%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET720+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:47:57 PM UTC 2026
% Result : Theorem 3.56s 1.27s
% Output : CNFRefutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 73 ( 14 unt; 0 def)
% Number of atoms : 283 ( 58 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 342 ( 132 ~; 134 |; 52 &)
% ( 6 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 244 ( 0 sgn 227 !; 17 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3,X5,X6] :
( ( member(X6,X2)
& member(X5,X2)
& member(X3,X1) )
=> ( ( apply(X0,X3,X6)
& apply(X0,X3,X5) )
=> X5 = X6 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',maps) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( equal_maps(X0,X1,X2,X3)
<=> ! [X4,X5,X6] :
( ( member(X6,X3)
& member(X5,X3)
& member(X4,X2) )
=> ( ( apply(X1,X4,X6)
& apply(X0,X4,X5) )
=> X5 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',equal_maps) ).
fof(f21,axiom,
! [X0,X1,X2,X3,X4] :
( ( member(X4,X2)
& member(X3,X1) )
=> ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',inverse_function) ).
fof(f29,conjecture,
! [X0,X1,X2] :
( ( one_to_one(X0,X1,X2)
& maps(X0,X1,X2) )
=> equal_maps(inverse_function(inverse_function(X0,X1,X2),X2,X1),X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII11) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2] :
( ( one_to_one(X0,X1,X2)
& maps(X0,X1,X2) )
=> equal_maps(inverse_function(inverse_function(X0,X1,X2),X2,X1),X0,X1,X2) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X5,X6,X7] :
( ( member(X7,X2)
& member(X6,X2)
& member(X5,X1) )
=> ( ( apply(X0,X5,X7)
& apply(X0,X5,X6) )
=> X6 = X7 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f35,plain,
! [X0,X1,X2,X3] :
( ! [X4,X5,X6] :
( ( member(X6,X3)
& member(X5,X3)
& member(X4,X2) )
=> ( ( apply(X1,X4,X6)
& apply(X0,X4,X5) )
=> X5 = X6 ) )
=> equal_maps(X0,X1,X2,X3) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f36,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> ( ! [X5,X6,X7] :
( ( member(X7,X2)
& member(X6,X2)
& member(X5,X1) )
=> ( ( apply(X0,X5,X7)
& apply(X0,X5,X6) )
=> X6 = X7 ) )
& ! [X3] :
( member(X3,X1)
=> ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f31]) ).
fof(f37,plain,
? [X0,X1,X2] :
( one_to_one(X0,X1,X2)
& maps(X0,X1,X2)
& ~ equal_maps(inverse_function(inverse_function(X0,X1,X2),X2,X1),X0,X1,X2) ),
inference(ennf_transformation,[],[f30]) ).
fof(f38,plain,
? [X0,X1,X2] :
( one_to_one(X0,X1,X2)
& maps(X0,X1,X2)
& ~ equal_maps(inverse_function(inverse_function(X0,X1,X2),X2,X1),X0,X1,X2) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ maps(X0,X1,X2)
| ( ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 )
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ maps(X0,X1,X2)
| ( ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 )
& ! [X3] :
( ~ member(X3,X1)
| ? [X4] :
( apply(X0,X3,X4)
& member(X4,X2) ) ) ) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6] :
( member(X6,X3)
& member(X5,X3)
& member(X4,X2)
& apply(X1,X4,X6)
& apply(X0,X4,X5)
& X5 != X6 )
| equal_maps(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f35]) ).
fof(f42,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6] :
( member(X6,X3)
& member(X5,X3)
& member(X4,X2)
& apply(X1,X4,X6)
& apply(X0,X4,X5)
& X5 != X6 )
| equal_maps(X0,X1,X2,X3) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(X4,X2)
| ~ member(X3,X1)
| ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(X4,X2)
| ~ member(X3,X1)
| ( apply(X0,X3,X4)
<=> apply(inverse_function(X0,X1,X2),X4,X3) ) ),
inference(flattening,[],[f43]) ).
fof(f49,plain,
( one_to_one(sK0,sK1,sK2)
& maps(sK0,sK1,sK2)
& ~ equal_maps(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f38]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ maps(X0,X1,X2)
| ( ! [X5,X6,X7] :
( ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 )
& ! [X3] :
( ~ member(X3,X1)
| ( apply(X0,X3,sK3(X0,X2,X3))
& member(sK3(X0,X2,X3),X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X0,X2,X3))],[f40]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( ( member(sK6(X0,X1,X2,X3),X3)
& member(sK5(X0,X1,X2,X3),X3)
& member(sK4(X0,X1,X2,X3),X2)
& apply(X1,sK4(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
& apply(X0,sK4(X0,X1,X2,X3),sK5(X0,X1,X2,X3))
& sK5(X0,X1,X2,X3) != sK6(X0,X1,X2,X3) )
| equal_maps(X0,X1,X2,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X4,sK4(X0,X1,X2,X3)),skolemize(X5,sK5(X0,X1,X2,X3)),skolemize(X6,sK6(X0,X1,X2,X3))],[f42]) ).
fof(f52,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(X4,X2)
| ~ member(X3,X1)
| ( ( ~ apply(X0,X3,X4)
| apply(inverse_function(X0,X1,X2),X4,X3) )
& ( ~ apply(inverse_function(X0,X1,X2),X4,X3)
| apply(X0,X3,X4) ) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f55,plain,
maps(sK0,sK1,sK2),
inference(cnf_transformation,[],[f49]) ).
fof(f56,plain,
~ equal_maps(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),
inference(cnf_transformation,[],[f49]) ).
fof(f57,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ maps(X0,X1,X2)
| ~ member(X7,X2)
| ~ member(X6,X2)
| ~ member(X5,X1)
| ~ apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| X6 = X7 ),
inference(cnf_transformation,[],[f50]) ).
fof(f58,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK3(X0,X2,X3)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f59,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK3(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f50]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( member(sK6(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f51]) ).
fof(f61,plain,
! [X2,X3,X0,X1] :
( member(sK5(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f51]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( member(sK4(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f51]) ).
fof(f63,plain,
! [X2,X3,X0,X1] :
( apply(X1,sK4(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f51]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( apply(X0,sK4(X0,X1,X2,X3),sK5(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f51]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( sK5(X0,X1,X2,X3) != sK6(X0,X1,X2,X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f51]) ).
fof(f67,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(X4,X2)
| ~ member(X3,X1)
| ~ apply(inverse_function(X0,X1,X2),X4,X3)
| apply(X0,X3,X4) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_49,negated_conjecture,
~ equal_maps(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),
inference(cnf_transformation,[],[f56]) ).
tcf(c_50,negated_conjecture,
maps(sK0,sK1,sK2),
inference(cnf_transformation,[],[f55]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK3(X0,X2,X3),X2)
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK3(X0,X2,X3))
| ~ member(X3,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1)
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| ( sK5(X0,X1,X2,X3) != sK6(X0,X1,X2,X3) ) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| apply(X0,sK4(X0,X1,X2,X3),sK5(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X1,X0,X2,X3)
| apply(X0,sK4(X1,X0,X2,X3),sK6(X1,X0,X2,X3)) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK4(X0,X1,X2,X3),X2) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK5(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK6(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,X4,X3)
| ~ member(X4,X1)
| ~ member(X3,X2)
| ~ apply(inverse_function(X0,X1,X2),X3,X4) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK6(X0,X1,X2,X3),X3)
| ( X3 != sK2 )
| ( X2 != sK1 )
| ( X1 != sK0 )
| ( inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_60]) ).
tcf(c_332,plain,
member(sK6(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK2),
inference(unflattening,[status(thm)],[c_331]) ).
tcf(c_336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK5(X0,X1,X2,X3),X3)
| ( X3 != sK2 )
| ( X2 != sK1 )
| ( X1 != sK0 )
| ( inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_59]) ).
tcf(c_337,plain,
member(sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK2),
inference(unflattening,[status(thm)],[c_336]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK4(X0,X1,X2,X3),X2)
| ( X3 != sK2 )
| ( X2 != sK1 )
| ( X1 != sK0 )
| ( inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_58]) ).
tcf(c_342,plain,
member(sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK1),
inference(unflattening,[status(thm)],[c_341]) ).
tcf(c_346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK4(X0,X1,X2,X3),sK5(X0,X1,X2,X3))
| ( X3 != sK2 )
| ( X2 != sK1 )
| ( X1 != sK0 )
| ( inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_56]) ).
tcf(c_347,plain,
apply(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2)),
inference(unflattening,[status(thm)],[c_346]) ).
tcf(c_351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 != sK2 )
| ( X2 != sK1 )
| ( X1 != sK0 )
| ( sK5(X0,X1,X2,X3) != sK6(X0,X1,X2,X3) )
| ( inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_55]) ).
tcf(c_352,plain,
sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2) != sK6(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),
inference(unflattening,[status(thm)],[c_351]) ).
tcf(c_356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,sK4(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
| ( X3 != sK2 )
| ( X2 != sK1 )
| ( X1 != sK0 )
| ( inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_57]) ).
tcf(c_357,plain,
apply(sK0,sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK6(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2)),
inference(unflattening,[status(thm)],[c_356]) ).
tcf(c_394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1)
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_54]) ).
tcf(c_395,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK2)
| ~ member(X1,sK2)
| ~ member(X0,sK1)
| ~ apply(sK0,X0,X2)
| ~ apply(sK0,X0,X1) ),
inference(unflattening,[status(thm)],[c_394]) ).
tcf(c_414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK3(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_53]) ).
tcf(c_415,plain,
! [X0: $i] :
( apply(sK0,X0,sK3(sK0,sK2,X0))
| ~ member(X0,sK1) ),
inference(unflattening,[status(thm)],[c_414]) ).
tcf(c_423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK3(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_52]) ).
tcf(c_424,plain,
! [X0: $i] :
( member(sK3(sK0,sK2,X0),sK2)
| ~ member(X0,sK1) ),
inference(unflattening,[status(thm)],[c_423]) ).
tcf(c_903,plain,
! [X0: $i,X1: $i] :
( ( sK3(sK0,sK2,X0) = X1 )
| ~ member(X1,sK2)
| ~ member(X0,sK1)
| ~ apply(sK0,X0,X1)
| ~ member(sK3(sK0,sK2,X0),sK2) ),
inference(superposition,[status(thm)],[c_415,c_395]) ).
tcf(c_977,plain,
! [X0: $i,X1: $i] :
( ( sK3(sK0,sK2,X0) = X1 )
| ~ member(X1,sK2)
| ~ member(X0,sK1)
| ~ apply(sK0,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_903,c_424,c_903]) ).
tcf(c_989,plain,
( ( sK3(sK0,sK2,sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2)) = sK6(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2) )
| ~ member(sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK1)
| ~ member(sK6(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK2) ),
inference(superposition,[status(thm)],[c_357,c_977]) ).
tcf(c_994,plain,
sK3(sK0,sK2,sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2)) = sK6(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_989,c_342,c_332]) ).
tcf(c_1031,plain,
( apply(inverse_function(sK0,sK1,sK2),sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2))
| ~ member(sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK1)
| ~ member(sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK2) ),
inference(superposition,[status(thm)],[c_347,c_61]) ).
tcf(c_1032,plain,
apply(inverse_function(sK0,sK1,sK2),sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_1031,c_342,c_337]) ).
tcf(c_1074,plain,
( apply(sK0,sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2))
| ~ member(sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK1)
| ~ member(sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK2) ),
inference(superposition,[status(thm)],[c_1032,c_61]) ).
tcf(c_1075,plain,
apply(sK0,sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_1074,c_342,c_337]) ).
tcf(c_1076,plain,
( ( sK3(sK0,sK2,sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2)) = sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2) )
| ~ member(sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK1)
| ~ member(sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK2) ),
inference(superposition,[status(thm)],[c_1075,c_977]) ).
tcf(c_1079,plain,
( ( sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2) = sK6(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2) )
| ~ member(sK4(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK1)
| ~ member(sK5(inverse_function(inverse_function(sK0,sK1,sK2),sK2,sK1),sK0,sK1,sK2),sK2) ),
inference(light_normalisation,[status(thm)],[c_1076,c_994]) ).
tcf(c_1080,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1079,c_352,c_342,c_337]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET720+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.42 % Computer : n019.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Thu Sep 24 11:45:50 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.23/0.49 Running first-order theorem proving
% 0.23/0.49 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.50
% 0.23/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.50
% 0.23/0.50 % Detected problem language: tptp
% 0.23/0.51 % Proving...
% 3.56/1.27 % SZS status Started for theBenchmark.p
% 3.56/1.27 % SZS status Theorem for theBenchmark.p
% 3.56/1.27
% 3.56/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.56/1.27
% 3.56/1.27 % ------ iProver source info
% 3.56/1.27
% 3.56/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.56/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.56/1.27 % git: non_committed_changes: false
% 3.56/1.27
% 3.56/1.27 % ------ Parsing...
% 3.56/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.56/1.27
% 3.56/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 3.56/1.27
% 3.56/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.56/1.27
% 3.56/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.56/1.27 % ------ Proving...
% 3.56/1.27 % ------ Problem Properties
% 3.56/1.27
% 3.56/1.27 %
% 3.56/1.27 % clauses 14
% 3.56/1.27 % conjectures 0
% 3.56/1.27 % EPR 2
% 3.56/1.27 % Horn 14
% 3.56/1.27 % unary 6
% 3.56/1.27 % binary 4
% 3.56/1.27 % lits 34
% 3.56/1.27 % lits eq 3
% 3.56/1.27 % fd_pure 0
% 3.56/1.27 % fd_pseudo 0
% 3.56/1.27 % fd_cond 0
% 3.56/1.27 % fd_pseudo_cond 2
% 3.56/1.27 % AC symbols 0
% 3.56/1.27
% 3.56/1.27 % ------ Schedule dynamic 5 is on
% 3.56/1.27
% 3.56/1.27 % ------ no conjectures: strip conj schedule
% 3.56/1.27
% 3.56/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.56/1.27
% 3.56/1.27
% 3.56/1.27 % ------
% 3.56/1.27 % Current options:
% 3.56/1.27 % ------
% 3.56/1.27
% 3.56/1.27
% 3.56/1.27 %
% 3.56/1.27
% 3.56/1.27 % ------ Proving...
% 3.56/1.27 %
% 3.56/1.27
% 3.56/1.27 % SZS status Theorem for theBenchmark.p
% 3.56/1.27
% 3.56/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.56/1.27
%------------------------------------------------------------------------------