TSTP Solution File: ITP006_2 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ITP006_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% 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 : Sat May 4 08:06:15 EDT 2024
% Result : Theorem 2.26s 0.81s
% Output : CNFRefutation 2.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 36
% Syntax : Number of formulae : 69 ( 9 unt; 30 typ; 0 def)
% Number of atoms : 350 ( 10 equ)
% Maximal formula atoms : 132 ( 8 avg)
% Number of connectives : 477 ( 166 ~; 158 |; 57 &)
% ( 21 <=>; 75 =>; 0 <=; 0 <~>)
% Maximal formula depth : 54 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 79 ( 21 >; 58 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-4 aty)
% Number of functors : 24 ( 24 usr; 6 con; 0-7 aty)
% Number of variables : 171 ( 0 sgn 159 !; 12 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
del: $tType ).
tff(decl_22,type,
bool: del ).
tff(decl_24,type,
arr: ( del * del ) > del ).
tff(decl_25,type,
mem: ( $i * del ) > $o ).
tff(decl_26,type,
ap: ( $i * $i ) > $i ).
tff(decl_29,type,
p: $i > $o ).
tff(decl_34,type,
c_2EquantHeuristics_2EGUESS__FORALL__GAP: ( del * del ) > $i ).
tff(decl_35,type,
c_2EquantHeuristics_2EGUESS__EXISTS__GAP: ( del * del ) > $i ).
tff(decl_36,type,
c_2EquantHeuristics_2EGUESS__FORALL__POINT: ( del * del ) > $i ).
tff(decl_37,type,
c_2EquantHeuristics_2EGUESS__EXISTS__POINT: ( del * del ) > $i ).
tff(decl_38,type,
c_2EquantHeuristics_2EGUESS__FORALL: ( del * del ) > $i ).
tff(decl_40,type,
c_2EquantHeuristics_2EGUESS__EXISTS: ( del * del ) > $i ).
tff(decl_54,type,
epred2_4: ( del * del * $i * $i ) > $o ).
tff(decl_55,type,
esk1_0: del ).
tff(decl_56,type,
esk2_0: del ).
tff(decl_57,type,
esk3_0: $i ).
tff(decl_58,type,
esk4_0: $i ).
tff(decl_59,type,
esk5_0: $i ).
tff(decl_61,type,
esk7_5: ( $i * $i * del * del * $i ) > $i ).
tff(decl_62,type,
esk8_4: ( $i * $i * del * del ) > $i ).
tff(decl_63,type,
esk9_5: ( $i * $i * del * del * $i ) > $i ).
tff(decl_64,type,
esk10_4: ( $i * $i * del * del ) > $i ).
tff(decl_65,type,
esk11_6: ( $i * $i * del * del * $i * $i ) > $i ).
tff(decl_66,type,
esk12_6: ( $i * $i * del * del * $i * $i ) > $i ).
tff(decl_67,type,
esk13_7: ( $i * $i * del * del * $i * $i * $i ) > $i ).
tff(decl_68,type,
esk14_6: ( $i * $i * del * del * $i * $i ) > $i ).
tff(decl_69,type,
esk15_7: ( $i * $i * del * del * $i * $i * $i ) > $i ).
tff(decl_70,type,
esk16_6: ( $i * $i * del * del * $i * $i ) > $i ).
tff(decl_71,type,
epred3_0: $o ).
tff(decl_72,type,
epred4_0: $o ).
tff(conj_thm_2EquantHeuristics_2EGUESS__REWRITES,axiom,
! [X11: del,X12: del,X25] :
( mem(X25,arr(X11,X12))
=> ! [X26] :
( mem(X26,arr(X12,bool))
=> ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X11,X12),X25),X26))
<=> ! [X27] :
( mem(X27,X12)
=> ( p(ap(X26,X27))
=> ? [X28] :
( mem(X28,X11)
& p(ap(X26,ap(X25,X28))) ) ) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X11,X12),X25),X26))
<=> ! [X29] :
( mem(X29,X12)
=> ( ~ p(ap(X26,X29))
=> ? [X30] :
( mem(X30,X11)
& ~ p(ap(X26,ap(X25,X30))) ) ) ) )
& ! [X31] :
( mem(X31,arr(X11,X12))
=> ! [X32] :
( mem(X32,arr(X12,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X11,X12),X31),X32))
<=> ! [X33] :
( mem(X33,X11)
=> p(ap(X32,ap(X31,X33))) ) ) ) )
& ! [X34] :
( mem(X34,arr(X11,X12))
=> ! [X35] :
( mem(X35,arr(X12,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X11,X12),X34),X35))
<=> ! [X36] :
( mem(X36,X11)
=> ~ p(ap(X35,ap(X34,X36))) ) ) ) )
& ! [X37] :
( mem(X37,arr(X11,X12))
=> ! [X38] :
( mem(X38,arr(X12,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X11,X12),X37),X38))
<=> ! [X39] :
( mem(X39,X12)
=> ( p(ap(X38,X39))
=> ? [X40] :
( mem(X40,X11)
& ( X39 = ap(X37,X40) ) ) ) ) ) ) )
& ! [X41] :
( mem(X41,arr(X11,X12))
=> ! [X42] :
( mem(X42,arr(X12,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X11,X12),X41),X42))
<=> ! [X43] :
( mem(X43,X12)
=> ( ~ p(ap(X42,X43))
=> ? [X44] :
( mem(X44,X11)
& ( X43 = ap(X41,X44) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mJsvFCayfW/E---3.1_14763.p',conj_thm_2EquantHeuristics_2EGUESS__REWRITES) ).
tff(conj_thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT,conjecture,
! [X11: del,X12: del,X25] :
( mem(X25,arr(X12,X11))
=> ! [X26] :
( mem(X26,arr(X11,bool))
=> ! [X50] :
( mem(X50,arr(X11,bool))
=> ( ! [X51] :
( mem(X51,X11)
=> ( p(ap(X50,X51))
=> p(ap(X26,X51)) ) )
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X12,X11),X25),X26))
=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X12,X11),X25),X50)) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mJsvFCayfW/E---3.1_14763.p',conj_thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT) ).
tff(ap_tp,axiom,
! [X1: del,X2: del,X3] :
( mem(X3,arr(X1,X2))
=> ! [X4] :
( mem(X4,X1)
=> mem(ap(X3,X4),X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.mJsvFCayfW/E---3.1_14763.p',ap_tp) ).
tff(c_0_3,plain,
! [X26,X25,X12: del,X11: del] :
( epred2_4(X11,X12,X25,X26)
<=> ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X11,X12),X25),X26))
<=> ! [X27] :
( mem(X27,X12)
=> ( p(ap(X26,X27))
=> ? [X28] :
( mem(X28,X11)
& p(ap(X26,ap(X25,X28))) ) ) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X11,X12),X25),X26))
<=> ! [X29] :
( mem(X29,X12)
=> ( ~ p(ap(X26,X29))
=> ? [X30] :
( mem(X30,X11)
& ~ p(ap(X26,ap(X25,X30))) ) ) ) )
& ! [X31] :
( mem(X31,arr(X11,X12))
=> ! [X32] :
( mem(X32,arr(X12,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X11,X12),X31),X32))
<=> ! [X33] :
( mem(X33,X11)
=> p(ap(X32,ap(X31,X33))) ) ) ) )
& ! [X34] :
( mem(X34,arr(X11,X12))
=> ! [X35] :
( mem(X35,arr(X12,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X11,X12),X34),X35))
<=> ! [X36] :
( mem(X36,X11)
=> ~ p(ap(X35,ap(X34,X36))) ) ) ) )
& ! [X37] :
( mem(X37,arr(X11,X12))
=> ! [X38] :
( mem(X38,arr(X12,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X11,X12),X37),X38))
<=> ! [X39] :
( mem(X39,X12)
=> ( p(ap(X38,X39))
=> ? [X40] :
( mem(X40,X11)
& ( X39 = ap(X37,X40) ) ) ) ) ) ) )
& ! [X41] :
( mem(X41,arr(X11,X12))
=> ! [X42] :
( mem(X42,arr(X12,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X11,X12),X41),X42))
<=> ! [X43] :
( mem(X43,X12)
=> ( ~ p(ap(X42,X43))
=> ? [X44] :
( mem(X44,X11)
& ( X43 = ap(X41,X44) ) ) ) ) ) ) ) ) ),
introduced(definition) ).
tff(c_0_4,plain,
! [X11: del,X12: del,X25] :
( mem(X25,arr(X11,X12))
=> ! [X26] :
( mem(X26,arr(X12,bool))
=> epred2_4(X11,X12,X25,X26) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[conj_thm_2EquantHeuristics_2EGUESS__REWRITES]),c_0_3]) ).
tff(c_0_5,negated_conjecture,
~ ! [X11: del,X12: del,X25] :
( mem(X25,arr(X12,X11))
=> ! [X26] :
( mem(X26,arr(X11,bool))
=> ! [X50] :
( mem(X50,arr(X11,bool))
=> ( ! [X51] :
( mem(X51,X11)
=> ( p(ap(X50,X51))
=> p(ap(X26,X51)) ) )
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X12,X11),X25),X26))
=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X12,X11),X25),X50)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT]) ).
tff(c_0_6,plain,
( ~ epred3_0
<=> ! [X3,X4] : ~ epred2_4(esk2_0,esk1_0,X3,X4) ),
introduced(definition) ).
tff(c_0_7,plain,
! [X101: del,X102: del,X103,X104] :
( ~ mem(X103,arr(X101,X102))
| ~ mem(X104,arr(X102,bool))
| epred2_4(X101,X102,X103,X104) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
tff(c_0_8,plain,
! [X90: del,X91: del,X92,X93] :
( ~ mem(X92,arr(X90,X91))
| ~ mem(X93,X90)
| mem(ap(X92,X93),X91) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])])]) ).
tff(c_0_9,negated_conjecture,
! [X57] :
( mem(esk3_0,arr(esk2_0,esk1_0))
& mem(esk4_0,arr(esk1_0,bool))
& mem(esk5_0,arr(esk1_0,bool))
& ( ~ mem(X57,esk1_0)
| ~ p(ap(esk5_0,X57))
| p(ap(esk4_0,X57)) )
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(esk2_0,esk1_0),esk3_0),esk4_0))
& ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(esk2_0,esk1_0),esk3_0),esk5_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_5])])])])]) ).
tff(c_0_10,plain,
! [X26,X25,X12: del,X11: del] :
( epred2_4(X11,X12,X25,X26)
=> ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X11,X12),X25),X26))
<=> ! [X27] :
( mem(X27,X12)
=> ( p(ap(X26,X27))
=> ? [X28] :
( mem(X28,X11)
& p(ap(X26,ap(X25,X28))) ) ) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X11,X12),X25),X26))
<=> ! [X29] :
( mem(X29,X12)
=> ( ~ p(ap(X26,X29))
=> ? [X30] :
( mem(X30,X11)
& ~ p(ap(X26,ap(X25,X30))) ) ) ) )
& ! [X31] :
( mem(X31,arr(X11,X12))
=> ! [X32] :
( mem(X32,arr(X12,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X11,X12),X31),X32))
<=> ! [X33] :
( mem(X33,X11)
=> p(ap(X32,ap(X31,X33))) ) ) ) )
& ! [X34] :
( mem(X34,arr(X11,X12))
=> ! [X35] :
( mem(X35,arr(X12,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X11,X12),X34),X35))
<=> ! [X36] :
( mem(X36,X11)
=> ~ p(ap(X35,ap(X34,X36))) ) ) ) )
& ! [X37] :
( mem(X37,arr(X11,X12))
=> ! [X38] :
( mem(X38,arr(X12,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X11,X12),X37),X38))
<=> ! [X39] :
( mem(X39,X12)
=> ( p(ap(X38,X39))
=> ? [X40] :
( mem(X40,X11)
& ( X39 = ap(X37,X40) ) ) ) ) ) ) )
& ! [X41] :
( mem(X41,arr(X11,X12))
=> ! [X42] :
( mem(X42,arr(X12,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X11,X12),X41),X42))
<=> ! [X43] :
( mem(X43,X12)
=> ( ~ p(ap(X42,X43))
=> ? [X44] :
( mem(X44,X11)
& ( X43 = ap(X41,X44) ) ) ) ) ) ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_3]) ).
tcf(c_0_11,negated_conjecture,
! [X3,X4] :
( epred3_0
| ~ epred2_4(esk2_0,esk1_0,X3,X4) ),
inference(split_equiv,[status(thm)],[c_0_6]) ).
tcf(c_0_12,plain,
! [X1: del,X4,X3,X2: del] :
( epred2_4(X1,X2,X3,X4)
| ~ mem(X3,arr(X1,X2))
| ~ mem(X4,arr(X2,bool)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
tcf(c_0_13,plain,
! [X2: del,X4,X3,X1: del] :
( mem(ap(X3,X4),X2)
| ~ mem(X3,arr(X1,X2))
| ~ mem(X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_14,negated_conjecture,
mem(esk3_0,arr(esk2_0,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tff(c_0_15,plain,
! [X122,X123,X124: del,X125: del,X126,X129,X130,X133,X134,X135,X136,X138,X139,X140,X142,X143,X144,X147,X148,X149,X150,X153] :
( ( mem(esk7_5(X122,X123,X124,X125,X126),X125)
| ~ p(ap(X122,X126))
| ~ mem(X126,X124)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X125,X124),X123),X122))
| ~ epred2_4(X125,X124,X123,X122) )
& ( p(ap(X122,ap(X123,esk7_5(X122,X123,X124,X125,X126))))
| ~ p(ap(X122,X126))
| ~ mem(X126,X124)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X125,X124),X123),X122))
| ~ epred2_4(X125,X124,X123,X122) )
& ( mem(esk8_4(X122,X123,X124,X125),X124)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X125,X124),X123),X122))
| ~ epred2_4(X125,X124,X123,X122) )
& ( p(ap(X122,esk8_4(X122,X123,X124,X125)))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X125,X124),X123),X122))
| ~ epred2_4(X125,X124,X123,X122) )
& ( ~ mem(X129,X125)
| ~ p(ap(X122,ap(X123,X129)))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X125,X124),X123),X122))
| ~ epred2_4(X125,X124,X123,X122) )
& ( mem(esk9_5(X122,X123,X124,X125,X130),X125)
| p(ap(X122,X130))
| ~ mem(X130,X124)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X125,X124),X123),X122))
| ~ epred2_4(X125,X124,X123,X122) )
& ( ~ p(ap(X122,ap(X123,esk9_5(X122,X123,X124,X125,X130))))
| p(ap(X122,X130))
| ~ mem(X130,X124)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X125,X124),X123),X122))
| ~ epred2_4(X125,X124,X123,X122) )
& ( mem(esk10_4(X122,X123,X124,X125),X124)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X125,X124),X123),X122))
| ~ epred2_4(X125,X124,X123,X122) )
& ( ~ p(ap(X122,esk10_4(X122,X123,X124,X125)))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X125,X124),X123),X122))
| ~ epred2_4(X125,X124,X123,X122) )
& ( ~ mem(X133,X125)
| p(ap(X122,ap(X123,X133)))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X125,X124),X123),X122))
| ~ epred2_4(X125,X124,X123,X122) )
& ( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X125,X124),X134),X135))
| ~ mem(X136,X125)
| p(ap(X135,ap(X134,X136)))
| ~ mem(X135,arr(X124,bool))
| ~ mem(X134,arr(X125,X124))
| ~ epred2_4(X125,X124,X123,X122) )
& ( mem(esk11_6(X122,X123,X124,X125,X134,X135),X125)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X125,X124),X134),X135))
| ~ mem(X135,arr(X124,bool))
| ~ mem(X134,arr(X125,X124))
| ~ epred2_4(X125,X124,X123,X122) )
& ( ~ p(ap(X135,ap(X134,esk11_6(X122,X123,X124,X125,X134,X135))))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X125,X124),X134),X135))
| ~ mem(X135,arr(X124,bool))
| ~ mem(X134,arr(X125,X124))
| ~ epred2_4(X125,X124,X123,X122) )
& ( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X125,X124),X138),X139))
| ~ mem(X140,X125)
| ~ p(ap(X139,ap(X138,X140)))
| ~ mem(X139,arr(X124,bool))
| ~ mem(X138,arr(X125,X124))
| ~ epred2_4(X125,X124,X123,X122) )
& ( mem(esk12_6(X122,X123,X124,X125,X138,X139),X125)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X125,X124),X138),X139))
| ~ mem(X139,arr(X124,bool))
| ~ mem(X138,arr(X125,X124))
| ~ epred2_4(X125,X124,X123,X122) )
& ( p(ap(X139,ap(X138,esk12_6(X122,X123,X124,X125,X138,X139))))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X125,X124),X138),X139))
| ~ mem(X139,arr(X124,bool))
| ~ mem(X138,arr(X125,X124))
| ~ epred2_4(X125,X124,X123,X122) )
& ( mem(esk13_7(X122,X123,X124,X125,X142,X143,X144),X125)
| ~ p(ap(X143,X144))
| ~ mem(X144,X124)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X125,X124),X142),X143))
| ~ mem(X143,arr(X124,bool))
| ~ mem(X142,arr(X125,X124))
| ~ epred2_4(X125,X124,X123,X122) )
& ( ( X144 = ap(X142,esk13_7(X122,X123,X124,X125,X142,X143,X144)) )
| ~ p(ap(X143,X144))
| ~ mem(X144,X124)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X125,X124),X142),X143))
| ~ mem(X143,arr(X124,bool))
| ~ mem(X142,arr(X125,X124))
| ~ epred2_4(X125,X124,X123,X122) )
& ( mem(esk14_6(X122,X123,X124,X125,X142,X143),X124)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X125,X124),X142),X143))
| ~ mem(X143,arr(X124,bool))
| ~ mem(X142,arr(X125,X124))
| ~ epred2_4(X125,X124,X123,X122) )
& ( p(ap(X143,esk14_6(X122,X123,X124,X125,X142,X143)))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X125,X124),X142),X143))
| ~ mem(X143,arr(X124,bool))
| ~ mem(X142,arr(X125,X124))
| ~ epred2_4(X125,X124,X123,X122) )
& ( ~ mem(X147,X125)
| ( esk14_6(X122,X123,X124,X125,X142,X143) != ap(X142,X147) )
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X125,X124),X142),X143))
| ~ mem(X143,arr(X124,bool))
| ~ mem(X142,arr(X125,X124))
| ~ epred2_4(X125,X124,X123,X122) )
& ( mem(esk15_7(X122,X123,X124,X125,X148,X149,X150),X125)
| p(ap(X149,X150))
| ~ mem(X150,X124)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X125,X124),X148),X149))
| ~ mem(X149,arr(X124,bool))
| ~ mem(X148,arr(X125,X124))
| ~ epred2_4(X125,X124,X123,X122) )
& ( ( X150 = ap(X148,esk15_7(X122,X123,X124,X125,X148,X149,X150)) )
| p(ap(X149,X150))
| ~ mem(X150,X124)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X125,X124),X148),X149))
| ~ mem(X149,arr(X124,bool))
| ~ mem(X148,arr(X125,X124))
| ~ epred2_4(X125,X124,X123,X122) )
& ( mem(esk16_6(X122,X123,X124,X125,X148,X149),X124)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X125,X124),X148),X149))
| ~ mem(X149,arr(X124,bool))
| ~ mem(X148,arr(X125,X124))
| ~ epred2_4(X125,X124,X123,X122) )
& ( ~ p(ap(X149,esk16_6(X122,X123,X124,X125,X148,X149)))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X125,X124),X148),X149))
| ~ mem(X149,arr(X124,bool))
| ~ mem(X148,arr(X125,X124))
| ~ epred2_4(X125,X124,X123,X122) )
& ( ~ mem(X153,X125)
| ( esk16_6(X122,X123,X124,X125,X148,X149) != ap(X148,X153) )
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X125,X124),X148),X149))
| ~ mem(X149,arr(X124,bool))
| ~ mem(X148,arr(X125,X124))
| ~ epred2_4(X125,X124,X123,X122) ) ),
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_10])])])])])]) ).
tcf(c_0_16,negated_conjecture,
! [X3,X4] :
( epred3_0
| ~ mem(X3,arr(esk1_0,bool))
| ~ mem(X4,arr(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
tcf(c_0_17,negated_conjecture,
mem(esk5_0,arr(esk1_0,bool)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_18,negated_conjecture,
! [X3] :
( p(ap(esk4_0,X3))
| ~ mem(X3,esk1_0)
| ~ p(ap(esk5_0,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_19,negated_conjecture,
! [X3] :
( mem(ap(esk3_0,X3),esk1_0)
| ~ mem(X3,esk2_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
tff(c_0_20,plain,
( ~ epred4_0
<=> ! [X5] :
( ~ mem(X5,esk2_0)
| ~ p(ap(esk4_0,ap(esk3_0,X5))) ) ),
introduced(definition) ).
tcf(c_0_21,plain,
! [X1: del,X2: del,X4,X3,X5,X6,X7] :
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X2),X3),X4))
| ~ mem(X5,X1)
| ~ p(ap(X4,ap(X3,X5)))
| ~ mem(X4,arr(X2,bool))
| ~ mem(X3,arr(X1,X2))
| ~ epred2_4(X1,X2,X6,X7) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
tcf(c_0_22,negated_conjecture,
p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(esk2_0,esk1_0),esk3_0),esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_23,negated_conjecture,
mem(esk4_0,arr(esk1_0,bool)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_24,negated_conjecture,
! [X3] :
( epred3_0
| ~ mem(X3,arr(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
tcf(c_0_25,negated_conjecture,
! [X3] :
( p(ap(esk4_0,ap(esk3_0,X3)))
| ~ p(ap(esk5_0,ap(esk3_0,X3)))
| ~ mem(X3,esk2_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
tcf(c_0_26,plain,
! [X1: del,X3,X4,X2: del,X6,X5] :
( p(ap(X3,ap(X4,esk12_6(X5,X6,X1,X2,X4,X3))))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X2,X1),X4),X3))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X4,arr(X2,X1))
| ~ epred2_4(X2,X1,X6,X5) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_27,negated_conjecture,
( ~ epred4_0
| ~ epred3_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_14])]),c_0_6]),c_0_20]) ).
cnf(c_0_28,negated_conjecture,
epred3_0,
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
tcf(c_0_29,negated_conjecture,
! [X3] :
( epred4_0
| ~ p(ap(esk4_0,ap(esk3_0,X3)))
| ~ mem(X3,esk2_0) ),
inference(split_equiv,[status(thm)],[c_0_20]) ).
tcf(c_0_30,plain,
! [X4,X3,X2: del,X1: del] :
( p(ap(esk4_0,ap(esk3_0,esk12_6(X3,X4,X1,X2,esk3_0,esk5_0))))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X2,X1),esk3_0),esk5_0))
| ~ epred2_4(X2,X1,X4,X3)
| ~ mem(esk12_6(X3,X4,X1,X2,esk3_0,esk5_0),esk2_0)
| ~ mem(esk5_0,arr(X1,bool))
| ~ mem(esk3_0,arr(X2,X1)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
~ epred4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
tcf(c_0_32,negated_conjecture,
! [X1: del,X4,X3,X2: del] :
( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X2),esk3_0),esk5_0))
| ~ epred2_4(X1,X2,X3,X4)
| ~ mem(esk12_6(X4,X3,X2,X1,esk3_0,esk5_0),esk2_0)
| ~ mem(esk5_0,arr(X2,bool))
| ~ mem(esk3_0,arr(X1,X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
tcf(c_0_33,plain,
! [X1: del,X2: del,X6,X5,X4,X3] :
( mem(esk12_6(X3,X4,X1,X2,X5,X6),X2)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X2,X1),X5),X6))
| ~ mem(X6,arr(X1,bool))
| ~ mem(X5,arr(X2,X1))
| ~ epred2_4(X2,X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
tcf(c_0_34,plain,
! [X4,X3,X1: del] :
( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(esk2_0,X1),esk3_0),esk5_0))
| ~ epred2_4(esk2_0,X1,X3,X4)
| ~ mem(esk5_0,arr(X1,bool))
| ~ mem(esk3_0,arr(esk2_0,X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
tcf(c_0_35,plain,
! [X4,X3,X1: del] :
( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(esk2_0,X1),esk3_0),esk5_0))
| ~ mem(esk5_0,arr(X1,bool))
| ~ mem(esk3_0,arr(esk2_0,X1))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X4,arr(esk2_0,X1)) ),
inference(spm,[status(thm)],[c_0_34,c_0_12]) ).
tcf(c_0_36,negated_conjecture,
~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(esk2_0,esk1_0),esk3_0),esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_37,negated_conjecture,
! [X3] : ~ mem(X3,arr(esk2_0,esk1_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_17]),c_0_17]),c_0_14])]),c_0_36]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_14,c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : ITP006_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.12/0.15 % Command : run_E %s %d THM
% 0.16/0.36 % Computer : n023.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 3 13:06:53 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.23/0.53 Running first-order theorem proving
% 0.23/0.53 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.mJsvFCayfW/E---3.1_14763.p
% 2.26/0.81 # Version: 3.1.0
% 2.26/0.81 # Preprocessing class: FSLSSMSMSSSNFFN.
% 2.26/0.81 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.26/0.81 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.26/0.81 # Starting new_bool_3 with 300s (1) cores
% 2.26/0.81 # Starting new_bool_1 with 300s (1) cores
% 2.26/0.81 # Starting sh5l with 300s (1) cores
% 2.26/0.81 # new_bool_3 with pid 14855 completed with status 0
% 2.26/0.81 # Result found by new_bool_3
% 2.26/0.81 # Preprocessing class: FSLSSMSMSSSNFFN.
% 2.26/0.81 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.26/0.81 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.26/0.81 # Starting new_bool_3 with 300s (1) cores
% 2.26/0.81 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.26/0.81 # Search class: FGHSM-FFMS33-MFFFFFNN
% 2.26/0.81 # partial match(1): FGHSM-FFMS31-MFFFFFNN
% 2.26/0.81 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 2.26/0.81 # Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 130s (1) cores
% 2.26/0.81 # G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with pid 14864 completed with status 0
% 2.26/0.81 # Result found by G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y
% 2.26/0.81 # Preprocessing class: FSLSSMSMSSSNFFN.
% 2.26/0.81 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.26/0.81 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.26/0.81 # Starting new_bool_3 with 300s (1) cores
% 2.26/0.81 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.26/0.81 # Search class: FGHSM-FFMS33-MFFFFFNN
% 2.26/0.81 # partial match(1): FGHSM-FFMS31-MFFFFFNN
% 2.26/0.81 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 2.26/0.81 # Starting G-E--_103_C18_F1_PI_AE_Q4_CS_SP_S0Y with 130s (1) cores
% 2.26/0.81 # Preprocessing time : 0.007 s
% 2.26/0.81
% 2.26/0.81 # Proof found!
% 2.26/0.81 # SZS status Theorem
% 2.26/0.81 # SZS output start CNFRefutation
% See solution above
% 2.26/0.81 # Parsed axioms : 91
% 2.26/0.81 # Removed by relevancy pruning/SinE : 62
% 2.26/0.81 # Initial clauses : 283
% 2.26/0.81 # Removed in clause preprocessing : 213
% 2.26/0.81 # Initial clauses in saturation : 70
% 2.26/0.81 # Processed clauses : 860
% 2.26/0.81 # ...of these trivial : 0
% 2.26/0.81 # ...subsumed : 264
% 2.26/0.81 # ...remaining for further processing : 596
% 2.26/0.81 # Other redundant clauses eliminated : 0
% 2.26/0.81 # Clauses deleted for lack of memory : 0
% 2.26/0.81 # Backward-subsumed : 15
% 2.26/0.81 # Backward-rewritten : 3
% 2.26/0.81 # Generated clauses : 8742
% 2.26/0.81 # ...of the previous two non-redundant : 8492
% 2.26/0.81 # ...aggressively subsumed : 0
% 2.26/0.81 # Contextual simplify-reflections : 10
% 2.26/0.81 # Paramodulations : 8721
% 2.26/0.81 # Factorizations : 14
% 2.26/0.81 # NegExts : 0
% 2.26/0.81 # Equation resolutions : 3
% 2.26/0.81 # Disequality decompositions : 0
% 2.26/0.81 # Total rewrite steps : 330
% 2.26/0.81 # ...of those cached : 321
% 2.26/0.81 # Propositional unsat checks : 0
% 2.26/0.81 # Propositional check models : 0
% 2.26/0.81 # Propositional check unsatisfiable : 0
% 2.26/0.81 # Propositional clauses : 0
% 2.26/0.81 # Propositional clauses after purity: 0
% 2.26/0.81 # Propositional unsat core size : 0
% 2.26/0.81 # Propositional preprocessing time : 0.000
% 2.26/0.81 # Propositional encoding time : 0.000
% 2.26/0.81 # Propositional solver time : 0.000
% 2.26/0.81 # Success case prop preproc time : 0.000
% 2.26/0.81 # Success case prop encoding time : 0.000
% 2.26/0.81 # Success case prop solver time : 0.000
% 2.26/0.81 # Current number of processed clauses : 576
% 2.26/0.81 # Positive orientable unit clauses : 11
% 2.26/0.81 # Positive unorientable unit clauses: 0
% 2.26/0.81 # Negative unit clauses : 3
% 2.26/0.81 # Non-unit-clauses : 562
% 2.26/0.81 # Current number of unprocessed clauses: 7647
% 2.26/0.81 # ...number of literals in the above : 62041
% 2.26/0.81 # Current number of archived formulas : 0
% 2.26/0.81 # Current number of archived clauses : 19
% 2.26/0.81 # Clause-clause subsumption calls (NU) : 23453
% 2.26/0.81 # Rec. Clause-clause subsumption calls : 2542
% 2.26/0.81 # Non-unit clause-clause subsumptions : 256
% 2.26/0.81 # Unit Clause-clause subsumption calls : 438
% 2.26/0.81 # Rewrite failures with RHS unbound : 0
% 2.26/0.81 # BW rewrite match attempts : 1
% 2.26/0.81 # BW rewrite match successes : 1
% 2.26/0.81 # Condensation attempts : 0
% 2.26/0.81 # Condensation successes : 0
% 2.26/0.81 # Termbank termtop insertions : 350956
% 2.26/0.81 # Search garbage collected termcells : 2991
% 2.26/0.81
% 2.26/0.81 # -------------------------------------------------
% 2.26/0.81 # User time : 0.252 s
% 2.26/0.81 # System time : 0.014 s
% 2.26/0.81 # Total time : 0.267 s
% 2.26/0.81 # Maximum resident set size: 2492 pages
% 2.26/0.81
% 2.26/0.81 # -------------------------------------------------
% 2.26/0.81 # User time : 0.256 s
% 2.26/0.81 # System time : 0.016 s
% 2.26/0.81 # Total time : 0.272 s
% 2.26/0.81 # Maximum resident set size: 1828 pages
% 2.26/0.81 % E---3.1 exiting
% 2.26/0.81 % E exiting
%------------------------------------------------------------------------------