%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ITP004+2 : TPTP v9.2.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:31:24 PM UTC 2026
% Result : Theorem 2.04s 1.93s
% Output : CNFRefutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 91 ( 16 unt; 0 def)
% Number of atoms : 316 ( 22 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 380 ( 155 ~; 178 |; 12 &)
% ( 6 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 125 ( 0 sgn 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_thm_2Epred__set_2EREST__SUBSET,conjecture,
! [X9] :
( ne(X9)
=> ! [X10] :
( mem(X10,arr(X9,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X9),ap(c_2Epred__set_2EREST(X9),X10)),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EREST__SUBSET) ).
fof(ap_tp,axiom,
! [X1,X2,X3] :
( mem(X3,arr(X1,X2))
=> ! [X4] :
( mem(X4,X1)
=> mem(ap(X3,X4),X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ITP001/ITP001+2.ax',ap_tp) ).
fof(mem_c_2Epred__set_2ESUBSET,axiom,
! [X9] :
( ne(X9)
=> mem(c_2Epred__set_2ESUBSET(X9),arr(arr(X9,bool),arr(arr(X9,bool),bool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Epred__set_2ESUBSET) ).
fof(ax_thm_2Epred__set_2ESUBSET__DEF,axiom,
! [X9] :
( ne(X9)
=> ! [X10] :
( mem(X10,arr(X9,bool))
=> ! [X11] :
( mem(X11,arr(X9,bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(X9),X10),X11))
<=> ! [X12] :
( mem(X12,X9)
=> ( p(ap(ap(c_2Ebool_2EIN(X9),X12),X10))
=> p(ap(ap(c_2Ebool_2EIN(X9),X12),X11)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Epred__set_2ESUBSET__DEF) ).
fof(boolext,axiom,
! [X5] :
( mem(X5,bool)
=> ! [X6] :
( mem(X6,bool)
=> ( ( p(X5)
<=> p(X6) )
=> X5 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ITP001/ITP001+2.ax',boolext) ).
fof(mem_c_2Epred__set_2EREST,axiom,
! [X9] :
( ne(X9)
=> mem(c_2Epred__set_2EREST(X9),arr(arr(X9,bool),arr(X9,bool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Epred__set_2EREST) ).
fof(mem_c_2Ebool_2E_7E,axiom,
mem(c_2Ebool_2E_7E,arr(bool,bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2E_7E) ).
fof(bool_ne,axiom,
ne(bool),
file('/export/starexec/sandbox2/benchmark/Axioms/ITP001/ITP001+2.ax',bool_ne) ).
fof(mem_c_2Ebool_2E_21,axiom,
! [X9] :
( ne(X9)
=> mem(c_2Ebool_2E_21(X9),arr(arr(X9,bool),bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2E_21) ).
fof(ax_all_p,axiom,
! [X1] :
( ne(X1)
=> ! [X5] :
( mem(X5,arr(X1,bool))
=> ( p(ap(c_2Ebool_2E_21(X1),X5))
<=> ! [X4] :
( mem(X4,X1)
=> p(ap(X5,X4)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_all_p) ).
fof(mem_c_2Epred__set_2ECHOICE,axiom,
! [X9] :
( ne(X9)
=> mem(c_2Epred__set_2ECHOICE(X9),arr(arr(X9,bool),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Epred__set_2ECHOICE) ).
fof(conj_thm_2Epred__set_2EIN__DELETE,axiom,
! [X9] :
( ne(X9)
=> ! [X10] :
( mem(X10,arr(X9,bool))
=> ! [X13] :
( mem(X13,X9)
=> ! [X14] :
( mem(X14,X9)
=> ( p(ap(ap(c_2Ebool_2EIN(X9),X13),ap(ap(c_2Epred__set_2EDELETE(X9),X10),X14)))
<=> ( p(ap(ap(c_2Ebool_2EIN(X9),X13),X10))
& X13 != X14 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EIN__DELETE) ).
fof(ax_thm_2Epred__set_2EREST__DEF,axiom,
! [X9] :
( ne(X9)
=> ! [X10] :
( mem(X10,arr(X9,bool))
=> ap(c_2Epred__set_2EREST(X9),X10) = ap(ap(c_2Epred__set_2EDELETE(X9),X10),ap(c_2Epred__set_2ECHOICE(X9),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Epred__set_2EREST__DEF) ).
fof(ax_neg_p,axiom,
! [X5] :
( mem(X5,bool)
=> ( p(ap(c_2Ebool_2E_7E,X5))
<=> ~ p(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_neg_p) ).
fof(c_0_14,negated_conjecture,
~ ! [X9] :
( ne(X9)
=> ! [X10] :
( mem(X10,arr(X9,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X9),ap(c_2Epred__set_2EREST(X9),X10)),X10)) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Epred__set_2EREST__SUBSET]) ).
fof(c_0_15,plain,
! [X65,X66,X67,X68] :
( ~ mem(X67,arr(X65,X66))
| ~ mem(X68,X65)
| mem(ap(X67,X68),X66) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])]) ).
fof(c_0_16,plain,
! [X83] :
( ~ ne(X83)
| mem(c_2Epred__set_2ESUBSET(X83),arr(arr(X83,bool),arr(arr(X83,bool),bool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mem_c_2Epred__set_2ESUBSET])]) ).
fof(c_0_17,plain,
! [X100,X101,X102,X103] :
( ( ~ p(ap(ap(c_2Epred__set_2ESUBSET(X100),X101),X102))
| ~ mem(X103,X100)
| ~ p(ap(ap(c_2Ebool_2EIN(X100),X103),X101))
| p(ap(ap(c_2Ebool_2EIN(X100),X103),X102))
| ~ mem(X102,arr(X100,bool))
| ~ mem(X101,arr(X100,bool))
| ~ ne(X100) )
& ( mem(esk3_3(X100,X101,X102),X100)
| p(ap(ap(c_2Epred__set_2ESUBSET(X100),X101),X102))
| ~ mem(X102,arr(X100,bool))
| ~ mem(X101,arr(X100,bool))
| ~ ne(X100) )
& ( p(ap(ap(c_2Ebool_2EIN(X100),esk3_3(X100,X101,X102)),X101))
| p(ap(ap(c_2Epred__set_2ESUBSET(X100),X101),X102))
| ~ mem(X102,arr(X100,bool))
| ~ mem(X101,arr(X100,bool))
| ~ ne(X100) )
& ( ~ p(ap(ap(c_2Ebool_2EIN(X100),esk3_3(X100,X101,X102)),X102))
| p(ap(ap(c_2Epred__set_2ESUBSET(X100),X101),X102))
| ~ mem(X102,arr(X100,bool))
| ~ mem(X101,arr(X100,bool))
| ~ ne(X100) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax_thm_2Epred__set_2ESUBSET__DEF])])])])]) ).
fof(c_0_18,negated_conjecture,
( ne(esk4_0)
& mem(esk5_0,arr(esk4_0,bool))
& ~ p(ap(ap(c_2Epred__set_2ESUBSET(esk4_0),ap(c_2Epred__set_2EREST(esk4_0),esk5_0)),esk5_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
cnf(c_0_19,plain,
( mem(ap(X1,X4),X3)
| ~ mem(X1,arr(X2,X3))
| ~ mem(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( mem(c_2Epred__set_2ESUBSET(X1),arr(arr(X1,bool),arr(arr(X1,bool),bool)))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( p(ap(ap(c_2Ebool_2EIN(X1),esk3_3(X1,X2,X3)),X2))
| p(ap(ap(c_2Epred__set_2ESUBSET(X1),X2),X3))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
mem(esk5_0,arr(esk4_0,bool)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
ne(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_24,plain,
! [X69,X70] :
( ( ~ p(X69)
| ~ p(X70)
| X69 = X70
| ~ mem(X70,bool)
| ~ mem(X69,bool) )
& ( p(X69)
| p(X70)
| X69 = X70
| ~ mem(X70,bool)
| ~ mem(X69,bool) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[boolext])])])]) ).
cnf(c_0_25,plain,
( mem(ap(c_2Epred__set_2ESUBSET(X1),X2),arr(arr(X1,bool),bool))
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
( p(ap(ap(c_2Ebool_2EIN(esk4_0),esk3_3(esk4_0,X1,esk5_0)),X1))
| p(ap(ap(c_2Epred__set_2ESUBSET(esk4_0),X1),esk5_0))
| ~ mem(X1,arr(esk4_0,bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_27,plain,
( p(X1)
| p(X2)
| X1 = X2
| ~ mem(X2,bool)
| ~ mem(X1,bool) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
( mem(ap(ap(c_2Epred__set_2ESUBSET(X1),X2),X3),bool)
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
fof(c_0_29,plain,
! [X90] :
( ~ ne(X90)
| mem(c_2Epred__set_2EREST(X90),arr(arr(X90,bool),arr(X90,bool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mem_c_2Epred__set_2EREST])]) ).
cnf(c_0_30,plain,
( X1 = X2
| ~ p(X1)
| ~ p(X2)
| ~ mem(X2,bool)
| ~ mem(X1,bool) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( p(ap(ap(c_2Epred__set_2ESUBSET(X1),X2),X3))
| ~ p(ap(ap(c_2Ebool_2EIN(X1),esk3_3(X1,X2,X3)),X3))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_32,negated_conjecture,
( p(ap(ap(c_2Ebool_2EIN(esk4_0),esk3_3(esk4_0,esk5_0,esk5_0)),esk5_0))
| p(ap(ap(c_2Epred__set_2ESUBSET(esk4_0),esk5_0),esk5_0)) ),
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_33,plain,
mem(c_2Ebool_2E_7E,arr(bool,bool)),
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2E_7E]) ).
cnf(c_0_34,plain,
ne(bool),
inference(split_conjunct,[status(thm)],[bool_ne]) ).
cnf(c_0_35,plain,
( X1 = ap(ap(c_2Epred__set_2ESUBSET(X2),X3),X4)
| p(ap(ap(c_2Epred__set_2ESUBSET(X2),X3),X4))
| p(X1)
| ~ mem(X4,arr(X2,bool))
| ~ mem(X3,arr(X2,bool))
| ~ mem(X1,bool)
| ~ ne(X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,plain,
( mem(c_2Epred__set_2EREST(X1),arr(arr(X1,bool),arr(X1,bool)))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,plain,
( X1 = ap(ap(c_2Epred__set_2ESUBSET(X2),X3),X4)
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X2),X3),X4))
| ~ p(X1)
| ~ mem(X4,arr(X2,bool))
| ~ mem(X3,arr(X2,bool))
| ~ mem(X1,bool)
| ~ ne(X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_28]) ).
cnf(c_0_38,negated_conjecture,
p(ap(ap(c_2Epred__set_2ESUBSET(esk4_0),esk5_0),esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_22]),c_0_23])]) ).
cnf(c_0_39,plain,
( p(ap(ap(c_2Ebool_2EIN(bool),esk3_3(bool,X1,c_2Ebool_2E_7E)),X1))
| p(ap(ap(c_2Epred__set_2ESUBSET(bool),X1),c_2Ebool_2E_7E))
| ~ mem(X1,arr(bool,bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_33]),c_0_34])]) ).
cnf(c_0_40,negated_conjecture,
( X1 = ap(ap(c_2Epred__set_2ESUBSET(esk4_0),X2),esk5_0)
| p(ap(ap(c_2Epred__set_2ESUBSET(esk4_0),X2),esk5_0))
| p(X1)
| ~ mem(X2,arr(esk4_0,bool))
| ~ mem(X1,bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_22]),c_0_23])]) ).
cnf(c_0_41,plain,
( mem(ap(c_2Epred__set_2EREST(X1),X2),arr(X1,bool))
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_36]) ).
fof(c_0_42,plain,
! [X95] :
( ~ ne(X95)
| mem(c_2Ebool_2E_21(X95),arr(arr(X95,bool),bool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mem_c_2Ebool_2E_21])]) ).
fof(c_0_43,plain,
! [X96,X97,X98] :
( ( ~ p(ap(c_2Ebool_2E_21(X96),X97))
| ~ mem(X98,X96)
| p(ap(X97,X98))
| ~ mem(X97,arr(X96,bool))
| ~ ne(X96) )
& ( mem(esk2_2(X96,X97),X96)
| p(ap(c_2Ebool_2E_21(X96),X97))
| ~ mem(X97,arr(X96,bool))
| ~ ne(X96) )
& ( ~ p(ap(X97,esk2_2(X96,X97)))
| p(ap(c_2Ebool_2E_21(X96),X97))
| ~ mem(X97,arr(X96,bool))
| ~ ne(X96) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax_all_p])])])])]) ).
cnf(c_0_44,negated_conjecture,
( X1 = ap(ap(c_2Epred__set_2ESUBSET(esk4_0),esk5_0),esk5_0)
| ~ p(X1)
| ~ mem(X1,bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_22]),c_0_23])]) ).
cnf(c_0_45,plain,
( p(ap(ap(c_2Ebool_2EIN(bool),esk3_3(bool,c_2Ebool_2E_7E,c_2Ebool_2E_7E)),c_2Ebool_2E_7E))
| p(ap(ap(c_2Epred__set_2ESUBSET(bool),c_2Ebool_2E_7E),c_2Ebool_2E_7E)) ),
inference(spm,[status(thm)],[c_0_39,c_0_33]) ).
fof(c_0_46,plain,
! [X88] :
( ~ ne(X88)
| mem(c_2Epred__set_2ECHOICE(X88),arr(arr(X88,bool),X88)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mem_c_2Epred__set_2ECHOICE])]) ).
cnf(c_0_47,negated_conjecture,
( X1 = ap(ap(c_2Epred__set_2ESUBSET(esk4_0),ap(c_2Epred__set_2EREST(esk4_0),X2)),esk5_0)
| p(ap(ap(c_2Epred__set_2ESUBSET(esk4_0),ap(c_2Epred__set_2EREST(esk4_0),X2)),esk5_0))
| p(X1)
| ~ mem(X2,arr(esk4_0,bool))
| ~ mem(X1,bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_23])]) ).
cnf(c_0_48,negated_conjecture,
~ p(ap(ap(c_2Epred__set_2ESUBSET(esk4_0),ap(c_2Epred__set_2EREST(esk4_0),esk5_0)),esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_49,plain,
( mem(c_2Ebool_2E_21(X1),arr(arr(X1,bool),bool))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,plain,
( mem(esk2_2(X1,X2),X1)
| p(ap(c_2Ebool_2E_21(X1),X2))
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_51,negated_conjecture,
( ap(ap(c_2Epred__set_2ESUBSET(X1),X2),X3) = ap(ap(c_2Epred__set_2ESUBSET(esk4_0),esk5_0),esk5_0)
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X1),X2),X3))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_28]) ).
cnf(c_0_52,plain,
p(ap(ap(c_2Epred__set_2ESUBSET(bool),c_2Ebool_2E_7E),c_2Ebool_2E_7E)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_45]),c_0_33]),c_0_34])]) ).
fof(c_0_53,plain,
! [X105,X106,X107,X108] :
( ( p(ap(ap(c_2Ebool_2EIN(X105),X107),X106))
| ~ p(ap(ap(c_2Ebool_2EIN(X105),X107),ap(ap(c_2Epred__set_2EDELETE(X105),X106),X108)))
| ~ mem(X108,X105)
| ~ mem(X107,X105)
| ~ mem(X106,arr(X105,bool))
| ~ ne(X105) )
& ( X107 != X108
| ~ p(ap(ap(c_2Ebool_2EIN(X105),X107),ap(ap(c_2Epred__set_2EDELETE(X105),X106),X108)))
| ~ mem(X108,X105)
| ~ mem(X107,X105)
| ~ mem(X106,arr(X105,bool))
| ~ ne(X105) )
& ( ~ p(ap(ap(c_2Ebool_2EIN(X105),X107),X106))
| X107 = X108
| p(ap(ap(c_2Ebool_2EIN(X105),X107),ap(ap(c_2Epred__set_2EDELETE(X105),X106),X108)))
| ~ mem(X108,X105)
| ~ mem(X107,X105)
| ~ mem(X106,arr(X105,bool))
| ~ ne(X105) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Epred__set_2EIN__DELETE])])])]) ).
fof(c_0_54,plain,
! [X109,X110] :
( ~ ne(X109)
| ~ mem(X110,arr(X109,bool))
| ap(c_2Epred__set_2EREST(X109),X110) = ap(ap(c_2Epred__set_2EDELETE(X109),X110),ap(c_2Epred__set_2ECHOICE(X109),X110)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax_thm_2Epred__set_2EREST__DEF])])]) ).
cnf(c_0_55,plain,
( mem(c_2Epred__set_2ECHOICE(X1),arr(arr(X1,bool),X1))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_56,negated_conjecture,
( X1 = ap(ap(c_2Epred__set_2ESUBSET(esk4_0),ap(c_2Epred__set_2EREST(esk4_0),esk5_0)),esk5_0)
| p(X1)
| ~ mem(X1,bool) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_22]),c_0_48]) ).
cnf(c_0_57,plain,
( mem(ap(c_2Ebool_2E_21(X1),X2),bool)
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_49]) ).
fof(c_0_58,plain,
! [X5] :
( mem(X5,bool)
=> ( p(ap(c_2Ebool_2E_7E,X5))
<=> ~ p(X5) ) ),
inference(fof_simplification,[status(thm)],[ax_neg_p]) ).
cnf(c_0_59,plain,
( p(ap(X2,X3))
| ~ p(ap(c_2Ebool_2E_21(X1),X2))
| ~ mem(X3,X1)
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_60,plain,
( p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| mem(esk2_2(bool,c_2Ebool_2E_7E),bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_33]),c_0_34])]) ).
cnf(c_0_61,negated_conjecture,
ap(ap(c_2Epred__set_2ESUBSET(esk4_0),esk5_0),esk5_0) = ap(ap(c_2Epred__set_2ESUBSET(bool),c_2Ebool_2E_7E),c_2Ebool_2E_7E),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_33]),c_0_34])]) ).
cnf(c_0_62,plain,
( p(ap(ap(c_2Ebool_2EIN(X1),X2),X3))
| ~ p(ap(ap(c_2Ebool_2EIN(X1),X2),ap(ap(c_2Epred__set_2EDELETE(X1),X3),X4)))
| ~ mem(X4,X1)
| ~ mem(X2,X1)
| ~ mem(X3,arr(X1,bool))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_63,plain,
( ap(c_2Epred__set_2EREST(X1),X2) = ap(ap(c_2Epred__set_2EDELETE(X1),X2),ap(c_2Epred__set_2ECHOICE(X1),X2))
| ~ ne(X1)
| ~ mem(X2,arr(X1,bool)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_64,plain,
( mem(ap(c_2Epred__set_2ECHOICE(X1),X2),X1)
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_55]) ).
cnf(c_0_65,negated_conjecture,
( p(ap(ap(c_2Ebool_2EIN(esk4_0),esk3_3(esk4_0,ap(c_2Epred__set_2EREST(esk4_0),X1),esk5_0)),ap(c_2Epred__set_2EREST(esk4_0),X1)))
| p(ap(ap(c_2Epred__set_2ESUBSET(esk4_0),ap(c_2Epred__set_2EREST(esk4_0),X1)),esk5_0))
| ~ mem(X1,arr(esk4_0,bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_41]),c_0_23])]) ).
cnf(c_0_66,negated_conjecture,
( ap(c_2Ebool_2E_21(X1),X2) = ap(ap(c_2Epred__set_2ESUBSET(esk4_0),ap(c_2Epred__set_2EREST(esk4_0),esk5_0)),esk5_0)
| p(ap(c_2Ebool_2E_21(X1),X2))
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
fof(c_0_67,plain,
! [X84] :
( ( ~ p(ap(c_2Ebool_2E_7E,X84))
| ~ p(X84)
| ~ mem(X84,bool) )
& ( p(X84)
| p(ap(c_2Ebool_2E_7E,X84))
| ~ mem(X84,bool) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])]) ).
cnf(c_0_68,plain,
( p(ap(c_2Ebool_2E_7E,X1))
| mem(esk2_2(bool,c_2Ebool_2E_7E),bool)
| ~ mem(X1,bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_33]),c_0_34])]) ).
cnf(c_0_69,negated_conjecture,
mem(ap(ap(c_2Epred__set_2ESUBSET(bool),c_2Ebool_2E_7E),c_2Ebool_2E_7E),bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_61]),c_0_22]),c_0_23])]) ).
cnf(c_0_70,plain,
( p(ap(ap(c_2Ebool_2EIN(X1),X2),X3))
| ~ p(ap(ap(c_2Ebool_2EIN(X1),X2),ap(c_2Epred__set_2EREST(X1),X3)))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,X1)
| ~ ne(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_71,negated_conjecture,
p(ap(ap(c_2Ebool_2EIN(esk4_0),esk3_3(esk4_0,ap(c_2Epred__set_2EREST(esk4_0),esk5_0),esk5_0)),ap(c_2Epred__set_2EREST(esk4_0),esk5_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_22]),c_0_48]) ).
cnf(c_0_72,plain,
( mem(esk3_3(X1,X2,X3),X1)
| p(ap(ap(c_2Epred__set_2ESUBSET(X1),X2),X3))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_73,negated_conjecture,
( ap(ap(c_2Epred__set_2ESUBSET(esk4_0),ap(c_2Epred__set_2EREST(esk4_0),esk5_0)),esk5_0) = ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E)
| p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_33]),c_0_34])]) ).
cnf(c_0_74,plain,
( ~ p(ap(c_2Ebool_2E_7E,X1))
| ~ p(X1)
| ~ mem(X1,bool) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_75,negated_conjecture,
( p(ap(c_2Ebool_2E_7E,ap(ap(c_2Epred__set_2ESUBSET(bool),c_2Ebool_2E_7E),c_2Ebool_2E_7E)))
| mem(esk2_2(bool,c_2Ebool_2E_7E),bool) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_76,negated_conjecture,
( p(ap(ap(c_2Ebool_2EIN(esk4_0),esk3_3(esk4_0,ap(c_2Epred__set_2EREST(esk4_0),esk5_0),esk5_0)),esk5_0))
| ~ mem(esk3_3(esk4_0,ap(c_2Epred__set_2EREST(esk4_0),esk5_0),esk5_0),esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_22]),c_0_23])]) ).
cnf(c_0_77,negated_conjecture,
( p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| mem(esk3_3(esk4_0,ap(c_2Epred__set_2EREST(esk4_0),esk5_0),esk5_0),esk4_0)
| ~ mem(ap(c_2Epred__set_2EREST(esk4_0),esk5_0),arr(esk4_0,bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_22]),c_0_23])]) ).
cnf(c_0_78,negated_conjecture,
mem(esk2_2(bool,c_2Ebool_2E_7E),bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_52]),c_0_69])]) ).
cnf(c_0_79,negated_conjecture,
( ~ mem(esk3_3(esk4_0,ap(c_2Epred__set_2EREST(esk4_0),esk5_0),esk5_0),esk4_0)
| ~ mem(ap(c_2Epred__set_2EREST(esk4_0),esk5_0),arr(esk4_0,bool)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_76]),c_0_22]),c_0_23])]),c_0_48]) ).
cnf(c_0_80,negated_conjecture,
( p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| mem(esk3_3(esk4_0,ap(c_2Epred__set_2EREST(esk4_0),esk5_0),esk5_0),esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_41]),c_0_22]),c_0_23])]) ).
cnf(c_0_81,negated_conjecture,
( ap(ap(c_2Epred__set_2ESUBSET(esk4_0),ap(c_2Epred__set_2EREST(esk4_0),esk5_0)),esk5_0) = esk2_2(bool,c_2Ebool_2E_7E)
| p(esk2_2(bool,c_2Ebool_2E_7E)) ),
inference(spm,[status(thm)],[c_0_56,c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| ~ mem(ap(c_2Epred__set_2EREST(esk4_0),esk5_0),arr(esk4_0,bool)) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_83,negated_conjecture,
( p(esk2_2(bool,c_2Ebool_2E_7E))
| mem(esk3_3(esk4_0,ap(c_2Epred__set_2EREST(esk4_0),esk5_0),esk5_0),esk4_0)
| ~ mem(ap(c_2Epred__set_2EREST(esk4_0),esk5_0),arr(esk4_0,bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_81]),c_0_22]),c_0_23])]) ).
cnf(c_0_84,negated_conjecture,
p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_41]),c_0_22]),c_0_23])]) ).
cnf(c_0_85,negated_conjecture,
( p(esk2_2(bool,c_2Ebool_2E_7E))
| mem(esk3_3(esk4_0,ap(c_2Epred__set_2EREST(esk4_0),esk5_0),esk5_0),esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_41]),c_0_22]),c_0_23])]) ).
cnf(c_0_86,negated_conjecture,
( p(ap(c_2Ebool_2E_7E,X1))
| ~ mem(X1,bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_84]),c_0_33]),c_0_34])]) ).
cnf(c_0_87,negated_conjecture,
( p(esk2_2(bool,c_2Ebool_2E_7E))
| ~ mem(ap(c_2Epred__set_2EREST(esk4_0),esk5_0),arr(esk4_0,bool)) ),
inference(spm,[status(thm)],[c_0_79,c_0_85]) ).
cnf(c_0_88,negated_conjecture,
( ~ p(X1)
| ~ mem(X1,bool) ),
inference(spm,[status(thm)],[c_0_74,c_0_86]) ).
cnf(c_0_89,negated_conjecture,
p(esk2_2(bool,c_2Ebool_2E_7E)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_41]),c_0_22]),c_0_23])]) ).
cnf(c_0_90,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_78])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP004+2 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n029.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 19:34:29 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.04/1.93 % Version : CSE_E---1.7
% 2.04/1.93 % Problem : theBenchmark.p
% 2.04/1.93 % SZS status Theorem for theBenchmark.p
% 2.04/1.93 % SZS output start CNFRefutation
% See solution above
% 2.04/1.94 % Total time : 1.371s
%------------------------------------------------------------------------------