%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ITP004+5 : 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 : n023.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 04:31:25 PM UTC 2026
% Result : Theorem 24.53s 15.22s
% Output : CNFRefutation 24.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 7 unt; 0 def)
% Number of atoms : 140 ( 20 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 159 ( 63 ~; 67 |; 5 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 69 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_thm_2Epred__set_2EREST__SUBSET,conjecture,
! [X9] :
( ne(X9)
=> ! [X168] :
( mem(X168,arr(X9,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X9),ap(c_2Epred__set_2EREST(X9),X168)),X168)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EREST__SUBSET) ).
fof(conj_thm_2Epred__set_2ECHOICE__INSERT__REST,axiom,
! [X9] :
( ne(X9)
=> ! [X168] :
( mem(X168,arr(X9,bool))
=> ( X168 != c_2Epred__set_2EEMPTY(X9)
=> ap(ap(c_2Epred__set_2EINSERT(X9),ap(c_2Epred__set_2ECHOICE(X9),X168)),ap(c_2Epred__set_2EREST(X9),X168)) = X168 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Epred__set_2ECHOICE__INSERT__REST) ).
fof(conj_thm_2Epred__set_2ESUBSET__OF__INSERT,axiom,
! [X9] :
( ne(X9)
=> ! [X32] :
( mem(X32,X9)
=> ! [X148] :
( mem(X148,arr(X9,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X9),X148),ap(ap(c_2Epred__set_2EINSERT(X9),X32),X148))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Epred__set_2ESUBSET__OF__INSERT) ).
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_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_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_2EEMPTY__DELETE,axiom,
! [X9] :
( ne(X9)
=> ! [X32] :
( mem(X32,X9)
=> ap(ap(c_2Epred__set_2EDELETE(X9),c_2Epred__set_2EEMPTY(X9)),X32) = c_2Epred__set_2EEMPTY(X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EEMPTY__DELETE) ).
fof(conj_thm_2Epred__set_2ESUBSET__applied,axiom,
! [X9] :
( ne(X9)
=> ! [X168] :
( mem(X168,arr(X9,bool))
=> ! [X42] :
( mem(X42,arr(X9,bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(X9),X168),X42))
<=> ! [X26] :
( mem(X26,X9)
=> ( p(ap(X168,X26))
=> p(ap(X42,X26)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Epred__set_2ESUBSET__applied) ).
fof(ax_thm_2Epred__set_2EREST__DEF,axiom,
! [X9] :
( ne(X9)
=> ! [X168] :
( mem(X168,arr(X9,bool))
=> ap(c_2Epred__set_2EREST(X9),X168) = ap(ap(c_2Epred__set_2EDELETE(X9),X168),ap(c_2Epred__set_2ECHOICE(X9),X168)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Epred__set_2EREST__DEF) ).
fof(c_0_9,negated_conjecture,
~ ! [X9] :
( ne(X9)
=> ! [X168] :
( mem(X168,arr(X9,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X9),ap(c_2Epred__set_2EREST(X9),X168)),X168)) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Epred__set_2EREST__SUBSET]) ).
fof(c_0_10,plain,
! [X2278,X2279] :
( ~ ne(X2278)
| ~ mem(X2279,arr(X2278,bool))
| X2279 = c_2Epred__set_2EEMPTY(X2278)
| ap(ap(c_2Epred__set_2EINSERT(X2278),ap(c_2Epred__set_2ECHOICE(X2278),X2279)),ap(c_2Epred__set_2EREST(X2278),X2279)) = X2279 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Epred__set_2ECHOICE__INSERT__REST])])]) ).
fof(c_0_11,negated_conjecture,
( ne(esk1_0)
& mem(esk2_0,arr(esk1_0,bool))
& ~ p(ap(ap(c_2Epred__set_2ESUBSET(esk1_0),ap(c_2Epred__set_2EREST(esk1_0),esk2_0)),esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_12,plain,
! [X2323,X2324,X2325] :
( ~ ne(X2323)
| ~ mem(X2324,X2323)
| ~ mem(X2325,arr(X2323,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(X2323),X2325),ap(ap(c_2Epred__set_2EINSERT(X2323),X2324),X2325))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Epred__set_2ESUBSET__OF__INSERT])])]) ).
cnf(c_0_13,plain,
( X2 = c_2Epred__set_2EEMPTY(X1)
| ap(ap(c_2Epred__set_2EINSERT(X1),ap(c_2Epred__set_2ECHOICE(X1),X2)),ap(c_2Epred__set_2EREST(X1),X2)) = X2
| ~ ne(X1)
| ~ mem(X2,arr(X1,bool)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
mem(esk2_0,arr(esk1_0,bool)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
ne(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X2328,X2329,X2330,X2331] :
( ~ mem(X2330,arr(X2328,X2329))
| ~ mem(X2331,X2328)
| mem(ap(X2330,X2331),X2329) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])]) ).
fof(c_0_17,plain,
! [X2267] :
( ~ ne(X2267)
| mem(c_2Epred__set_2EREST(X2267),arr(arr(X2267,bool),arr(X2267,bool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mem_c_2Epred__set_2EREST])]) ).
cnf(c_0_18,plain,
( p(ap(ap(c_2Epred__set_2ESUBSET(X1),X3),ap(ap(c_2Epred__set_2EINSERT(X1),X2),X3)))
| ~ ne(X1)
| ~ mem(X2,X1)
| ~ mem(X3,arr(X1,bool)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
( ap(ap(c_2Epred__set_2EINSERT(esk1_0),ap(c_2Epred__set_2ECHOICE(esk1_0),esk2_0)),ap(c_2Epred__set_2EREST(esk1_0),esk2_0)) = esk2_0
| c_2Epred__set_2EEMPTY(esk1_0) = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_20,negated_conjecture,
~ p(ap(ap(c_2Epred__set_2ESUBSET(esk1_0),ap(c_2Epred__set_2EREST(esk1_0),esk2_0)),esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,plain,
( mem(ap(X1,X4),X3)
| ~ mem(X1,arr(X2,X3))
| ~ mem(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( mem(c_2Epred__set_2EREST(X1),arr(arr(X1,bool),arr(X1,bool)))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X2387] :
( ~ ne(X2387)
| mem(c_2Epred__set_2ECHOICE(X2387),arr(arr(X2387,bool),X2387)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mem_c_2Epred__set_2ECHOICE])]) ).
cnf(c_0_24,negated_conjecture,
( c_2Epred__set_2EEMPTY(esk1_0) = esk2_0
| ~ mem(ap(c_2Epred__set_2EREST(esk1_0),esk2_0),arr(esk1_0,bool))
| ~ mem(ap(c_2Epred__set_2ECHOICE(esk1_0),esk2_0),esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_15])]),c_0_20]) ).
cnf(c_0_25,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_21,c_0_22]) ).
cnf(c_0_26,plain,
( mem(c_2Epred__set_2ECHOICE(X1),arr(arr(X1,bool),X1))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_27,plain,
! [X2412,X2413] :
( ~ ne(X2412)
| ~ mem(X2413,X2412)
| ap(ap(c_2Epred__set_2EDELETE(X2412),c_2Epred__set_2EEMPTY(X2412)),X2413) = c_2Epred__set_2EEMPTY(X2412) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Epred__set_2EEMPTY__DELETE])])]) ).
cnf(c_0_28,negated_conjecture,
( c_2Epred__set_2EEMPTY(esk1_0) = esk2_0
| ~ mem(ap(c_2Epred__set_2ECHOICE(esk1_0),esk2_0),esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_14]),c_0_15])]) ).
cnf(c_0_29,plain,
( mem(ap(c_2Epred__set_2ECHOICE(X1),X2),X1)
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
fof(c_0_30,plain,
! [X2290,X2291,X2292,X2293] :
( ( ~ p(ap(ap(c_2Epred__set_2ESUBSET(X2290),X2291),X2292))
| ~ mem(X2293,X2290)
| ~ p(ap(X2291,X2293))
| p(ap(X2292,X2293))
| ~ mem(X2292,arr(X2290,bool))
| ~ mem(X2291,arr(X2290,bool))
| ~ ne(X2290) )
& ( mem(esk79_3(X2290,X2291,X2292),X2290)
| p(ap(ap(c_2Epred__set_2ESUBSET(X2290),X2291),X2292))
| ~ mem(X2292,arr(X2290,bool))
| ~ mem(X2291,arr(X2290,bool))
| ~ ne(X2290) )
& ( p(ap(X2291,esk79_3(X2290,X2291,X2292)))
| p(ap(ap(c_2Epred__set_2ESUBSET(X2290),X2291),X2292))
| ~ mem(X2292,arr(X2290,bool))
| ~ mem(X2291,arr(X2290,bool))
| ~ ne(X2290) )
& ( ~ p(ap(X2292,esk79_3(X2290,X2291,X2292)))
| p(ap(ap(c_2Epred__set_2ESUBSET(X2290),X2291),X2292))
| ~ mem(X2292,arr(X2290,bool))
| ~ mem(X2291,arr(X2290,bool))
| ~ ne(X2290) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Epred__set_2ESUBSET__applied])])])])]) ).
fof(c_0_31,plain,
! [X2268,X2269] :
( ~ ne(X2268)
| ~ mem(X2269,arr(X2268,bool))
| ap(c_2Epred__set_2EREST(X2268),X2269) = ap(ap(c_2Epred__set_2EDELETE(X2268),X2269),ap(c_2Epred__set_2ECHOICE(X2268),X2269)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax_thm_2Epred__set_2EREST__DEF])])]) ).
cnf(c_0_32,plain,
( ap(ap(c_2Epred__set_2EDELETE(X1),c_2Epred__set_2EEMPTY(X1)),X2) = c_2Epred__set_2EEMPTY(X1)
| ~ ne(X1)
| ~ mem(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,negated_conjecture,
c_2Epred__set_2EEMPTY(esk1_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_14]),c_0_15])]) ).
cnf(c_0_34,plain,
( p(ap(X1,esk79_3(X2,X1,X3)))
| p(ap(ap(c_2Epred__set_2ESUBSET(X2),X1),X3))
| ~ mem(X3,arr(X2,bool))
| ~ mem(X1,arr(X2,bool))
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,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_31]) ).
cnf(c_0_36,negated_conjecture,
( ap(ap(c_2Epred__set_2EDELETE(esk1_0),esk2_0),X1) = esk2_0
| ~ mem(X1,esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_15])]) ).
cnf(c_0_37,negated_conjecture,
( p(ap(ap(c_2Epred__set_2ESUBSET(esk1_0),X1),esk2_0))
| p(ap(X1,esk79_3(esk1_0,X1,esk2_0)))
| ~ mem(X1,arr(esk1_0,bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_14]),c_0_15])]) ).
cnf(c_0_38,negated_conjecture,
( ap(c_2Epred__set_2EREST(esk1_0),esk2_0) = esk2_0
| ~ mem(ap(c_2Epred__set_2ECHOICE(esk1_0),esk2_0),esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_14]),c_0_15])]) ).
cnf(c_0_39,plain,
( p(ap(ap(c_2Epred__set_2ESUBSET(X2),X3),X1))
| ~ p(ap(X1,esk79_3(X2,X3,X1)))
| ~ mem(X1,arr(X2,bool))
| ~ mem(X3,arr(X2,bool))
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,negated_conjecture,
( p(ap(esk2_0,esk79_3(esk1_0,esk2_0,esk2_0)))
| p(ap(ap(c_2Epred__set_2ESUBSET(esk1_0),esk2_0),esk2_0)) ),
inference(spm,[status(thm)],[c_0_37,c_0_14]) ).
cnf(c_0_41,negated_conjecture,
ap(c_2Epred__set_2EREST(esk1_0),esk2_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_29]),c_0_14]),c_0_15])]) ).
cnf(c_0_42,negated_conjecture,
p(ap(ap(c_2Epred__set_2ESUBSET(esk1_0),esk2_0),esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_14]),c_0_15])]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_41]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : ITP004+5 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.12/0.14 % 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
% 0.16/0.35 % Computer : n023.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Mon May 4 19:35:54 EDT 2026
% 0.16/0.36 % CPUTime :
% 0.16/0.37 % start to proof: theBenchmark
% 24.53/15.22 % Version : CSE_E---1.7
% 24.53/15.22 % Problem : theBenchmark.p
% 24.53/15.22 % SZS status Theorem for theBenchmark.p
% 24.53/15.22 % SZS output start CNFRefutation
% See solution above
% 24.63/15.32 % Total time : 11.396s
%------------------------------------------------------------------------------