%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET711+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 : n020.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 02:47:56 PM UTC 2026
% Result : Theorem 0.82s 1.30s
% Output : CNFRefutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 100 ( 29 unt; 3 def)
% Number of atoms : 365 ( 66 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 373 ( 145 ~; 153 |; 51 &)
% ( 8 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 4 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 293 ( 0 sgn 277 !; 16 ?; 139 :)
% Comments :
%------------------------------------------------------------------------------
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(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/sandbox2/benchmark/Axioms/SET006+1.ax',injective) ).
fof(f19,axiom,
! [X0,X1,X2] :
( one_to_one(X0,X1,X2)
<=> ( surjective(X0,X1,X2)
& injective(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',one_to_one) ).
fof(f20,axiom,
! [X0,X1,X2,X3] :
( inverse_predicate(X0,X1,X2,X3)
<=> ! [X4,X5] :
( ( member(X5,X3)
& member(X4,X2) )
=> ( apply(X1,X4,X5)
<=> apply(X0,X5,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',inverse_predicate) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( inverse_predicate(X2,X0,X3,X4)
& inverse_predicate(X1,X0,X3,X4)
& one_to_one(X0,X3,X4)
& maps(X0,X3,X4) )
=> equal_maps(X1,X2,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII03a) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( inverse_predicate(X2,X0,X3,X4)
& inverse_predicate(X1,X0,X3,X4)
& one_to_one(X0,X3,X4)
& maps(X0,X3,X4) )
=> equal_maps(X1,X2,X4,X3) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,plain,
! [X0,X1,X2] :
( one_to_one(X0,X1,X2)
=> ( surjective(X0,X1,X2)
& injective(X0,X1,X2) ) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f34,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(unused_predicate_definition_removal,[],[f17]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( inverse_predicate(X0,X1,X2,X3)
=> ! [X4,X5] :
( ( member(X5,X3)
& member(X4,X2) )
=> ( apply(X1,X4,X5)
<=> apply(X0,X5,X4) ) ) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f37,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(f44,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,[],[f37]) ).
fof(f45,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,[],[f44]) ).
fof(f46,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,[],[f34]) ).
fof(f47,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,[],[f46]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ~ one_to_one(X0,X1,X2)
| ( surjective(X0,X1,X2)
& injective(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( ~ inverse_predicate(X0,X1,X2,X3)
| ! [X4,X5] :
( ~ member(X5,X3)
| ~ member(X4,X2)
| ( apply(X1,X4,X5)
<=> apply(X0,X5,X4) ) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( ~ inverse_predicate(X0,X1,X2,X3)
| ! [X4,X5] :
( ~ member(X5,X3)
| ~ member(X4,X2)
| ( apply(X1,X4,X5)
<=> apply(X0,X5,X4) ) ) ),
inference(flattening,[],[f50]) ).
fof(f54,plain,
? [X0,X1,X2,X3,X4] :
( inverse_predicate(X2,X0,X3,X4)
& inverse_predicate(X1,X0,X3,X4)
& one_to_one(X0,X3,X4)
& maps(X0,X3,X4)
& ~ equal_maps(X1,X2,X4,X3) ),
inference(ennf_transformation,[],[f30]) ).
fof(f55,plain,
? [X0,X1,X2,X3,X4] :
( inverse_predicate(X2,X0,X3,X4)
& inverse_predicate(X1,X0,X3,X4)
& one_to_one(X0,X3,X4)
& maps(X0,X3,X4)
& ~ equal_maps(X1,X2,X4,X3) ),
inference(flattening,[],[f54]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( ( member(sK7(X0,X1,X2,X3),X3)
& member(sK6(X0,X1,X2,X3),X3)
& member(sK5(X0,X1,X2,X3),X2)
& apply(X1,sK5(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
& apply(X0,sK5(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
& sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3) )
| equal_maps(X0,X1,X2,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X4,sK5(X0,X1,X2,X3)),skolemize(X5,sK6(X0,X1,X2,X3)),skolemize(X6,sK7(X0,X1,X2,X3))],[f45]) ).
fof(f81,plain,
! [X0,X1,X2,X3] :
( ~ inverse_predicate(X0,X1,X2,X3)
| ! [X4,X5] :
( ~ member(X5,X3)
| ~ member(X4,X2)
| ( ( ~ apply(X1,X4,X5)
| apply(X0,X5,X4) )
& ( ~ apply(X0,X5,X4)
| apply(X1,X4,X5) ) ) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f97,plain,
( inverse_predicate(sK15,sK13,sK16,sK17)
& inverse_predicate(sK14,sK13,sK16,sK17)
& one_to_one(sK13,sK16,sK17)
& maps(sK13,sK16,sK17)
& ~ equal_maps(sK14,sK15,sK17,sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15),skolemize(X3,sK16),skolemize(X4,sK17)],[f55]) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( member(sK7(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f132,plain,
! [X2,X3,X0,X1] :
( member(sK6(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f133,plain,
! [X2,X3,X0,X1] :
( member(sK5(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f134,plain,
! [X2,X3,X0,X1] :
( apply(X1,sK5(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f135,plain,
! [X2,X3,X0,X1] :
( apply(X0,sK5(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f136,plain,
! [X2,X3,X0,X1] :
( sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f137,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ injective(X0,X1,X2)
| ~ member(X5,X2)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X5)
| X3 = X4 ),
inference(cnf_transformation,[],[f47]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ one_to_one(X0,X1,X2)
| injective(X0,X1,X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f143,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ inverse_predicate(X0,X1,X2,X3)
| ~ member(X5,X3)
| ~ member(X4,X2)
| ~ apply(X0,X5,X4)
| apply(X1,X4,X5) ),
inference(cnf_transformation,[],[f81]) ).
fof(f160,plain,
inverse_predicate(sK15,sK13,sK16,sK17),
inference(cnf_transformation,[],[f97]) ).
fof(f161,plain,
inverse_predicate(sK14,sK13,sK16,sK17),
inference(cnf_transformation,[],[f97]) ).
fof(f162,plain,
one_to_one(sK13,sK16,sK17),
inference(cnf_transformation,[],[f97]) ).
fof(f164,plain,
~ equal_maps(sK14,sK15,sK17,sK16),
inference(cnf_transformation,[],[f97]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| ( sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3) ) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| apply(X0,sK5(X0,X1,X2,X3),sK6(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X1,X0,X2,X3)
| apply(X0,sK5(X1,X0,X2,X3),sK7(X1,X0,X2,X3)) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK5(X0,X1,X2,X3),X2) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_86,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,[],[f132]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK7(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_88,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,[],[f137]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| ~ one_to_one(X0,X1,X2) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( apply(X1,X5,X4)
| ~ member(X5,X2)
| ~ member(X4,X3)
| ~ apply(X0,X4,X5)
| ~ inverse_predicate(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_111,negated_conjecture,
~ equal_maps(sK14,sK15,sK17,sK16),
inference(cnf_transformation,[],[f164]) ).
tcf(c_113,negated_conjecture,
one_to_one(sK13,sK16,sK17),
inference(cnf_transformation,[],[f162]) ).
tcf(c_114,negated_conjecture,
inverse_predicate(sK14,sK13,sK16,sK17),
inference(cnf_transformation,[],[f161]) ).
tcf(c_115,negated_conjecture,
inverse_predicate(sK15,sK13,sK16,sK17),
inference(cnf_transformation,[],[f160]) ).
tcf(c_218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| ( sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3) ) ),
inference(prop_impl_just,[status(thm)],[c_82]) ).
tcf(c_224,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| ~ one_to_one(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_91]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK7(X0,X1,X2,X3),X3) ),
inference(prop_impl_just,[status(thm)],[c_87]) ).
tcf(c_268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK5(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_83]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| apply(X0,sK5(X0,X1,X2,X3),sK6(X0,X1,X2,X3)) ),
inference(renaming,[status(thm)],[c_268]) ).
tcf(c_270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK5(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_85]) ).
tcf(c_271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK5(X0,X1,X2,X3),X2) ),
inference(renaming,[status(thm)],[c_270]) ).
tcf(c_272,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK6(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_86]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK6(X0,X1,X2,X3),X3) ),
inference(renaming,[status(thm)],[c_272]) ).
tcf(c_292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X1,X0,X2,X3)
| apply(X0,sK5(X1,X0,X2,X3),sK7(X1,X0,X2,X3)) ),
inference(prop_impl_just,[status(thm)],[c_84]) ).
tcf(c_1095,plain,
! [X0: $i,X1: $i,X2: $i] :
( injective(X0,X1,X2)
| ( X2 != sK17 )
| ( X1 != sK16 )
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_224,c_113]) ).
tcf(c_1096,plain,
injective(sK13,sK16,sK17),
inference(unflattening,[status(thm)],[c_1095]) ).
tcf(c_1124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK7(X0,X1,X2,X3),X3)
| ( X3 != sK16 )
| ( X2 != sK17 )
| ( X1 != sK15 )
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_264,c_111]) ).
tcf(c_1125,plain,
member(sK7(sK14,sK15,sK17,sK16),sK16),
inference(unflattening,[status(thm)],[c_1124]) ).
tcf(c_1129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK6(X0,X1,X2,X3),X3)
| ( X3 != sK16 )
| ( X2 != sK17 )
| ( X1 != sK15 )
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_273,c_111]) ).
tcf(c_1130,plain,
member(sK6(sK14,sK15,sK17,sK16),sK16),
inference(unflattening,[status(thm)],[c_1129]) ).
tcf(c_1134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK5(X0,X1,X2,X3),X2)
| ( X3 != sK16 )
| ( X2 != sK17 )
| ( X1 != sK15 )
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_271,c_111]) ).
tcf(c_1135,plain,
member(sK5(sK14,sK15,sK17,sK16),sK17),
inference(unflattening,[status(thm)],[c_1134]) ).
tcf(c_1139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK5(X0,X1,X2,X3),sK6(X0,X1,X2,X3))
| ( X3 != sK16 )
| ( X2 != sK17 )
| ( X1 != sK15 )
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_269,c_111]) ).
tcf(c_1140,plain,
apply(sK14,sK5(sK14,sK15,sK17,sK16),sK6(sK14,sK15,sK17,sK16)),
inference(unflattening,[status(thm)],[c_1139]) ).
tcf(c_1144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 != sK16 )
| ( X2 != sK17 )
| ( X1 != sK15 )
| ( X0 != sK14 )
| ( sK6(X0,X1,X2,X3) != sK7(X0,X1,X2,X3) ) ),
inference(resolution_lifted,[status(thm)],[c_218,c_111]) ).
tcf(c_1145,plain,
sK6(sK14,sK15,sK17,sK16) != sK7(sK14,sK15,sK17,sK16),
inference(unflattening,[status(thm)],[c_1144]) ).
tcf(c_1149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK5(X1,X0,X2,X3),sK7(X1,X0,X2,X3))
| ( X3 != sK16 )
| ( X2 != sK17 )
| ( X1 != sK14 )
| ( X0 != sK15 ) ),
inference(resolution_lifted,[status(thm)],[c_292,c_111]) ).
tcf(c_1150,plain,
apply(sK15,sK5(sK14,sK15,sK17,sK16),sK7(sK14,sK15,sK17,sK16)),
inference(unflattening,[status(thm)],[c_1149]) ).
tcf(c_1160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X3 = X5 )
| ~ member(X5,X1)
| ~ member(X4,X2)
| ~ member(X3,X1)
| ~ apply(X0,X5,X4)
| ~ apply(X0,X3,X4)
| ( X2 != sK17 )
| ( X1 != sK16 )
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_88,c_1096]) ).
tcf(c_1161,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ member(X2,sK16)
| ~ member(X1,sK17)
| ~ member(X0,sK16)
| ~ apply(sK13,X2,X1)
| ~ apply(sK13,X0,X1) ),
inference(unflattening,[status(thm)],[c_1160]) ).
tcf(c_1316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( apply(X1,X5,X4)
| ~ member(X5,X2)
| ~ member(X4,X3)
| ~ apply(X0,X4,X5)
| ( X3 != sK17 )
| ( X2 != sK16 )
| ( X1 != sK13 )
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_93,c_114]) ).
tcf(c_1317,plain,
! [X0: $i,X1: $i] :
( apply(sK13,X1,X0)
| ~ member(X1,sK16)
| ~ member(X0,sK17)
| ~ apply(sK14,X0,X1) ),
inference(unflattening,[status(thm)],[c_1316]) ).
tcf(c_1346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( apply(X1,X5,X4)
| ~ member(X5,X2)
| ~ member(X4,X3)
| ~ apply(X0,X4,X5)
| ( X3 != sK17 )
| ( X2 != sK16 )
| ( X1 != sK13 )
| ( X0 != sK15 ) ),
inference(resolution_lifted,[status(thm)],[c_93,c_115]) ).
tcf(c_1347,plain,
! [X0: $i,X1: $i] :
( apply(sK13,X1,X0)
| ~ member(X1,sK16)
| ~ member(X0,sK17)
| ~ apply(sK15,X0,X1) ),
inference(unflattening,[status(thm)],[c_1346]) ).
tcf(c_2271,definition,
iPr_def_10 = sK5(sK14,sK15,sK17,sK16),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2272,definition,
iPr_def_11 = sK7(sK14,sK15,sK17,sK16),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2273,definition,
iPr_def_12 = sK6(sK14,sK15,sK17,sK16),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2274,plain,
! [X0: $i,X1: $i] :
( apply(sK13,X1,X0)
| ~ member(X1,sK16)
| ~ member(X0,sK17)
| ~ apply(sK15,X0,X1) ),
inference(demodulation,[status(thm)],[c_1347]) ).
tcf(c_2276,plain,
! [X0: $i,X1: $i] :
( apply(sK13,X1,X0)
| ~ member(X1,sK16)
| ~ member(X0,sK17)
| ~ apply(sK14,X0,X1) ),
inference(demodulation,[status(thm)],[c_1317]) ).
tcf(c_2279,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ member(X2,sK16)
| ~ member(X1,sK17)
| ~ member(X0,sK16)
| ~ apply(sK13,X2,X1)
| ~ apply(sK13,X0,X1) ),
inference(demodulation,[status(thm)],[c_1161]) ).
tcf(c_2280,plain,
apply(sK15,iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_1150,c_2272,c_2271]) ).
tcf(c_2281,plain,
iPr_def_12 != iPr_def_11,
inference(demodulation,[status(thm)],[c_1145,c_2273]) ).
tcf(c_2282,plain,
apply(sK14,iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_1140]) ).
tcf(c_2283,plain,
member(iPr_def_10,sK17),
inference(demodulation,[status(thm)],[c_1135]) ).
tcf(c_2284,plain,
member(iPr_def_12,sK16),
inference(demodulation,[status(thm)],[c_1130]) ).
tcf(c_2285,plain,
member(iPr_def_11,sK16),
inference(demodulation,[status(thm)],[c_1125]) ).
tcf(c_3548,plain,
( apply(sK13,iPr_def_11,iPr_def_10)
| ~ member(iPr_def_11,sK16)
| ~ member(iPr_def_10,sK17) ),
inference(superposition,[status(thm)],[c_2280,c_2274]) ).
tcf(c_3549,plain,
apply(sK13,iPr_def_11,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_3548,c_2285,c_2283]) ).
tcf(c_3577,plain,
( apply(sK13,iPr_def_12,iPr_def_10)
| ~ member(iPr_def_12,sK16)
| ~ member(iPr_def_10,sK17) ),
inference(superposition,[status(thm)],[c_2282,c_2276]) ).
tcf(c_3578,plain,
apply(sK13,iPr_def_12,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_3577,c_2284,c_2283]) ).
tcf(c_3694,plain,
! [X0: $i] :
( ( X0 = iPr_def_12 )
| ~ member(iPr_def_12,sK16)
| ~ member(iPr_def_10,sK17)
| ~ member(X0,sK16)
| ~ apply(sK13,X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_3578,c_2279]) ).
tcf(c_3695,plain,
! [X0: $i] :
( ( X0 = iPr_def_12 )
| ~ member(X0,sK16)
| ~ apply(sK13,X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3694,c_2284,c_2283]) ).
tcf(c_3711,plain,
( ( iPr_def_11 = iPr_def_12 )
| ~ member(iPr_def_11,sK16) ),
inference(superposition,[status(thm)],[c_3549,c_3695]) ).
tcf(c_3713,plain,
iPr_def_11 = iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_3711,c_2285]) ).
tcf(c_3719,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_2281,c_3713]) ).
tcf(c_3722,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_3719]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET711+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 11:45:18 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 0.82/1.30 % SZS status Started for theBenchmark.p
% 0.82/1.30 % SZS status Theorem for theBenchmark.p
% 0.82/1.30
% 0.82/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.82/1.30
% 0.82/1.30 % ------ iProver source info
% 0.82/1.30
% 0.82/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 0.82/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.82/1.30 % git: non_committed_changes: false
% 0.82/1.30
% 0.82/1.30 % ------ Parsing...
% 0.82/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.82/1.30
% 0.82/1.30 % ------ 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: 5 0s sf_e pe_s pe_e %
% 0.82/1.30
% 0.82/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.82/1.30
% 0.82/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.82/1.30 % ------ Proving...
% 0.82/1.30 % ------ Problem Properties
% 0.82/1.30
% 0.82/1.30 %
% 0.82/1.30 % clauses 65
% 0.82/1.30 % conjectures 0
% 0.82/1.30 % EPR 14
% 0.82/1.30 % Horn 60
% 0.82/1.30 % unary 13
% 0.82/1.30 % binary 29
% 0.82/1.30 % lits 160
% 0.82/1.30 % lits eq 9
% 0.82/1.30 % fd_pure 0
% 0.82/1.30 % fd_pseudo 0
% 0.82/1.30 % fd_cond 0
% 0.82/1.30 % fd_pseudo_cond 4
% 0.82/1.30 % AC symbols 0
% 0.82/1.30
% 0.82/1.30 % ------ Schedule dynamic 5 is on
% 0.82/1.30
% 0.82/1.30 % ------ no conjectures: strip conj schedule
% 0.82/1.30
% 0.82/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.82/1.30
% 0.82/1.30
% 0.82/1.30 % ------
% 0.82/1.30 % Current options:
% 0.82/1.30 % ------
% 0.82/1.30
% 0.82/1.30
% 0.82/1.30 %
% 0.82/1.30
% 0.82/1.30 % ------ Proving...
% 0.82/1.30 %
% 0.82/1.30
% 0.82/1.30 % SZS status Theorem for theBenchmark.p
% 0.82/1.30
% 0.82/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.94/1.30
% 3.94/1.30
%------------------------------------------------------------------------------