TSTP Solution File: SWC045+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWC045+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 : n015.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 20:19:21 EDT 2023
% Result : Theorem 93.94s 94.16s
% Output : CNFRefutation 93.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 91
% Syntax : Number of formulae : 154 ( 13 unt; 76 typ; 0 def)
% Number of atoms : 306 ( 88 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 391 ( 163 ~; 160 |; 28 &)
% ( 2 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 86 ( 69 >; 17 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 57 ( 57 usr; 7 con; 0-2 aty)
% Number of variables : 135 ( 0 sgn; 64 !; 6 ?; 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_1: $i > $i ).
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(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( nil != X2
| X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ( ( ~ memberP(X3,X5)
& ? [X6] :
( ssList(X6)
& segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) ) )
| ( ! [X6] :
( ssList(X6)
=> ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) )
& memberP(X3,X5) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax79) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax54,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X1) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax54) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).
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(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(c_0_15,plain,
! [X222,X223,X224] :
( ~ ssList(X222)
| ~ ssList(X223)
| ~ ssList(X224)
| app(app(X222,X223),X224) = app(X222,app(X223,X224)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
fof(c_0_16,plain,
! [X227] :
( ~ ssList(X227)
| app(X227,nil) = X227 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( nil != X2
| X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ( ( ~ memberP(X3,X5)
& ? [X6] :
( ssList(X6)
& segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) ) )
| ( ! [X6] :
( ssList(X6)
=> ~ segmentP(X4,app(app(cons(X5,nil),X6),cons(X5,nil))) )
& memberP(X3,X5) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_18,plain,
! [X214,X215,X216] :
( ~ ssList(X214)
| ~ ssList(X215)
| ~ ssList(X216)
| app(X216,X215) != app(X214,X215)
| X216 = X214 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])]) ).
fof(c_0_19,plain,
! [X135] :
( ~ ssList(X135)
| app(nil,X135) = X135 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
fof(c_0_20,plain,
! [X225,X226] :
( ( nil = X226
| nil != app(X225,X226)
| ~ ssList(X226)
| ~ ssList(X225) )
& ( nil = X225
| nil != app(X225,X226)
| ~ ssList(X226)
| ~ ssList(X225) )
& ( nil != X226
| nil != X225
| nil = app(X225,X226)
| ~ ssList(X226)
| ~ ssList(X225) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_21,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_24,negated_conjecture,
! [X255,X256] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& nil = esk49_0
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& nil != esk48_0
& ( memberP(esk50_0,X255)
| ~ ssList(X256)
| ~ segmentP(esk51_0,app(app(cons(X255,nil),X256),cons(X255,nil)))
| ~ ssItem(X255) )
& ( ssList(esk52_1(X255))
| ~ memberP(esk50_0,X255)
| ~ ssItem(X255) )
& ( segmentP(esk51_0,app(app(cons(X255,nil),esk52_1(X255)),cons(X255,nil)))
| ~ memberP(esk50_0,X255)
| ~ ssItem(X255) ) ),
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_17])])])])]) ).
cnf(c_0_25,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X3,X2) != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_27,plain,
! [X132,X133,X134] :
( ~ ssList(X132)
| ~ ssList(X133)
| ~ ssItem(X134)
| cons(X134,app(X133,X132)) = app(cons(X134,X133),X132) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
fof(c_0_28,plain,
! [X111,X112] :
( ~ ssList(X111)
| ~ ssItem(X112)
| ssList(cons(X112,X111)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
fof(c_0_29,plain,
! [X122,X123] :
( ~ ssList(X122)
| ~ ssItem(X123)
| nil != cons(X123,X122) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
cnf(c_0_30,plain,
( nil = X1
| nil != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,plain,
( app(X1,app(nil,X2)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
fof(c_0_32,plain,
! [X130,X131] :
( ~ ssList(X130)
| ~ ssList(X131)
| ssList(app(X130,X131)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_33,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,negated_conjecture,
nil = esk49_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_35,plain,
( X1 = nil
| app(X1,X2) != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_23])]) ).
cnf(c_0_36,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,plain,
( app(nil,X1) = nil
| app(X2,X1) != nil
| ~ ssList(app(nil,X1))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_42,plain,
! [X187,X188] :
( ~ ssList(X187)
| ~ ssList(X188)
| ~ segmentP(X187,X188)
| ~ segmentP(X188,X187)
| X187 = X188 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax54])])]) ).
cnf(c_0_43,negated_conjecture,
( segmentP(esk51_0,app(app(cons(X1,nil),esk52_1(X1)),cons(X1,nil)))
| ~ memberP(esk50_0,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_44,negated_conjecture,
esk51_0 = nil,
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
fof(c_0_45,plain,
! [X194] :
( ~ ssList(X194)
| segmentP(X194,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])]) ).
cnf(c_0_46,plain,
( cons(X1,app(X2,X3)) != X3
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38]) ).
cnf(c_0_47,plain,
( app(nil,X1) = nil
| app(X2,X1) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_23])]) ).
cnf(c_0_48,plain,
( app(nil,app(X1,X2)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_26]),c_0_23])]) ).
cnf(c_0_49,plain,
( ssList(cons(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_36]),c_0_37]) ).
cnf(c_0_50,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_41])]),c_0_23])]) ).
cnf(c_0_51,plain,
( X1 = X2
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_52,negated_conjecture,
( segmentP(nil,app(app(cons(X1,nil),esk52_1(X1)),cons(X1,nil)))
| ~ memberP(esk50_0,X1)
| ~ ssItem(X1) ),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_53,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_54,plain,
( cons(X1,app(X2,app(X3,X4))) != X4
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_21]),c_0_40]) ).
cnf(c_0_55,plain,
( app(nil,app(X1,X2)) = nil
| app(X1,X2) != nil
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_23])]),c_0_40]) ).
cnf(c_0_56,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_23])]) ).
cnf(c_0_57,negated_conjecture,
( app(app(cons(X1,nil),esk52_1(X1)),cons(X1,nil)) = nil
| ~ memberP(esk50_0,X1)
| ~ ssList(app(app(cons(X1,nil),esk52_1(X1)),cons(X1,nil)))
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_23])]),c_0_53]) ).
fof(c_0_58,plain,
! [X154,X155,X156] :
( ( ~ memberP(cons(X155,X156),X154)
| X154 = X155
| memberP(X156,X154)
| ~ ssList(X156)
| ~ ssItem(X155)
| ~ ssItem(X154) )
& ( X154 != X155
| memberP(cons(X155,X156),X154)
| ~ ssList(X156)
| ~ ssItem(X155)
| ~ ssItem(X154) )
& ( ~ memberP(X156,X154)
| memberP(cons(X155,X156),X154)
| ~ ssList(X156)
| ~ ssItem(X155)
| ~ ssItem(X154) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).
cnf(c_0_59,plain,
( app(X1,cons(X2,nil)) != nil
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_23])])]),c_0_56]) ).
cnf(c_0_60,negated_conjecture,
( app(app(cons(X1,nil),esk52_1(X1)),cons(X1,nil)) = nil
| ~ memberP(esk50_0,X1)
| ~ ssList(app(cons(X1,nil),esk52_1(X1)))
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_40]),c_0_56]) ).
cnf(c_0_61,plain,
( memberP(cons(X2,X3),X1)
| X1 != X2
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_62,plain,
! [X119] :
( ( ssList(esk44_1(X119))
| nil = X119
| ~ ssList(X119) )
& ( ssItem(esk45_1(X119))
| nil = X119
| ~ ssList(X119) )
& ( cons(esk45_1(X119),esk44_1(X119)) = X119
| nil = X119
| ~ ssList(X119) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).
cnf(c_0_63,negated_conjecture,
( ~ memberP(esk50_0,X1)
| ~ ssList(app(cons(X1,nil),esk52_1(X1)))
| ~ ssItem(X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,negated_conjecture,
( ssList(esk52_1(X1))
| ~ memberP(esk50_0,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_65,plain,
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(er,[status(thm)],[c_0_61]) ).
cnf(c_0_66,plain,
( cons(esk45_1(X1),esk44_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_67,plain,
( ssItem(esk45_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_68,plain,
( ssList(esk44_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_69,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_70,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_71,negated_conjecture,
nil != esk48_0,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_72,negated_conjecture,
( ~ memberP(esk50_0,X1)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_40]),c_0_64]),c_0_56]) ).
cnf(c_0_73,plain,
( nil = X1
| memberP(X1,esk45_1(X1))
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_68]) ).
cnf(c_0_74,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,negated_conjecture,
esk50_0 != nil,
inference(rw,[status(thm)],[c_0_71,c_0_70]) ).
cnf(c_0_76,negated_conjecture,
~ ssItem(esk45_1(esk50_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74])]),c_0_75]) ).
cnf(c_0_77,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_67]),c_0_74])]),c_0_75]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC045+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Aug 28 17:27:55 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.18/0.57 start to proof: theBenchmark
% 93.94/94.16 % Version : CSE_E---1.5
% 93.94/94.16 % Problem : theBenchmark.p
% 93.94/94.16 % Proof found
% 93.94/94.16 % SZS status Theorem for theBenchmark.p
% 93.94/94.16 % SZS output start Proof
% See solution above
% 93.94/94.17 % Total time : 93.533000 s
% 93.94/94.17 % SZS output end Proof
% 93.94/94.17 % Total time : 93.542000 s
%------------------------------------------------------------------------------