%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET708+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 : n026.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 02:47:50 PM UTC 2026
% Result : Theorem 4.09s 1.29s
% Output : CNFRefutation 4.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 7
% Syntax : Number of formulae : 154 ( 36 unt; 3 def)
% Number of atoms : 701 ( 133 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 807 ( 346 ~; 354 |; 79 &)
% ( 8 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 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 : 10 ( 8 usr; 4 prp; 0-6 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-5 aty)
% Number of variables : 500 ( 0 sgn 469 !; 31 ?; 266 :)
% 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/sandbox/benchmark/Axioms/SET006+1.ax',maps) ).
fof(f13,axiom,
! [X0,X1,X2,X3,X4,X5] :
( compose_predicate(X0,X1,X2,X3,X4,X5)
<=> ! [X6,X7] :
( ( member(X7,X5)
& member(X6,X3) )
=> ( apply(X0,X6,X7)
<=> ? [X8] :
( apply(X1,X8,X7)
& apply(X2,X6,X8)
& member(X8,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',compose_predicate) ).
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/sandbox/benchmark/Axioms/SET006+1.ax',equal_maps) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( compose_predicate(X3,X1,X0,X4,X5,X6)
& compose_predicate(X2,X1,X0,X4,X5,X6)
& maps(X1,X5,X6)
& maps(X0,X4,X5) )
=> equal_maps(X2,X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII01a) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6] :
( ( compose_predicate(X3,X1,X0,X4,X5,X6)
& compose_predicate(X2,X1,X0,X4,X5,X6)
& maps(X1,X5,X6)
& maps(X0,X4,X5) )
=> equal_maps(X2,X3,X4,X6) ),
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(f32,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(f33,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(f34,plain,
! [X0,X1,X2,X3,X4,X5] :
( compose_predicate(X0,X1,X2,X3,X4,X5)
=> ! [X6,X7] :
( ( member(X7,X5)
& member(X6,X3) )
=> ( apply(X0,X6,X7)
<=> ? [X8] :
( apply(X1,X8,X7)
& apply(X2,X6,X8)
& member(X8,X4) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f37,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,[],[f32]) ).
fof(f38,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,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ compose_predicate(X0,X1,X2,X3,X4,X5)
| ! [X6,X7] :
( ~ member(X7,X5)
| ~ member(X6,X3)
| ( apply(X0,X6,X7)
<=> ? [X8] :
( apply(X1,X8,X7)
& apply(X2,X6,X8)
& member(X8,X4) ) ) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f40,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ compose_predicate(X0,X1,X2,X3,X4,X5)
| ! [X6,X7] :
( ~ member(X7,X5)
| ~ member(X6,X3)
| ( apply(X0,X6,X7)
<=> ? [X8] :
( apply(X1,X8,X7)
& apply(X2,X6,X8)
& member(X8,X4) ) ) ) ),
inference(flattening,[],[f39]) ).
fof(f43,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,[],[f33]) ).
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(flattening,[],[f43]) ).
fof(f47,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( compose_predicate(X3,X1,X0,X4,X5,X6)
& compose_predicate(X2,X1,X0,X4,X5,X6)
& maps(X1,X5,X6)
& maps(X0,X4,X5)
& ~ equal_maps(X2,X3,X4,X6) ),
inference(ennf_transformation,[],[f30]) ).
fof(f48,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( compose_predicate(X3,X1,X0,X4,X5,X6)
& compose_predicate(X2,X1,X0,X4,X5,X6)
& maps(X1,X5,X6)
& maps(X0,X4,X5)
& ~ equal_maps(X2,X3,X4,X6) ),
inference(flattening,[],[f47]) ).
fof(f68,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))],[f38]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ compose_predicate(X0,X1,X2,X3,X4,X5)
| ! [X6,X7] :
( ~ member(X7,X5)
| ~ member(X6,X3)
| ( ( ~ apply(X0,X6,X7)
| ? [X8] :
( apply(X1,X8,X7)
& apply(X2,X6,X8)
& member(X8,X4) ) )
& ( ! [X8] :
( ~ apply(X1,X8,X7)
| ~ apply(X2,X6,X8)
| ~ member(X8,X4) )
| apply(X0,X6,X7) ) ) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f70,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ compose_predicate(X0,X1,X2,X3,X4,X5)
| ! [X6,X7] :
( ~ member(X7,X5)
| ~ member(X6,X3)
| ( ( ~ apply(X0,X6,X7)
| ? [X9] :
( apply(X1,X9,X7)
& apply(X2,X6,X9)
& member(X9,X4) ) )
& ( ! [X8] :
( ~ apply(X1,X8,X7)
| ~ apply(X2,X6,X8)
| ~ member(X8,X4) )
| apply(X0,X6,X7) ) ) ) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ compose_predicate(X0,X1,X2,X3,X4,X5)
| ! [X6,X7] :
( ~ member(X7,X5)
| ~ member(X6,X3)
| ( ( ~ apply(X0,X6,X7)
| ( apply(X1,sK4(X1,X2,X4,X6,X7),X7)
& apply(X2,X6,sK4(X1,X2,X4,X6,X7))
& member(sK4(X1,X2,X4,X6,X7),X4) ) )
& ( ! [X8] :
( ~ apply(X1,X8,X7)
| ~ apply(X2,X6,X8)
| ~ member(X8,X4) )
| apply(X0,X6,X7) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X9,sK4(X1,X2,X4,X6,X7))],[f70]) ).
fof(f75,plain,
! [X0,X1,X2,X3] :
( ( member(sK8(X0,X1,X2,X3),X3)
& member(sK7(X0,X1,X2,X3),X3)
& member(sK6(X0,X1,X2,X3),X2)
& apply(X1,sK6(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
& apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
& sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3) )
| equal_maps(X0,X1,X2,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X4,sK6(X0,X1,X2,X3)),skolemize(X5,sK7(X0,X1,X2,X3)),skolemize(X6,sK8(X0,X1,X2,X3))],[f44]) ).
fof(f91,plain,
( compose_predicate(sK16,sK14,sK13,sK17,sK18,sK19)
& compose_predicate(sK15,sK14,sK13,sK17,sK18,sK19)
& maps(sK14,sK18,sK19)
& maps(sK13,sK17,sK18)
& ~ equal_maps(sK15,sK16,sK17,sK19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17,sK18,sK19]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X2,sK15),skolemize(X3,sK16),skolemize(X4,sK17),skolemize(X5,sK18),skolemize(X6,sK19)],[f48]) ).
fof(f118,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,[],[f68]) ).
fof(f119,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK3(X0,X2,X3)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f120,plain,
! [X2,X3,X0,X1] :
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| member(sK3(X0,X2,X3),X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f121,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ compose_predicate(X0,X1,X2,X3,X4,X5)
| ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(X0,X6,X7)
| apply(X1,sK4(X1,X2,X4,X6,X7),X7) ),
inference(cnf_transformation,[],[f71]) ).
fof(f122,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ compose_predicate(X0,X1,X2,X3,X4,X5)
| ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(X0,X6,X7)
| apply(X2,X6,sK4(X1,X2,X4,X6,X7)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f123,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ compose_predicate(X0,X1,X2,X3,X4,X5)
| ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(X0,X6,X7)
| member(sK4(X1,X2,X4,X6,X7),X4) ),
inference(cnf_transformation,[],[f71]) ).
fof(f129,plain,
! [X2,X3,X0,X1] :
( member(sK8(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f75]) ).
fof(f130,plain,
! [X2,X3,X0,X1] :
( member(sK7(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f75]) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( member(sK6(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f75]) ).
fof(f132,plain,
! [X2,X3,X0,X1] :
( apply(X1,sK6(X0,X1,X2,X3),sK8(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f75]) ).
fof(f133,plain,
! [X2,X3,X0,X1] :
( apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f75]) ).
fof(f134,plain,
! [X2,X3,X0,X1] :
( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f75]) ).
fof(f151,plain,
compose_predicate(sK16,sK14,sK13,sK17,sK18,sK19),
inference(cnf_transformation,[],[f91]) ).
fof(f152,plain,
compose_predicate(sK15,sK14,sK13,sK17,sK18,sK19),
inference(cnf_transformation,[],[f91]) ).
fof(f153,plain,
maps(sK14,sK18,sK19),
inference(cnf_transformation,[],[f91]) ).
fof(f154,plain,
maps(sK13,sK17,sK18),
inference(cnf_transformation,[],[f91]) ).
fof(f155,plain,
~ equal_maps(sK15,sK16,sK17,sK19),
inference(cnf_transformation,[],[f91]) ).
tcf(c_75,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,[],[f120]) ).
tcf(c_76,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,[],[f119]) ).
tcf(c_77,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,[],[f118]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( member(sK4(X1,X2,X4,X6,X7),X4)
| ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(X0,X6,X7)
| ~ compose_predicate(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( apply(X2,X6,sK4(X1,X2,X4,X6,X7))
| ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(X0,X6,X7)
| ~ compose_predicate(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( apply(X1,sK4(X1,X2,X4,X6,X7),X7)
| ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(X0,X6,X7)
| ~ compose_predicate(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| ( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3) ) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3)) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X1,X0,X2,X3)
| apply(X0,sK6(X1,X0,X2,X3),sK8(X1,X0,X2,X3)) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK6(X0,X1,X2,X3),X2) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_90,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,[],[f130]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK8(X0,X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_108,negated_conjecture,
~ equal_maps(sK15,sK16,sK17,sK19),
inference(cnf_transformation,[],[f155]) ).
tcf(c_109,negated_conjecture,
maps(sK13,sK17,sK18),
inference(cnf_transformation,[],[f154]) ).
tcf(c_110,negated_conjecture,
maps(sK14,sK18,sK19),
inference(cnf_transformation,[],[f153]) ).
tcf(c_111,negated_conjecture,
compose_predicate(sK15,sK14,sK13,sK17,sK18,sK19),
inference(cnf_transformation,[],[f152]) ).
tcf(c_112,negated_conjecture,
compose_predicate(sK16,sK14,sK13,sK17,sK18,sK19),
inference(cnf_transformation,[],[f151]) ).
tcf(c_213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| ( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3) ) ),
inference(prop_impl_just,[status(thm)],[c_86]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK8(X0,X1,X2,X3),X3) ),
inference(prop_impl_just,[status(thm)],[c_91]) ).
tcf(c_255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
| equal_maps(X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_87]) ).
tcf(c_256,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3)) ),
inference(renaming,[status(thm)],[c_255]) ).
tcf(c_257,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK6(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_89]) ).
tcf(c_258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK6(X0,X1,X2,X3),X2) ),
inference(renaming,[status(thm)],[c_257]) ).
tcf(c_259,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK7(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_90]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X0,X1,X2,X3)
| member(sK7(X0,X1,X2,X3),X3) ),
inference(renaming,[status(thm)],[c_259]) ).
tcf(c_279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equal_maps(X1,X0,X2,X3)
| apply(X0,sK6(X1,X0,X2,X3),sK8(X1,X0,X2,X3)) ),
inference(prop_impl_just,[status(thm)],[c_88]) ).
tcf(c_1050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK8(X0,X1,X2,X3),X3)
| ( X3 != sK19 )
| ( X2 != sK17 )
| ( X1 != sK16 )
| ( X0 != sK15 ) ),
inference(resolution_lifted,[status(thm)],[c_251,c_108]) ).
tcf(c_1051,plain,
member(sK8(sK15,sK16,sK17,sK19),sK19),
inference(unflattening,[status(thm)],[c_1050]) ).
tcf(c_1055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK7(X0,X1,X2,X3),X3)
| ( X3 != sK19 )
| ( X2 != sK17 )
| ( X1 != sK16 )
| ( X0 != sK15 ) ),
inference(resolution_lifted,[status(thm)],[c_260,c_108]) ).
tcf(c_1056,plain,
member(sK7(sK15,sK16,sK17,sK19),sK19),
inference(unflattening,[status(thm)],[c_1055]) ).
tcf(c_1060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK6(X0,X1,X2,X3),X2)
| ( X3 != sK19 )
| ( X2 != sK17 )
| ( X1 != sK16 )
| ( X0 != sK15 ) ),
inference(resolution_lifted,[status(thm)],[c_258,c_108]) ).
tcf(c_1061,plain,
member(sK6(sK15,sK16,sK17,sK19),sK17),
inference(unflattening,[status(thm)],[c_1060]) ).
tcf(c_1065,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK6(X0,X1,X2,X3),sK7(X0,X1,X2,X3))
| ( X3 != sK19 )
| ( X2 != sK17 )
| ( X1 != sK16 )
| ( X0 != sK15 ) ),
inference(resolution_lifted,[status(thm)],[c_256,c_108]) ).
tcf(c_1066,plain,
apply(sK15,sK6(sK15,sK16,sK17,sK19),sK7(sK15,sK16,sK17,sK19)),
inference(unflattening,[status(thm)],[c_1065]) ).
tcf(c_1070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 != sK19 )
| ( X2 != sK17 )
| ( X1 != sK16 )
| ( X0 != sK15 )
| ( sK7(X0,X1,X2,X3) != sK8(X0,X1,X2,X3) ) ),
inference(resolution_lifted,[status(thm)],[c_213,c_108]) ).
tcf(c_1071,plain,
sK7(sK15,sK16,sK17,sK19) != sK8(sK15,sK16,sK17,sK19),
inference(unflattening,[status(thm)],[c_1070]) ).
tcf(c_1075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,sK6(X1,X0,X2,X3),sK8(X1,X0,X2,X3))
| ( X3 != sK19 )
| ( X2 != sK17 )
| ( X1 != sK15 )
| ( X0 != sK16 ) ),
inference(resolution_lifted,[status(thm)],[c_279,c_108]) ).
tcf(c_1076,plain,
apply(sK16,sK6(sK15,sK16,sK17,sK19),sK8(sK15,sK16,sK17,sK19)),
inference(unflattening,[status(thm)],[c_1075]) ).
tcf(c_1152,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 != sK18 )
| ( X1 != sK17 )
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_77,c_109]) ).
tcf(c_1153,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK18)
| ~ member(X1,sK18)
| ~ member(X0,sK17)
| ~ apply(sK13,X0,X2)
| ~ apply(sK13,X0,X1) ),
inference(unflattening,[status(thm)],[c_1152]) ).
tcf(c_1173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK3(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK18 )
| ( X1 != sK17 )
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_76,c_109]) ).
tcf(c_1174,plain,
! [X0: $i] :
( apply(sK13,X0,sK3(sK13,sK18,X0))
| ~ member(X0,sK17) ),
inference(unflattening,[status(thm)],[c_1173]) ).
tcf(c_1182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK3(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK18 )
| ( X1 != sK17 )
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_75,c_109]) ).
tcf(c_1183,plain,
! [X0: $i] :
( member(sK3(sK13,sK18,X0),sK18)
| ~ member(X0,sK17) ),
inference(unflattening,[status(thm)],[c_1182]) ).
tcf(c_1191,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 != sK19 )
| ( X1 != sK18 )
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_77,c_110]) ).
tcf(c_1192,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK19)
| ~ member(X1,sK19)
| ~ member(X0,sK18)
| ~ apply(sK14,X0,X2)
| ~ apply(sK14,X0,X1) ),
inference(unflattening,[status(thm)],[c_1191]) ).
tcf(c_1212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X0,X3,sK3(X0,X2,X3))
| ~ member(X3,X1)
| ( X2 != sK19 )
| ( X1 != sK18 )
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_76,c_110]) ).
tcf(c_1213,plain,
! [X0: $i] :
( apply(sK14,X0,sK3(sK14,sK19,X0))
| ~ member(X0,sK18) ),
inference(unflattening,[status(thm)],[c_1212]) ).
tcf(c_1221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK3(X0,X2,X3),X2)
| ~ member(X3,X1)
| ( X2 != sK19 )
| ( X1 != sK18 )
| ( X0 != sK14 ) ),
inference(resolution_lifted,[status(thm)],[c_75,c_110]) ).
tcf(c_1222,plain,
! [X0: $i] :
( member(sK3(sK14,sK19,X0),sK19)
| ~ member(X0,sK18) ),
inference(unflattening,[status(thm)],[c_1221]) ).
tcf(c_1250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( apply(X1,sK4(X1,X2,X4,X6,X7),X7)
| ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(X0,X6,X7)
| ( X5 != sK19 )
| ( X4 != sK18 )
| ( X3 != sK17 )
| ( X2 != sK13 )
| ( X1 != sK14 )
| ( X0 != sK15 ) ),
inference(resolution_lifted,[status(thm)],[c_81,c_111]) ).
tcf(c_1251,plain,
! [X0: $i,X1: $i] :
( apply(sK14,sK4(sK14,sK13,sK18,X0,X1),X1)
| ~ member(X1,sK19)
| ~ member(X0,sK17)
| ~ apply(sK15,X0,X1) ),
inference(unflattening,[status(thm)],[c_1250]) ).
tcf(c_1265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( apply(X2,X6,sK4(X1,X2,X4,X6,X7))
| ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(X0,X6,X7)
| ( X5 != sK19 )
| ( X4 != sK18 )
| ( X3 != sK17 )
| ( X2 != sK13 )
| ( X1 != sK14 )
| ( X0 != sK15 ) ),
inference(resolution_lifted,[status(thm)],[c_80,c_111]) ).
tcf(c_1266,plain,
! [X0: $i,X1: $i] :
( apply(sK13,X0,sK4(sK14,sK13,sK18,X0,X1))
| ~ member(X1,sK19)
| ~ member(X0,sK17)
| ~ apply(sK15,X0,X1) ),
inference(unflattening,[status(thm)],[c_1265]) ).
tcf(c_1280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( member(sK4(X1,X2,X4,X6,X7),X4)
| ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(X0,X6,X7)
| ( X5 != sK19 )
| ( X4 != sK18 )
| ( X3 != sK17 )
| ( X2 != sK13 )
| ( X1 != sK14 )
| ( X0 != sK15 ) ),
inference(resolution_lifted,[status(thm)],[c_79,c_111]) ).
tcf(c_1281,plain,
! [X0: $i,X1: $i] :
( member(sK4(sK14,sK13,sK18,X0,X1),sK18)
| ~ member(X1,sK19)
| ~ member(X0,sK17)
| ~ apply(sK15,X0,X1) ),
inference(unflattening,[status(thm)],[c_1280]) ).
tcf(c_1316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( apply(X1,sK4(X1,X2,X4,X6,X7),X7)
| ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(X0,X6,X7)
| ( X5 != sK19 )
| ( X4 != sK18 )
| ( X3 != sK17 )
| ( X2 != sK13 )
| ( X1 != sK14 )
| ( X0 != sK16 ) ),
inference(resolution_lifted,[status(thm)],[c_81,c_112]) ).
tcf(c_1317,plain,
! [X0: $i,X1: $i] :
( apply(sK14,sK4(sK14,sK13,sK18,X0,X1),X1)
| ~ member(X1,sK19)
| ~ member(X0,sK17)
| ~ apply(sK16,X0,X1) ),
inference(unflattening,[status(thm)],[c_1316]) ).
tcf(c_1331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( apply(X2,X6,sK4(X1,X2,X4,X6,X7))
| ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(X0,X6,X7)
| ( X5 != sK19 )
| ( X4 != sK18 )
| ( X3 != sK17 )
| ( X2 != sK13 )
| ( X1 != sK14 )
| ( X0 != sK16 ) ),
inference(resolution_lifted,[status(thm)],[c_80,c_112]) ).
tcf(c_1332,plain,
! [X0: $i,X1: $i] :
( apply(sK13,X0,sK4(sK14,sK13,sK18,X0,X1))
| ~ member(X1,sK19)
| ~ member(X0,sK17)
| ~ apply(sK16,X0,X1) ),
inference(unflattening,[status(thm)],[c_1331]) ).
tcf(c_1346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( member(sK4(X1,X2,X4,X6,X7),X4)
| ~ member(X7,X5)
| ~ member(X6,X3)
| ~ apply(X0,X6,X7)
| ( X5 != sK19 )
| ( X4 != sK18 )
| ( X3 != sK17 )
| ( X2 != sK13 )
| ( X1 != sK14 )
| ( X0 != sK16 ) ),
inference(resolution_lifted,[status(thm)],[c_79,c_112]) ).
tcf(c_1347,plain,
! [X0: $i,X1: $i] :
( member(sK4(sK14,sK13,sK18,X0,X1),sK18)
| ~ member(X1,sK19)
| ~ member(X0,sK17)
| ~ apply(sK16,X0,X1) ),
inference(unflattening,[status(thm)],[c_1346]) ).
tcf(c_1418,definition,
iPr_def_10 = sK6(sK15,sK16,sK17,sK19),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1419,definition,
iPr_def_11 = sK8(sK15,sK16,sK17,sK19),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1420,definition,
iPr_def_12 = sK7(sK15,sK16,sK17,sK19),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1422,plain,
! [X0: $i,X1: $i] :
( member(sK4(sK14,sK13,sK18,X0,X1),sK18)
| ~ member(X1,sK19)
| ~ member(X0,sK17)
| ~ apply(sK16,X0,X1) ),
inference(demodulation,[status(thm)],[c_1347]) ).
tcf(c_1423,plain,
! [X0: $i,X1: $i] :
( apply(sK13,X0,sK4(sK14,sK13,sK18,X0,X1))
| ~ member(X1,sK19)
| ~ member(X0,sK17)
| ~ apply(sK16,X0,X1) ),
inference(demodulation,[status(thm)],[c_1332]) ).
tcf(c_1424,plain,
! [X0: $i,X1: $i] :
( apply(sK14,sK4(sK14,sK13,sK18,X0,X1),X1)
| ~ member(X1,sK19)
| ~ member(X0,sK17)
| ~ apply(sK16,X0,X1) ),
inference(demodulation,[status(thm)],[c_1317]) ).
tcf(c_1426,plain,
! [X0: $i,X1: $i] :
( member(sK4(sK14,sK13,sK18,X0,X1),sK18)
| ~ member(X1,sK19)
| ~ member(X0,sK17)
| ~ apply(sK15,X0,X1) ),
inference(demodulation,[status(thm)],[c_1281]) ).
tcf(c_1427,plain,
! [X0: $i,X1: $i] :
( apply(sK13,X0,sK4(sK14,sK13,sK18,X0,X1))
| ~ member(X1,sK19)
| ~ member(X0,sK17)
| ~ apply(sK15,X0,X1) ),
inference(demodulation,[status(thm)],[c_1266]) ).
tcf(c_1428,plain,
! [X0: $i,X1: $i] :
( apply(sK14,sK4(sK14,sK13,sK18,X0,X1),X1)
| ~ member(X1,sK19)
| ~ member(X0,sK17)
| ~ apply(sK15,X0,X1) ),
inference(demodulation,[status(thm)],[c_1251]) ).
tcf(c_1430,plain,
! [X0: $i] :
( apply(sK14,X0,sK3(sK14,sK19,X0))
| ~ member(X0,sK18) ),
inference(demodulation,[status(thm)],[c_1213]) ).
tcf(c_1431,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK19)
| ~ member(X1,sK19)
| ~ member(X0,sK18)
| ~ apply(sK14,X0,X2)
| ~ apply(sK14,X0,X1) ),
inference(demodulation,[status(thm)],[c_1192]) ).
tcf(c_1433,plain,
! [X0: $i] :
( apply(sK13,X0,sK3(sK13,sK18,X0))
| ~ member(X0,sK17) ),
inference(demodulation,[status(thm)],[c_1174]) ).
tcf(c_1434,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ member(X2,sK18)
| ~ member(X1,sK18)
| ~ member(X0,sK17)
| ~ apply(sK13,X0,X2)
| ~ apply(sK13,X0,X1) ),
inference(demodulation,[status(thm)],[c_1153]) ).
tcf(c_1435,plain,
apply(sK16,iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_1076,c_1419,c_1418]) ).
tcf(c_1436,plain,
iPr_def_12 != iPr_def_11,
inference(demodulation,[status(thm)],[c_1071,c_1420]) ).
tcf(c_1437,plain,
apply(sK15,iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_1066]) ).
tcf(c_1438,plain,
member(iPr_def_10,sK17),
inference(demodulation,[status(thm)],[c_1061]) ).
tcf(c_1439,plain,
member(iPr_def_12,sK19),
inference(demodulation,[status(thm)],[c_1056]) ).
tcf(c_1440,plain,
member(iPr_def_11,sK19),
inference(demodulation,[status(thm)],[c_1051]) ).
tcf(c_3004,plain,
! [X0: $i,X1: $i] :
( ( sK3(sK14,sK19,X0) = X1 )
| ~ member(X1,sK19)
| ~ member(X0,sK18)
| ~ apply(sK14,X0,X1)
| ~ member(sK3(sK14,sK19,X0),sK19) ),
inference(superposition,[status(thm)],[c_1430,c_1431]) ).
tcf(c_3039,plain,
! [X0: $i,X1: $i] :
( ( sK3(sK13,sK18,X0) = X1 )
| ~ member(X1,sK18)
| ~ member(X0,sK17)
| ~ apply(sK13,X0,X1)
| ~ member(sK3(sK13,sK18,X0),sK18) ),
inference(superposition,[status(thm)],[c_1433,c_1434]) ).
tcf(c_3098,plain,
! [X0: $i,X1: $i] :
( ( sK3(sK14,sK19,X0) = X1 )
| ~ member(X1,sK19)
| ~ member(X0,sK18)
| ~ apply(sK14,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_3004,c_1222,c_3004]) ).
tcf(c_3110,plain,
! [X0: $i,X1: $i] :
( ( sK3(sK14,sK19,sK4(sK14,sK13,sK18,X0,X1)) = X1 )
| ~ member(X1,sK19)
| ~ member(X0,sK17)
| ~ apply(sK15,X0,X1)
| ~ member(sK4(sK14,sK13,sK18,X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_1428,c_3098]) ).
tcf(c_3111,plain,
! [X0: $i,X1: $i] :
( ( sK3(sK14,sK19,sK4(sK14,sK13,sK18,X0,X1)) = X1 )
| ~ member(X1,sK19)
| ~ member(X0,sK17)
| ~ apply(sK16,X0,X1)
| ~ member(sK4(sK14,sK13,sK18,X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_1424,c_3098]) ).
tcf(c_3124,plain,
! [X0: $i,X1: $i] :
( ( sK3(sK13,sK18,X0) = X1 )
| ~ member(X1,sK18)
| ~ member(X0,sK17)
| ~ apply(sK13,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_3039,c_1183,c_3039]) ).
tcf(c_3136,plain,
! [X0: $i,X1: $i] :
( ( sK4(sK14,sK13,sK18,X0,X1) = sK3(sK13,sK18,X0) )
| ~ member(X1,sK19)
| ~ member(X0,sK17)
| ~ apply(sK15,X0,X1)
| ~ member(sK4(sK14,sK13,sK18,X0,X1),sK18) ),
inference(superposition,[status(thm)],[c_1427,c_3124]) ).
tcf(c_3255,plain,
! [X0: $i,X1: $i] :
( ( sK3(sK14,sK19,sK4(sK14,sK13,sK18,X0,X1)) = X1 )
| ~ member(X1,sK19)
| ~ member(X0,sK17)
| ~ apply(sK15,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_3110,c_1281,c_3110]) ).
tcf(c_3266,plain,
( ( sK3(sK14,sK19,sK4(sK14,sK13,sK18,iPr_def_10,iPr_def_12)) = iPr_def_12 )
| ~ member(iPr_def_12,sK19)
| ~ member(iPr_def_10,sK17) ),
inference(superposition,[status(thm)],[c_1437,c_3255]) ).
tcf(c_3268,plain,
sK3(sK14,sK19,sK4(sK14,sK13,sK18,iPr_def_10,iPr_def_12)) = iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_3266,c_1439,c_1438]) ).
tcf(c_3301,plain,
! [X0: $i,X1: $i] :
( ( sK3(sK14,sK19,sK4(sK14,sK13,sK18,X0,X1)) = X1 )
| ~ member(X1,sK19)
| ~ member(X0,sK17)
| ~ apply(sK16,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_3111,c_1347,c_3111]) ).
tcf(c_3312,plain,
( ( sK3(sK14,sK19,sK4(sK14,sK13,sK18,iPr_def_10,iPr_def_11)) = iPr_def_11 )
| ~ member(iPr_def_11,sK19)
| ~ member(iPr_def_10,sK17) ),
inference(superposition,[status(thm)],[c_1435,c_3301]) ).
tcf(c_3314,plain,
sK3(sK14,sK19,sK4(sK14,sK13,sK18,iPr_def_10,iPr_def_11)) = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_3312,c_1440,c_1438]) ).
tcf(c_3418,plain,
! [X0: $i,X1: $i] :
( ( sK4(sK14,sK13,sK18,X0,X1) = sK3(sK13,sK18,X0) )
| ~ member(X1,sK19)
| ~ member(X0,sK17)
| ~ apply(sK15,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_3136,c_1281,c_3136]) ).
tcf(c_3429,plain,
( ( sK4(sK14,sK13,sK18,iPr_def_10,iPr_def_12) = sK3(sK13,sK18,iPr_def_10) )
| ~ member(iPr_def_12,sK19)
| ~ member(iPr_def_10,sK17) ),
inference(superposition,[status(thm)],[c_1437,c_3418]) ).
tcf(c_3431,plain,
sK4(sK14,sK13,sK18,iPr_def_10,iPr_def_12) = sK3(sK13,sK18,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_3429,c_1439,c_1438]) ).
tcf(c_3437,plain,
sK3(sK14,sK19,sK3(sK13,sK18,iPr_def_10)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_3268,c_3431]) ).
tcf(c_3447,plain,
( apply(sK13,iPr_def_10,sK3(sK13,sK18,iPr_def_10))
| ~ member(iPr_def_12,sK19)
| ~ member(iPr_def_10,sK17)
| ~ apply(sK15,iPr_def_10,iPr_def_12) ),
inference(superposition,[status(thm)],[c_3431,c_1427]) ).
tcf(c_3450,plain,
( member(sK3(sK13,sK18,iPr_def_10),sK18)
| ~ member(iPr_def_12,sK19)
| ~ member(iPr_def_10,sK17)
| ~ apply(sK15,iPr_def_10,iPr_def_12) ),
inference(superposition,[status(thm)],[c_3431,c_1426]) ).
tcf(c_3455,plain,
member(sK3(sK13,sK18,iPr_def_10),sK18),
inference(forward_subsumption_resolution,[status(thm)],[c_3450,c_1439,c_1438,c_1437]) ).
tcf(c_3462,plain,
apply(sK13,iPr_def_10,sK3(sK13,sK18,iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_3447,c_1439,c_1438,c_1437]) ).
tcf(c_3477,plain,
! [X0: $i] :
( ( sK3(sK13,sK18,iPr_def_10) = X0 )
| ~ member(iPr_def_10,sK17)
| ~ member(X0,sK18)
| ~ apply(sK13,iPr_def_10,X0)
| ~ member(sK3(sK13,sK18,iPr_def_10),sK18) ),
inference(superposition,[status(thm)],[c_3462,c_1434]) ).
tcf(c_3488,plain,
! [X0: $i] :
( ( sK3(sK13,sK18,iPr_def_10) = X0 )
| ~ member(X0,sK18)
| ~ apply(sK13,iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3477,c_1438,c_3455]) ).
tcf(c_4085,plain,
! [X0: $i] :
( member(sK4(sK14,sK13,sK18,iPr_def_10,X0),sK18)
| ~ member(iPr_def_10,sK17)
| ~ member(X0,sK19)
| ~ apply(sK16,iPr_def_10,X0) ),
inference(instantiation,[status(thm)],[c_1422]) ).
tcf(c_4549,plain,
! [X0: $i] :
( ( sK4(sK14,sK13,sK18,iPr_def_10,X0) = sK3(sK13,sK18,iPr_def_10) )
| ~ member(iPr_def_10,sK17)
| ~ member(X0,sK19)
| ~ apply(sK16,iPr_def_10,X0)
| ~ member(sK4(sK14,sK13,sK18,iPr_def_10,X0),sK18) ),
inference(superposition,[status(thm)],[c_1423,c_3488]) ).
tcf(c_4551,plain,
! [X0: $i] :
( ( sK4(sK14,sK13,sK18,iPr_def_10,X0) = sK3(sK13,sK18,iPr_def_10) )
| ~ member(X0,sK19)
| ~ apply(sK16,iPr_def_10,X0)
| ~ member(sK4(sK14,sK13,sK18,iPr_def_10,X0),sK18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4549,c_1438]) ).
tcf(c_5511,plain,
! [X0: $i] :
( ( sK4(sK14,sK13,sK18,iPr_def_10,X0) = sK3(sK13,sK18,iPr_def_10) )
| ~ member(X0,sK19)
| ~ apply(sK16,iPr_def_10,X0) ),
inference(global_subsumption_just,[status(thm)],[c_4551,c_1438,c_4085,c_4551]) ).
tcf(c_5521,plain,
( ( sK4(sK14,sK13,sK18,iPr_def_10,iPr_def_11) = sK3(sK13,sK18,iPr_def_10) )
| ~ member(iPr_def_11,sK19) ),
inference(superposition,[status(thm)],[c_1435,c_5511]) ).
tcf(c_5524,plain,
sK4(sK14,sK13,sK18,iPr_def_10,iPr_def_11) = sK3(sK13,sK18,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_5521,c_1440]) ).
tcf(c_5531,plain,
sK3(sK14,sK19,sK3(sK13,sK18,iPr_def_10)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_3314,c_5524]) ).
tcf(c_5532,plain,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_3437,c_5531]) ).
tcf(c_5543,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_1436,c_5532]) ).
tcf(c_5546,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_5543]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET708+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 11:46:23 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 4.09/1.29 % SZS status Started for theBenchmark.p
% 4.09/1.29 % SZS status Theorem for theBenchmark.p
% 4.09/1.29
% 4.09/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.09/1.29
% 4.09/1.29 % ------ iProver source info
% 4.09/1.29
% 4.09/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 4.09/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.09/1.29 % git: non_committed_changes: false
% 4.09/1.29
% 4.09/1.29 % ------ Parsing...
% 4.09/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.09/1.29
% 4.09/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 4.09/1.29
% 4.09/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.09/1.29
% 4.09/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.09/1.29 % ------ Proving...
% 4.09/1.29 % ------ Problem Properties
% 4.09/1.29
% 4.09/1.29 %
% 4.09/1.29 % clauses 69
% 4.09/1.29 % conjectures 0
% 4.09/1.29 % EPR 12
% 4.09/1.29 % Horn 64
% 4.09/1.29 % unary 13
% 4.09/1.29 % binary 29
% 4.09/1.29 % lits 180
% 4.09/1.29 % lits eq 9
% 4.09/1.29 % fd_pure 0
% 4.09/1.29 % fd_pseudo 0
% 4.09/1.29 % fd_cond 0
% 4.09/1.29 % fd_pseudo_cond 4
% 4.09/1.29 % AC symbols 0
% 4.09/1.29
% 4.09/1.29 % ------ Schedule dynamic 5 is on
% 4.09/1.29
% 4.09/1.29 % ------ no conjectures: strip conj schedule
% 4.09/1.29
% 4.09/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 4.09/1.29
% 4.09/1.29
% 4.09/1.29 % ------
% 4.09/1.29 % Current options:
% 4.09/1.29 % ------
% 4.09/1.29
% 4.09/1.29
% 4.09/1.29 %
% 4.09/1.29
% 4.09/1.29 % ------ Proving...
% 4.09/1.29 %
% 4.09/1.29
% 4.09/1.29 % SZS status Theorem for theBenchmark.p
% 4.09/1.29
% 4.09/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.09/1.29
% 4.09/1.29
%------------------------------------------------------------------------------