%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET732+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 02:47:59 PM UTC 2026
% Result : Theorem 3.18s 0.98s
% Output : CNFRefutation 3.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 101 ( 10 unt; 0 def)
% Number of atoms : 394 ( 37 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 494 ( 201 ~; 203 |; 66 &)
% ( 11 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 275 ( 0 sgn 248 !; 27 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f17,axiom,
! [X0,X1,X2] :
( injective(X0,X1,X2)
<=> ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X5)
& apply(X0,X3,X5) )
=> X3 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',injective) ).
fof(f18,axiom,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',surjective) ).
fof(f19,axiom,
! [X0,X1,X2] :
( one_to_one(X0,X1,X2)
<=> ( surjective(X0,X1,X2)
& injective(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',one_to_one) ).
fof(f22,axiom,
! [X0,X1,X2] :
( member(X2,image2(X0,X1))
<=> ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',image2) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( injective(X0,X2,X3)
& ! [X5,X6] :
( ( member(X6,X4)
& member(X5,X2) )
=> ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) ) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) )
=> one_to_one(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII23) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( injective(X0,X2,X3)
& ! [X5,X6] :
( ( member(X6,X4)
& member(X5,X2) )
=> ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) ) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) )
=> one_to_one(X1,X2,X4) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( surjective(X0,X1,X2)
& injective(X0,X1,X2) )
=> one_to_one(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) )
=> surjective(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f18]) ).
fof(f35,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f36,plain,
? [X0,X1,X2,X3,X4] :
( injective(X0,X2,X3)
& ! [X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) ) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3)
& ~ one_to_one(X1,X2,X4) ),
inference(ennf_transformation,[],[f30]) ).
fof(f37,plain,
? [X0,X1,X2,X3,X4] :
( injective(X0,X2,X3)
& ! [X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) ) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3)
& ~ one_to_one(X1,X2,X4) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2)
| one_to_one(X0,X1,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2)
| one_to_one(X0,X1,X2) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( injective(X0,X1,X2)
<=> ! [X3,X4,X5] :
( ~ member(X5,X2)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X5)
| X3 = X4 ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f44,plain,
! [X0,X1,X2] :
( injective(X0,X1,X2)
<=> ! [X3,X4,X5] :
( ~ member(X5,X2)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X5)
| X3 = X4 ) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ? [X3] :
( member(X3,X2)
& ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) ) )
| surjective(X0,X1,X2) ),
inference(ennf_transformation,[],[f33]) ).
fof(f46,plain,
? [X0,X1,X2,X3,X4] :
( injective(X0,X2,X3)
& ! [X5,X6] :
( ~ member(X6,X4)
| ~ member(X5,X2)
| ( ( ~ apply(X1,X5,X6)
| apply(X0,X5,X6) )
& ( ~ apply(X0,X5,X6)
| apply(X1,X5,X6) ) ) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3)
& ~ one_to_one(X1,X2,X4) ),
inference(nnf_transformation,[],[f37]) ).
fof(f47,plain,
( injective(sK0,sK2,sK3)
& ! [X5,X6] :
( ~ member(X6,sK4)
| ~ member(X5,sK2)
| ( ( ~ apply(sK1,X5,X6)
| apply(sK0,X5,X6) )
& ( ~ apply(sK0,X5,X6)
| apply(sK1,X5,X6) ) ) )
& sK4 = image2(sK0,sK2)
& subset(sK4,sK3)
& maps(sK0,sK2,sK3)
& ~ one_to_one(sK1,sK2,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)],[f46]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( ~ injective(X0,X1,X2)
| ! [X3,X4,X5] :
( ~ member(X5,X2)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X5)
| X3 = X4 ) )
& ( ? [X3,X4,X5] :
( member(X5,X2)
& member(X4,X1)
& member(X3,X1)
& apply(X0,X4,X5)
& apply(X0,X3,X5)
& X3 != X4 )
| injective(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( ~ injective(X0,X1,X2)
| ! [X6,X7,X8] :
( ~ member(X8,X2)
| ~ member(X7,X1)
| ~ member(X6,X1)
| ~ apply(X0,X7,X8)
| ~ apply(X0,X6,X8)
| X6 = X7 ) )
& ( ? [X3,X4,X5] :
( member(X5,X2)
& member(X4,X1)
& member(X3,X1)
& apply(X0,X4,X5)
& apply(X0,X3,X5)
& X3 != X4 )
| injective(X0,X1,X2) ) ),
inference(rectify,[],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( ~ injective(X0,X1,X2)
| ! [X6,X7,X8] :
( ~ member(X8,X2)
| ~ member(X7,X1)
| ~ member(X6,X1)
| ~ apply(X0,X7,X8)
| ~ apply(X0,X6,X8)
| X6 = X7 ) )
& ( ( member(sK8(X0,X1,X2),X2)
& member(sK7(X0,X1,X2),X1)
& member(sK6(X0,X1,X2),X1)
& apply(X0,sK7(X0,X1,X2),sK8(X0,X1,X2))
& apply(X0,sK6(X0,X1,X2),sK8(X0,X1,X2))
& sK6(X0,X1,X2) != sK7(X0,X1,X2) )
| injective(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X3,sK6(X0,X1,X2)),skolemize(X4,sK7(X0,X1,X2)),skolemize(X5,sK8(X0,X1,X2))],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( ~ member(X2,image2(X0,X1))
| ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) ) )
& ( ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) )
| member(X2,image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( ~ member(X2,image2(X0,X1))
| ? [X4] :
( apply(X0,X4,X2)
& member(X4,X1) ) )
& ( ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) )
| member(X2,image2(X0,X1)) ) ),
inference(rectify,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( ~ member(X2,image2(X0,X1))
| ( apply(X0,sK9(X0,X1,X2),X2)
& member(sK9(X0,X1,X2),X1) ) )
& ( ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) )
| member(X2,image2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X4,sK9(X0,X1,X2))],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( member(sK10(X0,X1,X2),X2)
& ! [X4] :
( ~ apply(X0,X4,sK10(X0,X1,X2))
| ~ member(X4,X1) ) )
| surjective(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X3,sK10(X0,X1,X2))],[f45]) ).
fof(f56,plain,
injective(sK0,sK2,sK3),
inference(cnf_transformation,[],[f47]) ).
fof(f57,plain,
! [X6,X5] :
( ~ member(X6,sK4)
| ~ member(X5,sK2)
| ~ apply(sK1,X5,X6)
| apply(sK0,X5,X6) ),
inference(cnf_transformation,[],[f47]) ).
fof(f58,plain,
! [X6,X5] :
( ~ member(X6,sK4)
| ~ member(X5,sK2)
| ~ apply(sK0,X5,X6)
| apply(sK1,X5,X6) ),
inference(cnf_transformation,[],[f47]) ).
fof(f59,plain,
sK4 = image2(sK0,sK2),
inference(cnf_transformation,[],[f47]) ).
fof(f60,plain,
subset(sK4,sK3),
inference(cnf_transformation,[],[f47]) ).
fof(f62,plain,
~ one_to_one(sK1,sK2,sK4),
inference(cnf_transformation,[],[f47]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2)
| one_to_one(X0,X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
fof(f68,plain,
! [X2,X0,X1,X8,X6,X7] :
( ~ injective(X0,X1,X2)
| ~ member(X8,X2)
| ~ member(X7,X1)
| ~ member(X6,X1)
| ~ apply(X0,X7,X8)
| ~ apply(X0,X6,X8)
| X6 = X7 ),
inference(cnf_transformation,[],[f51]) ).
fof(f69,plain,
! [X2,X0,X1] :
( member(sK8(X0,X1,X2),X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f70,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f71,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1,X2),X1)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f72,plain,
! [X2,X0,X1] :
( apply(X0,sK7(X0,X1,X2),sK8(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f73,plain,
! [X2,X0,X1] :
( apply(X0,sK6(X0,X1,X2),sK8(X0,X1,X2))
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f74,plain,
! [X2,X0,X1] :
( sK6(X0,X1,X2) != sK7(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f75,plain,
! [X2,X0,X1] :
( ~ member(X2,image2(X0,X1))
| apply(X0,sK9(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f76,plain,
! [X2,X0,X1] :
( ~ member(X2,image2(X0,X1))
| member(sK9(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1)
| member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f78,plain,
! [X2,X0,X1] :
( member(sK10(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f55]) ).
fof(f79,plain,
! [X2,X0,X1,X4] :
( ~ apply(X0,X4,sK10(X0,X1,X2))
| ~ member(X4,X1)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_49,negated_conjecture,
~ one_to_one(sK1,sK2,sK4),
inference(cnf_transformation,[],[f62]) ).
tcf(c_51,negated_conjecture,
subset(sK4,sK3),
inference(cnf_transformation,[],[f60]) ).
tcf(c_52,negated_conjecture,
image2(sK0,sK2) = sK4,
inference(cnf_transformation,[],[f59]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i] :
( apply(sK1,X0,X1)
| ~ member(X1,sK4)
| ~ member(X0,sK2)
| ~ apply(sK0,X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i] :
( apply(sK0,X0,X1)
| ~ member(X1,sK4)
| ~ member(X0,sK2)
| ~ apply(sK1,X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_55,negated_conjecture,
injective(sK0,sK2,sK3),
inference(cnf_transformation,[],[f56]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( one_to_one(X0,X1,X2)
| ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| ( sK6(X0,X1,X2) != sK7(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| apply(X0,sK6(X0,X1,X2),sK8(X0,X1,X2)) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| apply(X0,sK7(X0,X1,X2),sK8(X0,X1,X2)) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| member(sK6(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| member(sK7(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| member(sK8(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X1 = X3 )
| ~ member(X3,X4)
| ~ member(X2,X5)
| ~ member(X1,X4)
| ~ injective(X0,X4,X5)
| ~ apply(X0,X3,X2)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X2,image2(X0,X3))
| ~ member(X1,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK9(X1,X2,X0),X2)
| ~ member(X0,image2(X1,X2)) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X1,sK9(X1,X2,X0),X0)
| ~ member(X0,image2(X1,X2)) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( surjective(X0,X2,X3)
| ~ member(X1,X2)
| ~ apply(X0,X1,sK10(X0,X2,X3)) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( surjective(X0,X1,X2)
| member(sK10(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ surjective(X0,X1,X2)
| ~ injective(X0,X1,X2)
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_60]) ).
tcf(c_342,plain,
( ~ surjective(sK1,sK2,sK4)
| ~ injective(sK1,sK2,sK4) ),
inference(unflattening,[status(thm)],[c_341]) ).
tcf(c_351,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ( X1 != sK3 )
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_56]) ).
tcf(c_352,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,sK4) ),
inference(unflattening,[status(thm)],[c_351]) ).
tcf(c_362,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK10(X0,X1,X2),X2)
| ~ injective(sK1,sK2,sK4)
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_72,c_342]) ).
tcf(c_363,plain,
( member(sK10(sK1,sK2,sK4),sK4)
| ~ injective(sK1,sK2,sK4) ),
inference(unflattening,[status(thm)],[c_362]) ).
tcf(c_370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ member(X3,X1)
| ~ injective(sK1,sK2,sK4)
| ~ apply(X0,X3,sK10(X0,X1,X2))
| ( X2 != sK4 )
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_71,c_342]) ).
tcf(c_371,plain,
! [X0: $i] :
( ~ member(X0,sK2)
| ~ injective(sK1,sK2,sK4)
| ~ apply(sK1,X0,sK10(sK1,sK2,sK4)) ),
inference(unflattening,[status(thm)],[c_370]) ).
tcf(c_1919,plain,
! [X0: $i,X1: $i] :
( apply(sK1,sK9(sK0,X0,X1),X1)
| ~ member(X1,sK4)
| ~ member(X1,image2(sK0,X0))
| ~ member(sK9(sK0,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_70,c_53]) ).
tcf(c_1920,plain,
! [X0: $i] :
( ~ injective(sK1,sK2,sK4)
| ~ member(sK10(sK1,sK2,sK4),image2(sK1,X0))
| ~ member(sK9(sK1,X0,sK10(sK1,sK2,sK4)),sK2) ),
inference(superposition,[status(thm)],[c_70,c_371]) ).
tcf(c_2081,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X1,image2(sK1,X2))
| ~ member(X1,sK4)
| ~ member(X1,image2(sK0,X0))
| ~ member(sK9(sK0,X0,X1),sK2)
| ~ member(sK9(sK0,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_1919,c_68]) ).
tcf(c_2115,plain,
( injective(sK1,sK2,sK4)
| member(sK6(sK1,sK2,sK4),sK2) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_2116,plain,
( injective(sK1,sK2,sK4)
| member(sK7(sK1,sK2,sK4),sK2) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_2117,plain,
( injective(sK1,sK2,sK4)
| member(sK8(sK1,sK2,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_2191,plain,
( injective(sK1,sK2,sK4)
| ( sK6(sK1,sK2,sK4) != sK7(sK1,sK2,sK4) ) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_2192,plain,
( injective(sK1,sK2,sK4)
| apply(sK1,sK6(sK1,sK2,sK4),sK8(sK1,sK2,sK4)) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_2193,plain,
( injective(sK1,sK2,sK4)
| apply(sK1,sK7(sK1,sK2,sK4),sK8(sK1,sK2,sK4)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_2242,plain,
! [X0: $i] :
( apply(sK0,sK6(sK1,sK2,sK4),X0)
| ~ member(X0,sK4)
| ~ member(sK6(sK1,sK2,sK4),sK2)
| ~ apply(sK1,sK6(sK1,sK2,sK4),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_2331,plain,
! [X0: $i] :
( apply(sK0,sK7(sK1,sK2,sK4),X0)
| ~ member(X0,sK4)
| ~ member(sK7(sK1,sK2,sK4),sK2)
| ~ apply(sK1,sK7(sK1,sK2,sK4),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_2478,plain,
( member(sK8(sK1,sK2,sK4),sK3)
| ~ member(sK8(sK1,sK2,sK4),sK4) ),
inference(instantiation,[status(thm)],[c_352]) ).
tcf(c_2563,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK6(sK1,sK2,sK4) = sK7(sK1,sK2,sK4) )
| ~ member(X1,X3)
| ~ injective(X0,X2,X3)
| ~ member(sK7(sK1,sK2,sK4),X2)
| ~ member(sK6(sK1,sK2,sK4),X2)
| ~ apply(X0,sK7(sK1,sK2,sK4),X1)
| ~ apply(X0,sK6(sK1,sK2,sK4),X1) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_3087,plain,
! [X0: $i,X1: $i] :
( member(X0,image2(sK1,X1))
| ~ member(X0,sK4)
| ~ member(X0,image2(sK0,sK2))
| ~ member(sK9(sK0,sK2,X0),X1) ),
inference(superposition,[status(thm)],[c_69,c_2081]) ).
tcf(c_3088,plain,
! [X0: $i,X1: $i] :
( member(X0,image2(sK1,X1))
| ~ member(X0,sK4)
| ~ member(sK9(sK0,sK2,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_3087,c_52]) ).
tcf(c_3099,plain,
! [X0: $i] :
( member(X0,image2(sK1,sK2))
| ~ member(X0,sK4)
| ~ member(X0,image2(sK0,sK2)) ),
inference(superposition,[status(thm)],[c_69,c_3088]) ).
tcf(c_3100,plain,
! [X0: $i] :
( member(X0,image2(sK1,sK2))
| ~ member(X0,sK4) ),
inference(light_normalisation,[status(thm)],[c_3099,c_52]) ).
tcf(c_3133,plain,
( ~ injective(sK1,sK2,sK4)
| ~ member(sK10(sK1,sK2,sK4),image2(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_69,c_1920]) ).
tcf(c_3140,plain,
( ~ injective(sK1,sK2,sK4)
| ~ member(sK10(sK1,sK2,sK4),sK4) ),
inference(superposition,[status(thm)],[c_3100,c_3133]) ).
tcf(c_3155,plain,
~ injective(sK1,sK2,sK4),
inference(global_subsumption_just,[status(thm)],[c_3140,c_363,c_3140]) ).
tcf(c_3768,plain,
( apply(sK0,sK7(sK1,sK2,sK4),sK8(sK1,sK2,sK4))
| ~ member(sK8(sK1,sK2,sK4),sK4)
| ~ member(sK7(sK1,sK2,sK4),sK2)
| ~ apply(sK1,sK7(sK1,sK2,sK4),sK8(sK1,sK2,sK4)) ),
inference(instantiation,[status(thm)],[c_2331]) ).
tcf(c_3770,plain,
( apply(sK0,sK6(sK1,sK2,sK4),sK8(sK1,sK2,sK4))
| ~ member(sK8(sK1,sK2,sK4),sK4)
| ~ member(sK6(sK1,sK2,sK4),sK2)
| ~ apply(sK1,sK6(sK1,sK2,sK4),sK8(sK1,sK2,sK4)) ),
inference(instantiation,[status(thm)],[c_2242]) ).
tcf(c_4234,plain,
! [X0: $i,X1: $i] :
( ( sK6(sK1,sK2,sK4) = sK7(sK1,sK2,sK4) )
| ~ injective(X0,X1,sK3)
| ~ member(sK8(sK1,sK2,sK4),sK3)
| ~ member(sK7(sK1,sK2,sK4),X1)
| ~ member(sK6(sK1,sK2,sK4),X1)
| ~ apply(X0,sK7(sK1,sK2,sK4),sK8(sK1,sK2,sK4))
| ~ apply(X0,sK6(sK1,sK2,sK4),sK8(sK1,sK2,sK4)) ),
inference(instantiation,[status(thm)],[c_2563]) ).
tcf(c_5573,plain,
! [X0: $i] :
( ( sK6(sK1,sK2,sK4) = sK7(sK1,sK2,sK4) )
| ~ injective(sK0,X0,sK3)
| ~ member(sK8(sK1,sK2,sK4),sK3)
| ~ member(sK7(sK1,sK2,sK4),X0)
| ~ member(sK6(sK1,sK2,sK4),X0)
| ~ apply(sK0,sK7(sK1,sK2,sK4),sK8(sK1,sK2,sK4))
| ~ apply(sK0,sK6(sK1,sK2,sK4),sK8(sK1,sK2,sK4)) ),
inference(instantiation,[status(thm)],[c_4234]) ).
tcf(c_5574,plain,
( ( sK6(sK1,sK2,sK4) = sK7(sK1,sK2,sK4) )
| ~ injective(sK0,sK2,sK3)
| ~ member(sK8(sK1,sK2,sK4),sK3)
| ~ member(sK7(sK1,sK2,sK4),sK2)
| ~ member(sK6(sK1,sK2,sK4),sK2)
| ~ apply(sK0,sK7(sK1,sK2,sK4),sK8(sK1,sK2,sK4))
| ~ apply(sK0,sK6(sK1,sK2,sK4),sK8(sK1,sK2,sK4)) ),
inference(instantiation,[status(thm)],[c_5573]) ).
tcf(c_5575,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5574,c_3768,c_3770,c_3155,c_2478,c_2193,c_2192,c_2191,c_2117,c_2116,c_2115,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET732+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Thu Sep 24 11:47:05 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.32 Running first-order theorem proving
% 0.02/0.32 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.32
% 0.07/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.32
% 0.07/0.32 % Detected problem language: tptp
% 0.07/0.33 % Proving...
% 3.18/0.98 % SZS status Started for theBenchmark.p
% 3.18/0.98 % SZS status Theorem for theBenchmark.p
% 3.18/0.98
% 3.18/0.98 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.18/0.98
% 3.18/0.98 % ------ iProver source info
% 3.18/0.98
% 3.18/0.98 % git: date: 2026-07-19 20:42:38 +0200
% 3.18/0.98 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.18/0.98 % git: non_committed_changes: false
% 3.18/0.98
% 3.18/0.98 % ------ Parsing...
% 3.18/0.98 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.18/0.98
% 3.18/0.98 % ------ 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 %
% 3.18/0.98
% 3.18/0.98 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.18/0.98
% 3.18/0.98 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.18/0.98 % ------ Proving...
% 3.18/0.98 % ------ Problem Properties
% 3.18/0.98
% 3.18/0.98 %
% 3.18/0.98 % clauses 20
% 3.18/0.98 % conjectures 4
% 3.18/0.98 % EPR 6
% 3.18/0.98 % Horn 15
% 3.18/0.98 % unary 2
% 3.18/0.98 % binary 12
% 3.18/0.98 % lits 53
% 3.18/0.98 % lits eq 4
% 3.18/0.98 % fd_pure 0
% 3.18/0.98 % fd_pseudo 0
% 3.18/0.98 % fd_cond 0
% 3.18/0.98 % fd_pseudo_cond 2
% 3.18/0.98 % AC symbols 0
% 3.18/0.98
% 3.18/0.98 % ------ Schedule dynamic 5 is on
% 3.18/0.98
% 3.18/0.98 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.18/0.98
% 3.18/0.98
% 3.18/0.98 % ------
% 3.18/0.98 % Current options:
% 3.18/0.98 % ------
% 3.18/0.98
% 3.18/0.98
% 3.18/0.98 %
% 3.18/0.98
% 3.18/0.98 % ------ Proving...
% 3.18/0.98 %
% 3.18/0.98
% 3.18/0.98 % SZS status Theorem for theBenchmark.p
% 3.18/0.98
% 3.18/0.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.18/0.98
% 3.18/0.98
%------------------------------------------------------------------------------