%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ITP020+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.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 01:47:55 PM UTC 2026
% Result : Theorem 21.29s 4.98s
% Output : CNFRefutation 21.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 72 ( 25 unt; 7 def)
% Number of atoms : 321 ( 7 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 250 ( 113 ~; 107 |; 17 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 99 ( 0 sgn 88 !; 11 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( mem(X2,arr(X0,X1))
=> ! [X3] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax',ap_tp) ).
fof(f25,axiom,
! [X0] :
( ne(X0)
=> mem(c_2Epred__set_2EUNIV(X0),arr(X0,bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2EUNIV) ).
fof(f26,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ne(ty_2Epair_2Eprod(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ne_ty_2Epair_2Eprod) ).
fof(f27,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> mem(c_2Epred__set_2ECROSS(X0,X1),arr(arr(X0,bool),arr(arr(X1,bool),arr(ty_2Epair_2Eprod(X0,X1),bool)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2ECROSS) ).
fof(f29,axiom,
ne(ty_2Enum_2Enum),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ne_ty_2Enum_2Enum) ).
fof(f51,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( mem(X2,arr(X0,bool))
=> ! [X3] :
( mem(X3,arr(X1,bool))
=> ( ? [X4] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3))
& mem(X4,arr(X0,X1)) )
<=> ? [X5] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2))
& mem(X5,arr(X1,X0)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EBIJ__SYM) ).
fof(f62,axiom,
? [X0] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),X0),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))
& mem(X0,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eutil__prob_2ENUM__2D__BIJ) ).
fof(f63,conjecture,
? [X0] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))))
& mem(X0,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eutil__prob_2ENUM__2D__BIJ__INV) ).
fof(f64,negated_conjecture,
~ ? [X0] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))))
& mem(X0,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) ),
inference(negated_conjecture,[status(cth)],[f63]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ mem(X2,arr(X0,X1))
| ! [X3] :
( ~ mem(X3,X0)
| mem(ap(X2,X3),X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f98,plain,
! [X0] :
( ~ ne(X0)
| mem(c_2Epred__set_2EUNIV(X0),arr(X0,bool)) ),
inference(ennf_transformation,[],[f25]) ).
fof(f99,plain,
! [X0] :
( ~ ne(X0)
| ! [X1] :
( ~ ne(X1)
| ne(ty_2Epair_2Eprod(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f100,plain,
! [X0] :
( ~ ne(X0)
| ! [X1] :
( ~ ne(X1)
| mem(c_2Epred__set_2ECROSS(X0,X1),arr(arr(X0,bool),arr(arr(X1,bool),arr(ty_2Epair_2Eprod(X0,X1),bool)))) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f127,plain,
! [X0] :
( ~ ne(X0)
| ! [X1] :
( ~ ne(X1)
| ! [X2] :
( ~ mem(X2,arr(X0,bool))
| ! [X3] :
( ~ mem(X3,arr(X1,bool))
| ( ? [X4] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3))
& mem(X4,arr(X0,X1)) )
<=> ? [X5] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2))
& mem(X5,arr(X1,X0)) ) ) ) ) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f140,plain,
! [X0] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))))
| ~ mem(X0,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) ),
inference(ennf_transformation,[],[f64]) ).
fof(f225,plain,
! [X0] :
( ~ ne(X0)
| ! [X1] :
( ~ ne(X1)
| ! [X2] :
( ~ mem(X2,arr(X0,bool))
| ! [X3] :
( ~ mem(X3,arr(X1,bool))
| ( ( ! [X4] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3))
| ~ mem(X4,arr(X0,X1)) )
| ? [X5] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2))
& mem(X5,arr(X1,X0)) ) )
& ( ! [X5] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2))
| ~ mem(X5,arr(X1,X0)) )
| ? [X4] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3))
& mem(X4,arr(X0,X1)) ) ) ) ) ) ) ),
inference(nnf_transformation,[],[f127]) ).
fof(f226,plain,
! [X0] :
( ~ ne(X0)
| ! [X1] :
( ~ ne(X1)
| ! [X2] :
( ~ mem(X2,arr(X0,bool))
| ! [X3] :
( ~ mem(X3,arr(X1,bool))
| ( ( ! [X7] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X7),X2),X3))
| ~ mem(X7,arr(X0,X1)) )
| ? [X6] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X6),X3),X2))
& mem(X6,arr(X1,X0)) ) )
& ( ! [X5] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2))
| ~ mem(X5,arr(X1,X0)) )
| ? [X4] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X4),X2),X3))
& mem(X4,arr(X0,X1)) ) ) ) ) ) ) ),
inference(rectify,[],[f225]) ).
fof(f227,plain,
! [X0] :
( ~ ne(X0)
| ! [X1] :
( ~ ne(X1)
| ! [X2] :
( ~ mem(X2,arr(X0,bool))
| ! [X3] :
( ~ mem(X3,arr(X1,bool))
| ( ( ! [X7] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X7),X2),X3))
| ~ mem(X7,arr(X0,X1)) )
| ( p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),sK42(X0,X1,X2,X3)),X3),X2))
& mem(sK42(X0,X1,X2,X3),arr(X1,X0)) ) )
& ( ! [X5] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2))
| ~ mem(X5,arr(X1,X0)) )
| ( p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),sK41(X0,X1,X2,X3)),X2),X3))
& mem(sK41(X0,X1,X2,X3),arr(X0,X1)) ) ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41,sK42]),skolemize(X4,sK41(X0,X1,X2,X3)),skolemize(X6,sK42(X0,X1,X2,X3))],[f226]) ).
fof(f273,plain,
( p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),sK43),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))
& mem(sK43,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(X0,sK43)],[f62]) ).
fof(f277,plain,
! [X2,X3,X0,X1] :
( ~ mem(X2,arr(X0,X1))
| ~ mem(X3,X0)
| mem(ap(X2,X3),X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f310,plain,
! [X0] :
( ~ ne(X0)
| mem(c_2Epred__set_2EUNIV(X0),arr(X0,bool)) ),
inference(cnf_transformation,[],[f98]) ).
fof(f311,plain,
! [X0,X1] :
( ~ ne(X0)
| ~ ne(X1)
| ne(ty_2Epair_2Eprod(X0,X1)) ),
inference(cnf_transformation,[],[f99]) ).
fof(f312,plain,
! [X0,X1] :
( ~ ne(X0)
| ~ ne(X1)
| mem(c_2Epred__set_2ECROSS(X0,X1),arr(arr(X0,bool),arr(arr(X1,bool),arr(ty_2Epair_2Eprod(X0,X1),bool)))) ),
inference(cnf_transformation,[],[f100]) ).
fof(f314,plain,
ne(ty_2Enum_2Enum),
inference(cnf_transformation,[],[f29]) ).
fof(f420,plain,
! [X2,X3,X0,X1,X5] :
( ~ ne(X0)
| ~ ne(X1)
| ~ mem(X2,arr(X0,bool))
| ~ mem(X3,arr(X1,bool))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2))
| ~ mem(X5,arr(X1,X0))
| p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),sK41(X0,X1,X2,X3)),X2),X3)) ),
inference(cnf_transformation,[],[f227]) ).
fof(f421,plain,
! [X2,X3,X0,X1,X5] :
( ~ ne(X0)
| ~ ne(X1)
| ~ mem(X2,arr(X0,bool))
| ~ mem(X3,arr(X1,bool))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),X5),X3),X2))
| ~ mem(X5,arr(X1,X0))
| mem(sK41(X0,X1,X2,X3),arr(X0,X1)) ),
inference(cnf_transformation,[],[f227]) ).
fof(f527,plain,
p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),sK43),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),
inference(cnf_transformation,[],[f273]) ).
fof(f528,plain,
mem(sK43,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)),
inference(cnf_transformation,[],[f273]) ).
fof(f529,plain,
! [X0] :
( ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))))
| ~ mem(X0,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( mem(ap(X0,X3),X2)
| ~ mem(X3,X1)
| ~ mem(X0,arr(X1,X2)) ),
inference(cnf_transformation,[],[f277]) ).
tcf(c_85,plain,
! [X0: $i] :
( mem(c_2Epred__set_2EUNIV(X0),arr(X0,bool))
| ~ ne(X0) ),
inference(cnf_transformation,[],[f310]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( ne(ty_2Epair_2Eprod(X0,X1))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f311]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( mem(c_2Epred__set_2ECROSS(X0,X1),arr(arr(X0,bool),arr(arr(X1,bool),arr(ty_2Epair_2Eprod(X0,X1),bool))))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f312]) ).
tcf(c_89,plain,
ne(ty_2Enum_2Enum),
inference(cnf_transformation,[],[f314]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( mem(sK41(X1,X0,X4,X3),arr(X1,X0))
| ~ ne(X1)
| ~ ne(X0)
| ~ mem(X4,arr(X1,bool))
| ~ mem(X3,arr(X0,bool))
| ~ mem(X2,arr(X0,X1))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X2),X3),X4)) ),
inference(cnf_transformation,[],[f421]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( p(ap(ap(ap(c_2Epred__set_2EBIJ(X1,X0),sK41(X1,X0,X4,X3)),X4),X3))
| ~ ne(X1)
| ~ ne(X0)
| ~ mem(X4,arr(X1,bool))
| ~ mem(X3,arr(X0,bool))
| ~ mem(X2,arr(X0,X1))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(X0,X1),X2),X3),X4)) ),
inference(cnf_transformation,[],[f420]) ).
tcf(c_247,plain,
mem(sK43,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum)),
inference(cnf_transformation,[],[f528]) ).
tcf(c_248,plain,
p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),sK43),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),c_2Epred__set_2EUNIV(ty_2Enum_2Enum))),
inference(cnf_transformation,[],[f527]) ).
tcf(c_249,negated_conjecture,
! [X0: $i] :
( ~ mem(X0,arr(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)))
| ~ p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),X0),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),ap(ap(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)),c_2Epred__set_2EUNIV(ty_2Enum_2Enum)))) ),
inference(cnf_transformation,[],[f529]) ).
tcf(c_6281,definition,
iPr_def_28 = ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),
introduced(definition,[new_symbols(definition,[iPr_def_28])],[]) ).
tcf(c_6282,definition,
iPr_def_29 = c_2Epred__set_2EBIJ(ty_2Enum_2Enum,iPr_def_28),
introduced(definition,[new_symbols(definition,[iPr_def_29])],[]) ).
tcf(c_6283,definition,
iPr_def_30 = c_2Epred__set_2EUNIV(ty_2Enum_2Enum),
introduced(definition,[new_symbols(definition,[iPr_def_30])],[]) ).
tcf(c_6284,definition,
iPr_def_31 = c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),
introduced(definition,[new_symbols(definition,[iPr_def_31])],[]) ).
tcf(c_6285,definition,
iPr_def_32 = ap(iPr_def_31,iPr_def_30),
introduced(definition,[new_symbols(definition,[iPr_def_32])],[]) ).
tcf(c_6286,definition,
iPr_def_33 = ap(iPr_def_32,iPr_def_30),
introduced(definition,[new_symbols(definition,[iPr_def_33])],[]) ).
tcf(c_6287,definition,
iPr_def_34 = arr(ty_2Enum_2Enum,iPr_def_28),
introduced(definition,[new_symbols(definition,[iPr_def_34])],[]) ).
tcf(c_6288,negated_conjecture,
! [X0: $i] :
( ~ mem(X0,iPr_def_34)
| ~ p(ap(ap(ap(iPr_def_29,X0),iPr_def_30),iPr_def_33)) ),
inference(demodulation,[status(thm)],[c_249,c_6287,c_6284,c_6285,c_6286,c_6283,c_6281,c_6282]) ).
tcf(c_8552,plain,
mem(sK43,arr(iPr_def_28,ty_2Enum_2Enum)),
inference(light_normalisation,[status(thm)],[c_247,c_6281]) ).
tcf(c_8584,plain,
( mem(iPr_def_30,arr(ty_2Enum_2Enum,bool))
| ~ ne(ty_2Enum_2Enum) ),
inference(superposition,[status(thm)],[c_6283,c_85]) ).
tcf(c_8585,plain,
mem(iPr_def_30,arr(ty_2Enum_2Enum,bool)),
inference(forward_subsumption_resolution,[status(thm)],[c_8584,c_89]) ).
tcf(c_8598,plain,
( ne(iPr_def_28)
| ~ ne(ty_2Enum_2Enum) ),
inference(superposition,[status(thm)],[c_6281,c_86]) ).
tcf(c_8599,plain,
ne(iPr_def_28),
inference(forward_subsumption_resolution,[status(thm)],[c_8598,c_89]) ).
tcf(c_10571,plain,
p(ap(ap(ap(c_2Epred__set_2EBIJ(iPr_def_28,ty_2Enum_2Enum),sK43),iPr_def_33),iPr_def_30)),
inference(light_normalisation,[status(thm)],[c_248,c_6281,c_6283,c_6284,c_6285,c_6286]) ).
tcf(c_11536,plain,
( mem(c_2Epred__set_2ECROSS(ty_2Enum_2Enum,ty_2Enum_2Enum),arr(arr(ty_2Enum_2Enum,bool),arr(arr(ty_2Enum_2Enum,bool),arr(iPr_def_28,bool))))
| ~ ne(ty_2Enum_2Enum) ),
inference(superposition,[status(thm)],[c_6281,c_87]) ).
tcf(c_11541,plain,
( mem(iPr_def_31,arr(arr(ty_2Enum_2Enum,bool),arr(arr(ty_2Enum_2Enum,bool),arr(iPr_def_28,bool))))
| ~ ne(ty_2Enum_2Enum) ),
inference(light_normalisation,[status(thm)],[c_11536,c_6284]) ).
tcf(c_11542,plain,
mem(iPr_def_31,arr(arr(ty_2Enum_2Enum,bool),arr(arr(ty_2Enum_2Enum,bool),arr(iPr_def_28,bool)))),
inference(forward_subsumption_resolution,[status(thm)],[c_11541,c_89]) ).
tcf(c_11642,plain,
! [X0: $i] :
( mem(ap(iPr_def_31,X0),arr(arr(ty_2Enum_2Enum,bool),arr(iPr_def_28,bool)))
| ~ mem(X0,arr(ty_2Enum_2Enum,bool)) ),
inference(superposition,[status(thm)],[c_11542,c_52]) ).
tcf(c_29219,plain,
( mem(sK41(ty_2Enum_2Enum,iPr_def_28,iPr_def_30,iPr_def_33),arr(ty_2Enum_2Enum,iPr_def_28))
| ~ ne(iPr_def_28)
| ~ ne(ty_2Enum_2Enum)
| ~ mem(iPr_def_33,arr(iPr_def_28,bool))
| ~ mem(iPr_def_30,arr(ty_2Enum_2Enum,bool))
| ~ mem(sK43,arr(iPr_def_28,ty_2Enum_2Enum)) ),
inference(superposition,[status(thm)],[c_10571,c_152]) ).
tcf(c_29221,plain,
( mem(sK41(ty_2Enum_2Enum,iPr_def_28,iPr_def_30,iPr_def_33),iPr_def_34)
| ~ ne(iPr_def_28)
| ~ ne(ty_2Enum_2Enum)
| ~ mem(iPr_def_33,arr(iPr_def_28,bool))
| ~ mem(iPr_def_30,arr(ty_2Enum_2Enum,bool))
| ~ mem(sK43,arr(iPr_def_28,ty_2Enum_2Enum)) ),
inference(light_normalisation,[status(thm)],[c_29219,c_6287]) ).
tcf(c_29222,plain,
( mem(sK41(ty_2Enum_2Enum,iPr_def_28,iPr_def_30,iPr_def_33),iPr_def_34)
| ~ mem(iPr_def_33,arr(iPr_def_28,bool)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29221,c_8599,c_89,c_8585,c_8552]) ).
tcf(c_30861,plain,
( p(ap(ap(ap(c_2Epred__set_2EBIJ(ty_2Enum_2Enum,iPr_def_28),sK41(ty_2Enum_2Enum,iPr_def_28,iPr_def_30,iPr_def_33)),iPr_def_30),iPr_def_33))
| ~ ne(iPr_def_28)
| ~ ne(ty_2Enum_2Enum)
| ~ mem(iPr_def_33,arr(iPr_def_28,bool))
| ~ mem(iPr_def_30,arr(ty_2Enum_2Enum,bool))
| ~ mem(sK43,arr(iPr_def_28,ty_2Enum_2Enum)) ),
inference(superposition,[status(thm)],[c_10571,c_153]) ).
tcf(c_30863,plain,
( p(ap(ap(ap(iPr_def_29,sK41(ty_2Enum_2Enum,iPr_def_28,iPr_def_30,iPr_def_33)),iPr_def_30),iPr_def_33))
| ~ ne(iPr_def_28)
| ~ ne(ty_2Enum_2Enum)
| ~ mem(iPr_def_33,arr(iPr_def_28,bool))
| ~ mem(iPr_def_30,arr(ty_2Enum_2Enum,bool))
| ~ mem(sK43,arr(iPr_def_28,ty_2Enum_2Enum)) ),
inference(light_normalisation,[status(thm)],[c_30861,c_6282]) ).
tcf(c_30864,plain,
( p(ap(ap(ap(iPr_def_29,sK41(ty_2Enum_2Enum,iPr_def_28,iPr_def_30,iPr_def_33)),iPr_def_30),iPr_def_33))
| ~ mem(iPr_def_33,arr(iPr_def_28,bool)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30863,c_8599,c_89,c_8585,c_8552]) ).
tcf(c_35714,plain,
( mem(iPr_def_32,arr(arr(ty_2Enum_2Enum,bool),arr(iPr_def_28,bool)))
| ~ mem(iPr_def_30,arr(ty_2Enum_2Enum,bool)) ),
inference(superposition,[status(thm)],[c_6285,c_11642]) ).
tcf(c_35725,plain,
mem(iPr_def_32,arr(arr(ty_2Enum_2Enum,bool),arr(iPr_def_28,bool))),
inference(forward_subsumption_resolution,[status(thm)],[c_35714,c_8585]) ).
tcf(c_36061,plain,
! [X0: $i] :
( mem(ap(iPr_def_32,X0),arr(iPr_def_28,bool))
| ~ mem(X0,arr(ty_2Enum_2Enum,bool)) ),
inference(superposition,[status(thm)],[c_35725,c_52]) ).
tcf(c_36146,plain,
( mem(iPr_def_33,arr(iPr_def_28,bool))
| ~ mem(iPr_def_30,arr(ty_2Enum_2Enum,bool)) ),
inference(superposition,[status(thm)],[c_6286,c_36061]) ).
tcf(c_36161,plain,
mem(iPr_def_33,arr(iPr_def_28,bool)),
inference(forward_subsumption_resolution,[status(thm)],[c_36146,c_8585]) ).
tcf(c_36228,plain,
mem(sK41(ty_2Enum_2Enum,iPr_def_28,iPr_def_30,iPr_def_33),iPr_def_34),
inference(backward_subsumption_resolution,[status(thm)],[c_29222,c_36161]) ).
tcf(c_53066,plain,
p(ap(ap(ap(iPr_def_29,sK41(ty_2Enum_2Enum,iPr_def_28,iPr_def_30,iPr_def_33)),iPr_def_30),iPr_def_33)),
inference(global_subsumption_just,[status(thm)],[c_30864,c_30864,c_36161]) ).
tcf(c_53078,plain,
~ mem(sK41(ty_2Enum_2Enum,iPr_def_28,iPr_def_30,iPr_def_33),iPr_def_34),
inference(superposition,[status(thm)],[c_53066,c_6288]) ).
tcf(c_53079,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_53078,c_36228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ITP020+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.19/0.44 % Computer : n006.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Wed Sep 23 17:45:56 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.26/0.51 Running first-order theorem proving
% 0.26/0.51 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
% 0.26/0.52
% 0.26/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.26/0.52
% 0.26/0.52 % Detected problem language: tptp
% 0.26/0.54 % Proving...
% 21.29/4.98 % SZS status Started for theBenchmark.p
% 21.29/4.98 % SZS status Theorem for theBenchmark.p
% 21.29/4.98
% 21.29/4.98 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 21.29/4.98
% 21.29/4.98 % ------ iProver source info
% 21.29/4.98
% 21.29/4.98 % git: date: 2026-07-19 20:42:38 +0200
% 21.29/4.98 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 21.29/4.98 % git: non_committed_changes: false
% 21.29/4.98
% 21.29/4.98 % ------ Parsing...
% 21.29/4.98 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 21.29/4.98
% 21.29/4.98 % ------ Preprocessing... sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 21.29/4.98
% 21.29/4.98 % ------ Preprocessing... gs_s sp: 32 0s gs_e snvd_s sp: 0 0s snvd_e %
% 21.29/4.98
% 21.29/4.98 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 21.29/4.98 % ------ Proving...
% 21.29/4.98 % ------ Problem Properties
% 21.29/4.98
% 21.29/4.98 %
% 21.29/4.98 % clauses 125
% 21.29/4.98 % conjectures 1
% 21.29/4.98 % EPR 27
% 21.29/4.98 % Horn 85
% 21.29/4.98 % unary 20
% 21.29/4.98 % binary 23
% 21.29/4.98 % lits 508
% 21.29/4.98 % lits eq 15
% 21.29/4.98 % fd_pure 0
% 21.29/4.98 % fd_pseudo 0
% 21.29/4.98 % fd_cond 0
% 21.29/4.98 % fd_pseudo_cond 5
% 21.29/4.98 % AC symbols 0
% 21.29/4.98
% 21.29/4.98 % ------ Schedule dynamic 5 is on
% 21.29/4.98
% 21.29/4.98 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 21.29/4.98
% 21.29/4.98
% 21.29/4.98 % ------
% 21.29/4.98 % Current options:
% 21.29/4.98 % ------
% 21.29/4.98
% 21.29/4.98
% 21.29/4.98 %
% 21.29/4.98
% 21.29/4.98 % ------ Proving...
% 21.29/4.98 %
% 21.29/4.98
% 21.29/4.98 % SZS status Theorem for theBenchmark.p
% 21.29/4.98
% 21.29/4.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 21.29/4.98
% 21.29/4.98
%------------------------------------------------------------------------------