TSTP Solution File: SWC409+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWC409+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n025.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 20:22:22 EDT 2023
% Result : Theorem 6.00s 6.08s
% Output : CNFRefutation 6.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 100
% Syntax : Number of formulae : 230 ( 40 unt; 76 typ; 0 def)
% Number of atoms : 551 ( 146 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 659 ( 262 ~; 290 |; 41 &)
% ( 7 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 85 ( 68 >; 17 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 57 ( 57 usr; 8 con; 0-2 aty)
% Number of variables : 207 ( 0 sgn; 102 !; 10 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ssItem: $i > $o ).
tff(decl_23,type,
neq: ( $i * $i ) > $o ).
tff(decl_24,type,
ssList: $i > $o ).
tff(decl_25,type,
memberP: ( $i * $i ) > $o ).
tff(decl_26,type,
cons: ( $i * $i ) > $i ).
tff(decl_27,type,
app: ( $i * $i ) > $i ).
tff(decl_28,type,
singletonP: $i > $o ).
tff(decl_29,type,
nil: $i ).
tff(decl_30,type,
frontsegP: ( $i * $i ) > $o ).
tff(decl_31,type,
rearsegP: ( $i * $i ) > $o ).
tff(decl_32,type,
segmentP: ( $i * $i ) > $o ).
tff(decl_33,type,
cyclefreeP: $i > $o ).
tff(decl_34,type,
leq: ( $i * $i ) > $o ).
tff(decl_35,type,
totalorderP: $i > $o ).
tff(decl_36,type,
strictorderP: $i > $o ).
tff(decl_37,type,
lt: ( $i * $i ) > $o ).
tff(decl_38,type,
totalorderedP: $i > $o ).
tff(decl_39,type,
strictorderedP: $i > $o ).
tff(decl_40,type,
duplicatefreeP: $i > $o ).
tff(decl_41,type,
equalelemsP: $i > $o ).
tff(decl_42,type,
hd: $i > $i ).
tff(decl_43,type,
tl: $i > $i ).
tff(decl_44,type,
geq: ( $i * $i ) > $o ).
tff(decl_45,type,
gt: ( $i * $i ) > $o ).
tff(decl_46,type,
esk1_0: $i ).
tff(decl_47,type,
esk2_0: $i ).
tff(decl_48,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk5_1: $i > $i ).
tff(decl_51,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk10_1: $i > $i ).
tff(decl_56,type,
esk11_1: $i > $i ).
tff(decl_57,type,
esk12_1: $i > $i ).
tff(decl_58,type,
esk13_1: $i > $i ).
tff(decl_59,type,
esk14_1: $i > $i ).
tff(decl_60,type,
esk15_1: $i > $i ).
tff(decl_61,type,
esk16_1: $i > $i ).
tff(decl_62,type,
esk17_1: $i > $i ).
tff(decl_63,type,
esk18_1: $i > $i ).
tff(decl_64,type,
esk19_1: $i > $i ).
tff(decl_65,type,
esk20_1: $i > $i ).
tff(decl_66,type,
esk21_1: $i > $i ).
tff(decl_67,type,
esk22_1: $i > $i ).
tff(decl_68,type,
esk23_1: $i > $i ).
tff(decl_69,type,
esk24_1: $i > $i ).
tff(decl_70,type,
esk25_1: $i > $i ).
tff(decl_71,type,
esk26_1: $i > $i ).
tff(decl_72,type,
esk27_1: $i > $i ).
tff(decl_73,type,
esk28_1: $i > $i ).
tff(decl_74,type,
esk29_1: $i > $i ).
tff(decl_75,type,
esk30_1: $i > $i ).
tff(decl_76,type,
esk31_1: $i > $i ).
tff(decl_77,type,
esk32_1: $i > $i ).
tff(decl_78,type,
esk33_1: $i > $i ).
tff(decl_79,type,
esk34_1: $i > $i ).
tff(decl_80,type,
esk35_1: $i > $i ).
tff(decl_81,type,
esk36_1: $i > $i ).
tff(decl_82,type,
esk37_1: $i > $i ).
tff(decl_83,type,
esk38_1: $i > $i ).
tff(decl_84,type,
esk39_1: $i > $i ).
tff(decl_85,type,
esk40_1: $i > $i ).
tff(decl_86,type,
esk41_1: $i > $i ).
tff(decl_87,type,
esk42_1: $i > $i ).
tff(decl_88,type,
esk43_1: $i > $i ).
tff(decl_89,type,
esk44_1: $i > $i ).
tff(decl_90,type,
esk45_1: $i > $i ).
tff(decl_91,type,
esk46_1: $i > $i ).
tff(decl_92,type,
esk47_1: $i > $i ).
tff(decl_93,type,
esk48_0: $i ).
tff(decl_94,type,
esk49_0: $i ).
tff(decl_95,type,
esk50_0: $i ).
tff(decl_96,type,
esk51_0: $i ).
tff(decl_97,type,
esk52_0: $i ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) != X3
& app(cons(X5,nil),X6) = X4 ) )
| ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X2,X7)
| memberP(X1,X7) ) )
| ( nil != X3
& nil = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax43,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(X1,X2)
=> frontsegP(app(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax43) ).
fof(ax45,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax45) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax82,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax85) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax50,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( rearsegP(X1,X2)
=> rearsegP(app(X3,X1),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax50) ).
fof(ax51,axiom,
! [X1] :
( ssList(X1)
=> rearsegP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax51) ).
fof(ax6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax86,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax86) ).
fof(ax36,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X2,X1)
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(c_0_24,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) != X3
& app(cons(X5,nil),X6) = X4 ) )
| ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X2,X7)
| memberP(X1,X7) ) )
| ( nil != X3
& nil = X4 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_25,negated_conjecture,
! [X256,X257] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( ~ ssItem(X256)
| ~ ssList(X257)
| app(X257,cons(X256,nil)) = esk50_0
| app(cons(X256,nil),X257) != esk51_0 )
& ssItem(esk52_0)
& memberP(esk49_0,esk52_0)
& ~ memberP(esk48_0,esk52_0)
& ( nil = esk50_0
| nil != esk51_0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
fof(c_0_26,plain,
! [X21,X22,X24] :
( ( ssList(esk6_2(X21,X22))
| ~ frontsegP(X21,X22)
| ~ ssList(X22)
| ~ ssList(X21) )
& ( app(X22,esk6_2(X21,X22)) = X21
| ~ frontsegP(X21,X22)
| ~ ssList(X22)
| ~ ssList(X21) )
& ( ~ ssList(X24)
| app(X22,X24) != X21
| frontsegP(X21,X22)
| ~ ssList(X22)
| ~ ssList(X21) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).
fof(c_0_27,plain,
! [X131,X132] :
( ~ ssList(X131)
| ~ ssList(X132)
| ssList(app(X131,X132)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_28,plain,
! [X12,X13,X16,X17] :
( ( ssList(esk3_2(X12,X13))
| ~ memberP(X12,X13)
| ~ ssItem(X13)
| ~ ssList(X12) )
& ( ssList(esk4_2(X12,X13))
| ~ memberP(X12,X13)
| ~ ssItem(X13)
| ~ ssList(X12) )
& ( app(esk3_2(X12,X13),cons(X13,esk4_2(X12,X13))) = X12
| ~ memberP(X12,X13)
| ~ ssItem(X13)
| ~ ssList(X12) )
& ( ~ ssList(X16)
| ~ ssList(X17)
| app(X16,cons(X13,X17)) != X12
| memberP(X12,X13)
| ~ ssItem(X13)
| ~ ssList(X12) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])]) ).
cnf(c_0_29,negated_conjecture,
memberP(esk49_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
( app(esk3_2(X1,X2),cons(X2,esk4_2(X1,X2))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
memberP(esk51_0,esk52_0),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_37,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38,plain,
( ssList(esk3_2(X1,X2))
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_32]),c_0_33]) ).
cnf(c_0_40,negated_conjecture,
app(esk3_2(esk51_0,esk52_0),cons(esk52_0,esk4_2(esk51_0,esk52_0))) = esk51_0,
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])]) ).
cnf(c_0_41,negated_conjecture,
ssList(esk3_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_35]),c_0_36]),c_0_37])]) ).
fof(c_0_42,plain,
! [X112,X113] :
( ~ ssList(X112)
| ~ ssItem(X113)
| ssList(cons(X113,X112)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_43,plain,
( ssList(esk4_2(X1,X2))
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_44,plain,
! [X165,X166,X167] :
( ~ ssList(X165)
| ~ ssList(X166)
| ~ ssList(X167)
| ~ frontsegP(X165,X166)
| frontsegP(app(X165,X167),X166) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).
fof(c_0_45,plain,
! [X172] :
( ~ ssList(X172)
| frontsegP(X172,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
cnf(c_0_46,negated_conjecture,
( frontsegP(esk51_0,esk3_2(esk51_0,esk52_0))
| ~ ssList(cons(esk52_0,esk4_2(esk51_0,esk52_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
cnf(c_0_47,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,negated_conjecture,
ssList(esk4_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_35]),c_0_36]),c_0_37])]) ).
fof(c_0_49,plain,
! [X226,X227] :
( ( nil = X227
| nil != app(X226,X227)
| ~ ssList(X227)
| ~ ssList(X226) )
& ( nil = X226
| nil != app(X226,X227)
| ~ ssList(X227)
| ~ ssList(X226) )
& ( nil != X227
| nil != X226
| nil = app(X226,X227)
| ~ ssList(X227)
| ~ ssList(X226) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_50,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_53,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_54,negated_conjecture,
frontsegP(esk51_0,esk3_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_37])]) ).
cnf(c_0_55,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_56,plain,
! [X223,X224,X225] :
( ~ ssList(X223)
| ~ ssList(X224)
| ~ ssList(X225)
| app(app(X223,X224),X225) = app(X223,app(X224,X225)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_57,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_58,plain,
( frontsegP(app(X1,X2),nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).
cnf(c_0_59,negated_conjecture,
app(esk3_2(esk51_0,esk52_0),esk6_2(esk51_0,esk3_2(esk51_0,esk52_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_36]),c_0_41])]) ).
cnf(c_0_60,negated_conjecture,
ssList(esk6_2(esk51_0,esk3_2(esk51_0,esk52_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_54]),c_0_41]),c_0_36])]) ).
fof(c_0_61,plain,
! [X29,X30,X33,X34] :
( ( ssList(esk8_2(X29,X30))
| ~ segmentP(X29,X30)
| ~ ssList(X30)
| ~ ssList(X29) )
& ( ssList(esk9_2(X29,X30))
| ~ segmentP(X29,X30)
| ~ ssList(X30)
| ~ ssList(X29) )
& ( app(app(esk8_2(X29,X30),X30),esk9_2(X29,X30)) = X29
| ~ segmentP(X29,X30)
| ~ ssList(X30)
| ~ ssList(X29) )
& ( ~ ssList(X33)
| ~ ssList(X34)
| app(app(X33,X30),X34) != X29
| segmentP(X29,X30)
| ~ ssList(X30)
| ~ ssList(X29) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])]) ).
cnf(c_0_62,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_63,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_57])]),c_0_52])]) ).
cnf(c_0_64,negated_conjecture,
frontsegP(esk51_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_41])]) ).
cnf(c_0_65,plain,
( segmentP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,X3),X2) != X4
| ~ ssList(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_66,plain,
( app(nil,app(nil,X1)) = app(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_52])]) ).
cnf(c_0_67,negated_conjecture,
app(nil,esk6_2(esk51_0,nil)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_64]),c_0_36]),c_0_52])]) ).
cnf(c_0_68,negated_conjecture,
ssList(esk6_2(esk51_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_64]),c_0_52]),c_0_36])]) ).
cnf(c_0_69,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(app(app(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_65]) ).
cnf(c_0_70,negated_conjecture,
app(nil,esk51_0) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68])]) ).
fof(c_0_71,plain,
! [X228] :
( ~ ssList(X228)
| app(X228,nil) = X228 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_72,negated_conjecture,
( segmentP(app(esk51_0,X1),esk51_0)
| ~ ssList(app(esk51_0,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_36]),c_0_52])]) ).
cnf(c_0_73,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_74,plain,
( app(app(esk8_2(X1,X2),X2),esk9_2(X1,X2)) = X1
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_75,negated_conjecture,
segmentP(esk51_0,esk51_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_36]),c_0_52])]) ).
cnf(c_0_76,plain,
( ssList(esk9_2(X1,X2))
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_77,plain,
( ssList(esk8_2(X1,X2))
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_78,negated_conjecture,
app(app(esk8_2(esk51_0,esk51_0),esk51_0),esk9_2(esk51_0,esk51_0)) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_36])]) ).
cnf(c_0_79,negated_conjecture,
ssList(esk9_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_75]),c_0_36])]) ).
cnf(c_0_80,negated_conjecture,
ssList(esk8_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_75]),c_0_36])]) ).
fof(c_0_81,plain,
! [X229,X230] :
( ~ ssList(X229)
| ~ ssList(X230)
| nil = X229
| hd(app(X229,X230)) = hd(X229) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).
cnf(c_0_82,negated_conjecture,
app(esk8_2(esk51_0,esk51_0),app(esk51_0,esk9_2(esk51_0,esk51_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_78]),c_0_79]),c_0_36]),c_0_80])]) ).
fof(c_0_83,plain,
! [X125] :
( ~ ssList(X125)
| nil = X125
| ssItem(hd(X125)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
cnf(c_0_84,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
fof(c_0_85,plain,
! [X180,X181,X182] :
( ~ ssList(X180)
| ~ ssList(X181)
| ~ ssList(X182)
| ~ rearsegP(X180,X181)
| rearsegP(app(X182,X180),X181) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).
fof(c_0_86,plain,
! [X183] :
( ~ ssList(X183)
| rearsegP(X183,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).
cnf(c_0_87,negated_conjecture,
( frontsegP(esk51_0,esk8_2(esk51_0,esk51_0))
| ~ ssList(app(esk51_0,esk9_2(esk51_0,esk51_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_82]),c_0_80])]) ).
cnf(c_0_88,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_89,negated_conjecture,
( hd(esk3_2(esk51_0,esk52_0)) = hd(esk51_0)
| esk3_2(esk51_0,esk52_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_59]),c_0_60]),c_0_41])]) ).
cnf(c_0_90,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_91,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_92,negated_conjecture,
frontsegP(esk51_0,esk8_2(esk51_0,esk51_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_33]),c_0_79]),c_0_36])]) ).
fof(c_0_93,plain,
! [X25,X26,X28] :
( ( ssList(esk7_2(X25,X26))
| ~ rearsegP(X25,X26)
| ~ ssList(X26)
| ~ ssList(X25) )
& ( app(esk7_2(X25,X26),X26) = X25
| ~ rearsegP(X25,X26)
| ~ ssList(X26)
| ~ ssList(X25) )
& ( ~ ssList(X28)
| app(X28,X26) != X25
| rearsegP(X25,X26)
| ~ ssList(X26)
| ~ ssList(X25) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])])])]) ).
fof(c_0_94,plain,
! [X136] :
( ~ ssList(X136)
| app(nil,X136) = X136 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_95,negated_conjecture,
( esk3_2(esk51_0,esk52_0) = nil
| ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_41])]) ).
cnf(c_0_96,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_52])]) ).
cnf(c_0_97,negated_conjecture,
app(esk8_2(esk51_0,esk51_0),esk6_2(esk51_0,esk8_2(esk51_0,esk51_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_92]),c_0_36]),c_0_80])]) ).
cnf(c_0_98,negated_conjecture,
ssList(esk6_2(esk51_0,esk8_2(esk51_0,esk51_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_92]),c_0_80]),c_0_36])]) ).
cnf(c_0_99,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_100,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
fof(c_0_101,plain,
! [X221,X222] :
( ~ ssList(X221)
| ~ ssItem(X222)
| cons(X222,X221) = app(cons(X222,nil),X221) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_102,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_103,negated_conjecture,
( app(nil,cons(esk52_0,esk4_2(esk51_0,esk52_0))) = esk51_0
| ssItem(hd(esk51_0)) ),
inference(spm,[status(thm)],[c_0_40,c_0_95]) ).
fof(c_0_104,plain,
! [X214] :
( ~ ssList(X214)
| nil = X214
| cons(hd(X214),tl(X214)) = X214 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
cnf(c_0_105,negated_conjecture,
rearsegP(esk51_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_80]),c_0_98])]) ).
cnf(c_0_106,plain,
( app(esk7_2(X1,nil),nil) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_91]),c_0_52])]) ).
cnf(c_0_107,plain,
( ssList(esk7_2(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_91]),c_0_52])]) ).
cnf(c_0_108,negated_conjecture,
( app(X2,cons(X1,nil)) = esk50_0
| ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,nil),X2) != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_109,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_110,negated_conjecture,
( cons(esk52_0,esk4_2(esk51_0,esk52_0)) = esk51_0
| ssItem(hd(esk51_0))
| ~ ssList(cons(esk52_0,esk4_2(esk51_0,esk52_0))) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_111,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_112,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_113,negated_conjecture,
app(esk7_2(esk51_0,nil),nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_105]),c_0_52]),c_0_36])]) ).
cnf(c_0_114,plain,
( esk7_2(X1,nil) = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_106]),c_0_107]) ).
cnf(c_0_115,plain,
( memberP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,cons(X3,X2)) != X4
| ~ ssItem(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_116,negated_conjecture,
( app(X1,cons(X2,nil)) = esk50_0
| cons(X2,X1) != esk51_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_117,negated_conjecture,
( cons(esk52_0,esk4_2(esk51_0,esk52_0)) = esk51_0
| ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_47]),c_0_48]),c_0_37])]) ).
cnf(c_0_118,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_119,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_120,negated_conjecture,
~ memberP(esk48_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_121,plain,
! [X155,X156,X157] :
( ( ~ memberP(cons(X156,X157),X155)
| X155 = X156
| memberP(X157,X155)
| ~ ssList(X157)
| ~ ssItem(X156)
| ~ ssItem(X155) )
& ( X155 != X156
| memberP(cons(X156,X157),X155)
| ~ ssList(X157)
| ~ ssItem(X156)
| ~ ssItem(X155) )
& ( ~ memberP(X157,X155)
| memberP(cons(X156,X157),X155)
| ~ ssList(X157)
| ~ ssItem(X156)
| ~ ssItem(X155) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).
fof(c_0_122,plain,
! [X128] :
( ~ ssList(X128)
| nil = X128
| ssList(tl(X128)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
fof(c_0_123,plain,
! [X231,X232] :
( ~ ssList(X231)
| ~ ssList(X232)
| nil = X231
| tl(app(X231,X232)) = app(tl(X231),X232) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
cnf(c_0_124,plain,
( cons(hd(X1),tl(app(X1,X2))) = app(X1,X2)
| nil = X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_84]),c_0_33]),c_0_112]) ).
cnf(c_0_125,negated_conjecture,
app(esk51_0,nil) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_36])]) ).
cnf(c_0_126,plain,
( memberP(app(X1,cons(X2,X3)),X2)
| ~ ssList(app(X1,cons(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(er,[status(thm)],[c_0_115]) ).
cnf(c_0_127,negated_conjecture,
( app(esk4_2(esk51_0,esk52_0),cons(esk52_0,nil)) = esk50_0
| ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_48]),c_0_37])]) ).
cnf(c_0_128,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_129,negated_conjecture,
~ memberP(esk50_0,esk52_0),
inference(rw,[status(thm)],[c_0_120,c_0_119]) ).
cnf(c_0_130,plain,
( X3 = X1
| memberP(X2,X3)
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_131,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_132,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_133,negated_conjecture,
( cons(hd(esk51_0),tl(esk51_0)) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_52]),c_0_36])]) ).
cnf(c_0_134,negated_conjecture,
ssItem(hd(esk51_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_126,c_0_127]),c_0_128]),c_0_52]),c_0_48]),c_0_37])]),c_0_129]) ).
fof(c_0_135,plain,
! [X152,X153,X154] :
( ( ~ memberP(app(X153,X154),X152)
| memberP(X153,X152)
| memberP(X154,X152)
| ~ ssList(X154)
| ~ ssList(X153)
| ~ ssItem(X152) )
& ( ~ memberP(X153,X152)
| memberP(app(X153,X154),X152)
| ~ ssList(X154)
| ~ ssList(X153)
| ~ ssItem(X152) )
& ( ~ memberP(X154,X152)
| memberP(app(X153,X154),X152)
| ~ ssList(X154)
| ~ ssList(X153)
| ~ ssItem(X152) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])]) ).
cnf(c_0_136,plain,
( hd(X1) = X2
| nil = X1
| memberP(tl(X1),X2)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_111]),c_0_88]),c_0_131]) ).
cnf(c_0_137,plain,
( nil = X1
| ssList(app(tl(X1),X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_33]),c_0_112]) ).
cnf(c_0_138,negated_conjecture,
( app(tl(esk51_0),nil) = tl(esk51_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_125]),c_0_52]),c_0_36])]) ).
cnf(c_0_139,negated_conjecture,
( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk50_0
| esk51_0 = nil
| ~ ssList(tl(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_133]),c_0_134])]) ).
cnf(c_0_140,plain,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_141,negated_conjecture,
( hd(esk51_0) = esk52_0
| esk51_0 = nil
| memberP(tl(esk51_0),esk52_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_35]),c_0_36]),c_0_37])]) ).
cnf(c_0_142,negated_conjecture,
( esk51_0 = nil
| ssList(tl(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_52]),c_0_36])]) ).
cnf(c_0_143,negated_conjecture,
( app(tl(esk51_0),cons(hd(esk51_0),nil)) = esk50_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_131]),c_0_36])]) ).
cnf(c_0_144,negated_conjecture,
( hd(esk51_0) = esk52_0
| esk51_0 = nil
| memberP(app(tl(esk51_0),X1),esk52_0)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_37])]),c_0_142]) ).
cnf(c_0_145,negated_conjecture,
( esk51_0 = nil
| memberP(esk50_0,hd(esk51_0))
| ~ ssList(tl(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_143]),c_0_128]),c_0_52]),c_0_134])]) ).
cnf(c_0_146,negated_conjecture,
( hd(esk51_0) = esk52_0
| esk51_0 = nil
| ~ ssList(cons(hd(esk51_0),nil)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_143]),c_0_129]) ).
cnf(c_0_147,negated_conjecture,
( esk51_0 = nil
| memberP(esk50_0,hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_131]),c_0_36])]) ).
cnf(c_0_148,negated_conjecture,
( hd(esk51_0) = esk52_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_47]),c_0_52]),c_0_134])]) ).
cnf(c_0_149,negated_conjecture,
( nil = esk50_0
| nil != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_150,negated_conjecture,
esk51_0 = nil,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_129]) ).
cnf(c_0_151,negated_conjecture,
esk50_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_150])]) ).
cnf(c_0_152,negated_conjecture,
~ memberP(nil,esk52_0),
inference(rw,[status(thm)],[c_0_129,c_0_151]) ).
cnf(c_0_153,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_150]),c_0_152]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC409+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 17:29:24 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 6.00/6.08 % Version : CSE_E---1.5
% 6.00/6.08 % Problem : theBenchmark.p
% 6.00/6.08 % Proof found
% 6.00/6.08 % SZS status Theorem for theBenchmark.p
% 6.00/6.08 % SZS output start Proof
% See solution above
% 6.00/6.09 % Total time : 5.509000 s
% 6.00/6.09 % SZS output end Proof
% 6.00/6.09 % Total time : 5.513000 s
%------------------------------------------------------------------------------