%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET756+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 02:48:12 PM UTC 2026
% Result : Theorem 65.20s 12.38s
% Output : CNFRefutation 65.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 77 ( 4 unt; 0 def)
% Number of atoms : 221 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 247 ( 103 ~; 103 |; 32 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 151 ( 0 sgn 136 !; 15 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f5,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',union) ).
fof(f24,axiom,
! [X0,X1,X2] :
( member(X2,inverse_image2(X0,X1))
<=> ? [X3] :
( apply(X0,X2,X3)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',inverse_image2) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( subset(X4,X2)
& subset(X3,X2)
& maps(X0,X1,X2) )
=> equal_set(inverse_image2(X0,union(X3,X4)),union(inverse_image2(X0,X3),inverse_image2(X0,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIIa06) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( subset(X4,X2)
& subset(X3,X2)
& maps(X0,X1,X2) )
=> equal_set(inverse_image2(X0,union(X3,X4)),union(inverse_image2(X0,X3),inverse_image2(X0,X4))) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f34,plain,
? [X0,X1,X2,X3,X4] :
( subset(X4,X2)
& subset(X3,X2)
& maps(X0,X1,X2)
& ~ equal_set(inverse_image2(X0,union(X3,X4)),union(inverse_image2(X0,X3),inverse_image2(X0,X4))) ),
inference(ennf_transformation,[],[f30]) ).
fof(f35,plain,
? [X0,X1,X2,X3,X4] :
( subset(X4,X2)
& subset(X3,X2)
& maps(X0,X1,X2)
& ~ equal_set(inverse_image2(X0,union(X3,X4)),union(inverse_image2(X0,X3),inverse_image2(X0,X4))) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f37,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f38,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(flattening,[],[f37]) ).
fof(f41,plain,
( subset(sK4,sK2)
& subset(sK3,sK2)
& maps(sK0,sK1,sK2)
& ~ equal_set(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f35]) ).
fof(f42,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f43,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK5(X0,X1),X0)
& ~ member(sK5(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) )
& ( ( ~ member(X0,X2)
& ~ member(X0,X1) )
| member(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) )
& ( ( ~ member(X0,X2)
& ~ member(X0,X1) )
| member(X0,union(X1,X2)) ) ),
inference(flattening,[],[f45]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( ~ member(X2,inverse_image2(X0,X1))
| ? [X3] :
( apply(X0,X2,X3)
& member(X3,X1) ) )
& ( ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) )
| member(X2,inverse_image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( ~ member(X2,inverse_image2(X0,X1))
| ? [X4] :
( apply(X0,X2,X4)
& member(X4,X1) ) )
& ( ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) )
| member(X2,inverse_image2(X0,X1)) ) ),
inference(rectify,[],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( ~ member(X2,inverse_image2(X0,X1))
| ( apply(X0,X2,sK7(X0,X1,X2))
& member(sK7(X0,X1,X2),X1) ) )
& ( ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) )
| member(X2,inverse_image2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X4,sK7(X0,X1,X2))],[f49]) ).
fof(f54,plain,
~ equal_set(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),
inference(cnf_transformation,[],[f41]) ).
fof(f56,plain,
! [X0,X1] :
( member(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f57,plain,
! [X0,X1] :
( ~ member(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f58,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f59,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f60,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f61,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ~ member(X2,inverse_image2(X0,X1))
| apply(X0,X2,sK7(X0,X1,X2)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f66,plain,
! [X2,X0,X1] :
( ~ member(X2,inverse_image2(X0,X1))
| member(sK7(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1)
| member(X2,inverse_image2(X0,X1)) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_49,negated_conjecture,
~ equal_set(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),
inference(cnf_transformation,[],[f54]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,inverse_image2(X0,X3))
| ~ member(X2,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK7(X1,X2,X0),X2)
| ~ member(X0,inverse_image2(X1,X2)) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X1,X0,sK7(X1,X2,X0))
| ~ member(X0,inverse_image2(X1,X2)) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| ( inverse_image2(sK0,union(sK3,sK4)) != X1 )
| ( union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_59]) ).
tcf(c_242,plain,
( ~ subset(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))
| ~ subset(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))) ),
inference(unflattening,[status(thm)],[c_241]) ).
tcf(c_953,plain,
( subset(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))
| ~ member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,union(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_967,plain,
( subset(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))
| member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_991,plain,
( subset(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))
| member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,union(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_992,plain,
( subset(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))
| ~ member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_1028,plain,
( apply(sK0,sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))))
| ~ member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,union(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_1029,plain,
( member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),union(sK3,sK4))
| ~ member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,union(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_1104,plain,
( member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,sK4))
| member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,sK3))
| ~ member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_1310,plain,
( member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),sK4)
| member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),sK3)
| ~ member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_1809,plain,
! [X0: $i,X1: $i] :
( member(X1,inverse_image2(X0,sK3))
| ~ member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),sK3)
| ~ apply(X0,X1,sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))))) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_2175,plain,
( apply(sK0,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))))
| ~ member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,sK3)) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_2176,plain,
( member(sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),sK3)
| ~ member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,sK3)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_3268,plain,
! [X0: $i,X1: $i] :
( member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),union(X1,X0))
| ~ member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),X0) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_3269,plain,
! [X0: $i,X1: $i] :
( member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),union(X0,X1))
| ~ member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),X0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_3774,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X1,inverse_image2(X0,X2))
| ~ member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),X2)
| ~ apply(X0,X1,sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))))) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_6169,plain,
( apply(sK0,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),sK7(sK0,sK4,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))))
| ~ member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,sK4)) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_6170,plain,
( member(sK7(sK0,sK4,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),sK4)
| ~ member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,sK4)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_9654,plain,
! [X0: $i,X1: $i] :
( member(X1,inverse_image2(X0,sK4))
| ~ member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),sK4)
| ~ apply(X0,X1,sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))))) ),
inference(instantiation,[status(thm)],[c_3774]) ).
tcf(c_14577,plain,
( member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))
| ~ member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,sK4)) ),
inference(instantiation,[status(thm)],[c_3268]) ).
tcf(c_15797,plain,
( member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))
| ~ member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,sK3)) ),
inference(instantiation,[status(thm)],[c_3269]) ).
tcf(c_16980,plain,
( member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,sK3))
| ~ member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),sK3)
| ~ apply(sK0,sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))))) ),
inference(instantiation,[status(thm)],[c_1809]) ).
tcf(c_37266,plain,
( member(sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),inverse_image2(sK0,sK4))
| ~ member(sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),sK4)
| ~ apply(sK0,sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),sK7(sK0,union(sK3,sK4),sK5(inverse_image2(sK0,union(sK3,sK4)),union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))))) ),
inference(instantiation,[status(thm)],[c_9654]) ).
tcf(c_74582,plain,
! [X0: $i] :
( member(sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),union(sK3,X0))
| ~ member(sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),sK3) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_75008,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X1,inverse_image2(X0,X2))
| ~ member(sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),X2)
| ~ apply(X0,X1,sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))))) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_80489,plain,
! [X0: $i] :
( member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,X0))
| ~ member(sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),X0)
| ~ apply(sK0,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))))) ),
inference(instantiation,[status(thm)],[c_75008]) ).
tcf(c_89838,plain,
( member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,union(sK3,sK4)))
| ~ member(sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),union(sK3,sK4))
| ~ apply(sK0,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))))) ),
inference(instantiation,[status(thm)],[c_80489]) ).
tcf(c_111664,plain,
( member(sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),union(sK3,sK4))
| ~ member(sK7(sK0,sK3,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),sK3) ),
inference(instantiation,[status(thm)],[c_74582]) ).
tcf(c_115129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK7(X0,X1,X2),union(X3,X1))
| ~ member(sK7(X0,X1,X2),X1) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_119734,plain,
! [X0: $i,X1: $i] :
( member(sK7(X0,sK4,X1),union(sK3,sK4))
| ~ member(sK7(X0,sK4,X1),sK4) ),
inference(instantiation,[status(thm)],[c_115129]) ).
tcf(c_130420,plain,
~ subset(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),
inference(global_subsumption_just,[status(thm)],[c_242,c_242,c_992,c_991,c_1029,c_1028,c_1310,c_14577,c_15797,c_16980,c_37266]) ).
tcf(c_163619,plain,
( member(sK7(sK0,sK4,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),union(sK3,sK4))
| ~ member(sK7(sK0,sK4,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),sK4) ),
inference(instantiation,[status(thm)],[c_119734]) ).
tcf(c_174067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X1,inverse_image2(X0,X3))
| ~ member(sK7(X0,X2,X1),X3)
| ~ apply(X0,X1,sK7(X0,X2,X1)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_175600,plain,
! [X0: $i] :
( member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,union(sK3,sK4)))
| ~ member(sK7(sK0,X0,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),union(sK3,sK4))
| ~ apply(sK0,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),sK7(sK0,X0,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))))) ),
inference(instantiation,[status(thm)],[c_174067]) ).
tcf(c_187987,plain,
( member(sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),inverse_image2(sK0,union(sK3,sK4)))
| ~ member(sK7(sK0,sK4,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4)))),union(sK3,sK4))
| ~ apply(sK0,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))),sK7(sK0,sK4,sK5(union(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,union(sK3,sK4))))) ),
inference(instantiation,[status(thm)],[c_175600]) ).
tcf(c_189005,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_187987,c_163619,c_130420,c_111664,c_89838,c_6169,c_6170,c_2175,c_2176,c_1104,c_967,c_953]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET756+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 11:52:22 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.02/0.40 Running first-order theorem proving
% 0.02/0.40 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
% 0.02/0.41
% 0.02/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.02/0.41
% 0.02/0.41 % Detected problem language: tptp
% 0.02/0.42 % Proving...
% 65.20/12.38 % SZS status Started for theBenchmark.p
% 65.20/12.38 % SZS status Theorem for theBenchmark.p
% 65.20/12.38
% 65.20/12.38 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 65.20/12.38
% 65.20/12.38 % ------ iProver source info
% 65.20/12.38
% 65.20/12.38 % git: date: 2026-07-19 20:42:38 +0200
% 65.20/12.38 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 65.20/12.38 % git: non_committed_changes: false
% 65.20/12.38
% 65.20/12.38 % ------ Parsing...
% 65.20/12.38 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 65.20/12.38
% 65.20/12.38 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 65.20/12.38
% 65.20/12.38 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 65.20/12.38
% 65.20/12.38 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 65.20/12.38 % ------ Proving...
% 65.20/12.38 % ------ Problem Properties
% 65.20/12.38
% 65.20/12.38 %
% 65.20/12.38 % clauses 15
% 65.20/12.38 % conjectures 2
% 65.20/12.38 % EPR 4
% 65.20/12.38 % Horn 13
% 65.20/12.38 % unary 2
% 65.20/12.38 % binary 9
% 65.20/12.38 % lits 35
% 65.20/12.38 % lits eq 1
% 65.20/12.38 % fd_pure 0
% 65.20/12.38 % fd_pseudo 0
% 65.20/12.38 % fd_cond 0
% 65.20/12.38 % fd_pseudo_cond 1
% 65.20/12.38 % AC symbols 0
% 65.20/12.38
% 65.20/12.38 % ------ Schedule dynamic 5 is on
% 65.20/12.38
% 65.20/12.38 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 65.20/12.38
% 65.20/12.38
% 65.20/12.38 % ------
% 65.20/12.38 % Current options:
% 65.20/12.38 % ------
% 65.20/12.38
% 65.20/12.38
% 65.20/12.38 %
% 65.20/12.38
% 65.20/12.38 % ------ Proving...
% 65.20/12.38 % Proof_search_loop: time out after: 7775 full_loop iterations
% 65.20/12.38
% 65.20/12.38 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 65.20/12.38
% 65.20/12.38
% 65.20/12.38 % ------
% 65.20/12.38 % Current options:
% 65.20/12.38 % ------
% 65.20/12.38
% 65.20/12.38
% 65.20/12.38 %
% 65.20/12.38
% 65.20/12.38 % ------ Proving...
% 65.20/12.38 %
% 65.20/12.38
% 65.20/12.38 % SZS status Theorem for theBenchmark.p
% 65.20/12.38
% 65.20/12.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 65.20/12.38
% 65.20/12.38
%------------------------------------------------------------------------------