TSTP Solution File: SWC252+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWC252+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 : n012.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 20:21:07 EDT 2023
% Result : Theorem 0.19s 0.68s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 92
% Syntax : Number of formulae : 165 ( 26 unt; 77 typ; 0 def)
% Number of atoms : 359 ( 103 equ)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 454 ( 183 ~; 185 |; 40 &)
% ( 5 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 88 ( 69 >; 19 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 58 ( 58 usr; 8 con; 0-3 aty)
% Number of variables : 132 ( 0 sgn; 69 !; 8 ?; 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_3: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
esk53_0: $i ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ lt(X5,X8)
| leq(X5,X8) ) ) ) ) )
| ( ! [X9] :
( ssItem(X9)
=> ( cons(X9,nil) != X3
| ~ memberP(X4,X9) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax52,axiom,
! [X1] :
( ssList(X1)
=> ( rearsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax52) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(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(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
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(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(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(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(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(ax42,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax42) ).
fof(ax93,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
<=> ( X1 != X2
& leq(X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax93) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| nil = X1
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& app(app(X6,cons(X5,nil)),X7) = X1
& ! [X8] :
( ssItem(X8)
=> ( ~ memberP(X6,X8)
| ~ memberP(X7,X8)
| ~ lt(X5,X8)
| leq(X5,X8) ) ) ) ) )
| ( ! [X9] :
( ssItem(X9)
=> ( cons(X9,nil) != X3
| ~ memberP(X4,X9) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_16,plain,
! [X186] :
( ( ~ rearsegP(nil,X186)
| nil = X186
| ~ ssList(X186) )
& ( nil != X186
| rearsegP(nil,X186)
| ~ ssList(X186) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax52])])]) ).
fof(c_0_17,negated_conjecture,
! [X258,X259,X260] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& nil != esk48_0
& ( ssItem(esk52_3(X258,X259,X260))
| ~ ssList(X260)
| app(app(X259,cons(X258,nil)),X260) != esk48_0
| ~ ssList(X259)
| ~ ssItem(X258) )
& ( memberP(X259,esk52_3(X258,X259,X260))
| ~ ssList(X260)
| app(app(X259,cons(X258,nil)),X260) != esk48_0
| ~ ssList(X259)
| ~ ssItem(X258) )
& ( memberP(X260,esk52_3(X258,X259,X260))
| ~ ssList(X260)
| app(app(X259,cons(X258,nil)),X260) != esk48_0
| ~ ssList(X259)
| ~ ssItem(X258) )
& ( lt(X258,esk52_3(X258,X259,X260))
| ~ ssList(X260)
| app(app(X259,cons(X258,nil)),X260) != esk48_0
| ~ ssList(X259)
| ~ ssItem(X258) )
& ( ~ leq(X258,esk52_3(X258,X259,X260))
| ~ ssList(X260)
| app(app(X259,cons(X258,nil)),X260) != esk48_0
| ~ ssList(X259)
| ~ ssItem(X258) )
& ( nil = esk51_0
| ssItem(esk53_0) )
& ( nil = esk50_0
| ssItem(esk53_0) )
& ( nil = esk51_0
| cons(esk53_0,nil) = esk50_0 )
& ( nil = esk50_0
| cons(esk53_0,nil) = esk50_0 )
& ( nil = esk51_0
| memberP(esk51_0,esk53_0) )
& ( nil = esk50_0
| memberP(esk51_0,esk53_0) ) ),
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_15])])])])]) ).
fof(c_0_18,plain,
! [X182,X183,X184] :
( ~ ssList(X182)
| ~ ssList(X183)
| ~ ssList(X184)
| ~ rearsegP(X182,X183)
| rearsegP(app(X184,X182),X183) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).
cnf(c_0_19,plain,
( rearsegP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_21,plain,
! [X223,X224] :
( ~ ssList(X223)
| ~ ssItem(X224)
| cons(X224,X223) = app(cons(X224,nil),X223) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_22,negated_conjecture,
( nil = esk50_0
| cons(esk53_0,nil) = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
nil != esk48_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
( nil = esk50_0
| ssItem(esk53_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
rearsegP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_19]),c_0_20])]) ).
cnf(c_0_28,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,negated_conjecture,
cons(esk53_0,nil) = esk48_0,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_24]) ).
cnf(c_0_30,negated_conjecture,
ssItem(esk53_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_23]),c_0_24]) ).
fof(c_0_31,plain,
! [X27,X28,X30] :
( ( ssList(esk7_2(X27,X28))
| ~ rearsegP(X27,X28)
| ~ ssList(X28)
| ~ ssList(X27) )
& ( app(esk7_2(X27,X28),X28) = X27
| ~ rearsegP(X27,X28)
| ~ ssList(X28)
| ~ ssList(X27) )
& ( ~ ssList(X30)
| app(X30,X28) != X27
| rearsegP(X27,X28)
| ~ ssList(X28)
| ~ ssList(X27) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])])])]) ).
cnf(c_0_32,plain,
( rearsegP(app(X1,nil),nil)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_20])]) ).
cnf(c_0_33,negated_conjecture,
( app(esk48_0,X1) = cons(esk53_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_34,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_35,plain,
! [X230] :
( ~ ssList(X230)
| app(X230,nil) = X230 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_36,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,negated_conjecture,
rearsegP(esk48_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_29]),c_0_34]),c_0_20])]) ).
cnf(c_0_38,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_39,plain,
! [X228,X229] :
( ( nil = X229
| nil != app(X228,X229)
| ~ ssList(X229)
| ~ ssList(X228) )
& ( nil = X228
| nil != app(X228,X229)
| ~ ssList(X229)
| ~ ssList(X228) )
& ( nil != X229
| nil != X228
| nil = app(X228,X229)
| ~ ssList(X229)
| ~ ssList(X228) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
fof(c_0_40,plain,
! [X167,X168,X169] :
( ~ ssList(X167)
| ~ ssList(X168)
| ~ ssList(X169)
| ~ frontsegP(X167,X168)
| frontsegP(app(X167,X169),X168) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).
fof(c_0_41,plain,
! [X174] :
( ~ ssList(X174)
| frontsegP(X174,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
cnf(c_0_42,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,negated_conjecture,
app(esk7_2(esk48_0,nil),nil) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_20]),c_0_34])]) ).
cnf(c_0_44,negated_conjecture,
ssList(esk7_2(esk48_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_37]),c_0_20]),c_0_34])]) ).
cnf(c_0_45,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,negated_conjecture,
esk7_2(esk48_0,nil) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
fof(c_0_49,plain,
! [X225,X226,X227] :
( ~ ssList(X225)
| ~ ssList(X226)
| ~ ssList(X227)
| app(app(X225,X226),X227) = app(X225,app(X226,X227)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_50,plain,
( app(nil,X1) = nil
| nil != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_45]),c_0_20])]) ).
fof(c_0_51,plain,
! [X23,X24,X26] :
( ( ssList(esk6_2(X23,X24))
| ~ frontsegP(X23,X24)
| ~ ssList(X24)
| ~ ssList(X23) )
& ( app(X24,esk6_2(X23,X24)) = X23
| ~ frontsegP(X23,X24)
| ~ ssList(X24)
| ~ ssList(X23) )
& ( ~ ssList(X26)
| app(X24,X26) != X23
| frontsegP(X23,X24)
| ~ ssList(X24)
| ~ ssList(X23) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).
cnf(c_0_52,plain,
( frontsegP(app(X1,X2),nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_20])]) ).
cnf(c_0_53,negated_conjecture,
app(esk48_0,nil) = esk48_0,
inference(rw,[status(thm)],[c_0_43,c_0_48]) ).
cnf(c_0_54,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_55,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_50]),c_0_20])]) ).
cnf(c_0_56,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_57,negated_conjecture,
frontsegP(esk48_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_20]),c_0_34])]) ).
cnf(c_0_58,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_59,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_54,c_0_55]),c_0_20])]) ).
cnf(c_0_60,negated_conjecture,
app(nil,esk6_2(esk48_0,nil)) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_34]),c_0_20])]) ).
cnf(c_0_61,negated_conjecture,
ssList(esk6_2(esk48_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_57]),c_0_20]),c_0_34])]) ).
cnf(c_0_62,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_63,negated_conjecture,
app(nil,esk48_0) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).
fof(c_0_64,plain,
! [X220,X221,X222] :
( ~ ssList(X220)
| ~ ssList(X221)
| ~ ssList(X222)
| app(X221,X222) != app(X221,X220)
| X222 = X220 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])]) ).
cnf(c_0_65,negated_conjecture,
( frontsegP(X1,esk48_0)
| esk48_0 != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_53]),c_0_34]),c_0_20])]) ).
cnf(c_0_66,negated_conjecture,
( app(nil,app(esk48_0,X1)) = app(esk48_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_63]),c_0_34]),c_0_20])]) ).
fof(c_0_67,plain,
! [X166] :
( ~ ssList(X166)
| frontsegP(X166,X166) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax42])]) ).
cnf(c_0_68,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,X3) != app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_69,negated_conjecture,
frontsegP(esk48_0,esk48_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_65]),c_0_34])]) ).
cnf(c_0_70,negated_conjecture,
( lt(X1,esk52_3(X1,X2,X3))
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_71,negated_conjecture,
( app(nil,cons(esk53_0,X1)) = cons(esk53_0,X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_33]) ).
cnf(c_0_72,plain,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( X1 = nil
| app(esk48_0,X1) != esk48_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_53]),c_0_20]),c_0_34])]) ).
cnf(c_0_74,negated_conjecture,
app(esk48_0,esk6_2(esk48_0,esk48_0)) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_69]),c_0_34])]) ).
cnf(c_0_75,negated_conjecture,
ssList(esk6_2(esk48_0,esk48_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_69]),c_0_34])]) ).
cnf(c_0_76,negated_conjecture,
( ssItem(esk52_3(X1,X2,X3))
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_77,plain,
! [X247,X248] :
( ( X247 != X248
| ~ lt(X247,X248)
| ~ ssItem(X248)
| ~ ssItem(X247) )
& ( leq(X247,X248)
| ~ lt(X247,X248)
| ~ ssItem(X248)
| ~ ssItem(X247) )
& ( X247 = X248
| ~ leq(X247,X248)
| lt(X247,X248)
| ~ ssItem(X248)
| ~ ssItem(X247) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax93])])])]) ).
cnf(c_0_78,negated_conjecture,
( lt(esk53_0,esk52_3(esk53_0,nil,X1))
| app(esk48_0,X1) != esk48_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_29]),c_0_20]),c_0_30])]) ).
cnf(c_0_79,plain,
( app(X1,esk6_2(X1,X1)) = X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_72]) ).
cnf(c_0_80,negated_conjecture,
esk6_2(esk48_0,esk48_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75])]) ).
cnf(c_0_81,negated_conjecture,
( ssItem(esk52_3(esk53_0,nil,X1))
| app(esk48_0,X1) != esk48_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_71]),c_0_29]),c_0_20]),c_0_30])]) ).
cnf(c_0_82,plain,
( leq(X1,X2)
| ~ lt(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_83,negated_conjecture,
lt(esk53_0,esk52_3(esk53_0,nil,nil)),
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_78,c_0_79]),c_0_80]),c_0_80]),c_0_20]),c_0_34])]) ).
cnf(c_0_84,negated_conjecture,
ssItem(esk52_3(esk53_0,nil,nil)),
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_81,c_0_79]),c_0_80]),c_0_80]),c_0_20]),c_0_34])]) ).
cnf(c_0_85,negated_conjecture,
( ~ leq(X1,esk52_3(X1,X2,X3))
| ~ ssList(X3)
| app(app(X2,cons(X1,nil)),X3) != esk48_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_86,negated_conjecture,
leq(esk53_0,esk52_3(esk53_0,nil,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]),c_0_30])]) ).
cnf(c_0_87,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_29]),c_0_63]),c_0_53]),c_0_20]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC252+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
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 15:12:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.19/0.68 % Version : CSE_E---1.5
% 0.19/0.68 % Problem : theBenchmark.p
% 0.19/0.68 % Proof found
% 0.19/0.68 % SZS status Theorem for theBenchmark.p
% 0.19/0.68 % SZS output start Proof
% See solution above
% 0.19/0.69 % Total time : 0.120000 s
% 0.19/0.69 % SZS output end Proof
% 0.19/0.69 % Total time : 0.126000 s
%------------------------------------------------------------------------------