TSTP Solution File: ITP006+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ITP006+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n024.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 : Thu Aug 31 03:10:16 EDT 2023
% Result : Theorem 56.17s 56.24s
% Output : CNFRefutation 56.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 53
% Syntax : Number of formulae : 95 ( 14 unt; 46 typ; 0 def)
% Number of atoms : 390 ( 22 equ)
% Maximal formula atoms : 132 ( 7 avg)
% Number of connectives : 515 ( 174 ~; 175 |; 60 &)
% ( 20 <=>; 86 =>; 0 <=; 0 <~>)
% Maximal formula depth : 54 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 103 ( 33 >; 70 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 39 ( 39 usr; 13 con; 0-7 aty)
% Number of variables : 178 ( 10 sgn; 109 !; 12 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
bool: $i ).
tff(decl_23,type,
ne: $i > $o ).
tff(decl_24,type,
ind: $i ).
tff(decl_25,type,
arr: ( $i * $i ) > $i ).
tff(decl_26,type,
mem: ( $i * $i ) > $o ).
tff(decl_27,type,
ap: ( $i * $i ) > $i ).
tff(decl_28,type,
p: $i > $o ).
tff(decl_29,type,
k: ( $i * $i ) > $i ).
tff(decl_30,type,
i: $i > $i ).
tff(decl_31,type,
c_2Ebool_2ET: $i ).
tff(decl_32,type,
c_2EquantHeuristics_2EGUESS__FORALL__GAP: ( $i * $i ) > $i ).
tff(decl_33,type,
c_2EquantHeuristics_2EGUESS__EXISTS__GAP: ( $i * $i ) > $i ).
tff(decl_34,type,
c_2EquantHeuristics_2EGUESS__FORALL__POINT: ( $i * $i ) > $i ).
tff(decl_35,type,
c_2EquantHeuristics_2EGUESS__EXISTS__POINT: ( $i * $i ) > $i ).
tff(decl_36,type,
c_2EquantHeuristics_2EGUESS__FORALL: ( $i * $i ) > $i ).
tff(decl_37,type,
c_2Ebool_2E_3F: $i > $i ).
tff(decl_38,type,
c_2EquantHeuristics_2EGUESS__EXISTS: ( $i * $i ) > $i ).
tff(decl_39,type,
c_2Ebool_2EF: $i ).
tff(decl_40,type,
c_2Ebool_2E_5C_2F: $i ).
tff(decl_41,type,
c_2Ebool_2E_2F_5C: $i ).
tff(decl_42,type,
c_2Emin_2E_3D: $i > $i ).
tff(decl_43,type,
c_2Ebool_2E_7E: $i ).
tff(decl_44,type,
c_2Emin_2E_3D_3D_3E: $i ).
tff(decl_45,type,
c_2Ebool_2E_21: $i > $i ).
tff(decl_46,type,
epred1_4: ( $i * $i * $i * $i ) > $o ).
tff(decl_47,type,
epred2_3: ( $i * $i * $i ) > $o ).
tff(decl_48,type,
epred3_3: ( $i * $i * $i ) > $o ).
tff(decl_49,type,
epred4_3: ( $i * $i * $i ) > $o ).
tff(decl_50,type,
esk1_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_51,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk4_0: $i ).
tff(decl_54,type,
esk5_0: $i ).
tff(decl_55,type,
esk6_0: $i ).
tff(decl_56,type,
esk7_0: $i ).
tff(decl_57,type,
esk8_0: $i ).
tff(decl_58,type,
esk9_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_59,type,
esk10_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_60,type,
esk11_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_61,type,
esk12_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_62,type,
esk13_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_63,type,
esk14_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_64,type,
esk15_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_65,type,
esk16_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_66,type,
esk17_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_67,type,
esk18_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
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(ax_false_p,axiom,
~ p(c_2Ebool_2EF),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_false_p) ).
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))
=> ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X9,X10),X20),X21))
<=> ! [X22] :
( mem(X22,X10)
=> ( p(ap(X21,X22))
=> ? [X23] :
( mem(X23,X9)
& p(ap(X21,ap(X20,X23))) ) ) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X9,X10),X20),X21))
<=> ! [X24] :
( mem(X24,X10)
=> ( ~ p(ap(X21,X24))
=> ? [X25] :
( mem(X25,X9)
& ~ p(ap(X21,ap(X20,X25))) ) ) ) )
& ! [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))) ) ) ) )
& ! [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))) ) ) ) )
& ! [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] :
( mem(X35,X9)
& X34 = ap(X32,X35) ) ) ) ) ) )
& ! [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] :
( mem(X39,X9)
& X38 = ap(X36,X39) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2EquantHeuristics_2EGUESS__REWRITES) ).
fof(c_0_6,plain,
! [X21,X20,X10,X9] :
( epred1_4(X9,X10,X20,X21)
<=> ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X9,X10),X20),X21))
<=> ! [X22] :
( mem(X22,X10)
=> ( p(ap(X21,X22))
=> ? [X23] :
( mem(X23,X9)
& p(ap(X21,ap(X20,X23))) ) ) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X9,X10),X20),X21))
<=> ! [X24] :
( mem(X24,X10)
=> ( ~ p(ap(X21,X24))
=> ? [X25] :
( mem(X25,X9)
& ~ p(ap(X21,ap(X20,X25))) ) ) ) )
& ! [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))) ) ) ) )
& ! [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))) ) ) ) )
& ! [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] :
( mem(X35,X9)
& X34 = ap(X32,X35) ) ) ) ) ) )
& ! [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] :
( mem(X39,X9)
& X38 = ap(X36,X39) ) ) ) ) ) ) ) ),
introduced(definition) ).
fof(c_0_7,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_8,plain,
! [X21,X20,X10,X9] :
( epred1_4(X9,X10,X20,X21)
=> ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X9,X10),X20),X21))
<=> ! [X22] :
( mem(X22,X10)
=> ( p(ap(X21,X22))
=> ? [X23] :
( mem(X23,X9)
& p(ap(X21,ap(X20,X23))) ) ) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X9,X10),X20),X21))
<=> ! [X24] :
( mem(X24,X10)
=> ( ~ p(ap(X21,X24))
=> ? [X25] :
( mem(X25,X9)
& ~ p(ap(X21,ap(X20,X25))) ) ) ) )
& ! [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))) ) ) ) )
& ! [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))) ) ) ) )
& ! [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] :
( mem(X35,X9)
& X34 = ap(X32,X35) ) ) ) ) ) )
& ! [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] :
( mem(X39,X9)
& X38 = ap(X36,X39) ) ) ) ) ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X53,X54] :
( ( ~ p(X53)
| ~ p(X54)
| X53 = X54
| ~ mem(X54,bool)
| ~ mem(X53,bool) )
& ( p(X53)
| p(X54)
| X53 = X54
| ~ mem(X54,bool)
| ~ mem(X53,bool) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[boolext])])])]) ).
fof(c_0_10,plain,
~ p(c_2Ebool_2EF),
inference(fof_simplification,[status(thm)],[ax_false_p]) ).
fof(c_0_11,plain,
! [X49,X50,X51,X52] :
( ~ mem(X51,arr(X49,X50))
| ~ mem(X52,X49)
| mem(ap(X51,X52),X50) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])]) ).
fof(c_0_12,negated_conjecture,
! [X136] :
( ne(esk4_0)
& ne(esk5_0)
& mem(esk6_0,arr(esk5_0,esk4_0))
& mem(esk7_0,arr(esk4_0,bool))
& mem(esk8_0,arr(esk4_0,bool))
& ( ~ mem(X136,esk4_0)
| ~ p(ap(esk8_0,X136))
| p(ap(esk7_0,X136)) )
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(esk5_0,esk4_0),esk6_0),esk7_0))
& ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(esk5_0,esk4_0),esk6_0),esk8_0)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_13,plain,
! [X137,X138,X139,X140,X141,X144,X145,X148,X149,X150,X151,X153,X154,X155,X157,X158,X159,X162,X163,X164,X165,X168] :
( ( mem(esk9_5(X137,X138,X139,X140,X141),X140)
| ~ p(ap(X137,X141))
| ~ mem(X141,X139)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X140,X139),X138),X137))
| ~ epred1_4(X140,X139,X138,X137) )
& ( p(ap(X137,ap(X138,esk9_5(X137,X138,X139,X140,X141))))
| ~ p(ap(X137,X141))
| ~ mem(X141,X139)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X140,X139),X138),X137))
| ~ epred1_4(X140,X139,X138,X137) )
& ( mem(esk10_4(X137,X138,X139,X140),X139)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X140,X139),X138),X137))
| ~ epred1_4(X140,X139,X138,X137) )
& ( p(ap(X137,esk10_4(X137,X138,X139,X140)))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X140,X139),X138),X137))
| ~ epred1_4(X140,X139,X138,X137) )
& ( ~ mem(X144,X140)
| ~ p(ap(X137,ap(X138,X144)))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X140,X139),X138),X137))
| ~ epred1_4(X140,X139,X138,X137) )
& ( mem(esk11_5(X137,X138,X139,X140,X145),X140)
| p(ap(X137,X145))
| ~ mem(X145,X139)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X140,X139),X138),X137))
| ~ epred1_4(X140,X139,X138,X137) )
& ( ~ p(ap(X137,ap(X138,esk11_5(X137,X138,X139,X140,X145))))
| p(ap(X137,X145))
| ~ mem(X145,X139)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X140,X139),X138),X137))
| ~ epred1_4(X140,X139,X138,X137) )
& ( mem(esk12_4(X137,X138,X139,X140),X139)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X140,X139),X138),X137))
| ~ epred1_4(X140,X139,X138,X137) )
& ( ~ p(ap(X137,esk12_4(X137,X138,X139,X140)))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X140,X139),X138),X137))
| ~ epred1_4(X140,X139,X138,X137) )
& ( ~ mem(X148,X140)
| p(ap(X137,ap(X138,X148)))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X140,X139),X138),X137))
| ~ epred1_4(X140,X139,X138,X137) )
& ( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X140,X139),X149),X150))
| ~ mem(X151,X140)
| p(ap(X150,ap(X149,X151)))
| ~ mem(X150,arr(X139,bool))
| ~ mem(X149,arr(X140,X139))
| ~ epred1_4(X140,X139,X138,X137) )
& ( mem(esk13_6(X137,X138,X139,X140,X149,X150),X140)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X140,X139),X149),X150))
| ~ mem(X150,arr(X139,bool))
| ~ mem(X149,arr(X140,X139))
| ~ epred1_4(X140,X139,X138,X137) )
& ( ~ p(ap(X150,ap(X149,esk13_6(X137,X138,X139,X140,X149,X150))))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X140,X139),X149),X150))
| ~ mem(X150,arr(X139,bool))
| ~ mem(X149,arr(X140,X139))
| ~ epred1_4(X140,X139,X138,X137) )
& ( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X140,X139),X153),X154))
| ~ mem(X155,X140)
| ~ p(ap(X154,ap(X153,X155)))
| ~ mem(X154,arr(X139,bool))
| ~ mem(X153,arr(X140,X139))
| ~ epred1_4(X140,X139,X138,X137) )
& ( mem(esk14_6(X137,X138,X139,X140,X153,X154),X140)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X140,X139),X153),X154))
| ~ mem(X154,arr(X139,bool))
| ~ mem(X153,arr(X140,X139))
| ~ epred1_4(X140,X139,X138,X137) )
& ( p(ap(X154,ap(X153,esk14_6(X137,X138,X139,X140,X153,X154))))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X140,X139),X153),X154))
| ~ mem(X154,arr(X139,bool))
| ~ mem(X153,arr(X140,X139))
| ~ epred1_4(X140,X139,X138,X137) )
& ( mem(esk15_7(X137,X138,X139,X140,X157,X158,X159),X140)
| ~ p(ap(X158,X159))
| ~ mem(X159,X139)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X140,X139),X157),X158))
| ~ mem(X158,arr(X139,bool))
| ~ mem(X157,arr(X140,X139))
| ~ epred1_4(X140,X139,X138,X137) )
& ( X159 = ap(X157,esk15_7(X137,X138,X139,X140,X157,X158,X159))
| ~ p(ap(X158,X159))
| ~ mem(X159,X139)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X140,X139),X157),X158))
| ~ mem(X158,arr(X139,bool))
| ~ mem(X157,arr(X140,X139))
| ~ epred1_4(X140,X139,X138,X137) )
& ( mem(esk16_6(X137,X138,X139,X140,X157,X158),X139)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X140,X139),X157),X158))
| ~ mem(X158,arr(X139,bool))
| ~ mem(X157,arr(X140,X139))
| ~ epred1_4(X140,X139,X138,X137) )
& ( p(ap(X158,esk16_6(X137,X138,X139,X140,X157,X158)))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X140,X139),X157),X158))
| ~ mem(X158,arr(X139,bool))
| ~ mem(X157,arr(X140,X139))
| ~ epred1_4(X140,X139,X138,X137) )
& ( ~ mem(X162,X140)
| esk16_6(X137,X138,X139,X140,X157,X158) != ap(X157,X162)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X140,X139),X157),X158))
| ~ mem(X158,arr(X139,bool))
| ~ mem(X157,arr(X140,X139))
| ~ epred1_4(X140,X139,X138,X137) )
& ( mem(esk17_7(X137,X138,X139,X140,X163,X164,X165),X140)
| p(ap(X164,X165))
| ~ mem(X165,X139)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X140,X139),X163),X164))
| ~ mem(X164,arr(X139,bool))
| ~ mem(X163,arr(X140,X139))
| ~ epred1_4(X140,X139,X138,X137) )
& ( X165 = ap(X163,esk17_7(X137,X138,X139,X140,X163,X164,X165))
| p(ap(X164,X165))
| ~ mem(X165,X139)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X140,X139),X163),X164))
| ~ mem(X164,arr(X139,bool))
| ~ mem(X163,arr(X140,X139))
| ~ epred1_4(X140,X139,X138,X137) )
& ( mem(esk18_6(X137,X138,X139,X140,X163,X164),X139)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X140,X139),X163),X164))
| ~ mem(X164,arr(X139,bool))
| ~ mem(X163,arr(X140,X139))
| ~ epred1_4(X140,X139,X138,X137) )
& ( ~ p(ap(X164,esk18_6(X137,X138,X139,X140,X163,X164)))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X140,X139),X163),X164))
| ~ mem(X164,arr(X139,bool))
| ~ mem(X163,arr(X140,X139))
| ~ epred1_4(X140,X139,X138,X137) )
& ( ~ mem(X168,X140)
| esk18_6(X137,X138,X139,X140,X163,X164) != ap(X163,X168)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X140,X139),X163),X164))
| ~ mem(X164,arr(X139,bool))
| ~ mem(X163,arr(X140,X139))
| ~ epred1_4(X140,X139,X138,X137) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
cnf(c_0_14,plain,
( p(X1)
| p(X2)
| X1 = X2
| ~ mem(X2,bool)
| ~ mem(X1,bool) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
mem(c_2Ebool_2EF,bool),
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2EF]) ).
cnf(c_0_16,plain,
~ p(c_2Ebool_2EF),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( mem(ap(X1,X4),X3)
| ~ mem(X1,arr(X2,X3))
| ~ mem(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
mem(esk7_0,arr(esk4_0,bool)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_19,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_6]) ).
cnf(c_0_20,plain,
( ~ 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))
| ~ epred1_4(X1,X2,X6,X7) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,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_12]) ).
cnf(c_0_22,negated_conjecture,
mem(esk6_0,arr(esk5_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,plain,
( X1 = c_2Ebool_2EF
| p(X1)
| ~ mem(X1,bool) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( mem(ap(esk7_0,X1),bool)
| ~ mem(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_25,plain,
! [X108,X109,X110,X111] :
( ~ ne(X108)
| ~ ne(X109)
| ~ mem(X110,arr(X108,X109))
| ~ mem(X111,arr(X109,bool))
| epred1_4(X108,X109,X110,X111) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_26,negated_conjecture,
mem(esk8_0,arr(esk4_0,bool)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,negated_conjecture,
( ~ epred1_4(esk5_0,esk4_0,X1,X2)
| ~ p(ap(esk7_0,ap(esk6_0,X3)))
| ~ mem(X3,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_18]),c_0_22])]) ).
cnf(c_0_28,negated_conjecture,
( ap(esk7_0,X1) = c_2Ebool_2EF
| p(ap(esk7_0,X1))
| ~ mem(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( mem(ap(esk6_0,X1),esk4_0)
| ~ mem(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_30,plain,
( epred1_4(X1,X2,X3,X4)
| ~ ne(X1)
| ~ ne(X2)
| ~ mem(X3,arr(X1,X2))
| ~ mem(X4,arr(X2,bool)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,negated_conjecture,
ne(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_32,negated_conjecture,
( mem(ap(esk8_0,X1),bool)
| ~ mem(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
( ap(esk7_0,ap(esk6_0,X1)) = c_2Ebool_2EF
| ~ epred1_4(esk5_0,esk4_0,X2,X3)
| ~ mem(X1,esk5_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( epred1_4(X1,esk4_0,X2,esk8_0)
| ~ mem(X2,arr(X1,esk4_0))
| ~ ne(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_26]),c_0_31])]) ).
cnf(c_0_35,negated_conjecture,
ne(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_36,negated_conjecture,
( p(ap(esk7_0,X1))
| ~ mem(X1,esk4_0)
| ~ p(ap(esk8_0,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_37,negated_conjecture,
( ap(esk8_0,X1) = c_2Ebool_2EF
| p(ap(esk8_0,X1))
| ~ mem(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( ap(esk7_0,ap(esk6_0,X1)) = c_2Ebool_2EF
| ~ mem(X2,arr(esk5_0,esk4_0))
| ~ mem(X1,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_39,negated_conjecture,
( ap(esk8_0,X1) = c_2Ebool_2EF
| p(ap(esk7_0,X1))
| ~ mem(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( ap(esk7_0,ap(esk6_0,X1)) = c_2Ebool_2EF
| ~ mem(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_22]) ).
cnf(c_0_41,plain,
( p(ap(X1,ap(X2,esk14_6(X3,X4,X5,X6,X2,X1))))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X6,X5),X2),X1))
| ~ mem(X1,arr(X5,bool))
| ~ mem(X2,arr(X6,X5))
| ~ epred1_4(X6,X5,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_42,negated_conjecture,
( ap(esk8_0,ap(esk6_0,X1)) = c_2Ebool_2EF
| ~ mem(X1,esk5_0) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_16]),c_0_29]) ).
cnf(c_0_43,plain,
( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X2),esk6_0),esk8_0))
| ~ epred1_4(X1,X2,X3,X4)
| ~ mem(esk14_6(X4,X3,X2,X1,esk6_0,esk8_0),esk5_0)
| ~ mem(esk8_0,arr(X2,bool))
| ~ mem(esk6_0,arr(X1,X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_16]) ).
cnf(c_0_44,plain,
( mem(esk14_6(X1,X2,X3,X4,X5,X6),X4)
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X4,X3),X5),X6))
| ~ mem(X6,arr(X3,bool))
| ~ mem(X5,arr(X4,X3))
| ~ epred1_4(X4,X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_45,plain,
( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(esk5_0,X1),esk6_0),esk8_0))
| ~ epred1_4(esk5_0,X1,X2,X3)
| ~ mem(esk8_0,arr(X1,bool))
| ~ mem(esk6_0,arr(esk5_0,X1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_46,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_12]) ).
cnf(c_0_47,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(spm,[status(thm)],[c_0_45,c_0_34]),c_0_26]),c_0_22]),c_0_35])]),c_0_46]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_22,c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP006+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.12/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 11:49:39 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 56.17/56.24 % Version : CSE_E---1.5
% 56.17/56.24 % Problem : theBenchmark.p
% 56.17/56.24 % Proof found
% 56.17/56.24 % SZS status Theorem for theBenchmark.p
% 56.17/56.24 % SZS output start Proof
% See solution above
% 56.17/56.24 % Total time : 55.655000 s
% 56.17/56.24 % SZS output end Proof
% 56.17/56.24 % Total time : 55.662000 s
%------------------------------------------------------------------------------