 @ C_47 ) ) ) ) ) )).
+
+thf(fact_235_finite__subset__image,axiom,(
+    ! [F_45: pname > hoare_1167836817_state,A_125: pname > $o,B_91: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ B_91 )
+     => ( ( ord_le827224136tate_o @ B_91 @ ( image_575578384_state @ F_45 @ A_125 ) )
+       => ? [C_47: pname > $o] :
+            ( ( ord_less_eq_pname_o @ C_47 @ A_125 )
+            & ( finite_finite_pname @ C_47 )
+            & ( B_91
+              = ( image_575578384_state @ F_45 @ C_47 ) ) ) ) ) )).
+
+thf(fact_236_finite__dom__body,axiom,
+    ( finite_finite_pname @ ( dom_pname_com @ body ) )).
+
+thf(fact_237_finite__induct,axiom,(
+    ! [P_33: ( ( pname > $o ) > $o ) > $o,F_44: ( pname > $o ) > $o] :
+      ( ( finite297249702name_o @ F_44 )
+     => ( ( P_33 @ bot_bot_pname_o_o )
+       => ( ! [X_5: pname > $o,F_26: ( pname > $o ) > $o] :
+              ( ( finite297249702name_o @ F_26 )
+             => ( ~ ( member_pname_o @ X_5 @ F_26 )
+               => ( ( P_33 @ F_26 )
+                 => ( P_33 @ ( insert_pname_o @ X_5 @ F_26 ) ) ) ) )
+         => ( P_33 @ F_44 ) ) ) ) )).
+
+thf(fact_238_finite__induct,axiom,(
+    ! [P_33: ( ( hoare_1167836817_state > $o ) > $o ) > $o,F_44: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( finite1380128977tate_o @ F_44 )
+     => ( ( P_33 @ bot_bo691907561te_o_o )
+       => ( ! [X_5: hoare_1167836817_state > $o,F_26: ( hoare_1167836817_state > $o ) > $o] :
+              ( ( finite1380128977tate_o @ F_26 )
+             => ( ~ ( member864234961tate_o @ X_5 @ F_26 )
+               => ( ( P_33 @ F_26 )
+                 => ( P_33 @ ( insert999278200tate_o @ X_5 @ F_26 ) ) ) ) )
+         => ( P_33 @ F_44 ) ) ) ) )).
+
+thf(fact_239_finite__induct,axiom,(
+    ! [P_33: ( pname > $o ) > $o,F_44: pname > $o] :
+      ( ( finite_finite_pname @ F_44 )
+     => ( ( P_33 @ bot_bot_pname_o )
+       => ( ! [X_5: pname,F_26: pname > $o] :
+              ( ( finite_finite_pname @ F_26 )
+             => ( ~ ( member_pname @ X_5 @ F_26 )
+               => ( ( P_33 @ F_26 )
+                 => ( P_33 @ ( insert_pname @ X_5 @ F_26 ) ) ) ) )
+         => ( P_33 @ F_44 ) ) ) ) )).
+
+thf(fact_240_finite__induct,axiom,(
+    ! [P_33: ( hoare_1167836817_state > $o ) > $o,F_44: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ F_44 )
+     => ( ( P_33 @ bot_bo70021908tate_o )
+       => ( ! [X_5: hoare_1167836817_state,F_26: hoare_1167836817_state > $o] :
+              ( ( finite1084549118_state @ F_26 )
+             => ( ~ ( member2058392318_state @ X_5 @ F_26 )
+               => ( ( P_33 @ F_26 )
+                 => ( P_33 @ ( insert2134838167_state @ X_5 @ F_26 ) ) ) ) )
+         => ( P_33 @ F_44 ) ) ) ) )).
+
+thf(fact_241_finite_Osimps,axiom,(
+    ! [A_123: ( pname > $o ) > $o] :
+      ( ( finite297249702name_o @ A_123 )
+    <=> ( ( A_123 = bot_bot_pname_o_o )
+        | ? [A_124: ( pname > $o ) > $o,A_122: pname > $o] :
+            ( ( A_123
+              = ( insert_pname_o @ A_122 @ A_124 ) )
+            & ( finite297249702name_o @ A_124 ) ) ) ) )).
+
+thf(fact_242_finite_Osimps,axiom,(
+    ! [A_123: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( finite1380128977tate_o @ A_123 )
+    <=> ( ( A_123 = bot_bo691907561te_o_o )
+        | ? [A_124: ( hoare_1167836817_state > $o ) > $o,A_122: hoare_1167836817_state > $o] :
+            ( ( A_123
+              = ( insert999278200tate_o @ A_122 @ A_124 ) )
+            & ( finite1380128977tate_o @ A_124 ) ) ) ) )).
+
+thf(fact_243_finite_Osimps,axiom,(
+    ! [A_123: pname > $o] :
+      ( ( finite_finite_pname @ A_123 )
+    <=> ( ( A_123 = bot_bot_pname_o )
+        | ? [A_124: pname > $o,A_122: pname] :
+            ( ( A_123
+              = ( insert_pname @ A_122 @ A_124 ) )
+            & ( finite_finite_pname @ A_124 ) ) ) ) )).
+
+thf(fact_244_finite_Osimps,axiom,(
+    ! [A_123: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ A_123 )
+    <=> ( ( A_123 = bot_bo70021908tate_o )
+        | ? [A_124: hoare_1167836817_state > $o,A_122: hoare_1167836817_state] :
+            ( ( A_123
+              = ( insert2134838167_state @ A_122 @ A_124 ) )
+            & ( finite1084549118_state @ A_124 ) ) ) ) )).
+
+thf(fact_245_pigeonhole__infinite,axiom,(
+    ! [F_43: pname > pname > $o,A_121: pname > $o] :
+      ( ~ ( finite_finite_pname @ A_121 )
+     => ( ( finite297249702name_o @ ( image_pname_pname_o @ F_43 @ A_121 ) )
+       => ? [X_5: pname] :
+            ( ( member_pname @ X_5 @ A_121 )
+            & ~ ( finite_finite_pname
+                @ ( collect_pname
+                  @ ^ [A_122: pname] :
+                      ( (&) @ ( member_pname @ A_122 @ A_121 )
+                      @ ( ( F_43 @ A_122 )
+                        = ( F_43 @ X_5 ) ) ) ) ) ) ) ) )).
+
+thf(fact_246_pigeonhole__infinite,axiom,(
+    ! [F_43: pname > hoare_1167836817_state > $o,A_121: pname > $o] :
+      ( ~ ( finite_finite_pname @ A_121 )
+     => ( ( finite1380128977tate_o @ ( image_475339327tate_o @ F_43 @ A_121 ) )
+       => ? [X_5: pname] :
+            ( ( member_pname @ X_5 @ A_121 )
+            & ~ ( finite_finite_pname
+                @ ( collect_pname
+                  @ ^ [A_122: pname] :
+                      ( (&) @ ( member_pname @ A_122 @ A_121 )
+                      @ ( ( F_43 @ A_122 )
+                        = ( F_43 @ X_5 ) ) ) ) ) ) ) ) )).
+
+thf(fact_247_pigeonhole__infinite,axiom,(
+    ! [F_43: hoare_1167836817_state > hoare_1167836817_state,A_121: hoare_1167836817_state > $o] :
+      ( ~ ( finite1084549118_state @ A_121 )
+     => ( ( finite1084549118_state @ ( image_31595733_state @ F_43 @ A_121 ) )
+       => ? [X_5: hoare_1167836817_state] :
+            ( ( member2058392318_state @ X_5 @ A_121 )
+            & ~ ( finite1084549118_state
+                @ ( collec1027672124_state
+                  @ ^ [A_122: hoare_1167836817_state] :
+                      ( (&) @ ( member2058392318_state @ A_122 @ A_121 )
+                      @ ( ( F_43 @ A_122 )
+                        = ( F_43 @ X_5 ) ) ) ) ) ) ) ) )).
+
+thf(fact_248_pigeonhole__infinite,axiom,(
+    ! [F_43: ( pname > $o ) > hoare_1167836817_state,A_121: ( pname > $o ) > $o] :
+      ( ~ ( finite297249702name_o @ A_121 )
+     => ( ( finite1084549118_state @ ( image_1381916541_state @ F_43 @ A_121 ) )
+       => ? [X_5: pname > $o] :
+            ( ( member_pname_o @ X_5 @ A_121 )
+            & ~ ( finite297249702name_o
+                @ ( collect_pname_o
+                  @ ^ [A_122: pname > $o] :
+                      ( (&) @ ( member_pname_o @ A_122 @ A_121 )
+                      @ ( ( F_43 @ A_122 )
+                        = ( F_43 @ X_5 ) ) ) ) ) ) ) ) )).
+
+thf(fact_249_pigeonhole__infinite,axiom,(
+    ! [F_43: ( hoare_1167836817_state > $o ) > hoare_1167836817_state,A_121: ( hoare_1167836817_state > $o ) > $o] :
+      ( ~ ( finite1380128977tate_o @ A_121 )
+     => ( ( finite1084549118_state @ ( image_635813834_state @ F_43 @ A_121 ) )
+       => ? [X_5: hoare_1167836817_state > $o] :
+            ( ( member864234961tate_o @ X_5 @ A_121 )
+            & ~ ( finite1380128977tate_o
+                @ ( collec269976083tate_o
+                  @ ^ [A_122: hoare_1167836817_state > $o] :
+                      ( (&) @ ( member864234961tate_o @ A_122 @ A_121 )
+                      @ ( ( F_43 @ A_122 )
+                        = ( F_43 @ X_5 ) ) ) ) ) ) ) ) )).
+
+thf(fact_250_pigeonhole__infinite,axiom,(
+    ! [F_43: pname > pname,A_121: pname > $o] :
+      ( ~ ( finite_finite_pname @ A_121 )
+     => ( ( finite_finite_pname @ ( image_pname_pname @ F_43 @ A_121 ) )
+       => ? [X_5: pname] :
+            ( ( member_pname @ X_5 @ A_121 )
+            & ~ ( finite_finite_pname
+                @ ( collect_pname
+                  @ ^ [A_122: pname] :
+                      ( (&) @ ( member_pname @ A_122 @ A_121 )
+                      @ ( ( F_43 @ A_122 )
+                        = ( F_43 @ X_5 ) ) ) ) ) ) ) ) )).
+
+thf(fact_251_pigeonhole__infinite,axiom,(
+    ! [F_43: hoare_1167836817_state > pname,A_121: hoare_1167836817_state > $o] :
+      ( ~ ( finite1084549118_state @ A_121 )
+     => ( ( finite_finite_pname @ ( image_8178176_pname @ F_43 @ A_121 ) )
+       => ? [X_5: hoare_1167836817_state] :
+            ( ( member2058392318_state @ X_5 @ A_121 )
+            & ~ ( finite1084549118_state
+                @ ( collec1027672124_state
+                  @ ^ [A_122: hoare_1167836817_state] :
+                      ( (&) @ ( member2058392318_state @ A_122 @ A_121 )
+                      @ ( ( F_43 @ A_122 )
+                        = ( F_43 @ X_5 ) ) ) ) ) ) ) ) )).
+
+thf(fact_252_pigeonhole__infinite,axiom,(
+    ! [F_43: ( pname > $o ) > pname,A_121: ( pname > $o ) > $o] :
+      ( ~ ( finite297249702name_o @ A_121 )
+     => ( ( finite_finite_pname @ ( image_pname_o_pname @ F_43 @ A_121 ) )
+       => ? [X_5: pname > $o] :
+            ( ( member_pname_o @ X_5 @ A_121 )
+            & ~ ( finite297249702name_o
+                @ ( collect_pname_o
+                  @ ^ [A_122: pname > $o] :
+                      ( (&) @ ( member_pname_o @ A_122 @ A_121 )
+                      @ ( ( F_43 @ A_122 )
+                        = ( F_43 @ X_5 ) ) ) ) ) ) ) ) )).
+
+thf(fact_253_pigeonhole__infinite,axiom,(
+    ! [F_43: ( hoare_1167836817_state > $o ) > pname,A_121: ( hoare_1167836817_state > $o ) > $o] :
+      ( ~ ( finite1380128977tate_o @ A_121 )
+     => ( ( finite_finite_pname @ ( image_980295115_pname @ F_43 @ A_121 ) )
+       => ? [X_5: hoare_1167836817_state > $o] :
+            ( ( member864234961tate_o @ X_5 @ A_121 )
+            & ~ ( finite1380128977tate_o
+                @ ( collec269976083tate_o
+                  @ ^ [A_122: hoare_1167836817_state > $o] :
+                      ( (&) @ ( member864234961tate_o @ A_122 @ A_121 )
+                      @ ( ( F_43 @ A_122 )
+                        = ( F_43 @ X_5 ) ) ) ) ) ) ) ) )).
+
+thf(fact_254_pigeonhole__infinite,axiom,(
+    ! [F_43: hoare_1167836817_state > pname > $o,A_121: hoare_1167836817_state > $o] :
+      ( ~ ( finite1084549118_state @ A_121 )
+     => ( ( finite297249702name_o @ ( image_2066861949name_o @ F_43 @ A_121 ) )
+       => ? [X_5: hoare_1167836817_state] :
+            ( ( member2058392318_state @ X_5 @ A_121 )
+            & ~ ( finite1084549118_state
+                @ ( collec1027672124_state
+                  @ ^ [A_122: hoare_1167836817_state] :
+                      ( (&) @ ( member2058392318_state @ A_122 @ A_121 )
+                      @ ( ( F_43 @ A_122 )
+                        = ( F_43 @ X_5 ) ) ) ) ) ) ) ) )).
+
+thf(fact_255_pigeonhole__infinite,axiom,(
+    ! [F_43: hoare_1167836817_state > hoare_1167836817_state > $o,A_121: hoare_1167836817_state > $o] :
+      ( ~ ( finite1084549118_state @ A_121 )
+     => ( ( finite1380128977tate_o @ ( image_1745649338tate_o @ F_43 @ A_121 ) )
+       => ? [X_5: hoare_1167836817_state] :
+            ( ( member2058392318_state @ X_5 @ A_121 )
+            & ~ ( finite1084549118_state
+                @ ( collec1027672124_state
+                  @ ^ [A_122: hoare_1167836817_state] :
+                      ( (&) @ ( member2058392318_state @ A_122 @ A_121 )
+                      @ ( ( F_43 @ A_122 )
+                        = ( F_43 @ X_5 ) ) ) ) ) ) ) ) )).
+
+thf(fact_256_pigeonhole__infinite,axiom,(
+    ! [F_43: pname > hoare_1167836817_state,A_121: pname > $o] :
+      ( ~ ( finite_finite_pname @ A_121 )
+     => ( ( finite1084549118_state @ ( image_575578384_state @ F_43 @ A_121 ) )
+       => ? [X_5: pname] :
+            ( ( member_pname @ X_5 @ A_121 )
+            & ~ ( finite_finite_pname
+                @ ( collect_pname
+                  @ ^ [A_122: pname] :
+                      ( (&) @ ( member_pname @ A_122 @ A_121 )
+                      @ ( ( F_43 @ A_122 )
+                        = ( F_43 @ X_5 ) ) ) ) ) ) ) ) )).
+
+thf(fact_257_com_Osimps_I6_J,axiom,(
+    ! [Pname_1: pname,Pname: pname] :
+      ( ( ( body_1 @ Pname_1 )
+        = ( body_1 @ Pname ) )
+    <=> ( Pname_1 = Pname ) ) )).
+
+thf(fact_258_MGT__Body,axiom,(
+    ! [G_3: hoare_1167836817_state > $o,Procs_3: pname > $o] :
+      ( ( hoare_123228589_state
+        @ ( semila1172322802tate_o @ G_3
+          @ ( image_575578384_state
+            @ ^ [Pn: pname] :
+                ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
+            @ Procs_3 ) )
+        @ ( image_575578384_state
+          @ ^ [Pn: pname] :
+              ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn ) ) )
+          @ Procs_3 ) )
+     => ( ( finite_finite_pname @ Procs_3 )
+       => ( hoare_123228589_state @ G_3
+          @ ( image_575578384_state
+            @ ^ [Pn: pname] :
+                ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
+            @ Procs_3 ) ) ) ) )).
+
+thf(fact_259_domD,axiom,(
+    ! [A_120: pname,M_1: pname > option_com] :
+      ( ( member_pname @ A_120 @ ( dom_pname_com @ M_1 ) )
+     => ? [B_90: com] :
+          ( ( M_1 @ A_120 )
+          = ( some_com @ B_90 ) ) ) )).
+
+thf(fact_260_the__elem__eq,axiom,(
+    ! [X_84: pname] :
+      ( ( the_elem_pname @ ( insert_pname @ X_84 @ bot_bot_pname_o ) )
+      = X_84 ) )).
+
+thf(fact_261_the__elem__eq,axiom,(
+    ! [X_84: hoare_1167836817_state] :
+      ( ( the_el323660082_state @ ( insert2134838167_state @ X_84 @ bot_bo70021908tate_o ) )
+      = X_84 ) )).
+
+thf(fact_262_image__subsetI,axiom,(
+    ! [F_42: hoare_1167836817_state > pname,B_89: pname > $o,A_119: hoare_1167836817_state > $o] :
+      ( ! [X_5: hoare_1167836817_state] :
+          ( ( member2058392318_state @ X_5 @ A_119 )
+         => ( member_pname @ ( F_42 @ X_5 ) @ B_89 ) )
+     => ( ord_less_eq_pname_o @ ( image_8178176_pname @ F_42 @ A_119 ) @ B_89 ) ) )).
+
+thf(fact_263_image__subsetI,axiom,(
+    ! [F_42: pname > hoare_1167836817_state,B_89: hoare_1167836817_state > $o,A_119: pname > $o] :
+      ( ! [X_5: pname] :
+          ( ( member_pname @ X_5 @ A_119 )
+         => ( member2058392318_state @ ( F_42 @ X_5 ) @ B_89 ) )
+     => ( ord_le827224136tate_o @ ( image_575578384_state @ F_42 @ A_119 ) @ B_89 ) ) )).
+
+thf(fact_264_order__refl,axiom,(
+    ! [X_83: pname > $o] :
+      ( ord_less_eq_pname_o @ X_83 @ X_83 ) )).
+
+thf(fact_265_order__refl,axiom,(
+    ! [X_83: hoare_1167836817_state > $o] :
+      ( ord_le827224136tate_o @ X_83 @ X_83 ) )).
+
+thf(fact_266_nonempty__iff,axiom,(
+    ! [A_118: pname > $o] :
+      ( ( A_118 != bot_bot_pname_o )
+    <=> ? [X_5: pname,B_43: pname > $o] :
+          ( ( A_118
+            = ( insert_pname @ X_5 @ B_43 ) )
+          & ~ ( member_pname @ X_5 @ B_43 ) ) ) )).
+
+thf(fact_267_nonempty__iff,axiom,(
+    ! [A_118: hoare_1167836817_state > $o] :
+      ( ( A_118 != bot_bo70021908tate_o )
+    <=> ? [X_5: hoare_1167836817_state,B_43: hoare_1167836817_state > $o] :
+          ( ( A_118
+            = ( insert2134838167_state @ X_5 @ B_43 ) )
+          & ~ ( member2058392318_state @ X_5 @ B_43 ) ) ) )).
+
+thf(fact_268_the_Osimps,axiom,(
+    ! [X_82: com] :
+      ( ( the_com @ ( some_com @ X_82 ) )
+      = X_82 ) )).
+
+thf(fact_269_weak__Body,axiom,(
+    ! [G_27: hoare_1167836817_state > $o,P_32: state > state > $o,Pn_4: pname,Q_22: state > state > $o] :
+      ( ( hoare_123228589_state @ G_27 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_32 @ ( the_com @ ( body @ Pn_4 ) ) @ Q_22 ) @ bot_bo70021908tate_o ) )
+     => ( hoare_123228589_state @ G_27 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_32 @ ( body_1 @ Pn_4 ) @ Q_22 ) @ bot_bo70021908tate_o ) ) ) )).
+
+thf(fact_270_UnCI,axiom,(
+    ! [A_117: pname > $o,C_46: pname,B_88: pname > $o] :
+      ( ( ~ ( member_pname @ C_46 @ B_88 )
+       => ( member_pname @ C_46 @ A_117 ) )
+     => ( member_pname @ C_46 @ ( semila1780557381name_o @ A_117 @ B_88 ) ) ) )).
+
+thf(fact_271_UnCI,axiom,(
+    ! [A_117: hoare_1167836817_state > $o,C_46: hoare_1167836817_state,B_88: hoare_1167836817_state > $o] :
+      ( ( ~ ( member2058392318_state @ C_46 @ B_88 )
+       => ( member2058392318_state @ C_46 @ A_117 ) )
+     => ( member2058392318_state @ C_46 @ ( semila1172322802tate_o @ A_117 @ B_88 ) ) ) )).
+
+thf(fact_272_UnE,axiom,(
+    ! [C_45: pname,A_116: pname > $o,B_87: pname > $o] :
+      ( ( member_pname @ C_45 @ ( semila1780557381name_o @ A_116 @ B_87 ) )
+     => ( ~ ( member_pname @ C_45 @ A_116 )
+       => ( member_pname @ C_45 @ B_87 ) ) ) )).
+
+thf(fact_273_UnE,axiom,(
+    ! [C_45: hoare_1167836817_state,A_116: hoare_1167836817_state > $o,B_87: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ C_45 @ ( semila1172322802tate_o @ A_116 @ B_87 ) )
+     => ( ~ ( member2058392318_state @ C_45 @ A_116 )
+       => ( member2058392318_state @ C_45 @ B_87 ) ) ) )).
+
+thf(fact_274_Collect__disj__eq,axiom,(
+    ! [P_31: pname > $o,Q_21: pname > $o] :
+      ( ( collect_pname
+        @ ^ [X_5: pname] :
+            ( (|) @ ( P_31 @ X_5 ) @ ( Q_21 @ X_5 ) ) )
+      = ( semila1780557381name_o @ ( collect_pname @ P_31 ) @ ( collect_pname @ Q_21 ) ) ) )).
+
+thf(fact_275_Collect__disj__eq,axiom,(
+    ! [P_31: ( pname > $o ) > $o,Q_21: ( pname > $o ) > $o] :
+      ( ( collect_pname_o
+        @ ^ [X_5: pname > $o] :
+            ( (|) @ ( P_31 @ X_5 ) @ ( Q_21 @ X_5 ) ) )
+      = ( semila181081674me_o_o @ ( collect_pname_o @ P_31 ) @ ( collect_pname_o @ Q_21 ) ) ) )).
+
+thf(fact_276_Collect__disj__eq,axiom,(
+    ! [P_31: ( hoare_1167836817_state > $o ) > $o,Q_21: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( collec269976083tate_o
+        @ ^ [X_5: hoare_1167836817_state > $o] :
+            ( (|) @ ( P_31 @ X_5 ) @ ( Q_21 @ X_5 ) ) )
+      = ( semila866907787te_o_o @ ( collec269976083tate_o @ P_31 ) @ ( collec269976083tate_o @ Q_21 ) ) ) )).
+
+thf(fact_277_Collect__disj__eq,axiom,(
+    ! [P_31: hoare_1167836817_state > $o,Q_21: hoare_1167836817_state > $o] :
+      ( ( collec1027672124_state
+        @ ^ [X_5: hoare_1167836817_state] :
+            ( (|) @ ( P_31 @ X_5 ) @ ( Q_21 @ X_5 ) ) )
+      = ( semila1172322802tate_o @ ( collec1027672124_state @ P_31 ) @ ( collec1027672124_state @ Q_21 ) ) ) )).
+
+thf(fact_278_triple_Oinject,axiom,(
+    ! [Fun1_2: state > state > $o,Com_4: com,Fun2_2: state > state > $o,Fun1_1: state > state > $o,Com_3: com,Fun2_1: state > state > $o] :
+      ( ( ( hoare_908217195_state @ Fun1_2 @ Com_4 @ Fun2_2 )
+        = ( hoare_908217195_state @ Fun1_1 @ Com_3 @ Fun2_1 ) )
+    <=> ( ( Fun1_2 = Fun1_1 )
+        & ( Com_4 = Com_3 )
+        & ( Fun2_2 = Fun2_1 ) ) ) )).
+
+thf(fact_279_UnI2,axiom,(
+    ! [A_115: pname > $o,C_44: pname,B_86: pname > $o] :
+      ( ( member_pname @ C_44 @ B_86 )
+     => ( member_pname @ C_44 @ ( semila1780557381name_o @ A_115 @ B_86 ) ) ) )).
+
+thf(fact_280_UnI2,axiom,(
+    ! [A_115: hoare_1167836817_state > $o,C_44: hoare_1167836817_state,B_86: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ C_44 @ B_86 )
+     => ( member2058392318_state @ C_44 @ ( semila1172322802tate_o @ A_115 @ B_86 ) ) ) )).
+
+thf(fact_281_UnI1,axiom,(
+    ! [B_85: pname > $o,C_43: pname,A_114: pname > $o] :
+      ( ( member_pname @ C_43 @ A_114 )
+     => ( member_pname @ C_43 @ ( semila1780557381name_o @ A_114 @ B_85 ) ) ) )).
+
+thf(fact_282_UnI1,axiom,(
+    ! [B_85: hoare_1167836817_state > $o,C_43: hoare_1167836817_state,A_114: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ C_43 @ A_114 )
+     => ( member2058392318_state @ C_43 @ ( semila1172322802tate_o @ A_114 @ B_85 ) ) ) )).
+
+thf(fact_283_ball__Un,axiom,(
+    ! [P_30: hoare_1167836817_state > $o,A_113: hoare_1167836817_state > $o,B_84: hoare_1167836817_state > $o] :
+      ( ! [X_5: hoare_1167836817_state] :
+          ( ( member2058392318_state @ X_5 @ ( semila1172322802tate_o @ A_113 @ B_84 ) )
+         => ( P_30 @ X_5 ) )
+    <=> ( ! [X_5: hoare_1167836817_state] :
+            ( ( member2058392318_state @ X_5 @ A_113 )
+           => ( P_30 @ X_5 ) )
+        & ! [X_5: hoare_1167836817_state] :
+            ( ( member2058392318_state @ X_5 @ B_84 )
+           => ( P_30 @ X_5 ) ) ) ) )).
+
+thf(fact_284_bex__Un,axiom,(
+    ! [P_29: hoare_1167836817_state > $o,A_112: hoare_1167836817_state > $o,B_83: hoare_1167836817_state > $o] :
+      ( ? [X_5: hoare_1167836817_state] :
+          ( ( member2058392318_state @ X_5 @ ( semila1172322802tate_o @ A_112 @ B_83 ) )
+          & ( P_29 @ X_5 ) )
+    <=> ( ? [X_5: hoare_1167836817_state] :
+            ( ( member2058392318_state @ X_5 @ A_112 )
+            & ( P_29 @ X_5 ) )
+        | ? [X_5: hoare_1167836817_state] :
+            ( ( member2058392318_state @ X_5 @ B_83 )
+            & ( P_29 @ X_5 ) ) ) ) )).
+
+thf(fact_285_Un__assoc,axiom,(
+    ! [A_111: hoare_1167836817_state > $o,B_82: hoare_1167836817_state > $o,C_42: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ A_111 @ B_82 ) @ C_42 )
+      = ( semila1172322802tate_o @ A_111 @ ( semila1172322802tate_o @ B_82 @ C_42 ) ) ) )).
+
+thf(fact_286_Un__iff,axiom,(
+    ! [C_41: pname,A_110: pname > $o,B_81: pname > $o] :
+      ( ( member_pname @ C_41 @ ( semila1780557381name_o @ A_110 @ B_81 ) )
+    <=> ( ( member_pname @ C_41 @ A_110 )
+        | ( member_pname @ C_41 @ B_81 ) ) ) )).
+
+thf(fact_287_Un__iff,axiom,(
+    ! [C_41: hoare_1167836817_state,A_110: hoare_1167836817_state > $o,B_81: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ C_41 @ ( semila1172322802tate_o @ A_110 @ B_81 ) )
+    <=> ( ( member2058392318_state @ C_41 @ A_110 )
+        | ( member2058392318_state @ C_41 @ B_81 ) ) ) )).
+
+thf(fact_288_Un__left__commute,axiom,(
+    ! [A_109: hoare_1167836817_state > $o,B_80: hoare_1167836817_state > $o,C_40: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ A_109 @ ( semila1172322802tate_o @ B_80 @ C_40 ) )
+      = ( semila1172322802tate_o @ B_80 @ ( semila1172322802tate_o @ A_109 @ C_40 ) ) ) )).
+
+thf(fact_289_Un__left__absorb,axiom,(
+    ! [A_108: hoare_1167836817_state > $o,B_79: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ A_108 @ ( semila1172322802tate_o @ A_108 @ B_79 ) )
+      = ( semila1172322802tate_o @ A_108 @ B_79 ) ) )).
+
+thf(fact_290_Un__commute,axiom,(
+    ! [A_107: hoare_1167836817_state > $o,B_78: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ A_107 @ B_78 )
+      = ( semila1172322802tate_o @ B_78 @ A_107 ) ) )).
+
+thf(fact_291_Un__def,axiom,(
+    ! [A_106: pname > $o,B_77: pname > $o] :
+      ( ( semila1780557381name_o @ A_106 @ B_77 )
+      = ( collect_pname
+        @ ^ [X_5: pname] :
+            ( (|) @ ( member_pname @ X_5 @ A_106 ) @ ( member_pname @ X_5 @ B_77 ) ) ) ) )).
+
+thf(fact_292_Un__def,axiom,(
+    ! [A_106: ( pname > $o ) > $o,B_77: ( pname > $o ) > $o] :
+      ( ( semila181081674me_o_o @ A_106 @ B_77 )
+      = ( collect_pname_o
+        @ ^ [X_5: pname > $o] :
+            ( (|) @ ( member_pname_o @ X_5 @ A_106 ) @ ( member_pname_o @ X_5 @ B_77 ) ) ) ) )).
+
+thf(fact_293_Un__def,axiom,(
+    ! [A_106: ( hoare_1167836817_state > $o ) > $o,B_77: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( semila866907787te_o_o @ A_106 @ B_77 )
+      = ( collec269976083tate_o
+        @ ^ [X_5: hoare_1167836817_state > $o] :
+            ( (|) @ ( member864234961tate_o @ X_5 @ A_106 ) @ ( member864234961tate_o @ X_5 @ B_77 ) ) ) ) )).
+
+thf(fact_294_Un__def,axiom,(
+    ! [A_106: hoare_1167836817_state > $o,B_77: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ A_106 @ B_77 )
+      = ( collec1027672124_state
+        @ ^ [X_5: hoare_1167836817_state] :
+            ( (|) @ ( member2058392318_state @ X_5 @ A_106 ) @ ( member2058392318_state @ X_5 @ B_77 ) ) ) ) )).
+
+thf(fact_295_Un__absorb,axiom,(
+    ! [A_105: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ A_105 @ A_105 )
+      = A_105 ) )).
+
+thf(fact_296_Un__empty,axiom,(
+    ! [A_104: pname > $o,B_76: pname > $o] :
+      ( ( ( semila1780557381name_o @ A_104 @ B_76 )
+        = bot_bot_pname_o )
+    <=> ( ( A_104 = bot_bot_pname_o )
+        & ( B_76 = bot_bot_pname_o ) ) ) )).
+
+thf(fact_297_Un__empty,axiom,(
+    ! [A_104: hoare_1167836817_state > $o,B_76: hoare_1167836817_state > $o] :
+      ( ( ( semila1172322802tate_o @ A_104 @ B_76 )
+        = bot_bo70021908tate_o )
+    <=> ( ( A_104 = bot_bo70021908tate_o )
+        & ( B_76 = bot_bo70021908tate_o ) ) ) )).
+
+thf(fact_298_Un__empty__right,axiom,(
+    ! [A_103: pname > $o] :
+      ( ( semila1780557381name_o @ A_103 @ bot_bot_pname_o )
+      = A_103 ) )).
+
+thf(fact_299_Un__empty__right,axiom,(
+    ! [A_103: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ A_103 @ bot_bo70021908tate_o )
+      = A_103 ) )).
+
+thf(fact_300_Un__empty__left,axiom,(
+    ! [B_75: pname > $o] :
+      ( ( semila1780557381name_o @ bot_bot_pname_o @ B_75 )
+      = B_75 ) )).
+
+thf(fact_301_Un__empty__left,axiom,(
+    ! [B_75: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ bot_bo70021908tate_o @ B_75 )
+      = B_75 ) )).
+
+thf(fact_302_finite__UnI,axiom,(
+    ! [G_26: ( pname > $o ) > $o,F_41: ( pname > $o ) > $o] :
+      ( ( finite297249702name_o @ F_41 )
+     => ( ( finite297249702name_o @ G_26 )
+       => ( finite297249702name_o @ ( semila181081674me_o_o @ F_41 @ G_26 ) ) ) ) )).
+
+thf(fact_303_finite__UnI,axiom,(
+    ! [G_26: ( hoare_1167836817_state > $o ) > $o,F_41: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( finite1380128977tate_o @ F_41 )
+     => ( ( finite1380128977tate_o @ G_26 )
+       => ( finite1380128977tate_o @ ( semila866907787te_o_o @ F_41 @ G_26 ) ) ) ) )).
+
+thf(fact_304_finite__UnI,axiom,(
+    ! [G_26: pname > $o,F_41: pname > $o] :
+      ( ( finite_finite_pname @ F_41 )
+     => ( ( finite_finite_pname @ G_26 )
+       => ( finite_finite_pname @ ( semila1780557381name_o @ F_41 @ G_26 ) ) ) ) )).
+
+thf(fact_305_finite__UnI,axiom,(
+    ! [G_26: hoare_1167836817_state > $o,F_41: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ F_41 )
+     => ( ( finite1084549118_state @ G_26 )
+       => ( finite1084549118_state @ ( semila1172322802tate_o @ F_41 @ G_26 ) ) ) ) )).
+
+thf(fact_306_finite__Un,axiom,(
+    ! [F_40: ( pname > $o ) > $o,G_25: ( pname > $o ) > $o] :
+      ( ( finite297249702name_o @ ( semila181081674me_o_o @ F_40 @ G_25 ) )
+    <=> ( ( finite297249702name_o @ F_40 )
+        & ( finite297249702name_o @ G_25 ) ) ) )).
+
+thf(fact_307_finite__Un,axiom,(
+    ! [F_40: ( hoare_1167836817_state > $o ) > $o,G_25: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( finite1380128977tate_o @ ( semila866907787te_o_o @ F_40 @ G_25 ) )
+    <=> ( ( finite1380128977tate_o @ F_40 )
+        & ( finite1380128977tate_o @ G_25 ) ) ) )).
+
+thf(fact_308_finite__Un,axiom,(
+    ! [F_40: pname > $o,G_25: pname > $o] :
+      ( ( finite_finite_pname @ ( semila1780557381name_o @ F_40 @ G_25 ) )
+    <=> ( ( finite_finite_pname @ F_40 )
+        & ( finite_finite_pname @ G_25 ) ) ) )).
+
+thf(fact_309_finite__Un,axiom,(
+    ! [F_40: hoare_1167836817_state > $o,G_25: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ ( semila1172322802tate_o @ F_40 @ G_25 ) )
+    <=> ( ( finite1084549118_state @ F_40 )
+        & ( finite1084549118_state @ G_25 ) ) ) )).
+
+thf(fact_310_Un__insert__left,axiom,(
+    ! [A_102: pname,B_74: pname > $o,C_39: pname > $o] :
+      ( ( semila1780557381name_o @ ( insert_pname @ A_102 @ B_74 ) @ C_39 )
+      = ( insert_pname @ A_102 @ ( semila1780557381name_o @ B_74 @ C_39 ) ) ) )).
+
+thf(fact_311_Un__insert__left,axiom,(
+    ! [A_102: hoare_1167836817_state,B_74: hoare_1167836817_state > $o,C_39: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ ( insert2134838167_state @ A_102 @ B_74 ) @ C_39 )
+      = ( insert2134838167_state @ A_102 @ ( semila1172322802tate_o @ B_74 @ C_39 ) ) ) )).
+
+thf(fact_312_Un__insert__right,axiom,(
+    ! [A_101: pname > $o,A_100: pname,B_73: pname > $o] :
+      ( ( semila1780557381name_o @ A_101 @ ( insert_pname @ A_100 @ B_73 ) )
+      = ( insert_pname @ A_100 @ ( semila1780557381name_o @ A_101 @ B_73 ) ) ) )).
+
+thf(fact_313_Un__insert__right,axiom,(
+    ! [A_101: hoare_1167836817_state > $o,A_100: hoare_1167836817_state,B_73: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ A_101 @ ( insert2134838167_state @ A_100 @ B_73 ) )
+      = ( insert2134838167_state @ A_100 @ ( semila1172322802tate_o @ A_101 @ B_73 ) ) ) )).
+
+thf(fact_314_Un__mono,axiom,(
+    ! [B_72: pname > $o,D_4: pname > $o,A_99: pname > $o,C_38: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_99 @ C_38 )
+     => ( ( ord_less_eq_pname_o @ B_72 @ D_4 )
+       => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_99 @ B_72 ) @ ( semila1780557381name_o @ C_38 @ D_4 ) ) ) ) )).
+
+thf(fact_315_Un__mono,axiom,(
+    ! [B_72: hoare_1167836817_state > $o,D_4: hoare_1167836817_state > $o,A_99: hoare_1167836817_state > $o,C_38: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_99 @ C_38 )
+     => ( ( ord_le827224136tate_o @ B_72 @ D_4 )
+       => ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A_99 @ B_72 ) @ ( semila1172322802tate_o @ C_38 @ D_4 ) ) ) ) )).
+
+thf(fact_316_Un__least,axiom,(
+    ! [B_71: pname > $o,A_98: pname > $o,C_37: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_98 @ C_37 )
+     => ( ( ord_less_eq_pname_o @ B_71 @ C_37 )
+       => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_98 @ B_71 ) @ C_37 ) ) ) )).
+
+thf(fact_317_Un__least,axiom,(
+    ! [B_71: hoare_1167836817_state > $o,A_98: hoare_1167836817_state > $o,C_37: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_98 @ C_37 )
+     => ( ( ord_le827224136tate_o @ B_71 @ C_37 )
+       => ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A_98 @ B_71 ) @ C_37 ) ) ) )).
+
+thf(fact_318_Un__absorb2,axiom,(
+    ! [B_70: pname > $o,A_97: pname > $o] :
+      ( ( ord_less_eq_pname_o @ B_70 @ A_97 )
+     => ( ( semila1780557381name_o @ A_97 @ B_70 )
+        = A_97 ) ) )).
+
+thf(fact_319_Un__absorb2,axiom,(
+    ! [B_70: hoare_1167836817_state > $o,A_97: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ B_70 @ A_97 )
+     => ( ( semila1172322802tate_o @ A_97 @ B_70 )
+        = A_97 ) ) )).
+
+thf(fact_320_Un__absorb1,axiom,(
+    ! [A_96: pname > $o,B_69: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_96 @ B_69 )
+     => ( ( semila1780557381name_o @ A_96 @ B_69 )
+        = B_69 ) ) )).
+
+thf(fact_321_Un__absorb1,axiom,(
+    ! [A_96: hoare_1167836817_state > $o,B_69: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_96 @ B_69 )
+     => ( ( semila1172322802tate_o @ A_96 @ B_69 )
+        = B_69 ) ) )).
+
+thf(fact_322_subset__Un__eq,axiom,(
+    ! [A_95: pname > $o,B_68: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_95 @ B_68 )
+    <=> ( ( semila1780557381name_o @ A_95 @ B_68 )
+        = B_68 ) ) )).
+
+thf(fact_323_subset__Un__eq,axiom,(
+    ! [A_95: hoare_1167836817_state > $o,B_68: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_95 @ B_68 )
+    <=> ( ( semila1172322802tate_o @ A_95 @ B_68 )
+        = B_68 ) ) )).
+
+thf(fact_324_Un__upper2,axiom,(
+    ! [B_67: pname > $o,A_94: pname > $o] :
+      ( ord_less_eq_pname_o @ B_67 @ ( semila1780557381name_o @ A_94 @ B_67 ) ) )).
+
+thf(fact_325_Un__upper2,axiom,(
+    ! [B_67: hoare_1167836817_state > $o,A_94: hoare_1167836817_state > $o] :
+      ( ord_le827224136tate_o @ B_67 @ ( semila1172322802tate_o @ A_94 @ B_67 ) ) )).
+
+thf(fact_326_Un__upper1,axiom,(
+    ! [A_93: pname > $o,B_66: pname > $o] :
+      ( ord_less_eq_pname_o @ A_93 @ ( semila1780557381name_o @ A_93 @ B_66 ) ) )).
+
+thf(fact_327_Un__upper1,axiom,(
+    ! [A_93: hoare_1167836817_state > $o,B_66: hoare_1167836817_state > $o] :
+      ( ord_le827224136tate_o @ A_93 @ ( semila1172322802tate_o @ A_93 @ B_66 ) ) )).
+
+thf(fact_328_image__Un,axiom,(
+    ! [F_39: pname > hoare_1167836817_state,A_92: pname > $o,B_65: pname > $o] :
+      ( ( image_575578384_state @ F_39 @ ( semila1780557381name_o @ A_92 @ B_65 ) )
+      = ( semila1172322802tate_o @ ( image_575578384_state @ F_39 @ A_92 ) @ ( image_575578384_state @ F_39 @ B_65 ) ) ) )).
+
+thf(fact_329_insert__def,axiom,(
+    ! [A_91: pname,B_64: pname > $o] :
+      ( ( insert_pname @ A_91 @ B_64 )
+      = ( semila1780557381name_o
+        @ ( collect_pname
+          @ ^ [X_5: pname] : ( X_5 = A_91 ) )
+        @ B_64 ) ) )).
+
+thf(fact_330_insert__def,axiom,(
+    ! [A_91: hoare_1167836817_state,B_64: hoare_1167836817_state > $o] :
+      ( ( insert2134838167_state @ A_91 @ B_64 )
+      = ( semila1172322802tate_o
+        @ ( collec1027672124_state
+          @ ^ [X_5: hoare_1167836817_state] : ( X_5 = A_91 ) )
+        @ B_64 ) ) )).
+
+thf(fact_331_insert__def,axiom,(
+    ! [A_91: pname > $o,B_64: ( pname > $o ) > $o] :
+      ( ( insert_pname_o @ A_91 @ B_64 )
+      = ( semila181081674me_o_o
+        @ ( collect_pname_o
+          @ ^ [X_5: pname > $o] : ( X_5 = A_91 ) )
+        @ B_64 ) ) )).
+
+thf(fact_332_insert__def,axiom,(
+    ! [A_91: hoare_1167836817_state > $o,B_64: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( insert999278200tate_o @ A_91 @ B_64 )
+      = ( semila866907787te_o_o
+        @ ( collec269976083tate_o
+          @ ^ [X_5: hoare_1167836817_state > $o] : ( X_5 = A_91 ) )
+        @ B_64 ) ) )).
+
+thf(fact_333_insert__is__Un,axiom,(
+    ! [A_90: pname,A_89: pname > $o] :
+      ( ( insert_pname @ A_90 @ A_89 )
+      = ( semila1780557381name_o @ ( insert_pname @ A_90 @ bot_bot_pname_o ) @ A_89 ) ) )).
+
+thf(fact_334_insert__is__Un,axiom,(
+    ! [A_90: hoare_1167836817_state,A_89: hoare_1167836817_state > $o] :
+      ( ( insert2134838167_state @ A_90 @ A_89 )
+      = ( semila1172322802tate_o @ ( insert2134838167_state @ A_90 @ bot_bo70021908tate_o ) @ A_89 ) ) )).
+
+thf(fact_335_hoare__derivs_OBody,axiom,(
+    ! [G_24: hoare_1167836817_state > $o,P_28: pname > state > state > $o,Q_20: pname > state > state > $o,Procs_2: pname > $o] :
+      ( ( hoare_123228589_state
+        @ ( semila1172322802tate_o @ G_24
+          @ ( image_575578384_state
+            @ ^ [P_24: pname] :
+                ( hoare_908217195_state @ ( P_28 @ P_24 ) @ ( body_1 @ P_24 ) @ ( Q_20 @ P_24 ) )
+            @ Procs_2 ) )
+        @ ( image_575578384_state
+          @ ^ [P_24: pname] :
+              ( hoare_908217195_state @ ( P_28 @ P_24 ) @ ( the_com @ ( body @ P_24 ) ) @ ( Q_20 @ P_24 ) )
+          @ Procs_2 ) )
+     => ( hoare_123228589_state @ G_24
+        @ ( image_575578384_state
+          @ ^ [P_24: pname] :
+              ( hoare_908217195_state @ ( P_28 @ P_24 ) @ ( body_1 @ P_24 ) @ ( Q_20 @ P_24 ) )
+          @ Procs_2 ) ) ) )).
+
+thf(fact_336_xt1_I6_J,axiom,(
+    ! [Z_20: pname > $o,Y_46: pname > $o,X_81: pname > $o] :
+      ( ( ord_less_eq_pname_o @ Y_46 @ X_81 )
+     => ( ( ord_less_eq_pname_o @ Z_20 @ Y_46 )
+       => ( ord_less_eq_pname_o @ Z_20 @ X_81 ) ) ) )).
+
+thf(fact_337_xt1_I6_J,axiom,(
+    ! [Z_20: hoare_1167836817_state > $o,Y_46: hoare_1167836817_state > $o,X_81: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ Y_46 @ X_81 )
+     => ( ( ord_le827224136tate_o @ Z_20 @ Y_46 )
+       => ( ord_le827224136tate_o @ Z_20 @ X_81 ) ) ) )).
+
+thf(fact_338_xt1_I5_J,axiom,(
+    ! [Y_45: pname > $o,X_80: pname > $o] :
+      ( ( ord_less_eq_pname_o @ Y_45 @ X_80 )
+     => ( ( ord_less_eq_pname_o @ X_80 @ Y_45 )
+       => ( X_80 = Y_45 ) ) ) )).
+
+thf(fact_339_xt1_I5_J,axiom,(
+    ! [Y_45: hoare_1167836817_state > $o,X_80: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ Y_45 @ X_80 )
+     => ( ( ord_le827224136tate_o @ X_80 @ Y_45 )
+       => ( X_80 = Y_45 ) ) ) )).
+
+thf(fact_340_order__trans,axiom,(
+    ! [Z_19: pname > $o,X_79: pname > $o,Y_44: pname > $o] :
+      ( ( ord_less_eq_pname_o @ X_79 @ Y_44 )
+     => ( ( ord_less_eq_pname_o @ Y_44 @ Z_19 )
+       => ( ord_less_eq_pname_o @ X_79 @ Z_19 ) ) ) )).
+
+thf(fact_341_order__trans,axiom,(
+    ! [Z_19: hoare_1167836817_state > $o,X_79: hoare_1167836817_state > $o,Y_44: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ X_79 @ Y_44 )
+     => ( ( ord_le827224136tate_o @ Y_44 @ Z_19 )
+       => ( ord_le827224136tate_o @ X_79 @ Z_19 ) ) ) )).
+
+thf(fact_342_order__antisym,axiom,(
+    ! [X_78: pname > $o,Y_43: pname > $o] :
+      ( ( ord_less_eq_pname_o @ X_78 @ Y_43 )
+     => ( ( ord_less_eq_pname_o @ Y_43 @ X_78 )
+       => ( X_78 = Y_43 ) ) ) )).
+
+thf(fact_343_order__antisym,axiom,(
+    ! [X_78: hoare_1167836817_state > $o,Y_43: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ X_78 @ Y_43 )
+     => ( ( ord_le827224136tate_o @ Y_43 @ X_78 )
+       => ( X_78 = Y_43 ) ) ) )).
+
+thf(fact_344_xt1_I4_J,axiom,(
+    ! [C_36: pname > $o,B_63: pname > $o,A_88: pname > $o] :
+      ( ( ord_less_eq_pname_o @ B_63 @ A_88 )
+     => ( ( B_63 = C_36 )
+       => ( ord_less_eq_pname_o @ C_36 @ A_88 ) ) ) )).
+
+thf(fact_345_xt1_I4_J,axiom,(
+    ! [C_36: hoare_1167836817_state > $o,B_63: hoare_1167836817_state > $o,A_88: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ B_63 @ A_88 )
+     => ( ( B_63 = C_36 )
+       => ( ord_le827224136tate_o @ C_36 @ A_88 ) ) ) )).
+
+thf(fact_346_ord__le__eq__trans,axiom,(
+    ! [C_35: pname > $o,A_87: pname > $o,B_62: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_87 @ B_62 )
+     => ( ( B_62 = C_35 )
+       => ( ord_less_eq_pname_o @ A_87 @ C_35 ) ) ) )).
+
+thf(fact_347_ord__le__eq__trans,axiom,(
+    ! [C_35: hoare_1167836817_state > $o,A_87: hoare_1167836817_state > $o,B_62: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_87 @ B_62 )
+     => ( ( B_62 = C_35 )
+       => ( ord_le827224136tate_o @ A_87 @ C_35 ) ) ) )).
+
+thf(fact_348_xt1_I3_J,axiom,(
+    ! [C_34: pname > $o,A_86: pname > $o,B_61: pname > $o] :
+      ( ( A_86 = B_61 )
+     => ( ( ord_less_eq_pname_o @ C_34 @ B_61 )
+       => ( ord_less_eq_pname_o @ C_34 @ A_86 ) ) ) )).
+
+thf(fact_349_xt1_I3_J,axiom,(
+    ! [C_34: hoare_1167836817_state > $o,A_86: hoare_1167836817_state > $o,B_61: hoare_1167836817_state > $o] :
+      ( ( A_86 = B_61 )
+     => ( ( ord_le827224136tate_o @ C_34 @ B_61 )
+       => ( ord_le827224136tate_o @ C_34 @ A_86 ) ) ) )).
+
+thf(fact_350_ord__eq__le__trans,axiom,(
+    ! [C_33: pname > $o,A_85: pname > $o,B_60: pname > $o] :
+      ( ( A_85 = B_60 )
+     => ( ( ord_less_eq_pname_o @ B_60 @ C_33 )
+       => ( ord_less_eq_pname_o @ A_85 @ C_33 ) ) ) )).
+
+thf(fact_351_ord__eq__le__trans,axiom,(
+    ! [C_33: hoare_1167836817_state > $o,A_85: hoare_1167836817_state > $o,B_60: hoare_1167836817_state > $o] :
+      ( ( A_85 = B_60 )
+     => ( ( ord_le827224136tate_o @ B_60 @ C_33 )
+       => ( ord_le827224136tate_o @ A_85 @ C_33 ) ) ) )).
+
+thf(fact_352_order__antisym__conv,axiom,(
+    ! [Y_42: pname > $o,X_77: pname > $o] :
+      ( ( ord_less_eq_pname_o @ Y_42 @ X_77 )
+     => ( ( ord_less_eq_pname_o @ X_77 @ Y_42 )
+      <=> ( X_77 = Y_42 ) ) ) )).
+
+thf(fact_353_order__antisym__conv,axiom,(
+    ! [Y_42: hoare_1167836817_state > $o,X_77: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ Y_42 @ X_77 )
+     => ( ( ord_le827224136tate_o @ X_77 @ Y_42 )
+      <=> ( X_77 = Y_42 ) ) ) )).
+
+thf(fact_354_order__eq__refl,axiom,(
+    ! [X_76: pname > $o,Y_41: pname > $o] :
+      ( ( X_76 = Y_41 )
+     => ( ord_less_eq_pname_o @ X_76 @ Y_41 ) ) )).
+
+thf(fact_355_order__eq__refl,axiom,(
+    ! [X_76: hoare_1167836817_state > $o,Y_41: hoare_1167836817_state > $o] :
+      ( ( X_76 = Y_41 )
+     => ( ord_le827224136tate_o @ X_76 @ Y_41 ) ) )).
+
+thf(fact_356_order__eq__iff,axiom,(
+    ! [X_75: pname > $o,Y_40: pname > $o] :
+      ( ( X_75 = Y_40 )
+    <=> ( ( ord_less_eq_pname_o @ X_75 @ Y_40 )
+        & ( ord_less_eq_pname_o @ Y_40 @ X_75 ) ) ) )).
+
+thf(fact_357_order__eq__iff,axiom,(
+    ! [X_75: hoare_1167836817_state > $o,Y_40: hoare_1167836817_state > $o] :
+      ( ( X_75 = Y_40 )
+    <=> ( ( ord_le827224136tate_o @ X_75 @ Y_40 )
+        & ( ord_le827224136tate_o @ Y_40 @ X_75 ) ) ) )).
+
+thf(fact_358_option_Oinject,axiom,(
+    ! [A_84: com,A_83: com] :
+      ( ( ( some_com @ A_84 )
+        = ( some_com @ A_83 ) )
+    <=> ( A_84 = A_83 ) ) )).
+
+thf(fact_359_constant,axiom,(
+    ! [G_23: hoare_1167836817_state > $o,P_27: state > state > $o,C_32: com,Q_19: state > state > $o,C_31: $o] :
+      ( ( C_31
+       => ( hoare_123228589_state @ G_23 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_27 @ C_32 @ Q_19 ) @ bot_bo70021908tate_o ) ) )
+     => ( hoare_123228589_state @ G_23
+        @ ( insert2134838167_state
+          @ ( hoare_908217195_state
+            @ ^ [Z_11: state,S_3: state] :
+                ( (&) @ ( P_27 @ Z_11 @ S_3 ) @ C_31 )
+            @ C_32
+            @ Q_19 )
+          @ bot_bo70021908tate_o ) ) ) )).
+
+thf(fact_360_Body1,axiom,(
+    ! [Pn_3: pname,G_22: hoare_1167836817_state > $o,P_26: pname > state > state > $o,Q_18: pname > state > state > $o,Procs_1: pname > $o] :
+      ( ( hoare_123228589_state
+        @ ( semila1172322802tate_o @ G_22
+          @ ( image_575578384_state
+            @ ^ [P_24: pname] :
+                ( hoare_908217195_state @ ( P_26 @ P_24 ) @ ( body_1 @ P_24 ) @ ( Q_18 @ P_24 ) )
+            @ Procs_1 ) )
+        @ ( image_575578384_state
+          @ ^ [P_24: pname] :
+              ( hoare_908217195_state @ ( P_26 @ P_24 ) @ ( the_com @ ( body @ P_24 ) ) @ ( Q_18 @ P_24 ) )
+          @ Procs_1 ) )
+     => ( ( member_pname @ Pn_3 @ Procs_1 )
+       => ( hoare_123228589_state @ G_22 @ ( insert2134838167_state @ ( hoare_908217195_state @ ( P_26 @ Pn_3 ) @ ( body_1 @ Pn_3 ) @ ( Q_18 @ Pn_3 ) ) @ bot_bo70021908tate_o ) ) ) ) )).
+
+thf(fact_361_le__bot,axiom,(
+    ! [A_82: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_82 @ bot_bot_pname_o )
+     => ( A_82 = bot_bot_pname_o ) ) )).
+
+thf(fact_362_le__bot,axiom,(
+    ! [A_82: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_82 @ bot_bo70021908tate_o )
+     => ( A_82 = bot_bo70021908tate_o ) ) )).
+
+thf(fact_363_bot__unique,axiom,(
+    ! [A_81: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_81 @ bot_bot_pname_o )
+    <=> ( A_81 = bot_bot_pname_o ) ) )).
+
+thf(fact_364_bot__unique,axiom,(
+    ! [A_81: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_81 @ bot_bo70021908tate_o )
+    <=> ( A_81 = bot_bo70021908tate_o ) ) )).
+
+thf(fact_365_bot__least,axiom,(
+    ! [A_80: pname > $o] :
+      ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_80 ) )).
+
+thf(fact_366_bot__least,axiom,(
+    ! [A_80: hoare_1167836817_state > $o] :
+      ( ord_le827224136tate_o @ bot_bo70021908tate_o @ A_80 ) )).
+
+thf(fact_367_le__funE,axiom,(
+    ! [X_74: pname,F_38: pname > $o,G_21: pname > $o] :
+      ( ( ord_less_eq_pname_o @ F_38 @ G_21 )
+     => ( ord_less_eq_o @ ( F_38 @ X_74 ) @ ( G_21 @ X_74 ) ) ) )).
+
+thf(fact_368_le__funE,axiom,(
+    ! [X_74: hoare_1167836817_state,F_38: hoare_1167836817_state > $o,G_21: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ F_38 @ G_21 )
+     => ( ord_less_eq_o @ ( F_38 @ X_74 ) @ ( G_21 @ X_74 ) ) ) )).
+
+thf(fact_369_le__funD,axiom,(
+    ! [X_73: pname,F_37: pname > $o,G_20: pname > $o] :
+      ( ( ord_less_eq_pname_o @ F_37 @ G_20 )
+     => ( ord_less_eq_o @ ( F_37 @ X_73 ) @ ( G_20 @ X_73 ) ) ) )).
+
+thf(fact_370_le__funD,axiom,(
+    ! [X_73: hoare_1167836817_state,F_37: hoare_1167836817_state > $o,G_20: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ F_37 @ G_20 )
+     => ( ord_less_eq_o @ ( F_37 @ X_73 ) @ ( G_20 @ X_73 ) ) ) )).
+
+thf(fact_371_le__fun__def,axiom,(
+    ! [F_36: pname > $o,G_19: pname > $o] :
+      ( ( ord_less_eq_pname_o @ F_36 @ G_19 )
+    <=> ! [X_5: pname] :
+          ( ord_less_eq_o @ ( F_36 @ X_5 ) @ ( G_19 @ X_5 ) ) ) )).
+
+thf(fact_372_le__fun__def,axiom,(
+    ! [F_36: hoare_1167836817_state > $o,G_19: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ F_36 @ G_19 )
+    <=> ! [X_5: hoare_1167836817_state] :
+          ( ord_less_eq_o @ ( F_36 @ X_5 ) @ ( G_19 @ X_5 ) ) ) )).
+
+thf(fact_373_bot__apply,axiom,(
+    ! [X_72: pname] :
+      ( ( bot_bot_pname_o @ X_72 )
+    <=> bot_bot_o ) )).
+
+thf(fact_374_bot__apply,axiom,(
+    ! [X_72: hoare_1167836817_state] :
+      ( ( bot_bo70021908tate_o @ X_72 )
+    <=> bot_bot_o ) )).
+
+thf(fact_375_bot__fun__def,axiom,(
+    ! [X_5: pname] :
+      ( ( bot_bot_pname_o @ X_5 )
+    <=> bot_bot_o ) )).
+
+thf(fact_376_bot__fun__def,axiom,(
+    ! [X_5: hoare_1167836817_state] :
+      ( ( bot_bo70021908tate_o @ X_5 )
+    <=> bot_bot_o ) )).
+
+thf(fact_377_BodyN,axiom,(
+    ! [P_25: state > state > $o,Pn_2: pname,Q_17: state > state > $o,G_18: hoare_1167836817_state > $o] :
+      ( ( hoare_123228589_state @ ( insert2134838167_state @ ( hoare_908217195_state @ P_25 @ ( body_1 @ Pn_2 ) @ Q_17 ) @ G_18 ) @ ( insert2134838167_state @ ( hoare_908217195_state @ P_25 @ ( the_com @ ( body @ Pn_2 ) ) @ Q_17 ) @ bot_bo70021908tate_o ) )
+     => ( hoare_123228589_state @ G_18 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_25 @ ( body_1 @ Pn_2 ) @ Q_17 ) @ bot_bo70021908tate_o ) ) ) )).
+
+thf(fact_378_finite__pointwise,axiom,(
+    ! [P_23: pname > state > state > $o,Q_16: pname > state > state > $o,G_17: hoare_1167836817_state > $o,P_22: pname > state > state > $o,C0_1: pname > com,Q_15: pname > state > state > $o,U_1: pname > $o] :
+      ( ( finite_finite_pname @ U_1 )
+     => ( ! [P_24: pname] :
+            ( ( hoare_123228589_state @ G_17 @ ( insert2134838167_state @ ( hoare_908217195_state @ ( P_22 @ P_24 ) @ ( C0_1 @ P_24 ) @ ( Q_15 @ P_24 ) ) @ bot_bo70021908tate_o ) )
+           => ( hoare_123228589_state @ G_17 @ ( insert2134838167_state @ ( hoare_908217195_state @ ( P_23 @ P_24 ) @ ( C0_1 @ P_24 ) @ ( Q_16 @ P_24 ) ) @ bot_bo70021908tate_o ) ) )
+       => ( ( hoare_123228589_state @ G_17
+            @ ( image_575578384_state
+              @ ^ [P_24: pname] :
+                  ( hoare_908217195_state @ ( P_22 @ P_24 ) @ ( C0_1 @ P_24 ) @ ( Q_15 @ P_24 ) )
+              @ U_1 ) )
+         => ( hoare_123228589_state @ G_17
+            @ ( image_575578384_state
+              @ ^ [P_24: pname] :
+                  ( hoare_908217195_state @ ( P_23 @ P_24 ) @ ( C0_1 @ P_24 ) @ ( Q_16 @ P_24 ) )
+              @ U_1 ) ) ) ) ) )).
+
+thf(fact_379_escape,axiom,(
+    ! [G_16: hoare_1167836817_state > $o,C_30: com,Q_14: state > state > $o,P_21: state > state > $o] :
+      ( ! [Z_11: state,S_3: state] :
+          ( ( P_21 @ Z_11 @ S_3 )
+         => ( hoare_123228589_state @ G_16
+            @ ( insert2134838167_state
+              @ ( hoare_908217195_state
+                @ ^ [Za: state,S_4: state] : ( S_4 = S_3 )
+                @ C_30
+                @ ^ [Z_18: state] :
+                    ( Q_14 @ Z_11 ) )
+              @ bot_bo70021908tate_o ) ) )
+     => ( hoare_123228589_state @ G_16 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_21 @ C_30 @ Q_14 ) @ bot_bo70021908tate_o ) ) ) )).
+
+thf(fact_380_Body__sound__lemma,axiom,(
+    ! [G_15: hoare_1167836817_state > $o,P_20: pname > state > state > $o,Q_13: pname > state > state > $o,Procs: pname > $o] :
+      ( ( hoare_529639851_state
+        @ ( semila1172322802tate_o @ G_15
+          @ ( image_575578384_state
+            @ ^ [Pn: pname] :
+                ( hoare_908217195_state @ ( P_20 @ Pn ) @ ( body_1 @ Pn ) @ ( Q_13 @ Pn ) )
+            @ Procs ) )
+        @ ( image_575578384_state
+          @ ^ [Pn: pname] :
+              ( hoare_908217195_state @ ( P_20 @ Pn ) @ ( the_com @ ( body @ Pn ) ) @ ( Q_13 @ Pn ) )
+          @ Procs ) )
+     => ( hoare_529639851_state @ G_15
+        @ ( image_575578384_state
+          @ ^ [Pn: pname] :
+              ( hoare_908217195_state @ ( P_20 @ Pn ) @ ( body_1 @ Pn ) @ ( Q_13 @ Pn ) )
+          @ Procs ) ) ) )).
+
+thf(fact_381_conseq1,axiom,(
+    ! [P_19: state > state > $o,G_14: hoare_1167836817_state > $o,P_18: state > state > $o,C_29: com,Q_12: state > state > $o] :
+      ( ( hoare_123228589_state @ G_14 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_18 @ C_29 @ Q_12 ) @ bot_bo70021908tate_o ) )
+     => ( ! [Z_11: state,S_3: state] :
+            ( ( P_19 @ Z_11 @ S_3 )
+           => ( P_18 @ Z_11 @ S_3 ) )
+       => ( hoare_123228589_state @ G_14 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_19 @ C_29 @ Q_12 ) @ bot_bo70021908tate_o ) ) ) ) )).
+
+thf(fact_382_conseq2,axiom,(
+    ! [Q_11: state > state > $o,G_13: hoare_1167836817_state > $o,P_17: state > state > $o,C_28: com,Q_10: state > state > $o] :
+      ( ( hoare_123228589_state @ G_13 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_17 @ C_28 @ Q_10 ) @ bot_bo70021908tate_o ) )
+     => ( ! [Z_11: state,S_3: state] :
+            ( ( Q_10 @ Z_11 @ S_3 )
+           => ( Q_11 @ Z_11 @ S_3 ) )
+       => ( hoare_123228589_state @ G_13 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_17 @ C_28 @ Q_11 ) @ bot_bo70021908tate_o ) ) ) ) )).
+
+thf(fact_383_MGF__complete,axiom,(
+    ! [P: state > state > $o,Q_9: state > state > $o,C_21: com] :
+      ( ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ C_21 ) @ bot_bo70021908tate_o ) )
+     => ( ( hoare_529639851_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_908217195_state @ P @ C_21 @ Q_9 ) @ bot_bo70021908tate_o ) )
+       => ( hoare_123228589_state @ bot_bo70021908tate_o @ ( insert2134838167_state @ ( hoare_908217195_state @ P @ C_21 @ Q_9 ) @ bot_bo70021908tate_o ) ) ) ) )).
+
+thf(fact_384_sup1E,axiom,(
+    ! [A_79: hoare_1167836817_state > $o,B_59: hoare_1167836817_state > $o,X_71: hoare_1167836817_state] :
+      ( ( semila1172322802tate_o @ A_79 @ B_59 @ X_71 )
+     => ( ~ ( A_79 @ X_71 )
+       => ( B_59 @ X_71 ) ) ) )).
+
+thf(fact_385_sup1CI,axiom,(
+    ! [A_78: hoare_1167836817_state > $o,B_58: hoare_1167836817_state > $o,X_70: hoare_1167836817_state] :
+      ( ( ~ ( B_58 @ X_70 )
+       => ( A_78 @ X_70 ) )
+     => ( semila1172322802tate_o @ A_78 @ B_58 @ X_70 ) ) )).
+
+thf(fact_386_hoare__sound,axiom,(
+    ! [G_12: hoare_1167836817_state > $o,Ts: hoare_1167836817_state > $o] :
+      ( ( hoare_123228589_state @ G_12 @ Ts )
+     => ( hoare_529639851_state @ G_12 @ Ts ) ) )).
+
+thf(fact_387_bot__empty__eq,axiom,(
+    ! [X_5: pname] :
+      ( ( bot_bot_pname_o @ X_5 )
+    <=> ( member_pname @ X_5 @ bot_bot_pname_o ) ) )).
+
+thf(fact_388_bot__empty__eq,axiom,(
+    ! [X_5: hoare_1167836817_state] :
+      ( ( bot_bo70021908tate_o @ X_5 )
+    <=> ( member2058392318_state @ X_5 @ bot_bo70021908tate_o ) ) )).
+
+thf(fact_389_rev__predicate1D,axiom,(
+    ! [Q_8: pname > $o,P_16: pname > $o,X_69: pname] :
+      ( ( P_16 @ X_69 )
+     => ( ( ord_less_eq_pname_o @ P_16 @ Q_8 )
+       => ( Q_8 @ X_69 ) ) ) )).
+
+thf(fact_390_rev__predicate1D,axiom,(
+    ! [Q_8: hoare_1167836817_state > $o,P_16: hoare_1167836817_state > $o,X_69: hoare_1167836817_state] :
+      ( ( P_16 @ X_69 )
+     => ( ( ord_le827224136tate_o @ P_16 @ Q_8 )
+       => ( Q_8 @ X_69 ) ) ) )).
+
+thf(fact_391_predicate1D,axiom,(
+    ! [X_68: pname,P_15: pname > $o,Q_7: pname > $o] :
+      ( ( ord_less_eq_pname_o @ P_15 @ Q_7 )
+     => ( ( P_15 @ X_68 )
+       => ( Q_7 @ X_68 ) ) ) )).
+
+thf(fact_392_predicate1D,axiom,(
+    ! [X_68: hoare_1167836817_state,P_15: hoare_1167836817_state > $o,Q_7: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ P_15 @ Q_7 )
+     => ( ( P_15 @ X_68 )
+       => ( Q_7 @ X_68 ) ) ) )).
+
+thf(fact_393_sup1I2,axiom,(
+    ! [A_77: hoare_1167836817_state > $o,B_57: hoare_1167836817_state > $o,X_67: hoare_1167836817_state] :
+      ( ( B_57 @ X_67 )
+     => ( semila1172322802tate_o @ A_77 @ B_57 @ X_67 ) ) )).
+
+thf(fact_394_sup1I1,axiom,(
+    ! [B_56: hoare_1167836817_state > $o,A_76: hoare_1167836817_state > $o,X_66: hoare_1167836817_state] :
+      ( ( A_76 @ X_66 )
+     => ( semila1172322802tate_o @ A_76 @ B_56 @ X_66 ) ) )).
+
+thf(fact_395_pred__subset__eq,axiom,(
+    ! [R_3: pname > $o,S_6: pname > $o] :
+      ( ( ord_less_eq_pname_o
+        @ ^ [X_5: pname] :
+            ( member_pname @ X_5 @ R_3 )
+        @ ^ [X_5: pname] :
+            ( member_pname @ X_5 @ S_6 ) )
+    <=> ( ord_less_eq_pname_o @ R_3 @ S_6 ) ) )).
+
+thf(fact_396_pred__subset__eq,axiom,(
+    ! [R_3: hoare_1167836817_state > $o,S_6: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o
+        @ ^ [X_5: hoare_1167836817_state] :
+            ( member2058392318_state @ X_5 @ R_3 )
+        @ ^ [X_5: hoare_1167836817_state] :
+            ( member2058392318_state @ X_5 @ S_6 ) )
+    <=> ( ord_le827224136tate_o @ R_3 @ S_6 ) ) )).
+
+thf(fact_397_sup__Un__eq,axiom,(
+    ! [R_2: pname > $o,S_5: pname > $o,X_5: pname] :
+      ( ( semila1780557381name_o
+        @ ^ [Y_2: pname] :
+            ( member_pname @ Y_2 @ R_2 )
+        @ ^ [Y_2: pname] :
+            ( member_pname @ Y_2 @ S_5 )
+        @ X_5 )
+    <=> ( member_pname @ X_5 @ ( semila1780557381name_o @ R_2 @ S_5 ) ) ) )).
+
+thf(fact_398_sup__Un__eq,axiom,(
+    ! [R_2: hoare_1167836817_state > $o,S_5: hoare_1167836817_state > $o,X_5: hoare_1167836817_state] :
+      ( ( semila1172322802tate_o
+        @ ^ [Y_2: hoare_1167836817_state] :
+            ( member2058392318_state @ Y_2 @ R_2 )
+        @ ^ [Y_2: hoare_1167836817_state] :
+            ( member2058392318_state @ Y_2 @ S_5 )
+        @ X_5 )
+    <=> ( member2058392318_state @ X_5 @ ( semila1172322802tate_o @ R_2 @ S_5 ) ) ) )).
+
+thf(fact_399_conseq12,axiom,(
+    ! [Q_6: state > state > $o,P_14: state > state > $o,G_11: hoare_1167836817_state > $o,P_13: state > state > $o,C_27: com,Q_5: state > state > $o] :
+      ( ( hoare_123228589_state @ G_11 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_13 @ C_27 @ Q_5 ) @ bot_bo70021908tate_o ) )
+     => ( ! [Z_11: state,S_3: state] :
+            ( ( P_14 @ Z_11 @ S_3 )
+           => ! [S_4: state] :
+                ( ! [Z_18: state] :
+                    ( ( P_13 @ Z_18 @ S_3 )
+                   => ( Q_5 @ Z_18 @ S_4 ) )
+               => ( Q_6 @ Z_11 @ S_4 ) ) )
+       => ( hoare_123228589_state @ G_11 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_14 @ C_27 @ Q_6 ) @ bot_bo70021908tate_o ) ) ) ) )).
+
+thf(fact_400_le__funI,axiom,(
+    ! [F_35: pname > $o,G_10: pname > $o] :
+      ( ! [X_5: pname] :
+          ( ord_less_eq_o @ ( F_35 @ X_5 ) @ ( G_10 @ X_5 ) )
+     => ( ord_less_eq_pname_o @ F_35 @ G_10 ) ) )).
+
+thf(fact_401_le__funI,axiom,(
+    ! [F_35: hoare_1167836817_state > $o,G_10: hoare_1167836817_state > $o] :
+      ( ! [X_5: hoare_1167836817_state] :
+          ( ord_less_eq_o @ ( F_35 @ X_5 ) @ ( G_10 @ X_5 ) )
+     => ( ord_le827224136tate_o @ F_35 @ G_10 ) ) )).
+
+thf(fact_402_Option_Oset_Osimps_I2_J,axiom,(
+    ! [X_65: pname] :
+      ( ( set_pname @ ( some_pname @ X_65 ) )
+      = ( insert_pname @ X_65 @ bot_bot_pname_o ) ) )).
+
+thf(fact_403_Option_Oset_Osimps_I2_J,axiom,(
+    ! [X_65: hoare_1167836817_state] :
+      ( ( set_Ho2131684873_state @ ( some_H1433514562_state @ X_65 ) )
+      = ( insert2134838167_state @ X_65 @ bot_bo70021908tate_o ) ) )).
+
+thf(fact_404_Option_Oset_Osimps_I2_J,axiom,(
+    ! [X_65: com] :
+      ( ( set_com @ ( some_com @ X_65 ) )
+      = ( insert_com @ X_65 @ bot_bot_com_o ) ) )).
+
+thf(fact_405_elem__set,axiom,(
+    ! [X_64: pname,Xo: option_pname] :
+      ( ( member_pname @ X_64 @ ( set_pname @ Xo ) )
+    <=> ( Xo
+        = ( some_pname @ X_64 ) ) ) )).
+
+thf(fact_406_elem__set,axiom,(
+    ! [X_64: hoare_1167836817_state,Xo: option1574264306_state] :
+      ( ( member2058392318_state @ X_64 @ ( set_Ho2131684873_state @ Xo ) )
+    <=> ( Xo
+        = ( some_H1433514562_state @ X_64 ) ) ) )).
+
+thf(fact_407_elem__set,axiom,(
+    ! [X_64: com,Xo: option_com] :
+      ( ( member_com @ X_64 @ ( set_com @ Xo ) )
+    <=> ( Xo
+        = ( some_com @ X_64 ) ) ) )).
+
+thf(fact_408_ospec,axiom,(
+    ! [X_63: com,P_12: com > $o,A_75: option_com] :
+      ( ! [X_5: com] :
+          ( ( member_com @ X_5 @ ( set_com @ A_75 ) )
+         => ( P_12 @ X_5 ) )
+     => ( ( A_75
+          = ( some_com @ X_63 ) )
+       => ( P_12 @ X_63 ) ) ) )).
+
+thf(fact_409_sup__fun__def,axiom,(
+    ! [F_34: hoare_1167836817_state > $o,G_9: hoare_1167836817_state > $o,X_5: hoare_1167836817_state] :
+      ( ( semila1172322802tate_o @ F_34 @ G_9 @ X_5 )
+    <=> ( semila10642723_sup_o @ ( F_34 @ X_5 ) @ ( G_9 @ X_5 ) ) ) )).
+
+thf(fact_410_sup__apply,axiom,(
+    ! [F_33: hoare_1167836817_state > $o,G_8: hoare_1167836817_state > $o,X_62: hoare_1167836817_state] :
+      ( ( semila1172322802tate_o @ F_33 @ G_8 @ X_62 )
+    <=> ( semila10642723_sup_o @ ( F_33 @ X_62 ) @ ( G_8 @ X_62 ) ) ) )).
+
+thf(fact_411_single__stateE,axiom,
+    ( hoare_1201148605gleton
+   => ! [T_1: state] :
+        ~ ! [S_3: state] : ( S_3 = T_1 ) )).
+
+thf(fact_412_state__not__singleton__def,axiom,
+    ( hoare_1201148605gleton
+  <=> ? [S_3: state,T_1: state] : ( S_3 != T_1 ) )).
+
+thf(fact_413_sup__assoc,axiom,(
+    ! [X_61: hoare_1167836817_state > $o,Y_39: hoare_1167836817_state > $o,Z_17: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ X_61 @ Y_39 ) @ Z_17 )
+      = ( semila1172322802tate_o @ X_61 @ ( semila1172322802tate_o @ Y_39 @ Z_17 ) ) ) )).
+
+thf(fact_414_inf__sup__aci_I6_J,axiom,(
+    ! [X_60: hoare_1167836817_state > $o,Y_38: hoare_1167836817_state > $o,Z_16: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ X_60 @ Y_38 ) @ Z_16 )
+      = ( semila1172322802tate_o @ X_60 @ ( semila1172322802tate_o @ Y_38 @ Z_16 ) ) ) )).
+
+thf(fact_415_sup_Oassoc,axiom,(
+    ! [A_74: hoare_1167836817_state > $o,B_55: hoare_1167836817_state > $o,C_26: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ A_74 @ B_55 ) @ C_26 )
+      = ( semila1172322802tate_o @ A_74 @ ( semila1172322802tate_o @ B_55 @ C_26 ) ) ) )).
+
+thf(fact_416_sup__left__commute,axiom,(
+    ! [X_59: hoare_1167836817_state > $o,Y_37: hoare_1167836817_state > $o,Z_15: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ X_59 @ ( semila1172322802tate_o @ Y_37 @ Z_15 ) )
+      = ( semila1172322802tate_o @ Y_37 @ ( semila1172322802tate_o @ X_59 @ Z_15 ) ) ) )).
+
+thf(fact_417_inf__sup__aci_I7_J,axiom,(
+    ! [X_58: hoare_1167836817_state > $o,Y_36: hoare_1167836817_state > $o,Z_14: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ X_58 @ ( semila1172322802tate_o @ Y_36 @ Z_14 ) )
+      = ( semila1172322802tate_o @ Y_36 @ ( semila1172322802tate_o @ X_58 @ Z_14 ) ) ) )).
+
+thf(fact_418_sup_Oleft__commute,axiom,(
+    ! [B_54: hoare_1167836817_state > $o,A_73: hoare_1167836817_state > $o,C_25: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ B_54 @ ( semila1172322802tate_o @ A_73 @ C_25 ) )
+      = ( semila1172322802tate_o @ A_73 @ ( semila1172322802tate_o @ B_54 @ C_25 ) ) ) )).
+
+thf(fact_419_sup__left__idem,axiom,(
+    ! [X_57: hoare_1167836817_state > $o,Y_35: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ X_57 @ ( semila1172322802tate_o @ X_57 @ Y_35 ) )
+      = ( semila1172322802tate_o @ X_57 @ Y_35 ) ) )).
+
+thf(fact_420_inf__sup__aci_I8_J,axiom,(
+    ! [X_56: hoare_1167836817_state > $o,Y_34: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ X_56 @ ( semila1172322802tate_o @ X_56 @ Y_34 ) )
+      = ( semila1172322802tate_o @ X_56 @ Y_34 ) ) )).
+
+thf(fact_421_sup_Oleft__idem,axiom,(
+    ! [A_72: hoare_1167836817_state > $o,B_53: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ A_72 @ ( semila1172322802tate_o @ A_72 @ B_53 ) )
+      = ( semila1172322802tate_o @ A_72 @ B_53 ) ) )).
+
+thf(fact_422_sup__commute,axiom,(
+    ! [X_55: hoare_1167836817_state > $o,Y_33: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ X_55 @ Y_33 )
+      = ( semila1172322802tate_o @ Y_33 @ X_55 ) ) )).
+
+thf(fact_423_inf__sup__aci_I5_J,axiom,(
+    ! [X_54: hoare_1167836817_state > $o,Y_32: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ X_54 @ Y_32 )
+      = ( semila1172322802tate_o @ Y_32 @ X_54 ) ) )).
+
+thf(fact_424_sup_Ocommute,axiom,(
+    ! [A_71: hoare_1167836817_state > $o,B_52: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ A_71 @ B_52 )
+      = ( semila1172322802tate_o @ B_52 @ A_71 ) ) )).
+
+thf(fact_425_sup__idem,axiom,(
+    ! [X_53: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ X_53 @ X_53 )
+      = X_53 ) )).
+
+thf(fact_426_sup_Oidem,axiom,(
+    ! [A_70: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ A_70 @ A_70 )
+      = A_70 ) )).
+
+thf(fact_427_le__supE,axiom,(
+    ! [A_69: pname > $o,B_51: pname > $o,X_52: pname > $o] :
+      ( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_69 @ B_51 ) @ X_52 )
+     => ~ ( ( ord_less_eq_pname_o @ A_69 @ X_52 )
+         => ~ ( ord_less_eq_pname_o @ B_51 @ X_52 ) ) ) )).
+
+thf(fact_428_le__supE,axiom,(
+    ! [A_69: hoare_1167836817_state > $o,B_51: hoare_1167836817_state > $o,X_52: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A_69 @ B_51 ) @ X_52 )
+     => ~ ( ( ord_le827224136tate_o @ A_69 @ X_52 )
+         => ~ ( ord_le827224136tate_o @ B_51 @ X_52 ) ) ) )).
+
+thf(fact_429_sup__mono,axiom,(
+    ! [B_50: pname > $o,D_3: pname > $o,A_68: pname > $o,C_24: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_68 @ C_24 )
+     => ( ( ord_less_eq_pname_o @ B_50 @ D_3 )
+       => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_68 @ B_50 ) @ ( semila1780557381name_o @ C_24 @ D_3 ) ) ) ) )).
+
+thf(fact_430_sup__mono,axiom,(
+    ! [B_50: hoare_1167836817_state > $o,D_3: hoare_1167836817_state > $o,A_68: hoare_1167836817_state > $o,C_24: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_68 @ C_24 )
+     => ( ( ord_le827224136tate_o @ B_50 @ D_3 )
+       => ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A_68 @ B_50 ) @ ( semila1172322802tate_o @ C_24 @ D_3 ) ) ) ) )).
+
+thf(fact_431_sup__least,axiom,(
+    ! [Z_13: pname > $o,Y_31: pname > $o,X_51: pname > $o] :
+      ( ( ord_less_eq_pname_o @ Y_31 @ X_51 )
+     => ( ( ord_less_eq_pname_o @ Z_13 @ X_51 )
+       => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ Y_31 @ Z_13 ) @ X_51 ) ) ) )).
+
+thf(fact_432_sup__least,axiom,(
+    ! [Z_13: hoare_1167836817_state > $o,Y_31: hoare_1167836817_state > $o,X_51: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ Y_31 @ X_51 )
+     => ( ( ord_le827224136tate_o @ Z_13 @ X_51 )
+       => ( ord_le827224136tate_o @ ( semila1172322802tate_o @ Y_31 @ Z_13 ) @ X_51 ) ) ) )).
+
+thf(fact_433_le__supI,axiom,(
+    ! [B_49: pname > $o,A_67: pname > $o,X_50: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_67 @ X_50 )
+     => ( ( ord_less_eq_pname_o @ B_49 @ X_50 )
+       => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_67 @ B_49 ) @ X_50 ) ) ) )).
+
+thf(fact_434_le__supI,axiom,(
+    ! [B_49: hoare_1167836817_state > $o,A_67: hoare_1167836817_state > $o,X_50: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_67 @ X_50 )
+     => ( ( ord_le827224136tate_o @ B_49 @ X_50 )
+       => ( ord_le827224136tate_o @ ( semila1172322802tate_o @ A_67 @ B_49 ) @ X_50 ) ) ) )).
+
+thf(fact_435_sup__absorb1,axiom,(
+    ! [Y_30: pname > $o,X_49: pname > $o] :
+      ( ( ord_less_eq_pname_o @ Y_30 @ X_49 )
+     => ( ( semila1780557381name_o @ X_49 @ Y_30 )
+        = X_49 ) ) )).
+
+thf(fact_436_sup__absorb1,axiom,(
+    ! [Y_30: hoare_1167836817_state > $o,X_49: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ Y_30 @ X_49 )
+     => ( ( semila1172322802tate_o @ X_49 @ Y_30 )
+        = X_49 ) ) )).
+
+thf(fact_437_sup__absorb2,axiom,(
+    ! [X_48: pname > $o,Y_29: pname > $o] :
+      ( ( ord_less_eq_pname_o @ X_48 @ Y_29 )
+     => ( ( semila1780557381name_o @ X_48 @ Y_29 )
+        = Y_29 ) ) )).
+
+thf(fact_438_sup__absorb2,axiom,(
+    ! [X_48: hoare_1167836817_state > $o,Y_29: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ X_48 @ Y_29 )
+     => ( ( semila1172322802tate_o @ X_48 @ Y_29 )
+        = Y_29 ) ) )).
+
+thf(fact_439_le__supI2,axiom,(
+    ! [A_66: pname > $o,X_47: pname > $o,B_48: pname > $o] :
+      ( ( ord_less_eq_pname_o @ X_47 @ B_48 )
+     => ( ord_less_eq_pname_o @ X_47 @ ( semila1780557381name_o @ A_66 @ B_48 ) ) ) )).
+
+thf(fact_440_le__supI2,axiom,(
+    ! [A_66: hoare_1167836817_state > $o,X_47: hoare_1167836817_state > $o,B_48: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ X_47 @ B_48 )
+     => ( ord_le827224136tate_o @ X_47 @ ( semila1172322802tate_o @ A_66 @ B_48 ) ) ) )).
+
+thf(fact_441_le__supI1,axiom,(
+    ! [B_47: pname > $o,X_46: pname > $o,A_65: pname > $o] :
+      ( ( ord_less_eq_pname_o @ X_46 @ A_65 )
+     => ( ord_less_eq_pname_o @ X_46 @ ( semila1780557381name_o @ A_65 @ B_47 ) ) ) )).
+
+thf(fact_442_le__supI1,axiom,(
+    ! [B_47: hoare_1167836817_state > $o,X_46: hoare_1167836817_state > $o,A_65: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ X_46 @ A_65 )
+     => ( ord_le827224136tate_o @ X_46 @ ( semila1172322802tate_o @ A_65 @ B_47 ) ) ) )).
+
+thf(fact_443_le__sup__iff,axiom,(
+    ! [X_45: pname > $o,Y_28: pname > $o,Z_12: pname > $o] :
+      ( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ X_45 @ Y_28 ) @ Z_12 )
+    <=> ( ( ord_less_eq_pname_o @ X_45 @ Z_12 )
+        & ( ord_less_eq_pname_o @ Y_28 @ Z_12 ) ) ) )).
+
+thf(fact_444_le__sup__iff,axiom,(
+    ! [X_45: hoare_1167836817_state > $o,Y_28: hoare_1167836817_state > $o,Z_12: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ ( semila1172322802tate_o @ X_45 @ Y_28 ) @ Z_12 )
+    <=> ( ( ord_le827224136tate_o @ X_45 @ Z_12 )
+        & ( ord_le827224136tate_o @ Y_28 @ Z_12 ) ) ) )).
+
+thf(fact_445_le__iff__sup,axiom,(
+    ! [X_44: pname > $o,Y_27: pname > $o] :
+      ( ( ord_less_eq_pname_o @ X_44 @ Y_27 )
+    <=> ( ( semila1780557381name_o @ X_44 @ Y_27 )
+        = Y_27 ) ) )).
+
+thf(fact_446_le__iff__sup,axiom,(
+    ! [X_44: hoare_1167836817_state > $o,Y_27: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ X_44 @ Y_27 )
+    <=> ( ( semila1172322802tate_o @ X_44 @ Y_27 )
+        = Y_27 ) ) )).
+
+thf(fact_447_sup__ge2,axiom,(
+    ! [Y_26: pname > $o,X_43: pname > $o] :
+      ( ord_less_eq_pname_o @ Y_26 @ ( semila1780557381name_o @ X_43 @ Y_26 ) ) )).
+
+thf(fact_448_sup__ge2,axiom,(
+    ! [Y_26: hoare_1167836817_state > $o,X_43: hoare_1167836817_state > $o] :
+      ( ord_le827224136tate_o @ Y_26 @ ( semila1172322802tate_o @ X_43 @ Y_26 ) ) )).
+
+thf(fact_449_inf__sup__ord_I4_J,axiom,(
+    ! [Y_25: pname > $o,X_42: pname > $o] :
+      ( ord_less_eq_pname_o @ Y_25 @ ( semila1780557381name_o @ X_42 @ Y_25 ) ) )).
+
+thf(fact_450_inf__sup__ord_I4_J,axiom,(
+    ! [Y_25: hoare_1167836817_state > $o,X_42: hoare_1167836817_state > $o] :
+      ( ord_le827224136tate_o @ Y_25 @ ( semila1172322802tate_o @ X_42 @ Y_25 ) ) )).
+
+thf(fact_451_sup__ge1,axiom,(
+    ! [X_41: pname > $o,Y_24: pname > $o] :
+      ( ord_less_eq_pname_o @ X_41 @ ( semila1780557381name_o @ X_41 @ Y_24 ) ) )).
+
+thf(fact_452_sup__ge1,axiom,(
+    ! [X_41: hoare_1167836817_state > $o,Y_24: hoare_1167836817_state > $o] :
+      ( ord_le827224136tate_o @ X_41 @ ( semila1172322802tate_o @ X_41 @ Y_24 ) ) )).
+
+thf(fact_453_inf__sup__ord_I3_J,axiom,(
+    ! [X_40: pname > $o,Y_23: pname > $o] :
+      ( ord_less_eq_pname_o @ X_40 @ ( semila1780557381name_o @ X_40 @ Y_23 ) ) )).
+
+thf(fact_454_inf__sup__ord_I3_J,axiom,(
+    ! [X_40: hoare_1167836817_state > $o,Y_23: hoare_1167836817_state > $o] :
+      ( ord_le827224136tate_o @ X_40 @ ( semila1172322802tate_o @ X_40 @ Y_23 ) ) )).
+
+thf(fact_455_sup__eq__bot__iff,axiom,(
+    ! [X_39: pname > $o,Y_22: pname > $o] :
+      ( ( ( semila1780557381name_o @ X_39 @ Y_22 )
+        = bot_bot_pname_o )
+    <=> ( ( X_39 = bot_bot_pname_o )
+        & ( Y_22 = bot_bot_pname_o ) ) ) )).
+
+thf(fact_456_sup__eq__bot__iff,axiom,(
+    ! [X_39: hoare_1167836817_state > $o,Y_22: hoare_1167836817_state > $o] :
+      ( ( ( semila1172322802tate_o @ X_39 @ Y_22 )
+        = bot_bo70021908tate_o )
+    <=> ( ( X_39 = bot_bo70021908tate_o )
+        & ( Y_22 = bot_bo70021908tate_o ) ) ) )).
+
+thf(fact_457_sup__bot__right,axiom,(
+    ! [X_38: pname > $o] :
+      ( ( semila1780557381name_o @ X_38 @ bot_bot_pname_o )
+      = X_38 ) )).
+
+thf(fact_458_sup__bot__right,axiom,(
+    ! [X_38: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ X_38 @ bot_bo70021908tate_o )
+      = X_38 ) )).
+
+thf(fact_459_sup__bot__left,axiom,(
+    ! [X_37: pname > $o] :
+      ( ( semila1780557381name_o @ bot_bot_pname_o @ X_37 )
+      = X_37 ) )).
+
+thf(fact_460_sup__bot__left,axiom,(
+    ! [X_37: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ bot_bo70021908tate_o @ X_37 )
+      = X_37 ) )).
+
+thf(fact_461_folding__one__idem_Ounion__idem,axiom,(
+    ! [B_46: ( pname > $o ) > $o,A_64: ( pname > $o ) > $o,F_32: ( pname > $o ) > ( pname > $o ) > pname > $o,F_31: ( ( pname > $o ) > $o ) > pname > $o] :
+      ( ( finite697516351name_o @ F_32 @ F_31 )
+     => ( ( finite297249702name_o @ A_64 )
+       => ( ( A_64 != bot_bot_pname_o_o )
+         => ( ( finite297249702name_o @ B_46 )
+           => ( ( B_46 != bot_bot_pname_o_o )
+             => ( ( F_31 @ ( semila181081674me_o_o @ A_64 @ B_46 ) )
+                = ( F_32 @ ( F_31 @ A_64 ) @ ( F_31 @ B_46 ) ) ) ) ) ) ) ) )).
+
+thf(fact_462_folding__one__idem_Ounion__idem,axiom,(
+    ! [B_46: ( hoare_1167836817_state > $o ) > $o,A_64: ( hoare_1167836817_state > $o ) > $o,F_32: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_31: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
+      ( ( finite671847800tate_o @ F_32 @ F_31 )
+     => ( ( finite1380128977tate_o @ A_64 )
+       => ( ( A_64 != bot_bo691907561te_o_o )
+         => ( ( finite1380128977tate_o @ B_46 )
+           => ( ( B_46 != bot_bo691907561te_o_o )
+             => ( ( F_31 @ ( semila866907787te_o_o @ A_64 @ B_46 ) )
+                = ( F_32 @ ( F_31 @ A_64 ) @ ( F_31 @ B_46 ) ) ) ) ) ) ) ) )).
+
+thf(fact_463_folding__one__idem_Ounion__idem,axiom,(
+    ! [B_46: pname > $o,A_64: pname > $o,F_32: pname > pname > pname,F_31: ( pname > $o ) > pname] :
+      ( ( finite89670078_pname @ F_32 @ F_31 )
+     => ( ( finite_finite_pname @ A_64 )
+       => ( ( A_64 != bot_bot_pname_o )
+         => ( ( finite_finite_pname @ B_46 )
+           => ( ( B_46 != bot_bot_pname_o )
+             => ( ( F_31 @ ( semila1780557381name_o @ A_64 @ B_46 ) )
+                = ( F_32 @ ( F_31 @ A_64 ) @ ( F_31 @ B_46 ) ) ) ) ) ) ) ) )).
+
+thf(fact_464_folding__one__idem_Ounion__idem,axiom,(
+    ! [B_46: hoare_1167836817_state > $o,A_64: hoare_1167836817_state > $o,F_32: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_31: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
+      ( ( finite806517911_state @ F_32 @ F_31 )
+     => ( ( finite1084549118_state @ A_64 )
+       => ( ( A_64 != bot_bo70021908tate_o )
+         => ( ( finite1084549118_state @ B_46 )
+           => ( ( B_46 != bot_bo70021908tate_o )
+             => ( ( F_31 @ ( semila1172322802tate_o @ A_64 @ B_46 ) )
+                = ( F_32 @ ( F_31 @ A_64 ) @ ( F_31 @ B_46 ) ) ) ) ) ) ) ) )).
+
+thf(fact_465_folding__one__idem_Osubset__idem,axiom,(
+    ! [B_45: ( pname > $o ) > $o,A_63: ( pname > $o ) > $o,F_30: ( pname > $o ) > ( pname > $o ) > pname > $o,F_29: ( ( pname > $o ) > $o ) > pname > $o] :
+      ( ( finite697516351name_o @ F_30 @ F_29 )
+     => ( ( finite297249702name_o @ A_63 )
+       => ( ( B_45 != bot_bot_pname_o_o )
+         => ( ( ord_le1205211808me_o_o @ B_45 @ A_63 )
+           => ( ( F_30 @ ( F_29 @ B_45 ) @ ( F_29 @ A_63 ) )
+              = ( F_29 @ A_63 ) ) ) ) ) ) )).
+
+thf(fact_466_folding__one__idem_Osubset__idem,axiom,(
+    ! [B_45: ( hoare_1167836817_state > $o ) > $o,A_63: ( hoare_1167836817_state > $o ) > $o,F_30: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_29: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
+      ( ( finite671847800tate_o @ F_30 @ F_29 )
+     => ( ( finite1380128977tate_o @ A_63 )
+       => ( ( B_45 != bot_bo691907561te_o_o )
+         => ( ( ord_le741939125te_o_o @ B_45 @ A_63 )
+           => ( ( F_30 @ ( F_29 @ B_45 ) @ ( F_29 @ A_63 ) )
+              = ( F_29 @ A_63 ) ) ) ) ) ) )).
+
+thf(fact_467_folding__one__idem_Osubset__idem,axiom,(
+    ! [B_45: pname > $o,A_63: pname > $o,F_30: pname > pname > pname,F_29: ( pname > $o ) > pname] :
+      ( ( finite89670078_pname @ F_30 @ F_29 )
+     => ( ( finite_finite_pname @ A_63 )
+       => ( ( B_45 != bot_bot_pname_o )
+         => ( ( ord_less_eq_pname_o @ B_45 @ A_63 )
+           => ( ( F_30 @ ( F_29 @ B_45 ) @ ( F_29 @ A_63 ) )
+              = ( F_29 @ A_63 ) ) ) ) ) ) )).
+
+thf(fact_468_folding__one__idem_Osubset__idem,axiom,(
+    ! [B_45: hoare_1167836817_state > $o,A_63: hoare_1167836817_state > $o,F_30: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_29: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
+      ( ( finite806517911_state @ F_30 @ F_29 )
+     => ( ( finite1084549118_state @ A_63 )
+       => ( ( B_45 != bot_bo70021908tate_o )
+         => ( ( ord_le827224136tate_o @ B_45 @ A_63 )
+           => ( ( F_30 @ ( F_29 @ B_45 ) @ ( F_29 @ A_63 ) )
+              = ( F_29 @ A_63 ) ) ) ) ) ) )).
+
+thf(fact_469_hoare__derivs_OSkip,axiom,(
+    ! [G_7: hoare_1167836817_state > $o,P_11: state > state > $o] :
+      ( hoare_123228589_state @ G_7 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_11 @ skip @ P_11 ) @ bot_bo70021908tate_o ) ) )).
+
+thf(fact_470_folding__one__idem_Oinsert__idem,axiom,(
+    ! [X_36: pname,A_62: pname > $o,F_28: pname > pname > pname,F_27: ( pname > $o ) > pname] :
+      ( ( finite89670078_pname @ F_28 @ F_27 )
+     => ( ( finite_finite_pname @ A_62 )
+       => ( ( A_62 != bot_bot_pname_o )
+         => ( ( F_27 @ ( insert_pname @ X_36 @ A_62 ) )
+            = ( F_28 @ X_36 @ ( F_27 @ A_62 ) ) ) ) ) ) )).
+
+thf(fact_471_folding__one__idem_Oinsert__idem,axiom,(
+    ! [X_36: hoare_1167836817_state,A_62: hoare_1167836817_state > $o,F_28: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_27: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
+      ( ( finite806517911_state @ F_28 @ F_27 )
+     => ( ( finite1084549118_state @ A_62 )
+       => ( ( A_62 != bot_bo70021908tate_o )
+         => ( ( F_27 @ ( insert2134838167_state @ X_36 @ A_62 ) )
+            = ( F_28 @ X_36 @ ( F_27 @ A_62 ) ) ) ) ) ) )).
+
+thf(fact_472_folding__one__idem_Oinsert__idem,axiom,(
+    ! [X_36: pname > $o,A_62: ( pname > $o ) > $o,F_28: ( pname > $o ) > ( pname > $o ) > pname > $o,F_27: ( ( pname > $o ) > $o ) > pname > $o] :
+      ( ( finite697516351name_o @ F_28 @ F_27 )
+     => ( ( finite297249702name_o @ A_62 )
+       => ( ( A_62 != bot_bot_pname_o_o )
+         => ( ( F_27 @ ( insert_pname_o @ X_36 @ A_62 ) )
+            = ( F_28 @ X_36 @ ( F_27 @ A_62 ) ) ) ) ) ) )).
+
+thf(fact_473_folding__one__idem_Oinsert__idem,axiom,(
+    ! [X_36: hoare_1167836817_state > $o,A_62: ( hoare_1167836817_state > $o ) > $o,F_28: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_27: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
+      ( ( finite671847800tate_o @ F_28 @ F_27 )
+     => ( ( finite1380128977tate_o @ A_62 )
+       => ( ( A_62 != bot_bo691907561te_o_o )
+         => ( ( F_27 @ ( insert999278200tate_o @ X_36 @ A_62 ) )
+            = ( F_28 @ X_36 @ ( F_27 @ A_62 ) ) ) ) ) ) )).
+
+thf(fact_474_finite__ne__induct,axiom,(
+    ! [P_10: ( pname > $o ) > $o,F_25: pname > $o] :
+      ( ( finite_finite_pname @ F_25 )
+     => ( ( F_25 != bot_bot_pname_o )
+       => ( ! [X_5: pname] :
+              ( P_10 @ ( insert_pname @ X_5 @ bot_bot_pname_o ) )
+         => ( ! [X_5: pname,F_26: pname > $o] :
+                ( ( finite_finite_pname @ F_26 )
+               => ( ( F_26 != bot_bot_pname_o )
+                 => ( ~ ( member_pname @ X_5 @ F_26 )
+                   => ( ( P_10 @ F_26 )
+                     => ( P_10 @ ( insert_pname @ X_5 @ F_26 ) ) ) ) ) )
+           => ( P_10 @ F_25 ) ) ) ) ) )).
+
+thf(fact_475_finite__ne__induct,axiom,(
+    ! [P_10: ( hoare_1167836817_state > $o ) > $o,F_25: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ F_25 )
+     => ( ( F_25 != bot_bo70021908tate_o )
+       => ( ! [X_5: hoare_1167836817_state] :
+              ( P_10 @ ( insert2134838167_state @ X_5 @ bot_bo70021908tate_o ) )
+         => ( ! [X_5: hoare_1167836817_state,F_26: hoare_1167836817_state > $o] :
+                ( ( finite1084549118_state @ F_26 )
+               => ( ( F_26 != bot_bo70021908tate_o )
+                 => ( ~ ( member2058392318_state @ X_5 @ F_26 )
+                   => ( ( P_10 @ F_26 )
+                     => ( P_10 @ ( insert2134838167_state @ X_5 @ F_26 ) ) ) ) ) )
+           => ( P_10 @ F_25 ) ) ) ) ) )).
+
+thf(fact_476_finite__ne__induct,axiom,(
+    ! [P_10: ( ( pname > $o ) > $o ) > $o,F_25: ( pname > $o ) > $o] :
+      ( ( finite297249702name_o @ F_25 )
+     => ( ( F_25 != bot_bot_pname_o_o )
+       => ( ! [X_5: pname > $o] :
+              ( P_10 @ ( insert_pname_o @ X_5 @ bot_bot_pname_o_o ) )
+         => ( ! [X_5: pname > $o,F_26: ( pname > $o ) > $o] :
+                ( ( finite297249702name_o @ F_26 )
+               => ( ( F_26 != bot_bot_pname_o_o )
+                 => ( ~ ( member_pname_o @ X_5 @ F_26 )
+                   => ( ( P_10 @ F_26 )
+                     => ( P_10 @ ( insert_pname_o @ X_5 @ F_26 ) ) ) ) ) )
+           => ( P_10 @ F_25 ) ) ) ) ) )).
+
+thf(fact_477_finite__ne__induct,axiom,(
+    ! [P_10: ( ( hoare_1167836817_state > $o ) > $o ) > $o,F_25: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( finite1380128977tate_o @ F_25 )
+     => ( ( F_25 != bot_bo691907561te_o_o )
+       => ( ! [X_5: hoare_1167836817_state > $o] :
+              ( P_10 @ ( insert999278200tate_o @ X_5 @ bot_bo691907561te_o_o ) )
+         => ( ! [X_5: hoare_1167836817_state > $o,F_26: ( hoare_1167836817_state > $o ) > $o] :
+                ( ( finite1380128977tate_o @ F_26 )
+               => ( ( F_26 != bot_bo691907561te_o_o )
+                 => ( ~ ( member864234961tate_o @ X_5 @ F_26 )
+                   => ( ( P_10 @ F_26 )
+                     => ( P_10 @ ( insert999278200tate_o @ X_5 @ F_26 ) ) ) ) ) )
+           => ( P_10 @ F_25 ) ) ) ) ) )).
+
+thf(fact_478_com_Osimps_I19_J,axiom,(
+    ! [Pname: pname] :
+      ( ( body_1 @ Pname )
+     != skip ) )).
+
+thf(fact_479_com_Osimps_I18_J,axiom,(
+    ! [Pname: pname] :
+      ( skip
+     != ( body_1 @ Pname ) ) )).
+
+thf(fact_480_WT_OSkip,axiom,
+    ( wt @ skip )).
+
+thf(fact_481_folding__one__idem_Oin__idem,axiom,(
+    ! [X_35: pname,A_61: pname > $o,F_24: pname > pname > pname,F_23: ( pname > $o ) > pname] :
+      ( ( finite89670078_pname @ F_24 @ F_23 )
+     => ( ( finite_finite_pname @ A_61 )
+       => ( ( member_pname @ X_35 @ A_61 )
+         => ( ( F_24 @ X_35 @ ( F_23 @ A_61 ) )
+            = ( F_23 @ A_61 ) ) ) ) ) )).
+
+thf(fact_482_folding__one__idem_Oin__idem,axiom,(
+    ! [X_35: hoare_1167836817_state,A_61: hoare_1167836817_state > $o,F_24: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_23: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
+      ( ( finite806517911_state @ F_24 @ F_23 )
+     => ( ( finite1084549118_state @ A_61 )
+       => ( ( member2058392318_state @ X_35 @ A_61 )
+         => ( ( F_24 @ X_35 @ ( F_23 @ A_61 ) )
+            = ( F_23 @ A_61 ) ) ) ) ) )).
+
+thf(fact_483_folding__one__idem_Oin__idem,axiom,(
+    ! [X_35: pname > $o,A_61: ( pname > $o ) > $o,F_24: ( pname > $o ) > ( pname > $o ) > pname > $o,F_23: ( ( pname > $o ) > $o ) > pname > $o] :
+      ( ( finite697516351name_o @ F_24 @ F_23 )
+     => ( ( finite297249702name_o @ A_61 )
+       => ( ( member_pname_o @ X_35 @ A_61 )
+         => ( ( F_24 @ X_35 @ ( F_23 @ A_61 ) )
+            = ( F_23 @ A_61 ) ) ) ) ) )).
+
+thf(fact_484_folding__one__idem_Oin__idem,axiom,(
+    ! [X_35: hoare_1167836817_state > $o,A_61: ( hoare_1167836817_state > $o ) > $o,F_24: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_23: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
+      ( ( finite671847800tate_o @ F_24 @ F_23 )
+     => ( ( finite1380128977tate_o @ A_61 )
+       => ( ( member864234961tate_o @ X_35 @ A_61 )
+         => ( ( F_24 @ X_35 @ ( F_23 @ A_61 ) )
+            = ( F_23 @ A_61 ) ) ) ) ) )).
+
+thf(fact_485_folding__one__idem_Ohom__commute,axiom,(
+    ! [N_1: ( pname > $o ) > $o,H: ( pname > $o ) > pname > $o,F_22: ( pname > $o ) > ( pname > $o ) > pname > $o,F_21: ( ( pname > $o ) > $o ) > pname > $o] :
+      ( ( finite697516351name_o @ F_22 @ F_21 )
+     => ( ! [X_5: pname > $o,Y_2: pname > $o] :
+            ( ( H @ ( F_22 @ X_5 @ Y_2 ) )
+            = ( F_22 @ ( H @ X_5 ) @ ( H @ Y_2 ) ) )
+       => ( ( finite297249702name_o @ N_1 )
+         => ( ( N_1 != bot_bot_pname_o_o )
+           => ( ( H @ ( F_21 @ N_1 ) )
+              = ( F_21 @ ( image_1085733413name_o @ H @ N_1 ) ) ) ) ) ) ) )).
+
+thf(fact_486_folding__one__idem_Ohom__commute,axiom,(
+    ! [N_1: ( hoare_1167836817_state > $o ) > $o,H: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_22: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_21: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
+      ( ( finite671847800tate_o @ F_22 @ F_21 )
+     => ( ! [X_5: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o] :
+            ( ( H @ ( F_22 @ X_5 @ Y_2 ) )
+            = ( F_22 @ ( H @ X_5 ) @ ( H @ Y_2 ) ) )
+       => ( ( finite1380128977tate_o @ N_1 )
+         => ( ( N_1 != bot_bo691907561te_o_o )
+           => ( ( H @ ( F_21 @ N_1 ) )
+              = ( F_21 @ ( image_1488525317tate_o @ H @ N_1 ) ) ) ) ) ) ) )).
+
+thf(fact_487_folding__one__idem_Ohom__commute,axiom,(
+    ! [N_1: pname > $o,H: pname > pname,F_22: pname > pname > pname,F_21: ( pname > $o ) > pname] :
+      ( ( finite89670078_pname @ F_22 @ F_21 )
+     => ( ! [X_5: pname,Y_2: pname] :
+            ( ( H @ ( F_22 @ X_5 @ Y_2 ) )
+            = ( F_22 @ ( H @ X_5 ) @ ( H @ Y_2 ) ) )
+       => ( ( finite_finite_pname @ N_1 )
+         => ( ( N_1 != bot_bot_pname_o )
+           => ( ( H @ ( F_21 @ N_1 ) )
+              = ( F_21 @ ( image_pname_pname @ H @ N_1 ) ) ) ) ) ) ) )).
+
+thf(fact_488_folding__one__idem_Ohom__commute,axiom,(
+    ! [N_1: hoare_1167836817_state > $o,H: hoare_1167836817_state > hoare_1167836817_state,F_22: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_21: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
+      ( ( finite806517911_state @ F_22 @ F_21 )
+     => ( ! [X_5: hoare_1167836817_state,Y_2: hoare_1167836817_state] :
+            ( ( H @ ( F_22 @ X_5 @ Y_2 ) )
+            = ( F_22 @ ( H @ X_5 ) @ ( H @ Y_2 ) ) )
+       => ( ( finite1084549118_state @ N_1 )
+         => ( ( N_1 != bot_bo70021908tate_o )
+           => ( ( H @ ( F_21 @ N_1 ) )
+              = ( F_21 @ ( image_31595733_state @ H @ N_1 ) ) ) ) ) ) ) )).
+
+thf(fact_489_LoopF,axiom,(
+    ! [G_6: hoare_1167836817_state > $o,P_9: state > state > $o,B_44: state > $o,C_23: com] :
+      ( hoare_123228589_state @ G_6
+      @ ( insert2134838167_state
+        @ ( hoare_908217195_state
+          @ ^ [Z_11: state,S_3: state] :
+              ( (&) @ ( P_9 @ Z_11 @ S_3 ) @ ( (~) @ ( B_44 @ S_3 ) ) )
+          @ ( while @ B_44 @ C_23 )
+          @ P_9 )
+        @ bot_bo70021908tate_o ) ) )).
+
+thf(fact_490_Comp,axiom,(
+    ! [D_2: com,R_1: state > state > $o,G_5: hoare_1167836817_state > $o,P_8: state > state > $o,C_22: com,Q_4: state > state > $o] :
+      ( ( hoare_123228589_state @ G_5 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_8 @ C_22 @ Q_4 ) @ bot_bo70021908tate_o ) )
+     => ( ( hoare_123228589_state @ G_5 @ ( insert2134838167_state @ ( hoare_908217195_state @ Q_4 @ D_2 @ R_1 ) @ bot_bo70021908tate_o ) )
+       => ( hoare_123228589_state @ G_5 @ ( insert2134838167_state @ ( hoare_908217195_state @ P_8 @ ( semi @ C_22 @ D_2 ) @ R_1 ) @ bot_bo70021908tate_o ) ) ) ) )).
+
+thf(fact_491_the__elem__def,axiom,(
+    ! [X_34: pname > $o] :
+      ( ( the_elem_pname @ X_34 )
+      = ( the_pname
+        @ ^ [X_5: pname] :
+            ( X_34
+            = ( insert_pname @ X_5 @ bot_bot_pname_o ) ) ) ) )).
+
+thf(fact_492_the__elem__def,axiom,(
+    ! [X_34: hoare_1167836817_state > $o] :
+      ( ( the_el323660082_state @ X_34 )
+      = ( the_Ho310147232_state
+        @ ^ [X_5: hoare_1167836817_state] :
+            ( X_34
+            = ( insert2134838167_state @ X_5 @ bot_bo70021908tate_o ) ) ) ) )).
+
+thf(fact_493_WTs__elim__cases_I6_J,axiom,(
+    ! [B_42: state > $o,C_21: com] :
+      ( ( wt @ ( while @ B_42 @ C_21 ) )
+     => ( wt @ C_21 ) ) )).
+
+thf(fact_494_WTs__elim__cases_I4_J,axiom,(
+    ! [C1: com,C2: com] :
+      ( ( wt @ ( semi @ C1 @ C2 ) )
+     => ~ ( ( wt @ C1 )
+         => ~ ( wt @ C2 ) ) ) )).
+
+thf(fact_495_com_Osimps_I46_J,axiom,(
+    ! [Com1_1: com,Com2_1: com,Fun: state > $o,Com_1: com] :
+      ( ( semi @ Com1_1 @ Com2_1 )
+     != ( while @ Fun @ Com_1 ) ) )).
+
+thf(fact_496_com_Osimps_I47_J,axiom,(
+    ! [Fun: state > $o,Com_1: com,Com1_1: com,Com2_1: com] :
+      ( ( while @ Fun @ Com_1 )
+     != ( semi @ Com1_1 @ Com2_1 ) ) )).
+
+thf(fact_497_com_Osimps_I3_J,axiom,(
+    ! [Com1_1: com,Com2_1: com,Com1: com,Com2: com] :
+      ( ( ( semi @ Com1_1 @ Com2_1 )
+        = ( semi @ Com1 @ Com2 ) )
+    <=> ( ( Com1_1 = Com1 )
+        & ( Com2_1 = Com2 ) ) ) )).
+
+thf(fact_498_com_Osimps_I5_J,axiom,(
+    ! [Fun_1: state > $o,Com_2: com,Fun: state > $o,Com_1: com] :
+      ( ( ( while @ Fun_1 @ Com_2 )
+        = ( while @ Fun @ Com_1 ) )
+    <=> ( ( Fun_1 = Fun )
+        & ( Com_2 = Com_1 ) ) ) )).
+
+thf(fact_499_com_Osimps_I59_J,axiom,(
+    ! [Pname: pname,Fun_1: state > $o,Com_2: com] :
+      ( ( body_1 @ Pname )
+     != ( while @ Fun_1 @ Com_2 ) ) )).
+
+thf(fact_500_com_Osimps_I58_J,axiom,(
+    ! [Fun_1: state > $o,Com_2: com,Pname: pname] :
+      ( ( while @ Fun_1 @ Com_2 )
+     != ( body_1 @ Pname ) ) )).
+
+thf(fact_501_While,axiom,(
+    ! [B_42: state > $o,C_21: com] :
+      ( ( wt @ C_21 )
+     => ( wt @ ( while @ B_42 @ C_21 ) ) ) )).
+
+thf(fact_502_com_Osimps_I16_J,axiom,(
+    ! [Fun: state > $o,Com_1: com] :
+      ( skip
+     != ( while @ Fun @ Com_1 ) ) )).
+
+thf(fact_503_com_Osimps_I17_J,axiom,(
+    ! [Fun: state > $o,Com_1: com] :
+      ( ( while @ Fun @ Com_1 )
+     != skip ) )).
+
+thf(fact_504_com_Osimps_I49_J,axiom,(
+    ! [Pname: pname,Com1_1: com,Com2_1: com] :
+      ( ( body_1 @ Pname )
+     != ( semi @ Com1_1 @ Com2_1 ) ) )).
+
+thf(fact_505_com_Osimps_I48_J,axiom,(
+    ! [Com1_1: com,Com2_1: com,Pname: pname] :
+      ( ( semi @ Com1_1 @ Com2_1 )
+     != ( body_1 @ Pname ) ) )).
+
+thf(fact_506_WT_OSemi,axiom,(
+    ! [C1: com,C0: com] :
+      ( ( wt @ C0 )
+     => ( ( wt @ C1 )
+       => ( wt @ ( semi @ C0 @ C1 ) ) ) ) )).
+
+thf(fact_507_com_Osimps_I12_J,axiom,(
+    ! [Com1: com,Com2: com] :
+      ( skip
+     != ( semi @ Com1 @ Com2 ) ) )).
+
+thf(fact_508_com_Osimps_I13_J,axiom,(
+    ! [Com1: com,Com2: com] :
+      ( ( semi @ Com1 @ Com2 )
+     != skip ) )).
+
+thf(fact_509_folding__one_Oinsert,axiom,(
+    ! [X_33: pname,A_60: pname > $o,F_20: pname > pname > pname,F_19: ( pname > $o ) > pname] :
+      ( ( finite1282449217_pname @ F_20 @ F_19 )
+     => ( ( finite_finite_pname @ A_60 )
+       => ( ~ ( member_pname @ X_33 @ A_60 )
+         => ( ( A_60 != bot_bot_pname_o )
+           => ( ( F_19 @ ( insert_pname @ X_33 @ A_60 ) )
+              = ( F_20 @ X_33 @ ( F_19 @ A_60 ) ) ) ) ) ) ) )).
+
+thf(fact_510_folding__one_Oinsert,axiom,(
+    ! [X_33: hoare_1167836817_state,A_60: hoare_1167836817_state > $o,F_20: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_19: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
+      ( ( finite1074406356_state @ F_20 @ F_19 )
+     => ( ( finite1084549118_state @ A_60 )
+       => ( ~ ( member2058392318_state @ X_33 @ A_60 )
+         => ( ( A_60 != bot_bo70021908tate_o )
+           => ( ( F_19 @ ( insert2134838167_state @ X_33 @ A_60 ) )
+              = ( F_20 @ X_33 @ ( F_19 @ A_60 ) ) ) ) ) ) ) )).
+
+thf(fact_511_folding__one_Oinsert,axiom,(
+    ! [X_33: pname > $o,A_60: ( pname > $o ) > $o,F_20: ( pname > $o ) > ( pname > $o ) > pname > $o,F_19: ( ( pname > $o ) > $o ) > pname > $o] :
+      ( ( finite349908348name_o @ F_20 @ F_19 )
+     => ( ( finite297249702name_o @ A_60 )
+       => ( ~ ( member_pname_o @ X_33 @ A_60 )
+         => ( ( A_60 != bot_bot_pname_o_o )
+           => ( ( F_19 @ ( insert_pname_o @ X_33 @ A_60 ) )
+              = ( F_20 @ X_33 @ ( F_19 @ A_60 ) ) ) ) ) ) ) )).
+
+thf(fact_512_folding__one_Oinsert,axiom,(
+    ! [X_33: hoare_1167836817_state > $o,A_60: ( hoare_1167836817_state > $o ) > $o,F_20: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_19: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
+      ( ( finite979047547tate_o @ F_20 @ F_19 )
+     => ( ( finite1380128977tate_o @ A_60 )
+       => ( ~ ( member864234961tate_o @ X_33 @ A_60 )
+         => ( ( A_60 != bot_bo691907561te_o_o )
+           => ( ( F_19 @ ( insert999278200tate_o @ X_33 @ A_60 ) )
+              = ( F_20 @ X_33 @ ( F_19 @ A_60 ) ) ) ) ) ) ) )).
+
+thf(fact_513_folding__one_Osingleton,axiom,(
+    ! [X_32: pname,F_18: pname > pname > pname,F_17: ( pname > $o ) > pname] :
+      ( ( finite1282449217_pname @ F_18 @ F_17 )
+     => ( ( F_17 @ ( insert_pname @ X_32 @ bot_bot_pname_o ) )
+        = X_32 ) ) )).
+
+thf(fact_514_folding__one_Osingleton,axiom,(
+    ! [X_32: hoare_1167836817_state,F_18: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_17: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
+      ( ( finite1074406356_state @ F_18 @ F_17 )
+     => ( ( F_17 @ ( insert2134838167_state @ X_32 @ bot_bo70021908tate_o ) )
+        = X_32 ) ) )).
+
+thf(fact_515_folding__one_Oclosed,axiom,(
+    ! [A_59: pname > $o,F_16: pname > pname > pname,F_15: ( pname > $o ) > pname] :
+      ( ( finite1282449217_pname @ F_16 @ F_15 )
+     => ( ( finite_finite_pname @ A_59 )
+       => ( ( A_59 != bot_bot_pname_o )
+         => ( ! [X_5: pname,Y_2: pname] :
+                ( member_pname @ ( F_16 @ X_5 @ Y_2 ) @ ( insert_pname @ X_5 @ ( insert_pname @ Y_2 @ bot_bot_pname_o ) ) )
+           => ( member_pname @ ( F_15 @ A_59 ) @ A_59 ) ) ) ) ) )).
+
+thf(fact_516_folding__one_Oclosed,axiom,(
+    ! [A_59: hoare_1167836817_state > $o,F_16: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_15: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
+      ( ( finite1074406356_state @ F_16 @ F_15 )
+     => ( ( finite1084549118_state @ A_59 )
+       => ( ( A_59 != bot_bo70021908tate_o )
+         => ( ! [X_5: hoare_1167836817_state,Y_2: hoare_1167836817_state] :
+                ( member2058392318_state @ ( F_16 @ X_5 @ Y_2 ) @ ( insert2134838167_state @ X_5 @ ( insert2134838167_state @ Y_2 @ bot_bo70021908tate_o ) ) )
+           => ( member2058392318_state @ ( F_15 @ A_59 ) @ A_59 ) ) ) ) ) )).
+
+thf(fact_517_folding__one_Oclosed,axiom,(
+    ! [A_59: ( pname > $o ) > $o,F_16: ( pname > $o ) > ( pname > $o ) > pname > $o,F_15: ( ( pname > $o ) > $o ) > pname > $o] :
+      ( ( finite349908348name_o @ F_16 @ F_15 )
+     => ( ( finite297249702name_o @ A_59 )
+       => ( ( A_59 != bot_bot_pname_o_o )
+         => ( ! [X_5: pname > $o,Y_2: pname > $o] :
+                ( member_pname_o @ ( F_16 @ X_5 @ Y_2 ) @ ( insert_pname_o @ X_5 @ ( insert_pname_o @ Y_2 @ bot_bot_pname_o_o ) ) )
+           => ( member_pname_o @ ( F_15 @ A_59 ) @ A_59 ) ) ) ) ) )).
+
+thf(fact_518_folding__one_Oclosed,axiom,(
+    ! [A_59: ( hoare_1167836817_state > $o ) > $o,F_16: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_15: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
+      ( ( finite979047547tate_o @ F_16 @ F_15 )
+     => ( ( finite1380128977tate_o @ A_59 )
+       => ( ( A_59 != bot_bo691907561te_o_o )
+         => ( ! [X_5: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o] :
+                ( member864234961tate_o @ ( F_16 @ X_5 @ Y_2 ) @ ( insert999278200tate_o @ X_5 @ ( insert999278200tate_o @ Y_2 @ bot_bo691907561te_o_o ) ) )
+           => ( member864234961tate_o @ ( F_15 @ A_59 ) @ A_59 ) ) ) ) ) )).
+
+thf(fact_519_triple_Oexhaust,axiom,(
+    ! [Y_21: hoare_1167836817_state] :
+      ~ ! [Fun1: state > state > $o,Com: com,Fun2: state > state > $o] :
+          ( Y_21
+         != ( hoare_908217195_state @ Fun1 @ Com @ Fun2 ) ) )).
+
+thf(fact_520_image__cong,axiom,(
+    ! [F_14: pname > hoare_1167836817_state,G_4: pname > hoare_1167836817_state,M: pname > $o,N: pname > $o] :
+      ( ( M = N )
+     => ( ! [X_5: pname] :
+            ( ( member_pname @ X_5 @ N )
+           => ( ( F_14 @ X_5 )
+              = ( G_4 @ X_5 ) ) )
+       => ( ( image_575578384_state @ F_14 @ M )
+          = ( image_575578384_state @ G_4 @ N ) ) ) ) )).
+
+thf(fact_521_Collect__mono,axiom,(
+    ! [Q_3: hoare_1167836817_state > $o,P_7: hoare_1167836817_state > $o] :
+      ( ! [X_5: hoare_1167836817_state] :
+          ( ( P_7 @ X_5 )
+         => ( Q_3 @ X_5 ) )
+     => ( ord_le827224136tate_o @ ( collec1027672124_state @ P_7 ) @ ( collec1027672124_state @ Q_3 ) ) ) )).
+
+thf(fact_522_Collect__mono,axiom,(
+    ! [Q_3: pname > $o,P_7: pname > $o] :
+      ( ! [X_5: pname] :
+          ( ( P_7 @ X_5 )
+         => ( Q_3 @ X_5 ) )
+     => ( ord_less_eq_pname_o @ ( collect_pname @ P_7 ) @ ( collect_pname @ Q_3 ) ) ) )).
+
+thf(fact_523_Collect__mono,axiom,(
+    ! [Q_3: ( pname > $o ) > $o,P_7: ( pname > $o ) > $o] :
+      ( ! [X_5: pname > $o] :
+          ( ( P_7 @ X_5 )
+         => ( Q_3 @ X_5 ) )
+     => ( ord_le1205211808me_o_o @ ( collect_pname_o @ P_7 ) @ ( collect_pname_o @ Q_3 ) ) ) )).
+
+thf(fact_524_Collect__mono,axiom,(
+    ! [Q_3: ( hoare_1167836817_state > $o ) > $o,P_7: ( hoare_1167836817_state > $o ) > $o] :
+      ( ! [X_5: hoare_1167836817_state > $o] :
+          ( ( P_7 @ X_5 )
+         => ( Q_3 @ X_5 ) )
+     => ( ord_le741939125te_o_o @ ( collec269976083tate_o @ P_7 ) @ ( collec269976083tate_o @ Q_3 ) ) ) )).
+
+thf(fact_525_predicate1I,axiom,(
+    ! [Q_2: pname > $o,P_6: pname > $o] :
+      ( ! [X_5: pname] :
+          ( ( P_6 @ X_5 )
+         => ( Q_2 @ X_5 ) )
+     => ( ord_less_eq_pname_o @ P_6 @ Q_2 ) ) )).
+
+thf(fact_526_predicate1I,axiom,(
+    ! [Q_2: hoare_1167836817_state > $o,P_6: hoare_1167836817_state > $o] :
+      ( ! [X_5: hoare_1167836817_state] :
+          ( ( P_6 @ X_5 )
+         => ( Q_2 @ X_5 ) )
+     => ( ord_le827224136tate_o @ P_6 @ Q_2 ) ) )).
+
+thf(fact_527_mk__disjoint__insert,axiom,(
+    ! [A_58: pname,A_57: pname > $o] :
+      ( ( member_pname @ A_58 @ A_57 )
+     => ? [B_43: pname > $o] :
+          ( ( A_57
+            = ( insert_pname @ A_58 @ B_43 ) )
+          & ~ ( member_pname @ A_58 @ B_43 ) ) ) )).
+
+thf(fact_528_mk__disjoint__insert,axiom,(
+    ! [A_58: hoare_1167836817_state,A_57: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ A_58 @ A_57 )
+     => ? [B_43: hoare_1167836817_state > $o] :
+          ( ( A_57
+            = ( insert2134838167_state @ A_58 @ B_43 ) )
+          & ~ ( member2058392318_state @ A_58 @ B_43 ) ) ) )).
+
+thf(fact_529_Set_Oset__insert,axiom,(
+    ! [X_31: pname,A_56: pname > $o] :
+      ( ( member_pname @ X_31 @ A_56 )
+     => ~ ! [B_43: pname > $o] :
+            ( ( A_56
+              = ( insert_pname @ X_31 @ B_43 ) )
+           => ( member_pname @ X_31 @ B_43 ) ) ) )).
+
+thf(fact_530_Set_Oset__insert,axiom,(
+    ! [X_31: hoare_1167836817_state,A_56: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ X_31 @ A_56 )
+     => ~ ! [B_43: hoare_1167836817_state > $o] :
+            ( ( A_56
+              = ( insert2134838167_state @ X_31 @ B_43 ) )
+           => ( member2058392318_state @ X_31 @ B_43 ) ) ) )).
+
+thf(fact_531_equals0I,axiom,(
+    ! [A_55: pname > $o] :
+      ( ! [Y_2: pname] :
+          ~ ( member_pname @ Y_2 @ A_55 )
+     => ( A_55 = bot_bot_pname_o ) ) )).
+
+thf(fact_532_equals0I,axiom,(
+    ! [A_55: hoare_1167836817_state > $o] :
+      ( ! [Y_2: hoare_1167836817_state] :
+          ~ ( member2058392318_state @ Y_2 @ A_55 )
+     => ( A_55 = bot_bo70021908tate_o ) ) )).
+
+thf(fact_533_MGT__alternD,axiom,(
+    ! [G_3: hoare_1167836817_state > $o,C_21: com] :
+      ( hoare_1201148605gleton
+     => ( ( hoare_123228589_state @ G_3
+          @ ( insert2134838167_state
+            @ ( hoare_908217195_state
+              @ ^ [Z_11: state,S0_1: state] :
+                ! [S1: state] :
+                  ( (=>) @ ( evalc @ C_21 @ S0_1 @ S1 ) @ ( Z_11 = S1 ) )
+              @ C_21
+              @ fequal_state )
+            @ bot_bo70021908tate_o ) )
+       => ( hoare_123228589_state @ G_3 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ C_21 ) @ bot_bo70021908tate_o ) ) ) ) )).
+
+thf(fact_534_MGT__alternI,axiom,(
+    ! [G_3: hoare_1167836817_state > $o,C_21: com] :
+      ( ( hoare_123228589_state @ G_3 @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ C_21 ) @ bot_bo70021908tate_o ) )
+     => ( hoare_123228589_state @ G_3
+        @ ( insert2134838167_state
+          @ ( hoare_908217195_state
+            @ ^ [Z_11: state,S0_1: state] :
+              ! [S1: state] :
+                ( (=>) @ ( evalc @ C_21 @ S0_1 @ S1 ) @ ( Z_11 = S1 ) )
+            @ C_21
+            @ fequal_state )
+          @ bot_bo70021908tate_o ) ) ) )).
+
+thf(fact_535_MGT__def,axiom,(
+    ! [C_21: com] :
+      ( ( hoare_Mirabelle_MGT @ C_21 )
+      = ( hoare_908217195_state @ fequal_state @ C_21 @ ( evalc @ C_21 ) ) ) )).
+
+thf(fact_536_evalc_OBody,axiom,(
+    ! [Pn_1: pname,S0: state,S1_1: state] :
+      ( ( evalc @ ( the_com @ ( body @ Pn_1 ) ) @ S0 @ S1_1 )
+     => ( evalc @ ( body_1 @ Pn_1 ) @ S0 @ S1_1 ) ) )).
+
+thf(fact_537_evalc__elim__cases_I6_J,axiom,(
+    ! [P: pname,S_2: state,S1_1: state] :
+      ( ( evalc @ ( body_1 @ P ) @ S_2 @ S1_1 )
+     => ( evalc @ ( the_com @ ( body @ P ) ) @ S_2 @ S1_1 ) ) )).
+
+thf(fact_538_evalc__elim__cases_I1_J,axiom,(
+    ! [S_2: state,T: state] :
+      ( ( evalc @ skip @ S_2 @ T )
+     => ( T = S_2 ) ) )).
+
+thf(fact_539_evalc_OWhileFalse,axiom,(
+    ! [C_21: com,B_42: state > $o,S_2: state] :
+      ( ~ ( B_42 @ S_2 )
+     => ( evalc @ ( while @ B_42 @ C_21 ) @ S_2 @ S_2 ) ) )).
+
+thf(fact_540_evalc_OWhileTrue,axiom,(
+    ! [S2: state,C_21: com,S1_1: state,B_42: state > $o,S0: state] :
+      ( ( B_42 @ S0 )
+     => ( ( evalc @ C_21 @ S0 @ S1_1 )
+       => ( ( evalc @ ( while @ B_42 @ C_21 ) @ S1_1 @ S2 )
+         => ( evalc @ ( while @ B_42 @ C_21 ) @ S0 @ S2 ) ) ) ) )).
+
+thf(fact_541_evalc_OSemi,axiom,(
+    ! [C1: com,S2: state,C0: com,S0: state,S1_1: state] :
+      ( ( evalc @ C0 @ S0 @ S1_1 )
+     => ( ( evalc @ C1 @ S1_1 @ S2 )
+       => ( evalc @ ( semi @ C0 @ C1 ) @ S0 @ S2 ) ) ) )).
+
+thf(fact_542_evalc_OSkip,axiom,(
+    ! [S_2: state] :
+      ( evalc @ skip @ S_2 @ S_2 ) )).
+
+thf(fact_543_com__det,axiom,(
+    ! [U: state,C_21: com,S_2: state,T: state] :
+      ( ( evalc @ C_21 @ S_2 @ T )
+     => ( ( evalc @ C_21 @ S_2 @ U )
+       => ( U = T ) ) ) )).
+
+thf(fact_544_evalc__elim__cases_I4_J,axiom,(
+    ! [C1: com,C2: com,S_2: state,T: state] :
+      ( ( evalc @ ( semi @ C1 @ C2 ) @ S_2 @ T )
+     => ~ ! [S1: state] :
+            ( ( evalc @ C1 @ S_2 @ S1 )
+           => ~ ( evalc @ C2 @ S1 @ T ) ) ) )).
+
+thf(fact_545_evalc__WHILE__case,axiom,(
+    ! [B_42: state > $o,C_21: com,S_2: state,T: state] :
+      ( ( evalc @ ( while @ B_42 @ C_21 ) @ S_2 @ T )
+     => ( ( ( T = S_2 )
+         => ( B_42 @ S_2 ) )
+       => ~ ( ( B_42 @ S_2 )
+           => ! [S1: state] :
+                ( ( evalc @ C_21 @ S_2 @ S1 )
+               => ~ ( evalc @ ( while @ B_42 @ C_21 ) @ S1 @ T ) ) ) ) ) )).
+
+thf(fact_546_xt1_I15_J,axiom,(
+    ! [C_20: pname > $o,A_54: pname > $o,F_13: ( pname > $o ) > pname > $o,B_41: pname > $o] :
+      ( ( A_54
+        = ( F_13 @ B_41 ) )
+     => ( ( ord_less_eq_pname_o @ C_20 @ B_41 )
+       => ( ! [X_5: pname > $o,Y_2: pname > $o] :
+              ( ( ord_less_eq_pname_o @ Y_2 @ X_5 )
+             => ( ord_less_eq_pname_o @ ( F_13 @ Y_2 ) @ ( F_13 @ X_5 ) ) )
+         => ( ord_less_eq_pname_o @ ( F_13 @ C_20 ) @ A_54 ) ) ) ) )).
+
+thf(fact_547_xt1_I15_J,axiom,(
+    ! [C_20: hoare_1167836817_state > $o,A_54: hoare_1167836817_state > $o,F_13: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,B_41: hoare_1167836817_state > $o] :
+      ( ( A_54
+        = ( F_13 @ B_41 ) )
+     => ( ( ord_le827224136tate_o @ C_20 @ B_41 )
+       => ( ! [X_5: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o] :
+              ( ( ord_le827224136tate_o @ Y_2 @ X_5 )
+             => ( ord_le827224136tate_o @ ( F_13 @ Y_2 ) @ ( F_13 @ X_5 ) ) )
+         => ( ord_le827224136tate_o @ ( F_13 @ C_20 ) @ A_54 ) ) ) ) )).
+
+thf(fact_548_xt1_I16_J,axiom,(
+    ! [F_12: ( pname > $o ) > pname > $o,C_19: pname > $o,B_40: pname > $o,A_53: pname > $o] :
+      ( ( ord_less_eq_pname_o @ B_40 @ A_53 )
+     => ( ( ( F_12 @ B_40 )
+          = C_19 )
+       => ( ! [X_5: pname > $o,Y_2: pname > $o] :
+              ( ( ord_less_eq_pname_o @ Y_2 @ X_5 )
+             => ( ord_less_eq_pname_o @ ( F_12 @ Y_2 ) @ ( F_12 @ X_5 ) ) )
+         => ( ord_less_eq_pname_o @ C_19 @ ( F_12 @ A_53 ) ) ) ) ) )).
+
+thf(fact_549_xt1_I16_J,axiom,(
+    ! [F_12: ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,C_19: hoare_1167836817_state > $o,B_40: hoare_1167836817_state > $o,A_53: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ B_40 @ A_53 )
+     => ( ( ( F_12 @ B_40 )
+          = C_19 )
+       => ( ! [X_5: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o] :
+              ( ( ord_le827224136tate_o @ Y_2 @ X_5 )
+             => ( ord_le827224136tate_o @ ( F_12 @ Y_2 ) @ ( F_12 @ X_5 ) ) )
+         => ( ord_le827224136tate_o @ C_19 @ ( F_12 @ A_53 ) ) ) ) ) )).
+
+thf(fact_550_folding__one_Ounion__inter,axiom,(
+    ! [B_39: ( pname > $o ) > $o,A_52: ( pname > $o ) > $o,F_11: ( pname > $o ) > ( pname > $o ) > pname > $o,F_10: ( ( pname > $o ) > $o ) > pname > $o] :
+      ( ( finite349908348name_o @ F_11 @ F_10 )
+     => ( ( finite297249702name_o @ A_52 )
+       => ( ( finite297249702name_o @ B_39 )
+         => ( ( ( semila2013987940me_o_o @ A_52 @ B_39 )
+             != bot_bot_pname_o_o )
+           => ( ( F_11 @ ( F_10 @ ( semila181081674me_o_o @ A_52 @ B_39 ) ) @ ( F_10 @ ( semila2013987940me_o_o @ A_52 @ B_39 ) ) )
+              = ( F_11 @ ( F_10 @ A_52 ) @ ( F_10 @ B_39 ) ) ) ) ) ) ) )).
+
+thf(fact_551_folding__one_Ounion__inter,axiom,(
+    ! [B_39: ( hoare_1167836817_state > $o ) > $o,A_52: ( hoare_1167836817_state > $o ) > $o,F_11: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_10: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
+      ( ( finite979047547tate_o @ F_11 @ F_10 )
+     => ( ( finite1380128977tate_o @ A_52 )
+       => ( ( finite1380128977tate_o @ B_39 )
+         => ( ( ( semila1758709489te_o_o @ A_52 @ B_39 )
+             != bot_bo691907561te_o_o )
+           => ( ( F_11 @ ( F_10 @ ( semila866907787te_o_o @ A_52 @ B_39 ) ) @ ( F_10 @ ( semila1758709489te_o_o @ A_52 @ B_39 ) ) )
+              = ( F_11 @ ( F_10 @ A_52 ) @ ( F_10 @ B_39 ) ) ) ) ) ) ) )).
+
+thf(fact_552_folding__one_Ounion__inter,axiom,(
+    ! [B_39: pname > $o,A_52: pname > $o,F_11: pname > pname > pname,F_10: ( pname > $o ) > pname] :
+      ( ( finite1282449217_pname @ F_11 @ F_10 )
+     => ( ( finite_finite_pname @ A_52 )
+       => ( ( finite_finite_pname @ B_39 )
+         => ( ( ( semila1673364395name_o @ A_52 @ B_39 )
+             != bot_bot_pname_o )
+           => ( ( F_11 @ ( F_10 @ ( semila1780557381name_o @ A_52 @ B_39 ) ) @ ( F_10 @ ( semila1673364395name_o @ A_52 @ B_39 ) ) )
+              = ( F_11 @ ( F_10 @ A_52 ) @ ( F_10 @ B_39 ) ) ) ) ) ) ) )).
+
+thf(fact_553_folding__one_Ounion__inter,axiom,(
+    ! [B_39: hoare_1167836817_state > $o,A_52: hoare_1167836817_state > $o,F_11: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_10: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
+      ( ( finite1074406356_state @ F_11 @ F_10 )
+     => ( ( finite1084549118_state @ A_52 )
+       => ( ( finite1084549118_state @ B_39 )
+         => ( ( ( semila179895820tate_o @ A_52 @ B_39 )
+             != bot_bo70021908tate_o )
+           => ( ( F_11 @ ( F_10 @ ( semila1172322802tate_o @ A_52 @ B_39 ) ) @ ( F_10 @ ( semila179895820tate_o @ A_52 @ B_39 ) ) )
+              = ( F_11 @ ( F_10 @ A_52 ) @ ( F_10 @ B_39 ) ) ) ) ) ) ) )).
+
+thf(fact_554_folding__one_Ounion__disjoint,axiom,(
+    ! [B_38: ( pname > $o ) > $o,A_51: ( pname > $o ) > $o,F_9: ( pname > $o ) > ( pname > $o ) > pname > $o,F_8: ( ( pname > $o ) > $o ) > pname > $o] :
+      ( ( finite349908348name_o @ F_9 @ F_8 )
+     => ( ( finite297249702name_o @ A_51 )
+       => ( ( A_51 != bot_bot_pname_o_o )
+         => ( ( finite297249702name_o @ B_38 )
+           => ( ( B_38 != bot_bot_pname_o_o )
+             => ( ( ( semila2013987940me_o_o @ A_51 @ B_38 )
+                  = bot_bot_pname_o_o )
+               => ( ( F_8 @ ( semila181081674me_o_o @ A_51 @ B_38 ) )
+                  = ( F_9 @ ( F_8 @ A_51 ) @ ( F_8 @ B_38 ) ) ) ) ) ) ) ) ) )).
+
+thf(fact_555_folding__one_Ounion__disjoint,axiom,(
+    ! [B_38: ( hoare_1167836817_state > $o ) > $o,A_51: ( hoare_1167836817_state > $o ) > $o,F_9: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_8: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
+      ( ( finite979047547tate_o @ F_9 @ F_8 )
+     => ( ( finite1380128977tate_o @ A_51 )
+       => ( ( A_51 != bot_bo691907561te_o_o )
+         => ( ( finite1380128977tate_o @ B_38 )
+           => ( ( B_38 != bot_bo691907561te_o_o )
+             => ( ( ( semila1758709489te_o_o @ A_51 @ B_38 )
+                  = bot_bo691907561te_o_o )
+               => ( ( F_8 @ ( semila866907787te_o_o @ A_51 @ B_38 ) )
+                  = ( F_9 @ ( F_8 @ A_51 ) @ ( F_8 @ B_38 ) ) ) ) ) ) ) ) ) )).
+
+thf(fact_556_folding__one_Ounion__disjoint,axiom,(
+    ! [B_38: pname > $o,A_51: pname > $o,F_9: pname > pname > pname,F_8: ( pname > $o ) > pname] :
+      ( ( finite1282449217_pname @ F_9 @ F_8 )
+     => ( ( finite_finite_pname @ A_51 )
+       => ( ( A_51 != bot_bot_pname_o )
+         => ( ( finite_finite_pname @ B_38 )
+           => ( ( B_38 != bot_bot_pname_o )
+             => ( ( ( semila1673364395name_o @ A_51 @ B_38 )
+                  = bot_bot_pname_o )
+               => ( ( F_8 @ ( semila1780557381name_o @ A_51 @ B_38 ) )
+                  = ( F_9 @ ( F_8 @ A_51 ) @ ( F_8 @ B_38 ) ) ) ) ) ) ) ) ) )).
+
+thf(fact_557_folding__one_Ounion__disjoint,axiom,(
+    ! [B_38: hoare_1167836817_state > $o,A_51: hoare_1167836817_state > $o,F_9: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_8: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
+      ( ( finite1074406356_state @ F_9 @ F_8 )
+     => ( ( finite1084549118_state @ A_51 )
+       => ( ( A_51 != bot_bo70021908tate_o )
+         => ( ( finite1084549118_state @ B_38 )
+           => ( ( B_38 != bot_bo70021908tate_o )
+             => ( ( ( semila179895820tate_o @ A_51 @ B_38 )
+                  = bot_bo70021908tate_o )
+               => ( ( F_8 @ ( semila1172322802tate_o @ A_51 @ B_38 ) )
+                  = ( F_9 @ ( F_8 @ A_51 ) @ ( F_8 @ B_38 ) ) ) ) ) ) ) ) ) )).
+
+thf(fact_558_IntI,axiom,(
+    ! [B_37: pname > $o,C_18: pname,A_50: pname > $o] :
+      ( ( member_pname @ C_18 @ A_50 )
+     => ( ( member_pname @ C_18 @ B_37 )
+       => ( member_pname @ C_18 @ ( semila1673364395name_o @ A_50 @ B_37 ) ) ) ) )).
+
+thf(fact_559_IntI,axiom,(
+    ! [B_37: hoare_1167836817_state > $o,C_18: hoare_1167836817_state,A_50: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ C_18 @ A_50 )
+     => ( ( member2058392318_state @ C_18 @ B_37 )
+       => ( member2058392318_state @ C_18 @ ( semila179895820tate_o @ A_50 @ B_37 ) ) ) ) )).
+
+thf(fact_560_IntE,axiom,(
+    ! [C_17: pname,A_49: pname > $o,B_36: pname > $o] :
+      ( ( member_pname @ C_17 @ ( semila1673364395name_o @ A_49 @ B_36 ) )
+     => ~ ( ( member_pname @ C_17 @ A_49 )
+         => ~ ( member_pname @ C_17 @ B_36 ) ) ) )).
+
+thf(fact_561_IntE,axiom,(
+    ! [C_17: hoare_1167836817_state,A_49: hoare_1167836817_state > $o,B_36: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ C_17 @ ( semila179895820tate_o @ A_49 @ B_36 ) )
+     => ~ ( ( member2058392318_state @ C_17 @ A_49 )
+         => ~ ( member2058392318_state @ C_17 @ B_36 ) ) ) )).
+
+thf(fact_562_finite__Int,axiom,(
+    ! [G_2: ( pname > $o ) > $o,F_7: ( pname > $o ) > $o] :
+      ( ( ( finite297249702name_o @ F_7 )
+        | ( finite297249702name_o @ G_2 ) )
+     => ( finite297249702name_o @ ( semila2013987940me_o_o @ F_7 @ G_2 ) ) ) )).
+
+thf(fact_563_finite__Int,axiom,(
+    ! [G_2: ( hoare_1167836817_state > $o ) > $o,F_7: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( ( finite1380128977tate_o @ F_7 )
+        | ( finite1380128977tate_o @ G_2 ) )
+     => ( finite1380128977tate_o @ ( semila1758709489te_o_o @ F_7 @ G_2 ) ) ) )).
+
+thf(fact_564_finite__Int,axiom,(
+    ! [G_2: pname > $o,F_7: pname > $o] :
+      ( ( ( finite_finite_pname @ F_7 )
+        | ( finite_finite_pname @ G_2 ) )
+     => ( finite_finite_pname @ ( semila1673364395name_o @ F_7 @ G_2 ) ) ) )).
+
+thf(fact_565_finite__Int,axiom,(
+    ! [G_2: hoare_1167836817_state > $o,F_7: hoare_1167836817_state > $o] :
+      ( ( ( finite1084549118_state @ F_7 )
+        | ( finite1084549118_state @ G_2 ) )
+     => ( finite1084549118_state @ ( semila179895820tate_o @ F_7 @ G_2 ) ) ) )).
+
+thf(fact_566_disjoint__iff__not__equal,axiom,(
+    ! [A_48: pname > $o,B_35: pname > $o] :
+      ( ( ( semila1673364395name_o @ A_48 @ B_35 )
+        = bot_bot_pname_o )
+    <=> ! [X_5: pname] :
+          ( ( member_pname @ X_5 @ A_48 )
+         => ! [Xa: pname] :
+              ( ( member_pname @ Xa @ B_35 )
+             => ( X_5 != Xa ) ) ) ) )).
+
+thf(fact_567_disjoint__iff__not__equal,axiom,(
+    ! [A_48: hoare_1167836817_state > $o,B_35: hoare_1167836817_state > $o] :
+      ( ( ( semila179895820tate_o @ A_48 @ B_35 )
+        = bot_bo70021908tate_o )
+    <=> ! [X_5: hoare_1167836817_state] :
+          ( ( member2058392318_state @ X_5 @ A_48 )
+         => ! [Xa: hoare_1167836817_state] :
+              ( ( member2058392318_state @ Xa @ B_35 )
+             => ( X_5 != Xa ) ) ) ) )).
+
+thf(fact_568_Int__empty__right,axiom,(
+    ! [A_47: pname > $o] :
+      ( ( semila1673364395name_o @ A_47 @ bot_bot_pname_o )
+      = bot_bot_pname_o ) )).
+
+thf(fact_569_Int__empty__right,axiom,(
+    ! [A_47: hoare_1167836817_state > $o] :
+      ( ( semila179895820tate_o @ A_47 @ bot_bo70021908tate_o )
+      = bot_bo70021908tate_o ) )).
+
+thf(fact_570_Int__empty__left,axiom,(
+    ! [B_34: pname > $o] :
+      ( ( semila1673364395name_o @ bot_bot_pname_o @ B_34 )
+      = bot_bot_pname_o ) )).
+
+thf(fact_571_Int__empty__left,axiom,(
+    ! [B_34: hoare_1167836817_state > $o] :
+      ( ( semila179895820tate_o @ bot_bo70021908tate_o @ B_34 )
+      = bot_bo70021908tate_o ) )).
+
+thf(fact_572_Int__def,axiom,(
+    ! [A_46: pname > $o,B_33: pname > $o] :
+      ( ( semila1673364395name_o @ A_46 @ B_33 )
+      = ( collect_pname
+        @ ^ [X_5: pname] :
+            ( (&) @ ( member_pname @ X_5 @ A_46 ) @ ( member_pname @ X_5 @ B_33 ) ) ) ) )).
+
+thf(fact_573_Int__def,axiom,(
+    ! [A_46: hoare_1167836817_state > $o,B_33: hoare_1167836817_state > $o] :
+      ( ( semila179895820tate_o @ A_46 @ B_33 )
+      = ( collec1027672124_state
+        @ ^ [X_5: hoare_1167836817_state] :
+            ( (&) @ ( member2058392318_state @ X_5 @ A_46 ) @ ( member2058392318_state @ X_5 @ B_33 ) ) ) ) )).
+
+thf(fact_574_Int__def,axiom,(
+    ! [A_46: ( pname > $o ) > $o,B_33: ( pname > $o ) > $o] :
+      ( ( semila2013987940me_o_o @ A_46 @ B_33 )
+      = ( collect_pname_o
+        @ ^ [X_5: pname > $o] :
+            ( (&) @ ( member_pname_o @ X_5 @ A_46 ) @ ( member_pname_o @ X_5 @ B_33 ) ) ) ) )).
+
+thf(fact_575_Int__def,axiom,(
+    ! [A_46: ( hoare_1167836817_state > $o ) > $o,B_33: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( semila1758709489te_o_o @ A_46 @ B_33 )
+      = ( collec269976083tate_o
+        @ ^ [X_5: hoare_1167836817_state > $o] :
+            ( (&) @ ( member864234961tate_o @ X_5 @ A_46 ) @ ( member864234961tate_o @ X_5 @ B_33 ) ) ) ) )).
+
+thf(fact_576_Int__iff,axiom,(
+    ! [C_16: pname,A_45: pname > $o,B_32: pname > $o] :
+      ( ( member_pname @ C_16 @ ( semila1673364395name_o @ A_45 @ B_32 ) )
+    <=> ( ( member_pname @ C_16 @ A_45 )
+        & ( member_pname @ C_16 @ B_32 ) ) ) )).
+
+thf(fact_577_Int__iff,axiom,(
+    ! [C_16: hoare_1167836817_state,A_45: hoare_1167836817_state > $o,B_32: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ C_16 @ ( semila179895820tate_o @ A_45 @ B_32 ) )
+    <=> ( ( member2058392318_state @ C_16 @ A_45 )
+        & ( member2058392318_state @ C_16 @ B_32 ) ) ) )).
+
+thf(fact_578_IntD1,axiom,(
+    ! [C_15: pname,A_44: pname > $o,B_31: pname > $o] :
+      ( ( member_pname @ C_15 @ ( semila1673364395name_o @ A_44 @ B_31 ) )
+     => ( member_pname @ C_15 @ A_44 ) ) )).
+
+thf(fact_579_IntD1,axiom,(
+    ! [C_15: hoare_1167836817_state,A_44: hoare_1167836817_state > $o,B_31: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ C_15 @ ( semila179895820tate_o @ A_44 @ B_31 ) )
+     => ( member2058392318_state @ C_15 @ A_44 ) ) )).
+
+thf(fact_580_IntD2,axiom,(
+    ! [C_14: pname,A_43: pname > $o,B_30: pname > $o] :
+      ( ( member_pname @ C_14 @ ( semila1673364395name_o @ A_43 @ B_30 ) )
+     => ( member_pname @ C_14 @ B_30 ) ) )).
+
+thf(fact_581_IntD2,axiom,(
+    ! [C_14: hoare_1167836817_state,A_43: hoare_1167836817_state > $o,B_30: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ C_14 @ ( semila179895820tate_o @ A_43 @ B_30 ) )
+     => ( member2058392318_state @ C_14 @ B_30 ) ) )).
+
+thf(fact_582_Collect__conj__eq,axiom,(
+    ! [P_5: hoare_1167836817_state > $o,Q_1: hoare_1167836817_state > $o] :
+      ( ( collec1027672124_state
+        @ ^ [X_5: hoare_1167836817_state] :
+            ( (&) @ ( P_5 @ X_5 ) @ ( Q_1 @ X_5 ) ) )
+      = ( semila179895820tate_o @ ( collec1027672124_state @ P_5 ) @ ( collec1027672124_state @ Q_1 ) ) ) )).
+
+thf(fact_583_Collect__conj__eq,axiom,(
+    ! [P_5: pname > $o,Q_1: pname > $o] :
+      ( ( collect_pname
+        @ ^ [X_5: pname] :
+            ( (&) @ ( P_5 @ X_5 ) @ ( Q_1 @ X_5 ) ) )
+      = ( semila1673364395name_o @ ( collect_pname @ P_5 ) @ ( collect_pname @ Q_1 ) ) ) )).
+
+thf(fact_584_Collect__conj__eq,axiom,(
+    ! [P_5: ( pname > $o ) > $o,Q_1: ( pname > $o ) > $o] :
+      ( ( collect_pname_o
+        @ ^ [X_5: pname > $o] :
+            ( (&) @ ( P_5 @ X_5 ) @ ( Q_1 @ X_5 ) ) )
+      = ( semila2013987940me_o_o @ ( collect_pname_o @ P_5 ) @ ( collect_pname_o @ Q_1 ) ) ) )).
+
+thf(fact_585_Collect__conj__eq,axiom,(
+    ! [P_5: ( hoare_1167836817_state > $o ) > $o,Q_1: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( collec269976083tate_o
+        @ ^ [X_5: hoare_1167836817_state > $o] :
+            ( (&) @ ( P_5 @ X_5 ) @ ( Q_1 @ X_5 ) ) )
+      = ( semila1758709489te_o_o @ ( collec269976083tate_o @ P_5 ) @ ( collec269976083tate_o @ Q_1 ) ) ) )).
+
+thf(fact_586_Int__Collect,axiom,(
+    ! [X_30: pname,A_42: pname > $o,P_4: pname > $o] :
+      ( ( member_pname @ X_30 @ ( semila1673364395name_o @ A_42 @ ( collect_pname @ P_4 ) ) )
+    <=> ( ( member_pname @ X_30 @ A_42 )
+        & ( P_4 @ X_30 ) ) ) )).
+
+thf(fact_587_Int__Collect,axiom,(
+    ! [X_30: hoare_1167836817_state,A_42: hoare_1167836817_state > $o,P_4: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ X_30 @ ( semila179895820tate_o @ A_42 @ ( collec1027672124_state @ P_4 ) ) )
+    <=> ( ( member2058392318_state @ X_30 @ A_42 )
+        & ( P_4 @ X_30 ) ) ) )).
+
+thf(fact_588_Int__Collect,axiom,(
+    ! [X_30: pname > $o,A_42: ( pname > $o ) > $o,P_4: ( pname > $o ) > $o] :
+      ( ( member_pname_o @ X_30 @ ( semila2013987940me_o_o @ A_42 @ ( collect_pname_o @ P_4 ) ) )
+    <=> ( ( member_pname_o @ X_30 @ A_42 )
+        & ( P_4 @ X_30 ) ) ) )).
+
+thf(fact_589_Int__Collect,axiom,(
+    ! [X_30: hoare_1167836817_state > $o,A_42: ( hoare_1167836817_state > $o ) > $o,P_4: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( member864234961tate_o @ X_30 @ ( semila1758709489te_o_o @ A_42 @ ( collec269976083tate_o @ P_4 ) ) )
+    <=> ( ( member864234961tate_o @ X_30 @ A_42 )
+        & ( P_4 @ X_30 ) ) ) )).
+
+thf(fact_590_inf__Int__eq,axiom,(
+    ! [R: pname > $o,S_1: pname > $o,X_5: pname] :
+      ( ( semila1673364395name_o
+        @ ^ [Y_2: pname] :
+            ( member_pname @ Y_2 @ R )
+        @ ^ [Y_2: pname] :
+            ( member_pname @ Y_2 @ S_1 )
+        @ X_5 )
+    <=> ( member_pname @ X_5 @ ( semila1673364395name_o @ R @ S_1 ) ) ) )).
+
+thf(fact_591_inf__Int__eq,axiom,(
+    ! [R: hoare_1167836817_state > $o,S_1: hoare_1167836817_state > $o,X_5: hoare_1167836817_state] :
+      ( ( semila179895820tate_o
+        @ ^ [Y_2: hoare_1167836817_state] :
+            ( member2058392318_state @ Y_2 @ R )
+        @ ^ [Y_2: hoare_1167836817_state] :
+            ( member2058392318_state @ Y_2 @ S_1 )
+        @ X_5 )
+    <=> ( member2058392318_state @ X_5 @ ( semila179895820tate_o @ R @ S_1 ) ) ) )).
+
+thf(fact_592_Un__Int__crazy,axiom,(
+    ! [A_41: hoare_1167836817_state > $o,B_29: hoare_1167836817_state > $o,C_13: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ ( semila1172322802tate_o @ ( semila179895820tate_o @ A_41 @ B_29 ) @ ( semila179895820tate_o @ B_29 @ C_13 ) ) @ ( semila179895820tate_o @ C_13 @ A_41 ) )
+      = ( semila179895820tate_o @ ( semila179895820tate_o @ ( semila1172322802tate_o @ A_41 @ B_29 ) @ ( semila1172322802tate_o @ B_29 @ C_13 ) ) @ ( semila1172322802tate_o @ C_13 @ A_41 ) ) ) )).
+
+thf(fact_593_Un__Int__distrib2,axiom,(
+    ! [B_28: hoare_1167836817_state > $o,C_12: hoare_1167836817_state > $o,A_40: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ ( semila179895820tate_o @ B_28 @ C_12 ) @ A_40 )
+      = ( semila179895820tate_o @ ( semila1172322802tate_o @ B_28 @ A_40 ) @ ( semila1172322802tate_o @ C_12 @ A_40 ) ) ) )).
+
+thf(fact_594_Int__Un__distrib2,axiom,(
+    ! [B_27: hoare_1167836817_state > $o,C_11: hoare_1167836817_state > $o,A_39: hoare_1167836817_state > $o] :
+      ( ( semila179895820tate_o @ ( semila1172322802tate_o @ B_27 @ C_11 ) @ A_39 )
+      = ( semila1172322802tate_o @ ( semila179895820tate_o @ B_27 @ A_39 ) @ ( semila179895820tate_o @ C_11 @ A_39 ) ) ) )).
+
+thf(fact_595_Un__Int__distrib,axiom,(
+    ! [A_38: hoare_1167836817_state > $o,B_26: hoare_1167836817_state > $o,C_10: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ A_38 @ ( semila179895820tate_o @ B_26 @ C_10 ) )
+      = ( semila179895820tate_o @ ( semila1172322802tate_o @ A_38 @ B_26 ) @ ( semila1172322802tate_o @ A_38 @ C_10 ) ) ) )).
+
+thf(fact_596_Int__Un__distrib,axiom,(
+    ! [A_37: hoare_1167836817_state > $o,B_25: hoare_1167836817_state > $o,C_9: hoare_1167836817_state > $o] :
+      ( ( semila179895820tate_o @ A_37 @ ( semila1172322802tate_o @ B_25 @ C_9 ) )
+      = ( semila1172322802tate_o @ ( semila179895820tate_o @ A_37 @ B_25 ) @ ( semila179895820tate_o @ A_37 @ C_9 ) ) ) )).
+
+thf(fact_597_Int__mono,axiom,(
+    ! [B_24: pname > $o,D_1: pname > $o,A_36: pname > $o,C_8: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_36 @ C_8 )
+     => ( ( ord_less_eq_pname_o @ B_24 @ D_1 )
+       => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_36 @ B_24 ) @ ( semila1673364395name_o @ C_8 @ D_1 ) ) ) ) )).
+
+thf(fact_598_Int__mono,axiom,(
+    ! [B_24: hoare_1167836817_state > $o,D_1: hoare_1167836817_state > $o,A_36: hoare_1167836817_state > $o,C_8: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_36 @ C_8 )
+     => ( ( ord_le827224136tate_o @ B_24 @ D_1 )
+       => ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_36 @ B_24 ) @ ( semila179895820tate_o @ C_8 @ D_1 ) ) ) ) )).
+
+thf(fact_599_Int__greatest,axiom,(
+    ! [B_23: pname > $o,C_7: pname > $o,A_35: pname > $o] :
+      ( ( ord_less_eq_pname_o @ C_7 @ A_35 )
+     => ( ( ord_less_eq_pname_o @ C_7 @ B_23 )
+       => ( ord_less_eq_pname_o @ C_7 @ ( semila1673364395name_o @ A_35 @ B_23 ) ) ) ) )).
+
+thf(fact_600_Int__greatest,axiom,(
+    ! [B_23: hoare_1167836817_state > $o,C_7: hoare_1167836817_state > $o,A_35: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ C_7 @ A_35 )
+     => ( ( ord_le827224136tate_o @ C_7 @ B_23 )
+       => ( ord_le827224136tate_o @ C_7 @ ( semila179895820tate_o @ A_35 @ B_23 ) ) ) ) )).
+
+thf(fact_601_Int__absorb1,axiom,(
+    ! [B_22: pname > $o,A_34: pname > $o] :
+      ( ( ord_less_eq_pname_o @ B_22 @ A_34 )
+     => ( ( semila1673364395name_o @ A_34 @ B_22 )
+        = B_22 ) ) )).
+
+thf(fact_602_Int__absorb1,axiom,(
+    ! [B_22: hoare_1167836817_state > $o,A_34: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ B_22 @ A_34 )
+     => ( ( semila179895820tate_o @ A_34 @ B_22 )
+        = B_22 ) ) )).
+
+thf(fact_603_Int__absorb2,axiom,(
+    ! [A_33: pname > $o,B_21: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_33 @ B_21 )
+     => ( ( semila1673364395name_o @ A_33 @ B_21 )
+        = A_33 ) ) )).
+
+thf(fact_604_Int__absorb2,axiom,(
+    ! [A_33: hoare_1167836817_state > $o,B_21: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_33 @ B_21 )
+     => ( ( semila179895820tate_o @ A_33 @ B_21 )
+        = A_33 ) ) )).
+
+thf(fact_605_Int__lower2,axiom,(
+    ! [A_32: pname > $o,B_20: pname > $o] :
+      ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_32 @ B_20 ) @ B_20 ) )).
+
+thf(fact_606_Int__lower2,axiom,(
+    ! [A_32: hoare_1167836817_state > $o,B_20: hoare_1167836817_state > $o] :
+      ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_32 @ B_20 ) @ B_20 ) )).
+
+thf(fact_607_Int__lower1,axiom,(
+    ! [A_31: pname > $o,B_19: pname > $o] :
+      ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_31 @ B_19 ) @ A_31 ) )).
+
+thf(fact_608_Int__lower1,axiom,(
+    ! [A_31: hoare_1167836817_state > $o,B_19: hoare_1167836817_state > $o] :
+      ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_31 @ B_19 ) @ A_31 ) )).
+
+thf(fact_609_Int__insert__left__if1,axiom,(
+    ! [B_18: pname > $o,A_30: pname,C_6: pname > $o] :
+      ( ( member_pname @ A_30 @ C_6 )
+     => ( ( semila1673364395name_o @ ( insert_pname @ A_30 @ B_18 ) @ C_6 )
+        = ( insert_pname @ A_30 @ ( semila1673364395name_o @ B_18 @ C_6 ) ) ) ) )).
+
+thf(fact_610_Int__insert__left__if1,axiom,(
+    ! [B_18: hoare_1167836817_state > $o,A_30: hoare_1167836817_state,C_6: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ A_30 @ C_6 )
+     => ( ( semila179895820tate_o @ ( insert2134838167_state @ A_30 @ B_18 ) @ C_6 )
+        = ( insert2134838167_state @ A_30 @ ( semila179895820tate_o @ B_18 @ C_6 ) ) ) ) )).
+
+thf(fact_611_Int__insert__right__if1,axiom,(
+    ! [B_17: pname > $o,A_29: pname,A_28: pname > $o] :
+      ( ( member_pname @ A_29 @ A_28 )
+     => ( ( semila1673364395name_o @ A_28 @ ( insert_pname @ A_29 @ B_17 ) )
+        = ( insert_pname @ A_29 @ ( semila1673364395name_o @ A_28 @ B_17 ) ) ) ) )).
+
+thf(fact_612_Int__insert__right__if1,axiom,(
+    ! [B_17: hoare_1167836817_state > $o,A_29: hoare_1167836817_state,A_28: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ A_29 @ A_28 )
+     => ( ( semila179895820tate_o @ A_28 @ ( insert2134838167_state @ A_29 @ B_17 ) )
+        = ( insert2134838167_state @ A_29 @ ( semila179895820tate_o @ A_28 @ B_17 ) ) ) ) )).
+
+thf(fact_613_Int__insert__left__if0,axiom,(
+    ! [B_16: pname > $o,A_27: pname,C_5: pname > $o] :
+      ( ~ ( member_pname @ A_27 @ C_5 )
+     => ( ( semila1673364395name_o @ ( insert_pname @ A_27 @ B_16 ) @ C_5 )
+        = ( semila1673364395name_o @ B_16 @ C_5 ) ) ) )).
+
+thf(fact_614_Int__insert__left__if0,axiom,(
+    ! [B_16: hoare_1167836817_state > $o,A_27: hoare_1167836817_state,C_5: hoare_1167836817_state > $o] :
+      ( ~ ( member2058392318_state @ A_27 @ C_5 )
+     => ( ( semila179895820tate_o @ ( insert2134838167_state @ A_27 @ B_16 ) @ C_5 )
+        = ( semila179895820tate_o @ B_16 @ C_5 ) ) ) )).
+
+thf(fact_615_Int__insert__right__if0,axiom,(
+    ! [B_15: pname > $o,A_26: pname,A_25: pname > $o] :
+      ( ~ ( member_pname @ A_26 @ A_25 )
+     => ( ( semila1673364395name_o @ A_25 @ ( insert_pname @ A_26 @ B_15 ) )
+        = ( semila1673364395name_o @ A_25 @ B_15 ) ) ) )).
+
+thf(fact_616_Int__insert__right__if0,axiom,(
+    ! [B_15: hoare_1167836817_state > $o,A_26: hoare_1167836817_state,A_25: hoare_1167836817_state > $o] :
+      ( ~ ( member2058392318_state @ A_26 @ A_25 )
+     => ( ( semila179895820tate_o @ A_25 @ ( insert2134838167_state @ A_26 @ B_15 ) )
+        = ( semila179895820tate_o @ A_25 @ B_15 ) ) ) )).
+
+thf(fact_617_insert__inter__insert,axiom,(
+    ! [A_24: pname,A_23: pname > $o,B_14: pname > $o] :
+      ( ( semila1673364395name_o @ ( insert_pname @ A_24 @ A_23 ) @ ( insert_pname @ A_24 @ B_14 ) )
+      = ( insert_pname @ A_24 @ ( semila1673364395name_o @ A_23 @ B_14 ) ) ) )).
+
+thf(fact_618_insert__inter__insert,axiom,(
+    ! [A_24: hoare_1167836817_state,A_23: hoare_1167836817_state > $o,B_14: hoare_1167836817_state > $o] :
+      ( ( semila179895820tate_o @ ( insert2134838167_state @ A_24 @ A_23 ) @ ( insert2134838167_state @ A_24 @ B_14 ) )
+      = ( insert2134838167_state @ A_24 @ ( semila179895820tate_o @ A_23 @ B_14 ) ) ) )).
+
+thf(fact_619_Int__insert__left,axiom,(
+    ! [B_13: pname > $o,A_22: pname,C_4: pname > $o] :
+      ( ( ( member_pname @ A_22 @ C_4 )
+       => ( ( semila1673364395name_o @ ( insert_pname @ A_22 @ B_13 ) @ C_4 )
+          = ( insert_pname @ A_22 @ ( semila1673364395name_o @ B_13 @ C_4 ) ) ) )
+      & ( ~ ( member_pname @ A_22 @ C_4 )
+       => ( ( semila1673364395name_o @ ( insert_pname @ A_22 @ B_13 ) @ C_4 )
+          = ( semila1673364395name_o @ B_13 @ C_4 ) ) ) ) )).
+
+thf(fact_620_Int__insert__left,axiom,(
+    ! [B_13: hoare_1167836817_state > $o,A_22: hoare_1167836817_state,C_4: hoare_1167836817_state > $o] :
+      ( ( ( member2058392318_state @ A_22 @ C_4 )
+       => ( ( semila179895820tate_o @ ( insert2134838167_state @ A_22 @ B_13 ) @ C_4 )
+          = ( insert2134838167_state @ A_22 @ ( semila179895820tate_o @ B_13 @ C_4 ) ) ) )
+      & ( ~ ( member2058392318_state @ A_22 @ C_4 )
+       => ( ( semila179895820tate_o @ ( insert2134838167_state @ A_22 @ B_13 ) @ C_4 )
+          = ( semila179895820tate_o @ B_13 @ C_4 ) ) ) ) )).
+
+thf(fact_621_Int__insert__right,axiom,(
+    ! [B_12: pname > $o,A_21: pname,A_20: pname > $o] :
+      ( ( ( member_pname @ A_21 @ A_20 )
+       => ( ( semila1673364395name_o @ A_20 @ ( insert_pname @ A_21 @ B_12 ) )
+          = ( insert_pname @ A_21 @ ( semila1673364395name_o @ A_20 @ B_12 ) ) ) )
+      & ( ~ ( member_pname @ A_21 @ A_20 )
+       => ( ( semila1673364395name_o @ A_20 @ ( insert_pname @ A_21 @ B_12 ) )
+          = ( semila1673364395name_o @ A_20 @ B_12 ) ) ) ) )).
+
+thf(fact_622_Int__insert__right,axiom,(
+    ! [B_12: hoare_1167836817_state > $o,A_21: hoare_1167836817_state,A_20: hoare_1167836817_state > $o] :
+      ( ( ( member2058392318_state @ A_21 @ A_20 )
+       => ( ( semila179895820tate_o @ A_20 @ ( insert2134838167_state @ A_21 @ B_12 ) )
+          = ( insert2134838167_state @ A_21 @ ( semila179895820tate_o @ A_20 @ B_12 ) ) ) )
+      & ( ~ ( member2058392318_state @ A_21 @ A_20 )
+       => ( ( semila179895820tate_o @ A_20 @ ( insert2134838167_state @ A_21 @ B_12 ) )
+          = ( semila179895820tate_o @ A_20 @ B_12 ) ) ) ) )).
+
+thf(fact_623_inf__sup__ord_I1_J,axiom,(
+    ! [X_29: pname > $o,Y_20: pname > $o] :
+      ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_29 @ Y_20 ) @ X_29 ) )).
+
+thf(fact_624_inf__sup__ord_I1_J,axiom,(
+    ! [X_29: hoare_1167836817_state > $o,Y_20: hoare_1167836817_state > $o] :
+      ( ord_le827224136tate_o @ ( semila179895820tate_o @ X_29 @ Y_20 ) @ X_29 ) )).
+
+thf(fact_625_inf__le1,axiom,(
+    ! [X_28: pname > $o,Y_19: pname > $o] :
+      ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_28 @ Y_19 ) @ X_28 ) )).
+
+thf(fact_626_inf__le1,axiom,(
+    ! [X_28: hoare_1167836817_state > $o,Y_19: hoare_1167836817_state > $o] :
+      ( ord_le827224136tate_o @ ( semila179895820tate_o @ X_28 @ Y_19 ) @ X_28 ) )).
+
+thf(fact_627_inf__sup__ord_I2_J,axiom,(
+    ! [X_27: pname > $o,Y_18: pname > $o] :
+      ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_27 @ Y_18 ) @ Y_18 ) )).
+
+thf(fact_628_inf__sup__ord_I2_J,axiom,(
+    ! [X_27: hoare_1167836817_state > $o,Y_18: hoare_1167836817_state > $o] :
+      ( ord_le827224136tate_o @ ( semila179895820tate_o @ X_27 @ Y_18 ) @ Y_18 ) )).
+
+thf(fact_629_inf__le2,axiom,(
+    ! [X_26: pname > $o,Y_17: pname > $o] :
+      ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_26 @ Y_17 ) @ Y_17 ) )).
+
+thf(fact_630_inf__le2,axiom,(
+    ! [X_26: hoare_1167836817_state > $o,Y_17: hoare_1167836817_state > $o] :
+      ( ord_le827224136tate_o @ ( semila179895820tate_o @ X_26 @ Y_17 ) @ Y_17 ) )).
+
+thf(fact_631_le__iff__inf,axiom,(
+    ! [X_25: pname > $o,Y_16: pname > $o] :
+      ( ( ord_less_eq_pname_o @ X_25 @ Y_16 )
+    <=> ( ( semila1673364395name_o @ X_25 @ Y_16 )
+        = X_25 ) ) )).
+
+thf(fact_632_le__iff__inf,axiom,(
+    ! [X_25: hoare_1167836817_state > $o,Y_16: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ X_25 @ Y_16 )
+    <=> ( ( semila179895820tate_o @ X_25 @ Y_16 )
+        = X_25 ) ) )).
+
+thf(fact_633_le__inf__iff,axiom,(
+    ! [X_24: pname > $o,Y_15: pname > $o,Z_10: pname > $o] :
+      ( ( ord_less_eq_pname_o @ X_24 @ ( semila1673364395name_o @ Y_15 @ Z_10 ) )
+    <=> ( ( ord_less_eq_pname_o @ X_24 @ Y_15 )
+        & ( ord_less_eq_pname_o @ X_24 @ Z_10 ) ) ) )).
+
+thf(fact_634_le__inf__iff,axiom,(
+    ! [X_24: hoare_1167836817_state > $o,Y_15: hoare_1167836817_state > $o,Z_10: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ X_24 @ ( semila179895820tate_o @ Y_15 @ Z_10 ) )
+    <=> ( ( ord_le827224136tate_o @ X_24 @ Y_15 )
+        & ( ord_le827224136tate_o @ X_24 @ Z_10 ) ) ) )).
+
+thf(fact_635_le__infI1,axiom,(
+    ! [B_11: pname > $o,A_19: pname > $o,X_23: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_19 @ X_23 )
+     => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_19 @ B_11 ) @ X_23 ) ) )).
+
+thf(fact_636_le__infI1,axiom,(
+    ! [B_11: hoare_1167836817_state > $o,A_19: hoare_1167836817_state > $o,X_23: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_19 @ X_23 )
+     => ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_19 @ B_11 ) @ X_23 ) ) )).
+
+thf(fact_637_le__infI2,axiom,(
+    ! [A_18: pname > $o,B_10: pname > $o,X_22: pname > $o] :
+      ( ( ord_less_eq_pname_o @ B_10 @ X_22 )
+     => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_18 @ B_10 ) @ X_22 ) ) )).
+
+thf(fact_638_le__infI2,axiom,(
+    ! [A_18: hoare_1167836817_state > $o,B_10: hoare_1167836817_state > $o,X_22: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ B_10 @ X_22 )
+     => ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_18 @ B_10 ) @ X_22 ) ) )).
+
+thf(fact_639_inf__absorb1,axiom,(
+    ! [X_21: pname > $o,Y_14: pname > $o] :
+      ( ( ord_less_eq_pname_o @ X_21 @ Y_14 )
+     => ( ( semila1673364395name_o @ X_21 @ Y_14 )
+        = X_21 ) ) )).
+
+thf(fact_640_inf__absorb1,axiom,(
+    ! [X_21: hoare_1167836817_state > $o,Y_14: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ X_21 @ Y_14 )
+     => ( ( semila179895820tate_o @ X_21 @ Y_14 )
+        = X_21 ) ) )).
+
+thf(fact_641_inf__absorb2,axiom,(
+    ! [Y_13: pname > $o,X_20: pname > $o] :
+      ( ( ord_less_eq_pname_o @ Y_13 @ X_20 )
+     => ( ( semila1673364395name_o @ X_20 @ Y_13 )
+        = Y_13 ) ) )).
+
+thf(fact_642_inf__absorb2,axiom,(
+    ! [Y_13: hoare_1167836817_state > $o,X_20: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ Y_13 @ X_20 )
+     => ( ( semila179895820tate_o @ X_20 @ Y_13 )
+        = Y_13 ) ) )).
+
+thf(fact_643_le__infI,axiom,(
+    ! [B_9: pname > $o,X_19: pname > $o,A_17: pname > $o] :
+      ( ( ord_less_eq_pname_o @ X_19 @ A_17 )
+     => ( ( ord_less_eq_pname_o @ X_19 @ B_9 )
+       => ( ord_less_eq_pname_o @ X_19 @ ( semila1673364395name_o @ A_17 @ B_9 ) ) ) ) )).
+
+thf(fact_644_le__infI,axiom,(
+    ! [B_9: hoare_1167836817_state > $o,X_19: hoare_1167836817_state > $o,A_17: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ X_19 @ A_17 )
+     => ( ( ord_le827224136tate_o @ X_19 @ B_9 )
+       => ( ord_le827224136tate_o @ X_19 @ ( semila179895820tate_o @ A_17 @ B_9 ) ) ) ) )).
+
+thf(fact_645_inf__greatest,axiom,(
+    ! [Z_9: pname > $o,X_18: pname > $o,Y_12: pname > $o] :
+      ( ( ord_less_eq_pname_o @ X_18 @ Y_12 )
+     => ( ( ord_less_eq_pname_o @ X_18 @ Z_9 )
+       => ( ord_less_eq_pname_o @ X_18 @ ( semila1673364395name_o @ Y_12 @ Z_9 ) ) ) ) )).
+
+thf(fact_646_inf__greatest,axiom,(
+    ! [Z_9: hoare_1167836817_state > $o,X_18: hoare_1167836817_state > $o,Y_12: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ X_18 @ Y_12 )
+     => ( ( ord_le827224136tate_o @ X_18 @ Z_9 )
+       => ( ord_le827224136tate_o @ X_18 @ ( semila179895820tate_o @ Y_12 @ Z_9 ) ) ) ) )).
+
+thf(fact_647_inf__mono,axiom,(
+    ! [B_8: pname > $o,D: pname > $o,A_16: pname > $o,C_3: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_16 @ C_3 )
+     => ( ( ord_less_eq_pname_o @ B_8 @ D )
+       => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_16 @ B_8 ) @ ( semila1673364395name_o @ C_3 @ D ) ) ) ) )).
+
+thf(fact_648_inf__mono,axiom,(
+    ! [B_8: hoare_1167836817_state > $o,D: hoare_1167836817_state > $o,A_16: hoare_1167836817_state > $o,C_3: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_16 @ C_3 )
+     => ( ( ord_le827224136tate_o @ B_8 @ D )
+       => ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_16 @ B_8 ) @ ( semila179895820tate_o @ C_3 @ D ) ) ) ) )).
+
+thf(fact_649_le__infE,axiom,(
+    ! [X_17: pname > $o,A_15: pname > $o,B_7: pname > $o] :
+      ( ( ord_less_eq_pname_o @ X_17 @ ( semila1673364395name_o @ A_15 @ B_7 ) )
+     => ~ ( ( ord_less_eq_pname_o @ X_17 @ A_15 )
+         => ~ ( ord_less_eq_pname_o @ X_17 @ B_7 ) ) ) )).
+
+thf(fact_650_le__infE,axiom,(
+    ! [X_17: hoare_1167836817_state > $o,A_15: hoare_1167836817_state > $o,B_7: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ X_17 @ ( semila179895820tate_o @ A_15 @ B_7 ) )
+     => ~ ( ( ord_le827224136tate_o @ X_17 @ A_15 )
+         => ~ ( ord_le827224136tate_o @ X_17 @ B_7 ) ) ) )).
+
+thf(fact_651_inf__sup__absorb,axiom,(
+    ! [X_16: hoare_1167836817_state > $o,Y_11: hoare_1167836817_state > $o] :
+      ( ( semila179895820tate_o @ X_16 @ ( semila1172322802tate_o @ X_16 @ Y_11 ) )
+      = X_16 ) )).
+
+thf(fact_652_sup__inf__absorb,axiom,(
+    ! [X_15: hoare_1167836817_state > $o,Y_10: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ X_15 @ ( semila179895820tate_o @ X_15 @ Y_10 ) )
+      = X_15 ) )).
+
+thf(fact_653_inf__sup__distrib1,axiom,(
+    ! [X_14: hoare_1167836817_state > $o,Y_9: hoare_1167836817_state > $o,Z_8: hoare_1167836817_state > $o] :
+      ( ( semila179895820tate_o @ X_14 @ ( semila1172322802tate_o @ Y_9 @ Z_8 ) )
+      = ( semila1172322802tate_o @ ( semila179895820tate_o @ X_14 @ Y_9 ) @ ( semila179895820tate_o @ X_14 @ Z_8 ) ) ) )).
+
+thf(fact_654_sup__inf__distrib1,axiom,(
+    ! [X_13: hoare_1167836817_state > $o,Y_8: hoare_1167836817_state > $o,Z_7: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ X_13 @ ( semila179895820tate_o @ Y_8 @ Z_7 ) )
+      = ( semila179895820tate_o @ ( semila1172322802tate_o @ X_13 @ Y_8 ) @ ( semila1172322802tate_o @ X_13 @ Z_7 ) ) ) )).
+
+thf(fact_655_inf__sup__distrib2,axiom,(
+    ! [Y_7: hoare_1167836817_state > $o,Z_6: hoare_1167836817_state > $o,X_12: hoare_1167836817_state > $o] :
+      ( ( semila179895820tate_o @ ( semila1172322802tate_o @ Y_7 @ Z_6 ) @ X_12 )
+      = ( semila1172322802tate_o @ ( semila179895820tate_o @ Y_7 @ X_12 ) @ ( semila179895820tate_o @ Z_6 @ X_12 ) ) ) )).
+
+thf(fact_656_sup__inf__distrib2,axiom,(
+    ! [Y_6: hoare_1167836817_state > $o,Z_5: hoare_1167836817_state > $o,X_11: hoare_1167836817_state > $o] :
+      ( ( semila1172322802tate_o @ ( semila179895820tate_o @ Y_6 @ Z_5 ) @ X_11 )
+      = ( semila179895820tate_o @ ( semila1172322802tate_o @ Y_6 @ X_11 ) @ ( semila1172322802tate_o @ Z_5 @ X_11 ) ) ) )).
+
+thf(fact_657_inf__bot__right,axiom,(
+    ! [X_10: pname > $o] :
+      ( ( semila1673364395name_o @ X_10 @ bot_bot_pname_o )
+      = bot_bot_pname_o ) )).
+
+thf(fact_658_inf__bot__right,axiom,(
+    ! [X_10: hoare_1167836817_state > $o] :
+      ( ( semila179895820tate_o @ X_10 @ bot_bo70021908tate_o )
+      = bot_bo70021908tate_o ) )).
+
+thf(fact_659_inf__bot__left,axiom,(
+    ! [X_9: pname > $o] :
+      ( ( semila1673364395name_o @ bot_bot_pname_o @ X_9 )
+      = bot_bot_pname_o ) )).
+
+thf(fact_660_inf__bot__left,axiom,(
+    ! [X_9: hoare_1167836817_state > $o] :
+      ( ( semila179895820tate_o @ bot_bo70021908tate_o @ X_9 )
+      = bot_bo70021908tate_o ) )).
+
+thf(fact_661_distrib__sup__le,axiom,(
+    ! [X_8: pname > $o,Y_5: pname > $o,Z_4: pname > $o] :
+      ( ord_less_eq_pname_o @ ( semila1780557381name_o @ X_8 @ ( semila1673364395name_o @ Y_5 @ Z_4 ) ) @ ( semila1673364395name_o @ ( semila1780557381name_o @ X_8 @ Y_5 ) @ ( semila1780557381name_o @ X_8 @ Z_4 ) ) ) )).
+
+thf(fact_662_distrib__sup__le,axiom,(
+    ! [X_8: hoare_1167836817_state > $o,Y_5: hoare_1167836817_state > $o,Z_4: hoare_1167836817_state > $o] :
+      ( ord_le827224136tate_o @ ( semila1172322802tate_o @ X_8 @ ( semila179895820tate_o @ Y_5 @ Z_4 ) ) @ ( semila179895820tate_o @ ( semila1172322802tate_o @ X_8 @ Y_5 ) @ ( semila1172322802tate_o @ X_8 @ Z_4 ) ) ) )).
+
+thf(fact_663_distrib__inf__le,axiom,(
+    ! [X_7: pname > $o,Y_4: pname > $o,Z_3: pname > $o] :
+      ( ord_less_eq_pname_o @ ( semila1780557381name_o @ ( semila1673364395name_o @ X_7 @ Y_4 ) @ ( semila1673364395name_o @ X_7 @ Z_3 ) ) @ ( semila1673364395name_o @ X_7 @ ( semila1780557381name_o @ Y_4 @ Z_3 ) ) ) )).
+
+thf(fact_664_distrib__inf__le,axiom,(
+    ! [X_7: hoare_1167836817_state > $o,Y_4: hoare_1167836817_state > $o,Z_3: hoare_1167836817_state > $o] :
+      ( ord_le827224136tate_o @ ( semila1172322802tate_o @ ( semila179895820tate_o @ X_7 @ Y_4 ) @ ( semila179895820tate_o @ X_7 @ Z_3 ) ) @ ( semila179895820tate_o @ X_7 @ ( semila1172322802tate_o @ Y_4 @ Z_3 ) ) ) )).
+
+thf(fact_665_image__Int__subset,axiom,(
+    ! [F_6: pname > hoare_1167836817_state,A_14: pname > $o,B_6: pname > $o] :
+      ( ord_le827224136tate_o @ ( image_575578384_state @ F_6 @ ( semila1673364395name_o @ A_14 @ B_6 ) ) @ ( semila179895820tate_o @ ( image_575578384_state @ F_6 @ A_14 ) @ ( image_575578384_state @ F_6 @ B_6 ) ) ) )).
+
+thf(fact_666_Un__Int__assoc__eq,axiom,(
+    ! [A_13: pname > $o,B_5: pname > $o,C_2: pname > $o] :
+      ( ( ( semila1780557381name_o @ ( semila1673364395name_o @ A_13 @ B_5 ) @ C_2 )
+        = ( semila1673364395name_o @ A_13 @ ( semila1780557381name_o @ B_5 @ C_2 ) ) )
+    <=> ( ord_less_eq_pname_o @ C_2 @ A_13 ) ) )).
+
+thf(fact_667_Un__Int__assoc__eq,axiom,(
+    ! [A_13: hoare_1167836817_state > $o,B_5: hoare_1167836817_state > $o,C_2: hoare_1167836817_state > $o] :
+      ( ( ( semila1172322802tate_o @ ( semila179895820tate_o @ A_13 @ B_5 ) @ C_2 )
+        = ( semila179895820tate_o @ A_13 @ ( semila1172322802tate_o @ B_5 @ C_2 ) ) )
+    <=> ( ord_le827224136tate_o @ C_2 @ A_13 ) ) )).
+
+thf(fact_668_if__image__distrib,axiom,(
+    ! [P_3: pname > $o,F_5: pname > hoare_1167836817_state,G_1: pname > hoare_1167836817_state,S: pname > $o] :
+      ( ( image_575578384_state
+        @ ^ [X_5: pname] :
+            ( if_Hoa833675553_state @ ( P_3 @ X_5 ) @ ( F_5 @ X_5 ) @ ( G_1 @ X_5 ) )
+        @ S )
+      = ( semila1172322802tate_o @ ( image_575578384_state @ F_5 @ ( semila1673364395name_o @ S @ ( collect_pname @ P_3 ) ) )
+        @ ( image_575578384_state @ G_1
+          @ ( semila1673364395name_o @ S
+            @ ( collect_pname
+              @ ^ [X_5: pname] :
+                  ( (~) @ ( P_3 @ X_5 ) ) ) ) ) ) ) )).
+
+thf(fact_669_dom__if,axiom,(
+    ! [P_2: pname > $o,F_4: pname > option_com,G: pname > option_com] :
+      ( ( dom_pname_com
+        @ ^ [X_5: pname] :
+            ( if_option_com @ ( P_2 @ X_5 ) @ ( F_4 @ X_5 ) @ ( G @ X_5 ) ) )
+      = ( semila1780557381name_o @ ( semila1673364395name_o @ ( dom_pname_com @ F_4 ) @ ( collect_pname @ P_2 ) )
+        @ ( semila1673364395name_o @ ( dom_pname_com @ G )
+          @ ( collect_pname
+            @ ^ [X_5: pname] :
+                ( (~) @ ( P_2 @ X_5 ) ) ) ) ) ) )).
+
+thf(fact_670_Int__Collect__mono,axiom,(
+    ! [Q: pname > $o,P_1: pname > $o,A_12: pname > $o,B_4: pname > $o] :
+      ( ( ord_less_eq_pname_o @ A_12 @ B_4 )
+     => ( ! [X_5: pname] :
+            ( ( member_pname @ X_5 @ A_12 )
+           => ( ( P_1 @ X_5 )
+             => ( Q @ X_5 ) ) )
+       => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_12 @ ( collect_pname @ P_1 ) ) @ ( semila1673364395name_o @ B_4 @ ( collect_pname @ Q ) ) ) ) ) )).
+
+thf(fact_671_Int__Collect__mono,axiom,(
+    ! [Q: hoare_1167836817_state > $o,P_1: hoare_1167836817_state > $o,A_12: hoare_1167836817_state > $o,B_4: hoare_1167836817_state > $o] :
+      ( ( ord_le827224136tate_o @ A_12 @ B_4 )
+     => ( ! [X_5: hoare_1167836817_state] :
+            ( ( member2058392318_state @ X_5 @ A_12 )
+           => ( ( P_1 @ X_5 )
+             => ( Q @ X_5 ) ) )
+       => ( ord_le827224136tate_o @ ( semila179895820tate_o @ A_12 @ ( collec1027672124_state @ P_1 ) ) @ ( semila179895820tate_o @ B_4 @ ( collec1027672124_state @ Q ) ) ) ) ) )).
+
+thf(fact_672_Int__Collect__mono,axiom,(
+    ! [Q: ( pname > $o ) > $o,P_1: ( pname > $o ) > $o,A_12: ( pname > $o ) > $o,B_4: ( pname > $o ) > $o] :
+      ( ( ord_le1205211808me_o_o @ A_12 @ B_4 )
+     => ( ! [X_5: pname > $o] :
+            ( ( member_pname_o @ X_5 @ A_12 )
+           => ( ( P_1 @ X_5 )
+             => ( Q @ X_5 ) ) )
+       => ( ord_le1205211808me_o_o @ ( semila2013987940me_o_o @ A_12 @ ( collect_pname_o @ P_1 ) ) @ ( semila2013987940me_o_o @ B_4 @ ( collect_pname_o @ Q ) ) ) ) ) )).
+
+thf(fact_673_Int__Collect__mono,axiom,(
+    ! [Q: ( hoare_1167836817_state > $o ) > $o,P_1: ( hoare_1167836817_state > $o ) > $o,A_12: ( hoare_1167836817_state > $o ) > $o,B_4: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( ord_le741939125te_o_o @ A_12 @ B_4 )
+     => ( ! [X_5: hoare_1167836817_state > $o] :
+            ( ( member864234961tate_o @ X_5 @ A_12 )
+           => ( ( P_1 @ X_5 )
+             => ( Q @ X_5 ) ) )
+       => ( ord_le741939125te_o_o @ ( semila1758709489te_o_o @ A_12 @ ( collec269976083tate_o @ P_1 ) ) @ ( semila1758709489te_o_o @ B_4 @ ( collec269976083tate_o @ Q ) ) ) ) ) )).
+
+thf(fact_674_distrib__imp1,axiom,(
+    ! [X_6: hoare_1167836817_state > $o,Y_3: hoare_1167836817_state > $o,Z_2: hoare_1167836817_state > $o] :
+      ( ! [X_5: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o,Z_1: hoare_1167836817_state > $o] :
+          ( ( semila179895820tate_o @ X_5 @ ( semila1172322802tate_o @ Y_2 @ Z_1 ) )
+          = ( semila1172322802tate_o @ ( semila179895820tate_o @ X_5 @ Y_2 ) @ ( semila179895820tate_o @ X_5 @ Z_1 ) ) )
+     => ( ( semila1172322802tate_o @ X_6 @ ( semila179895820tate_o @ Y_3 @ Z_2 ) )
+        = ( semila179895820tate_o @ ( semila1172322802tate_o @ X_6 @ Y_3 ) @ ( semila1172322802tate_o @ X_6 @ Z_2 ) ) ) ) )).
+
+thf(fact_675_distrib__imp2,axiom,(
+    ! [X_4: hoare_1167836817_state > $o,Y_1: hoare_1167836817_state > $o,Z: hoare_1167836817_state > $o] :
+      ( ! [X_5: hoare_1167836817_state > $o,Y_2: hoare_1167836817_state > $o,Z_1: hoare_1167836817_state > $o] :
+          ( ( semila1172322802tate_o @ X_5 @ ( semila179895820tate_o @ Y_2 @ Z_1 ) )
+          = ( semila179895820tate_o @ ( semila1172322802tate_o @ X_5 @ Y_2 ) @ ( semila1172322802tate_o @ X_5 @ Z_1 ) ) )
+     => ( ( semila179895820tate_o @ X_4 @ ( semila1172322802tate_o @ Y_1 @ Z ) )
+        = ( semila1172322802tate_o @ ( semila179895820tate_o @ X_4 @ Y_1 ) @ ( semila179895820tate_o @ X_4 @ Z ) ) ) ) )).
+
+thf(fact_676_folding__one_Oremove,axiom,(
+    ! [X_3: pname,A_11: pname > $o,F_3: pname > pname > pname,F_2: ( pname > $o ) > pname] :
+      ( ( finite1282449217_pname @ F_3 @ F_2 )
+     => ( ( finite_finite_pname @ A_11 )
+       => ( ( member_pname @ X_3 @ A_11 )
+         => ( ( ( ( minus_minus_pname_o @ A_11 @ ( insert_pname @ X_3 @ bot_bot_pname_o ) )
+                = bot_bot_pname_o )
+             => ( ( F_2 @ A_11 )
+                = X_3 ) )
+            & ( ( ( minus_minus_pname_o @ A_11 @ ( insert_pname @ X_3 @ bot_bot_pname_o ) )
+               != bot_bot_pname_o )
+             => ( ( F_2 @ A_11 )
+                = ( F_3 @ X_3 @ ( F_2 @ ( minus_minus_pname_o @ A_11 @ ( insert_pname @ X_3 @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ) )).
+
+thf(fact_677_folding__one_Oremove,axiom,(
+    ! [X_3: hoare_1167836817_state,A_11: hoare_1167836817_state > $o,F_3: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F_2: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
+      ( ( finite1074406356_state @ F_3 @ F_2 )
+     => ( ( finite1084549118_state @ A_11 )
+       => ( ( member2058392318_state @ X_3 @ A_11 )
+         => ( ( ( ( minus_2107060239tate_o @ A_11 @ ( insert2134838167_state @ X_3 @ bot_bo70021908tate_o ) )
+                = bot_bo70021908tate_o )
+             => ( ( F_2 @ A_11 )
+                = X_3 ) )
+            & ( ( ( minus_2107060239tate_o @ A_11 @ ( insert2134838167_state @ X_3 @ bot_bo70021908tate_o ) )
+               != bot_bo70021908tate_o )
+             => ( ( F_2 @ A_11 )
+                = ( F_3 @ X_3 @ ( F_2 @ ( minus_2107060239tate_o @ A_11 @ ( insert2134838167_state @ X_3 @ bot_bo70021908tate_o ) ) ) ) ) ) ) ) ) ) )).
+
+thf(fact_678_folding__one_Oremove,axiom,(
+    ! [X_3: pname > $o,A_11: ( pname > $o ) > $o,F_3: ( pname > $o ) > ( pname > $o ) > pname > $o,F_2: ( ( pname > $o ) > $o ) > pname > $o] :
+      ( ( finite349908348name_o @ F_3 @ F_2 )
+     => ( ( finite297249702name_o @ A_11 )
+       => ( ( member_pname_o @ X_3 @ A_11 )
+         => ( ( ( ( minus_1480864103me_o_o @ A_11 @ ( insert_pname_o @ X_3 @ bot_bot_pname_o_o ) )
+                = bot_bot_pname_o_o )
+             => ( ( F_2 @ A_11 )
+                = X_3 ) )
+            & ( ( ( minus_1480864103me_o_o @ A_11 @ ( insert_pname_o @ X_3 @ bot_bot_pname_o_o ) )
+               != bot_bot_pname_o_o )
+             => ( ( F_2 @ A_11 )
+                = ( F_3 @ X_3 @ ( F_2 @ ( minus_1480864103me_o_o @ A_11 @ ( insert_pname_o @ X_3 @ bot_bot_pname_o_o ) ) ) ) ) ) ) ) ) ) )).
+
+thf(fact_679_folding__one_Oremove,axiom,(
+    ! [X_3: hoare_1167836817_state > $o,A_11: ( hoare_1167836817_state > $o ) > $o,F_3: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F_2: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
+      ( ( finite979047547tate_o @ F_3 @ F_2 )
+     => ( ( finite1380128977tate_o @ A_11 )
+       => ( ( member864234961tate_o @ X_3 @ A_11 )
+         => ( ( ( ( minus_1708687022te_o_o @ A_11 @ ( insert999278200tate_o @ X_3 @ bot_bo691907561te_o_o ) )
+                = bot_bo691907561te_o_o )
+             => ( ( F_2 @ A_11 )
+                = X_3 ) )
+            & ( ( ( minus_1708687022te_o_o @ A_11 @ ( insert999278200tate_o @ X_3 @ bot_bo691907561te_o_o ) )
+               != bot_bo691907561te_o_o )
+             => ( ( F_2 @ A_11 )
+                = ( F_3 @ X_3 @ ( F_2 @ ( minus_1708687022te_o_o @ A_11 @ ( insert999278200tate_o @ X_3 @ bot_bo691907561te_o_o ) ) ) ) ) ) ) ) ) ) )).
+
+thf(fact_680_folding__one_Oinsert__remove,axiom,(
+    ! [X_2: pname,A_10: pname > $o,F_1: pname > pname > pname,F: ( pname > $o ) > pname] :
+      ( ( finite1282449217_pname @ F_1 @ F )
+     => ( ( finite_finite_pname @ A_10 )
+       => ( ( ( ( minus_minus_pname_o @ A_10 @ ( insert_pname @ X_2 @ bot_bot_pname_o ) )
+              = bot_bot_pname_o )
+           => ( ( F @ ( insert_pname @ X_2 @ A_10 ) )
+              = X_2 ) )
+          & ( ( ( minus_minus_pname_o @ A_10 @ ( insert_pname @ X_2 @ bot_bot_pname_o ) )
+             != bot_bot_pname_o )
+           => ( ( F @ ( insert_pname @ X_2 @ A_10 ) )
+              = ( F_1 @ X_2 @ ( F @ ( minus_minus_pname_o @ A_10 @ ( insert_pname @ X_2 @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) )).
+
+thf(fact_681_folding__one_Oinsert__remove,axiom,(
+    ! [X_2: hoare_1167836817_state,A_10: hoare_1167836817_state > $o,F_1: hoare_1167836817_state > hoare_1167836817_state > hoare_1167836817_state,F: ( hoare_1167836817_state > $o ) > hoare_1167836817_state] :
+      ( ( finite1074406356_state @ F_1 @ F )
+     => ( ( finite1084549118_state @ A_10 )
+       => ( ( ( ( minus_2107060239tate_o @ A_10 @ ( insert2134838167_state @ X_2 @ bot_bo70021908tate_o ) )
+              = bot_bo70021908tate_o )
+           => ( ( F @ ( insert2134838167_state @ X_2 @ A_10 ) )
+              = X_2 ) )
+          & ( ( ( minus_2107060239tate_o @ A_10 @ ( insert2134838167_state @ X_2 @ bot_bo70021908tate_o ) )
+             != bot_bo70021908tate_o )
+           => ( ( F @ ( insert2134838167_state @ X_2 @ A_10 ) )
+              = ( F_1 @ X_2 @ ( F @ ( minus_2107060239tate_o @ A_10 @ ( insert2134838167_state @ X_2 @ bot_bo70021908tate_o ) ) ) ) ) ) ) ) ) )).
+
+thf(fact_682_folding__one_Oinsert__remove,axiom,(
+    ! [X_2: pname > $o,A_10: ( pname > $o ) > $o,F_1: ( pname > $o ) > ( pname > $o ) > pname > $o,F: ( ( pname > $o ) > $o ) > pname > $o] :
+      ( ( finite349908348name_o @ F_1 @ F )
+     => ( ( finite297249702name_o @ A_10 )
+       => ( ( ( ( minus_1480864103me_o_o @ A_10 @ ( insert_pname_o @ X_2 @ bot_bot_pname_o_o ) )
+              = bot_bot_pname_o_o )
+           => ( ( F @ ( insert_pname_o @ X_2 @ A_10 ) )
+              = X_2 ) )
+          & ( ( ( minus_1480864103me_o_o @ A_10 @ ( insert_pname_o @ X_2 @ bot_bot_pname_o_o ) )
+             != bot_bot_pname_o_o )
+           => ( ( F @ ( insert_pname_o @ X_2 @ A_10 ) )
+              = ( F_1 @ X_2 @ ( F @ ( minus_1480864103me_o_o @ A_10 @ ( insert_pname_o @ X_2 @ bot_bot_pname_o_o ) ) ) ) ) ) ) ) ) )).
+
+thf(fact_683_folding__one_Oinsert__remove,axiom,(
+    ! [X_2: hoare_1167836817_state > $o,A_10: ( hoare_1167836817_state > $o ) > $o,F_1: ( hoare_1167836817_state > $o ) > ( hoare_1167836817_state > $o ) > hoare_1167836817_state > $o,F: ( ( hoare_1167836817_state > $o ) > $o ) > hoare_1167836817_state > $o] :
+      ( ( finite979047547tate_o @ F_1 @ F )
+     => ( ( finite1380128977tate_o @ A_10 )
+       => ( ( ( ( minus_1708687022te_o_o @ A_10 @ ( insert999278200tate_o @ X_2 @ bot_bo691907561te_o_o ) )
+              = bot_bo691907561te_o_o )
+           => ( ( F @ ( insert999278200tate_o @ X_2 @ A_10 ) )
+              = X_2 ) )
+          & ( ( ( minus_1708687022te_o_o @ A_10 @ ( insert999278200tate_o @ X_2 @ bot_bo691907561te_o_o ) )
+             != bot_bo691907561te_o_o )
+           => ( ( F @ ( insert999278200tate_o @ X_2 @ A_10 ) )
+              = ( F_1 @ X_2 @ ( F @ ( minus_1708687022te_o_o @ A_10 @ ( insert999278200tate_o @ X_2 @ bot_bo691907561te_o_o ) ) ) ) ) ) ) ) ) )).
+
+thf(fact_684_DiffI,axiom,(
+    ! [B_3: pname > $o,C_1: pname,A_9: pname > $o] :
+      ( ( member_pname @ C_1 @ A_9 )
+     => ( ~ ( member_pname @ C_1 @ B_3 )
+       => ( member_pname @ C_1 @ ( minus_minus_pname_o @ A_9 @ B_3 ) ) ) ) )).
+
+thf(fact_685_DiffI,axiom,(
+    ! [B_3: hoare_1167836817_state > $o,C_1: hoare_1167836817_state,A_9: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ C_1 @ A_9 )
+     => ( ~ ( member2058392318_state @ C_1 @ B_3 )
+       => ( member2058392318_state @ C_1 @ ( minus_2107060239tate_o @ A_9 @ B_3 ) ) ) ) )).
+
+thf(fact_686_DiffE,axiom,(
+    ! [C: pname,A_8: pname > $o,B_2: pname > $o] :
+      ( ( member_pname @ C @ ( minus_minus_pname_o @ A_8 @ B_2 ) )
+     => ~ ( ( member_pname @ C @ A_8 )
+         => ( member_pname @ C @ B_2 ) ) ) )).
+
+thf(fact_687_DiffE,axiom,(
+    ! [C: hoare_1167836817_state,A_8: hoare_1167836817_state > $o,B_2: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ C @ ( minus_2107060239tate_o @ A_8 @ B_2 ) )
+     => ~ ( ( member2058392318_state @ C @ A_8 )
+         => ( member2058392318_state @ C @ B_2 ) ) ) )).
+
+thf(fact_688_finite__Diff,axiom,(
+    ! [B_1: ( pname > $o ) > $o,A_7: ( pname > $o ) > $o] :
+      ( ( finite297249702name_o @ A_7 )
+     => ( finite297249702name_o @ ( minus_1480864103me_o_o @ A_7 @ B_1 ) ) ) )).
+
+thf(fact_689_finite__Diff,axiom,(
+    ! [B_1: ( hoare_1167836817_state > $o ) > $o,A_7: ( hoare_1167836817_state > $o ) > $o] :
+      ( ( finite1380128977tate_o @ A_7 )
+     => ( finite1380128977tate_o @ ( minus_1708687022te_o_o @ A_7 @ B_1 ) ) ) )).
+
+thf(fact_690_finite__Diff,axiom,(
+    ! [B_1: pname > $o,A_7: pname > $o] :
+      ( ( finite_finite_pname @ A_7 )
+     => ( finite_finite_pname @ ( minus_minus_pname_o @ A_7 @ B_1 ) ) ) )).
+
+thf(fact_691_finite__Diff,axiom,(
+    ! [B_1: hoare_1167836817_state > $o,A_7: hoare_1167836817_state > $o] :
+      ( ( finite1084549118_state @ A_7 )
+     => ( finite1084549118_state @ ( minus_2107060239tate_o @ A_7 @ B_1 ) ) ) )).
+
+thf(fact_692_insert__Diff,axiom,(
+    ! [A_6: pname,A_5: pname > $o] :
+      ( ( member_pname @ A_6 @ A_5 )
+     => ( ( insert_pname @ A_6 @ ( minus_minus_pname_o @ A_5 @ ( insert_pname @ A_6 @ bot_bot_pname_o ) ) )
+        = A_5 ) ) )).
+
+thf(fact_693_insert__Diff,axiom,(
+    ! [A_6: hoare_1167836817_state,A_5: hoare_1167836817_state > $o] :
+      ( ( member2058392318_state @ A_6 @ A_5 )
+     => ( ( insert2134838167_state @ A_6 @ ( minus_2107060239tate_o @ A_5 @ ( insert2134838167_state @ A_6 @ bot_bo70021908tate_o ) ) )
+        = A_5 ) ) )).
+
+thf(fact_694_Diff__insert__absorb,axiom,(
+    ! [X_1: pname,A_4: pname > $o] :
+      ( ~ ( member_pname @ X_1 @ A_4 )
+     => ( ( minus_minus_pname_o @ ( insert_pname @ X_1 @ A_4 ) @ ( insert_pname @ X_1 @ bot_bot_pname_o ) )
+        = A_4 ) ) )).
+
+thf(fact_695_Diff__insert__absorb,axiom,(
+    ! [X_1: hoare_1167836817_state,A_4: hoare_1167836817_state > $o] :
+      ( ~ ( member2058392318_state @ X_1 @ A_4 )
+     => ( ( minus_2107060239tate_o @ ( insert2134838167_state @ X_1 @ A_4 ) @ ( insert2134838167_state @ X_1 @ bot_bo70021908tate_o ) )
+        = A_4 ) ) )).
+
+thf(fact_696_insert__Diff__single,axiom,(
+    ! [A_3: pname,A_2: pname > $o] :
+      ( ( insert_pname @ A_3 @ ( minus_minus_pname_o @ A_2 @ ( insert_pname @ A_3 @ bot_bot_pname_o ) ) )
+      = ( insert_pname @ A_3 @ A_2 ) ) )).
+
+thf(fact_697_insert__Diff__single,axiom,(
+    ! [A_3: hoare_1167836817_state,A_2: hoare_1167836817_state > $o] :
+      ( ( insert2134838167_state @ A_3 @ ( minus_2107060239tate_o @ A_2 @ ( insert2134838167_state @ A_3 @ bot_bo70021908tate_o ) ) )
+      = ( insert2134838167_state @ A_3 @ A_2 ) ) )).
+
+thf(fact_698_Diff__insert2,axiom,(
+    ! [A_1: hoare_1167836817_state > $o,A: hoare_1167836817_state,B: hoare_1167836817_state > $o] :
+      ( ( minus_2107060239tate_o @ A_1 @ ( insert2134838167_state @ A @ B ) )
+      = ( minus_2107060239tate_o @ ( minus_2107060239tate_o @ A_1 @ ( insert2134838167_state @ A @ bot_bo70021908tate_o ) ) @ B ) ) )).
+
+%----Helper facts (16)
+thf(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,(
+    ! [X: pname,Y: pname] :
+      ( ~ ( fequal_pname @ X @ Y )
+      | ( X = Y ) ) )).
+
+thf(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,(
+    ! [X: pname,Y: pname] :
+      ( ( X != Y )
+      | ( fequal_pname @ X @ Y ) ) )).
+
+thf(help_fequal_1_1_fequal_000tc__Com__Ostate_T,axiom,(
+    ! [X: state,Y: state] :
+      ( ~ ( fequal_state @ X @ Y )
+      | ( X = Y ) ) )).
+
+thf(help_fequal_2_1_fequal_000tc__Com__Ostate_T,axiom,(
+    ! [X: state,Y: state] :
+      ( ( X != Y )
+      | ( fequal_state @ X @ Y ) ) )).
+
+thf(help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,(
+    ! [X: pname > $o,Y: pname > $o] :
+      ( ~ ( fequal_pname_o @ X @ Y )
+      | ( X = Y ) ) )).
+
+thf(help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,(
+    ! [X: pname > $o,Y: pname > $o] :
+      ( ( X != Y )
+      | ( fequal_pname_o @ X @ Y ) ) )).
+
+thf(help_If_1_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,(
+    ! [X: option_com,Y: option_com] :
+      ( ( if_option_com @ $true @ X @ Y )
+      = X ) )).
+
+thf(help_If_2_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,(
+    ! [X: option_com,Y: option_com] :
+      ( ( if_option_com @ $false @ X @ Y )
+      = Y ) )).
+
+thf(help_If_3_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,(
+    ! [P: $o] :
+      ( ( P = $true )
+      | ( P = $false ) ) )).
+
+thf(help_If_1_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate,axiom,(
+    ! [X: hoare_1167836817_state,Y: hoare_1167836817_state] :
+      ( ( if_Hoa833675553_state @ $true @ X @ Y )
+      = X ) )).
+
+thf(help_If_2_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate,axiom,(
+    ! [X: hoare_1167836817_state,Y: hoare_1167836817_state] :
+      ( ( if_Hoa833675553_state @ $false @ X @ Y )
+      = Y ) )).
+
+thf(help_If_3_1_If_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com__Ostate,axiom,(
+    ! [P: $o] :
+      ( ( P = $true )
+      | ( P = $false ) ) )).
+
+thf(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com,axiom,(
+    ! [X: hoare_1167836817_state,Y: hoare_1167836817_state] :
+      ( ~ ( fequal1831255762_state @ X @ Y )
+      | ( X = Y ) ) )).
+
+thf(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____srushsumbx__Otriple_Itc__Com,axiom,(
+    ! [X: hoare_1167836817_state,Y: hoare_1167836817_state] :
+      ( ( X != Y )
+      | ( fequal1831255762_state @ X @ Y ) ) )).
+
+thf(help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_It,axiom,(
+    ! [X: hoare_1167836817_state > $o,Y: hoare_1167836817_state > $o] :
+      ( ~ ( fequal1486222077tate_o @ X @ Y )
+      | ( X = Y ) ) )).
+
+thf(help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____srushsumbx__Otriple_It,axiom,(
+    ! [X: hoare_1167836817_state > $o,Y: hoare_1167836817_state > $o] :
+      ( ( X != Y )
+      | ( fequal1486222077tate_o @ X @ Y ) ) )).
+
+%----Conjectures (8)
+thf(conj_0,hypothesis,(
+    hoare_1201148605gleton )).
+
+thf(conj_1,hypothesis,(
+    wT_bodies )).
+
+thf(conj_2,hypothesis,
+    ( finite1084549118_state @ fa )).
+
+thf(conj_3,hypothesis,(
+    ~ ( member2058392318_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ) )).
+
+thf(conj_4,hypothesis,
+    ( ord_le827224136tate_o @ fa
+    @ ( image_575578384_state
+      @ ^ [Pn: pname] :
+          ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn ) ) )
+      @ ( dom_pname_com @ body ) ) )).
+
+thf(conj_5,hypothesis,
+    ( ( body @ pn )
+    = ( some_com @ y ) )).
+
+thf(conj_6,hypothesis,
+    ( hoare_123228589_state
+    @ ( image_575578384_state
+      @ ^ [Pn: pname] :
+          ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
+      @ ( dom_pname_com @ body ) )
+    @ fa )).
+
+thf(conj_7,conjecture,
+    ( hoare_123228589_state
+    @ ( image_575578384_state
+      @ ^ [Pn: pname] :
+          ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
+      @ ( dom_pname_com @ body ) )
+    @ ( insert2134838167_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo70021908tate_o ) )).
+
+%------------------------------------------------------------------------------