%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP006+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 : Thu Sep 24 12:53:30 PM UTC 2026
% Result : Theorem 6.83s 1.59s
% Output : CNFRefutation 6.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 16 unt; 0 def)
% Number of atoms : 416 ( 23 equ)
% Maximal formula atoms : 132 ( 7 avg)
% Number of connectives : 554 ( 193 ~; 193 |; 60 &)
% ( 20 <=>; 88 =>; 0 <=; 0 <~>)
% Maximal formula depth : 54 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 25 ( 25 usr; 7 con; 0-7 aty)
% Number of variables : 196 ( 14 sgn 113 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax_false_p,axiom,
~ p(c_2Ebool_2EF),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_false_p) ).
fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT,conjecture,
! [X9] :
( ne(X9)
=> ! [X10] :
( ne(X10)
=> ! [X20] :
( mem(X20,arr(X10,X9))
=> ! [X21] :
( mem(X21,arr(X9,bool))
=> ! [X45] :
( mem(X45,arr(X9,bool))
=> ( ! [X46] :
( mem(X46,X9)
=> ( p(ap(X45,X46))
=> p(ap(X21,X46)) ) )
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X10,X9),X20),X21))
=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X10,X9),X20),X45)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT) ).
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(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_2Ebool_2EF,axiom,
mem(c_2Ebool_2EF,bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
fof(conj_thm_2EquantHeuristics_2EGUESS__REWRITES,axiom,
! [X9] :
( ne(X9)
=> ! [X10] :
( ne(X10)
=> ! [X20] :
( mem(X20,arr(X9,X10))
=> ! [X21] :
( mem(X21,arr(X10,bool))
=> ( ! [X36] :
( mem(X36,arr(X9,X10))
=> ! [X37] :
( mem(X37,arr(X10,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X9,X10),X36),X37))
<=> ! [X38] :
( mem(X38,X10)
=> ( ~ p(ap(X37,X38))
=> ? [X39] :
( X38 = ap(X36,X39)
& mem(X39,X9) ) ) ) ) ) )
& ! [X32] :
( mem(X32,arr(X9,X10))
=> ! [X33] :
( mem(X33,arr(X10,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X9,X10),X32),X33))
<=> ! [X34] :
( mem(X34,X10)
=> ( p(ap(X33,X34))
=> ? [X35] :
( X34 = ap(X32,X35)
& mem(X35,X9) ) ) ) ) ) )
& ! [X29] :
( mem(X29,arr(X9,X10))
=> ! [X30] :
( mem(X30,arr(X10,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X9,X10),X29),X30))
<=> ! [X31] :
( mem(X31,X9)
=> ~ p(ap(X30,ap(X29,X31))) ) ) ) )
& ! [X26] :
( mem(X26,arr(X9,X10))
=> ! [X27] :
( mem(X27,arr(X10,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X9,X10),X26),X27))
<=> ! [X28] :
( mem(X28,X9)
=> p(ap(X27,ap(X26,X28))) ) ) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X9,X10),X20),X21))
<=> ! [X24] :
( mem(X24,X10)
=> ( ~ p(ap(X21,X24))
=> ? [X25] :
( ~ p(ap(X21,ap(X20,X25)))
& mem(X25,X9) ) ) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X9,X10),X20),X21))
<=> ! [X22] :
( mem(X22,X10)
=> ( p(ap(X21,X22))
=> ? [X23] :
( p(ap(X21,ap(X20,X23)))
& mem(X23,X9) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2EquantHeuristics_2EGUESS__REWRITES) ).
fof(mem_c_2EquantHeuristics_2EGUESS__FORALL__POINT,axiom,
! [X9] :
( ne(X9)
=> ! [X10] :
( ne(X10)
=> mem(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X9,X10),arr(arr(X9,X10),arr(arr(X10,bool),bool))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2EquantHeuristics_2EGUESS__FORALL__POINT) ).
fof(c_0_7,plain,
~ p(c_2Ebool_2EF),
inference(fof_simplification,[status(thm)],[ax_false_p]) ).
fof(c_0_8,negated_conjecture,
~ ! [X9] :
( ne(X9)
=> ! [X10] :
( ne(X10)
=> ! [X20] :
( mem(X20,arr(X10,X9))
=> ! [X21] :
( mem(X21,arr(X9,bool))
=> ! [X45] :
( mem(X45,arr(X9,bool))
=> ( ! [X46] :
( mem(X46,X9)
=> ( p(ap(X45,X46))
=> p(ap(X21,X46)) ) )
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X10,X9),X20),X21))
=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X10,X9),X20),X45)) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT]) ).
fof(c_0_9,plain,
! [X21,X20,X10,X9] :
( epred1_4(X9,X10,X20,X21)
<=> ( ! [X36] :
( mem(X36,arr(X9,X10))
=> ! [X37] :
( mem(X37,arr(X10,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X9,X10),X36),X37))
<=> ! [X38] :
( mem(X38,X10)
=> ( ~ p(ap(X37,X38))
=> ? [X39] :
( X38 = ap(X36,X39)
& mem(X39,X9) ) ) ) ) ) )
& ! [X32] :
( mem(X32,arr(X9,X10))
=> ! [X33] :
( mem(X33,arr(X10,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X9,X10),X32),X33))
<=> ! [X34] :
( mem(X34,X10)
=> ( p(ap(X33,X34))
=> ? [X35] :
( X34 = ap(X32,X35)
& mem(X35,X9) ) ) ) ) ) )
& ! [X29] :
( mem(X29,arr(X9,X10))
=> ! [X30] :
( mem(X30,arr(X10,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X9,X10),X29),X30))
<=> ! [X31] :
( mem(X31,X9)
=> ~ p(ap(X30,ap(X29,X31))) ) ) ) )
& ! [X26] :
( mem(X26,arr(X9,X10))
=> ! [X27] :
( mem(X27,arr(X10,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X9,X10),X26),X27))
<=> ! [X28] :
( mem(X28,X9)
=> p(ap(X27,ap(X26,X28))) ) ) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X9,X10),X20),X21))
<=> ! [X24] :
( mem(X24,X10)
=> ( ~ p(ap(X21,X24))
=> ? [X25] :
( ~ p(ap(X21,ap(X20,X25)))
& mem(X25,X9) ) ) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X9,X10),X20),X21))
<=> ! [X22] :
( mem(X22,X10)
=> ( p(ap(X21,X22))
=> ? [X23] :
( p(ap(X21,ap(X20,X23)))
& mem(X23,X9) ) ) ) ) ) ),
introduced(definition) ).
fof(c_0_10,plain,
! [X53,X54] :
( ( ~ mem(X53,bool)
| ~ mem(X54,bool)
| X53 = X54
| p(X54)
| p(X53) )
& ( ~ mem(X53,bool)
| ~ mem(X54,bool)
| X53 = X54
| ~ p(X54)
| ~ p(X53) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[boolext])])])])]) ).
fof(c_0_11,plain,
~ p(c_2Ebool_2EF),
inference(fof_nnf,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X49,X50,X51,X52] :
( mem(ap(X51,X52),X50)
| ~ mem(X52,X49)
| ~ mem(X51,arr(X49,X50)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])])]) ).
fof(c_0_13,negated_conjecture,
! [X140] :
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(esk5_0,esk4_0),esk6_0),esk8_0))
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(esk5_0,esk4_0),esk6_0),esk7_0))
& ( p(ap(esk7_0,X140))
| ~ p(ap(esk8_0,X140))
| ~ mem(X140,esk4_0) )
& mem(esk8_0,arr(esk4_0,bool))
& mem(esk7_0,arr(esk4_0,bool))
& mem(esk6_0,arr(esk5_0,esk4_0))
& ne(esk5_0)
& ne(esk4_0) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
fof(c_0_14,plain,
! [X21,X20,X10,X9] :
( epred1_4(X9,X10,X20,X21)
=> ( ! [X36] :
( mem(X36,arr(X9,X10))
=> ! [X37] :
( mem(X37,arr(X10,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X9,X10),X36),X37))
<=> ! [X38] :
( mem(X38,X10)
=> ( ~ p(ap(X37,X38))
=> ? [X39] :
( X38 = ap(X36,X39)
& mem(X39,X9) ) ) ) ) ) )
& ! [X32] :
( mem(X32,arr(X9,X10))
=> ! [X33] :
( mem(X33,arr(X10,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X9,X10),X32),X33))
<=> ! [X34] :
( mem(X34,X10)
=> ( p(ap(X33,X34))
=> ? [X35] :
( X34 = ap(X32,X35)
& mem(X35,X9) ) ) ) ) ) )
& ! [X29] :
( mem(X29,arr(X9,X10))
=> ! [X30] :
( mem(X30,arr(X10,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X9,X10),X29),X30))
<=> ! [X31] :
( mem(X31,X9)
=> ~ p(ap(X30,ap(X29,X31))) ) ) ) )
& ! [X26] :
( mem(X26,arr(X9,X10))
=> ! [X27] :
( mem(X27,arr(X10,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X9,X10),X26),X27))
<=> ! [X28] :
( mem(X28,X9)
=> p(ap(X27,ap(X26,X28))) ) ) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X9,X10),X20),X21))
<=> ! [X24] :
( mem(X24,X10)
=> ( ~ p(ap(X21,X24))
=> ? [X25] :
( ~ p(ap(X21,ap(X20,X25)))
& mem(X25,X9) ) ) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X9,X10),X20),X21))
<=> ! [X22] :
( mem(X22,X10)
=> ( p(ap(X21,X22))
=> ? [X23] :
( p(ap(X21,ap(X20,X23)))
& mem(X23,X9) ) ) ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ mem(X1,bool)
| ~ mem(X2,bool)
| X1 = X2
| p(X2)
| p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
mem(c_2Ebool_2EF,bool),
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2EF]) ).
cnf(c_0_17,plain,
~ p(c_2Ebool_2EF),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( ~ mem(X4,X2)
| ~ mem(X1,arr(X2,X3))
| mem(ap(X1,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
mem(esk8_0,arr(esk4_0,bool)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,plain,
! [X141,X142,X143,X144,X145,X148,X149,X152,X153,X154,X155,X157,X158,X159,X161,X162,X163,X166,X167,X168,X169,X172] :
( ( ~ epred1_4(X144,X143,X142,X141)
| ~ mem(X167,arr(X144,X143))
| ~ mem(X168,arr(X143,bool))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X144,X143),X167),X168))
| esk18_6(X141,X142,X143,X144,X167,X168) != ap(X167,X172)
| ~ mem(X172,X144) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ mem(X167,arr(X144,X143))
| ~ mem(X168,arr(X143,bool))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X144,X143),X167),X168))
| ~ p(ap(X168,esk18_6(X141,X142,X143,X144,X167,X168))) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ mem(X167,arr(X144,X143))
| ~ mem(X168,arr(X143,bool))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X144,X143),X167),X168))
| mem(esk18_6(X141,X142,X143,X144,X167,X168),X143) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ mem(X167,arr(X144,X143))
| ~ mem(X168,arr(X143,bool))
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X144,X143),X167),X168))
| ~ mem(X169,X143)
| p(ap(X168,X169))
| X169 = ap(X167,esk17_7(X141,X142,X143,X144,X167,X168,X169)) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ mem(X167,arr(X144,X143))
| ~ mem(X168,arr(X143,bool))
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X144,X143),X167),X168))
| ~ mem(X169,X143)
| p(ap(X168,X169))
| mem(esk17_7(X141,X142,X143,X144,X167,X168,X169),X144) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ mem(X161,arr(X144,X143))
| ~ mem(X162,arr(X143,bool))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X144,X143),X161),X162))
| esk16_6(X141,X142,X143,X144,X161,X162) != ap(X161,X166)
| ~ mem(X166,X144) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ mem(X161,arr(X144,X143))
| ~ mem(X162,arr(X143,bool))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X144,X143),X161),X162))
| p(ap(X162,esk16_6(X141,X142,X143,X144,X161,X162))) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ mem(X161,arr(X144,X143))
| ~ mem(X162,arr(X143,bool))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X144,X143),X161),X162))
| mem(esk16_6(X141,X142,X143,X144,X161,X162),X143) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ mem(X161,arr(X144,X143))
| ~ mem(X162,arr(X143,bool))
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X144,X143),X161),X162))
| ~ mem(X163,X143)
| ~ p(ap(X162,X163))
| X163 = ap(X161,esk15_7(X141,X142,X143,X144,X161,X162,X163)) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ mem(X161,arr(X144,X143))
| ~ mem(X162,arr(X143,bool))
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X144,X143),X161),X162))
| ~ mem(X163,X143)
| ~ p(ap(X162,X163))
| mem(esk15_7(X141,X142,X143,X144,X161,X162,X163),X144) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ mem(X157,arr(X144,X143))
| ~ mem(X158,arr(X143,bool))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X144,X143),X157),X158))
| p(ap(X158,ap(X157,esk14_6(X141,X142,X143,X144,X157,X158)))) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ mem(X157,arr(X144,X143))
| ~ mem(X158,arr(X143,bool))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X144,X143),X157),X158))
| mem(esk14_6(X141,X142,X143,X144,X157,X158),X144) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ mem(X157,arr(X144,X143))
| ~ mem(X158,arr(X143,bool))
| ~ p(ap(X158,ap(X157,X159)))
| ~ mem(X159,X144)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X144,X143),X157),X158)) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ mem(X153,arr(X144,X143))
| ~ mem(X154,arr(X143,bool))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X144,X143),X153),X154))
| ~ p(ap(X154,ap(X153,esk13_6(X141,X142,X143,X144,X153,X154)))) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ mem(X153,arr(X144,X143))
| ~ mem(X154,arr(X143,bool))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X144,X143),X153),X154))
| mem(esk13_6(X141,X142,X143,X144,X153,X154),X144) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ mem(X153,arr(X144,X143))
| ~ mem(X154,arr(X143,bool))
| p(ap(X154,ap(X153,X155)))
| ~ mem(X155,X144)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X144,X143),X153),X154)) )
& ( ~ epred1_4(X144,X143,X142,X141)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X144,X143),X142),X141))
| p(ap(X141,ap(X142,X152)))
| ~ mem(X152,X144) )
& ( ~ epred1_4(X144,X143,X142,X141)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X144,X143),X142),X141))
| ~ p(ap(X141,esk12_4(X141,X142,X143,X144))) )
& ( ~ epred1_4(X144,X143,X142,X141)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X144,X143),X142),X141))
| mem(esk12_4(X141,X142,X143,X144),X143) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X144,X143),X142),X141))
| ~ mem(X149,X143)
| p(ap(X141,X149))
| ~ p(ap(X141,ap(X142,esk11_5(X141,X142,X143,X144,X149)))) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X144,X143),X142),X141))
| ~ mem(X149,X143)
| p(ap(X141,X149))
| mem(esk11_5(X141,X142,X143,X144,X149),X144) )
& ( ~ epred1_4(X144,X143,X142,X141)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X144,X143),X142),X141))
| ~ p(ap(X141,ap(X142,X148)))
| ~ mem(X148,X144) )
& ( ~ epred1_4(X144,X143,X142,X141)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X144,X143),X142),X141))
| p(ap(X141,esk10_4(X141,X142,X143,X144))) )
& ( ~ epred1_4(X144,X143,X142,X141)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X144,X143),X142),X141))
| mem(esk10_4(X141,X142,X143,X144),X143) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X144,X143),X142),X141))
| ~ mem(X145,X143)
| ~ p(ap(X141,X145))
| p(ap(X141,ap(X142,esk9_5(X141,X142,X143,X144,X145)))) )
& ( ~ epred1_4(X144,X143,X142,X141)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X144,X143),X142),X141))
| ~ mem(X145,X143)
| ~ p(ap(X141,X145))
| mem(esk9_5(X141,X142,X143,X144,X145),X144) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])])])]) ).
cnf(c_0_21,plain,
( ~ mem(X1,bool)
| p(X1)
| X1 = c_2Ebool_2EF ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( ~ mem(X1,esk4_0)
| mem(ap(esk8_0,X1),bool) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( ~ epred1_4(X1,X2,X6,X7)
| ~ mem(X3,arr(X1,X2))
| ~ mem(X4,arr(X2,bool))
| ~ p(ap(X4,ap(X3,X5)))
| ~ mem(X5,X1)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(esk5_0,esk4_0),esk6_0),esk7_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_25,negated_conjecture,
mem(esk7_0,arr(esk4_0,bool)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_26,negated_conjecture,
mem(esk6_0,arr(esk5_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_27,negated_conjecture,
( ~ p(ap(esk8_0,X1))
| ~ mem(X1,esk4_0)
| p(ap(esk7_0,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_28,negated_conjecture,
( ~ mem(X1,esk4_0)
| p(ap(esk8_0,X1))
| ap(esk8_0,X1) = c_2Ebool_2EF ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_29,plain,
! [X9] :
( ne(X9)
=> ! [X10] :
( ne(X10)
=> ! [X20] :
( mem(X20,arr(X9,X10))
=> ! [X21] :
( mem(X21,arr(X10,bool))
=> epred1_4(X9,X10,X20,X21) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[conj_thm_2EquantHeuristics_2EGUESS__REWRITES]),c_0_9]) ).
cnf(c_0_30,negated_conjecture,
( ~ mem(X3,esk5_0)
| ~ p(ap(esk7_0,ap(esk6_0,X3)))
| ~ epred1_4(esk5_0,esk4_0,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_31,negated_conjecture,
( ~ mem(X1,esk4_0)
| p(ap(esk7_0,X1))
| ap(esk8_0,X1) = c_2Ebool_2EF ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( ~ mem(X1,esk5_0)
| mem(ap(esk6_0,X1),esk4_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
fof(c_0_33,plain,
! [X110,X111,X112,X113] :
( epred1_4(X110,X111,X112,X113)
| ~ mem(X113,arr(X111,bool))
| ~ mem(X112,arr(X110,X111))
| ~ ne(X111)
| ~ ne(X110) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])]) ).
cnf(c_0_34,negated_conjecture,
( ~ mem(X1,esk5_0)
| ~ epred1_4(esk5_0,esk4_0,X2,X3)
| ap(esk8_0,ap(esk6_0,X1)) = c_2Ebool_2EF ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_35,plain,
( ~ mem(X4,arr(X2,bool))
| ~ mem(X3,arr(X1,X2))
| ~ ne(X2)
| ~ ne(X1)
| epred1_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_36,negated_conjecture,
ne(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_37,negated_conjecture,
ne(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_38,negated_conjecture,
( ~ mem(X1,esk5_0)
| ~ mem(X3,arr(esk5_0,esk4_0))
| ~ mem(X2,arr(esk4_0,bool))
| ap(esk8_0,ap(esk6_0,X1)) = c_2Ebool_2EF ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37])]) ).
fof(c_0_39,plain,
! [X69,X70] :
( mem(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X69,X70),arr(arr(X69,X70),arr(arr(X70,bool),bool)))
| ~ ne(X70)
| ~ ne(X69) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mem_c_2EquantHeuristics_2EGUESS__FORALL__POINT])])])]) ).
cnf(c_0_40,negated_conjecture,
( ~ mem(X1,esk5_0)
| ~ mem(X2,arr(esk5_0,esk4_0))
| ap(esk8_0,ap(esk6_0,X1)) = c_2Ebool_2EF ),
inference(spm,[status(thm)],[c_0_38,c_0_19]) ).
cnf(c_0_41,plain,
( ~ ne(X2)
| ~ ne(X1)
| mem(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X2),arr(arr(X1,X2),arr(arr(X2,bool),bool))) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_42,plain,
( ~ epred1_4(X6,X5,X4,X3)
| ~ mem(X2,arr(X6,X5))
| ~ mem(X1,arr(X5,bool))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X6,X5),X2),X1))
| p(ap(X1,ap(X2,esk14_6(X3,X4,X5,X6,X2,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_43,negated_conjecture,
( ~ mem(X1,esk5_0)
| ap(esk8_0,ap(esk6_0,X1)) = c_2Ebool_2EF ),
inference(spm,[status(thm)],[c_0_40,c_0_26]) ).
cnf(c_0_44,plain,
( ~ ne(X1)
| ~ ne(X2)
| ~ mem(X3,arr(X1,X2))
| mem(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X2),X3),arr(arr(X2,bool),bool)) ),
inference(spm,[status(thm)],[c_0_18,c_0_41]) ).
cnf(c_0_45,plain,
( ~ mem(esk6_0,arr(X1,X2))
| ~ mem(esk8_0,arr(X2,bool))
| ~ mem(esk14_6(X4,X3,X2,X1,esk6_0,esk8_0),esk5_0)
| ~ epred1_4(X1,X2,X3,X4)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X2),esk6_0),esk8_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_17]) ).
cnf(c_0_46,plain,
( ~ epred1_4(X4,X3,X2,X1)
| ~ mem(X5,arr(X4,X3))
| ~ mem(X6,arr(X3,bool))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X4,X3),X5),X6))
| mem(esk14_6(X1,X2,X3,X4,X5,X6),X4) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_47,plain,
( ~ ne(X1)
| ~ ne(X2)
| ~ mem(X3,arr(X1,X2))
| ~ mem(X4,arr(X2,bool))
| mem(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X2),X3),X4),bool) ),
inference(spm,[status(thm)],[c_0_18,c_0_44]) ).
cnf(c_0_48,plain,
( ~ mem(esk6_0,arr(esk5_0,X1))
| ~ mem(esk8_0,arr(X1,bool))
| ~ epred1_4(esk5_0,X1,X2,X3)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(esk5_0,X1),esk6_0),esk8_0)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,negated_conjecture,
~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(esk5_0,esk4_0),esk6_0),esk8_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_50,plain,
( ~ ne(X1)
| ~ ne(X2)
| ~ mem(X3,arr(X1,X2))
| ~ mem(X4,arr(X2,bool))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X2),X3),X4))
| ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X2),X3),X4) = c_2Ebool_2EF ),
inference(spm,[status(thm)],[c_0_21,c_0_47]) ).
cnf(c_0_51,plain,
( ~ ne(X1)
| ~ mem(X3,arr(esk5_0,X1))
| ~ mem(X2,arr(X1,bool))
| ~ mem(esk6_0,arr(esk5_0,X1))
| ~ mem(esk8_0,arr(X1,bool))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(esk5_0,X1),esk6_0),esk8_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_35]),c_0_37])]) ).
cnf(c_0_52,negated_conjecture,
ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(esk5_0,esk4_0),esk6_0),esk8_0) = c_2Ebool_2EF,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_19]),c_0_26]),c_0_36]),c_0_37])]) ).
cnf(c_0_53,negated_conjecture,
~ mem(X1,arr(esk5_0,esk4_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_19]),c_0_52]),c_0_19]),c_0_26]),c_0_36])]),c_0_17]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_26,c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP006+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.57 % Computer : n016.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Sun Sep 20 21:46:23 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.62 Running first-order theorem proving
% 0.14/0.62 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.83/1.59 % Version: 3.5.1
% 6.83/1.59 % Preprocessing class: FSLSSMSMSSSNFFN.
% 6.83/1.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.83/1.59 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 6.83/1.59 % Starting new_bool_3 with 300s (1) cores
% 6.83/1.59 % Starting new_bool_1 with 300s (1) cores
% 6.83/1.59 % Starting sh5l with 300s (1) cores
% 6.83/1.59 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 834766 completed with status 0
% 6.83/1.59 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 6.83/1.59 % Preprocessing class: FSLSSMSMSSSNFFN.
% 6.83/1.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.83/1.59 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 6.83/1.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.83/1.59 % No SInE strategy applied
% 6.83/1.59 % Search class: FGHSF-FSLM33-MFFFFFNN
% 6.83/1.59 % partial match(1): FGHSF-FSLM33-SFFFFFNN
% 6.83/1.59 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 6.83/1.59 % Starting SubtermCWHack with 136s (1) cores
% 6.83/1.59 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 6.83/1.59 % Starting G-E--_302_C18_F1_URBAN_S0Y with 136s (1) cores
% 6.83/1.59 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S0Y with 136s (1) cores
% 6.83/1.59 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 6.83/1.59 % G-E--_302_C18_F1_URBAN_S0Y with pid 834782 completed with status 0
% 6.83/1.59 % Result found by G-E--_302_C18_F1_URBAN_S0Y
% 6.83/1.59 % Preprocessing class: FSLSSMSMSSSNFFN.
% 6.83/1.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.83/1.59 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 6.83/1.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.83/1.59 % No SInE strategy applied
% 6.83/1.59 % Search class: FGHSF-FSLM33-MFFFFFNN
% 6.83/1.59 % partial match(1): FGHSF-FSLM33-SFFFFFNN
% 6.83/1.59 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 6.83/1.59 % Starting SubtermCWHack with 136s (1) cores
% 6.83/1.59 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 6.83/1.59 % Starting G-E--_302_C18_F1_URBAN_S0Y with 136s (1) cores
% 6.83/1.59 % Preprocessing time : 0.008 s
% 6.83/1.59
% 6.83/1.59 % Proof found!
% 6.83/1.59 % SZS status Theorem
% 6.83/1.59 % SZS output start CNFRefutation
% See solution above
% 6.83/1.59 % Parsed axioms : 52
% 6.83/1.59 % Removed by relevancy pruning/SinE : 0
% 6.83/1.59 % Initial clauses : 322
% 6.83/1.59 % Removed in clause preprocessing : 214
% 6.83/1.59 % Initial clauses in saturation : 108
% 6.83/1.59 % Processed clauses : 1909
% 6.83/1.59 % ...of these trivial : 16
% 6.83/1.59 % ...subsumed : 796
% 6.83/1.59 % ...remaining for further processing : 1097
% 6.83/1.59 % Other redundant clauses eliminated : 3
% 6.83/1.59 % Clauses deleted for lack of memory : 0
% 6.83/1.59 % Backward-subsumed : 79
% 6.83/1.59 % Backward-rewritten : 43
% 6.83/1.59 % Generated clauses : 21480
% 6.83/1.59 % ...of the previous two non-redundant : 20831
% 6.83/1.59 % ...aggressively subsumed : 0
% 6.83/1.59 % Contextual simplify-reflections : 57
% 6.83/1.59 % Paramodulations : 21433
% 6.83/1.59 % Factorizations : 39
% 6.83/1.59 % NegExts : 0
% 6.83/1.59 % Equation resolutions : 6
% 6.83/1.59 % Disequality decompositions : 0
% 6.83/1.59 % Total rewrite steps : 3316
% 6.83/1.59 % ...of those cached : 3297
% 6.83/1.59 % Propositional unsat checks : 0
% 6.83/1.59 % Propositional check models : 0
% 6.83/1.59 % Propositional check unsatisfiable : 0
% 6.83/1.59 % Propositional clauses : 0
% 6.83/1.59 % Propositional clauses after purity: 0
% 6.83/1.59 % Propositional unsat core size : 0
% 6.83/1.59 % Propositional preprocessing time : 0.000
% 6.83/1.59 % Propositional encoding time : 0.000
% 6.83/1.59 % Propositional solver time : 0.000
% 6.83/1.59 % Success case prop preproc time : 0.000
% 6.83/1.59 % Success case prop encoding time : 0.000
% 6.83/1.59 % Success case prop solver time : 0.000
% 6.83/1.59 % Current number of processed clauses : 972
% 6.83/1.59 % Positive orientable unit clauses : 18
% 6.83/1.59 % Positive unorientable unit clauses: 0
% 6.83/1.59 % Negative unit clauses : 2
% 6.83/1.59 % Non-unit-clauses : 952
% 6.83/1.59 % Current number of unprocessed clauses: 18849
% 6.83/1.59 % ...number of literals in the above : 176516
% 6.83/1.59 % Current number of archived formulas : 0
% 6.83/1.59 % Current number of archived clauses : 124
% 6.83/1.59 % Clause-clause subsumption calls (NU) : 175369
% 6.83/1.59 % Rec. Clause-clause subsumption calls : 8557
% 6.83/1.59 % Non-unit clause-clause subsumptions : 777
% 6.83/1.59 % Unit Clause-clause subsumption calls : 885
% 6.83/1.59 % Rewrite failures with RHS unbound : 0
% 6.83/1.59 % BW rewrite match attempts : 5
% 6.83/1.59 % BW rewrite match successes : 5
% 6.83/1.59 % Condensation attempts : 0
% 6.83/1.59 % Condensation successes : 0
% 6.83/1.59 % Termbank termtop insertions : 769166
% 6.83/1.59 % Search garbage collected termcells : 4607
% 6.83/1.59
% 6.83/1.59 % -------------------------------------------------
% 6.83/1.59 % User time : 0.890 s
% 6.83/1.59 % System time : 0.029 s
% 6.83/1.59 % Total time : 0.919 s
% 6.83/1.59 % Maximum resident set size: 4256 pages
% 6.83/1.59
% 6.83/1.59 % -------------------------------------------------
% 6.83/1.59 % User time : 4.300 s
% 6.83/1.59 % System time : 0.138 s
% 6.83/1.59 % Total time : 4.438 s
% 6.83/1.59 % Maximum resident set size: 4864 pages
% 6.83/1.59 % E exiting
%------------------------------------------------------------------------------