TSTP Solution File: SWC343+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWC343+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 : n031.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 20:21:48 EDT 2023
% Result : Theorem 0.73s 0.79s
% Output : CNFRefutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 90
% Syntax : Number of formulae : 168 ( 20 unt; 80 typ; 0 def)
% Number of atoms : 422 ( 179 equ)
% Maximal formula atoms : 88 ( 4 avg)
% Number of connectives : 560 ( 226 ~; 246 |; 53 &)
% ( 3 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 89 ( 72 >; 17 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 61 ( 61 usr; 8 con; 0-2 aty)
% Number of variables : 114 ( 0 sgn; 52 !; 11 ?; 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 ).
tff(decl_98,type,
esk53_1: $i > $i ).
tff(decl_99,type,
esk54_1: $i > $i ).
tff(decl_100,type,
esk55_1: $i > $i ).
tff(decl_101,type,
esk56_1: $i > $i ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ( app(X3,X5) != X4
| ~ strictorderedP(X3)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X5
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(X9,cons(X8,nil)) = X3
& lt(X8,X6) ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( ? [X10] :
( ssList(X10)
& app(X1,X10) = X2
& ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ( app(cons(X11,nil),X12) != X10
| ! [X13] :
( ssItem(X13)
=> ! [X14] :
( ssList(X14)
=> ( app(X14,cons(X13,nil)) != X1
| ~ lt(X13,X11) ) ) ) ) ) )
& strictorderedP(X1) )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
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(ax42,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax42) ).
fof(ax46,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax46) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ( app(X3,X5) != X4
| ~ strictorderedP(X3)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X5
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(X9,cons(X8,nil)) = X3
& lt(X8,X6) ) ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( ? [X10] :
( ssList(X10)
& app(X1,X10) = X2
& ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ( app(cons(X11,nil),X12) != X10
| ! [X13] :
( ssItem(X13)
=> ! [X14] :
( ssList(X14)
=> ( app(X14,cons(X13,nil)) != X1
| ~ lt(X13,X11) ) ) ) ) ) )
& strictorderedP(X1) )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_11,negated_conjecture,
! [X264,X265,X266,X267,X268] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ssList(esk52_0)
& app(esk50_0,esk52_0) = esk51_0
& strictorderedP(esk50_0)
& ( ~ ssItem(X264)
| ~ ssList(X265)
| app(cons(X264,nil),X265) != esk52_0
| ~ ssItem(X266)
| ~ ssList(X267)
| app(X267,cons(X266,nil)) != esk50_0
| ~ lt(X266,X264) )
& ( nil = esk51_0
| nil != esk50_0 )
& ( nil = esk48_0
| ssItem(esk53_1(X268))
| ~ ssList(X268)
| app(esk48_0,X268) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil != esk49_0
| ssItem(esk53_1(X268))
| ~ ssList(X268)
| app(esk48_0,X268) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil = esk48_0
| ssList(esk54_1(X268))
| ~ ssList(X268)
| app(esk48_0,X268) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil != esk49_0
| ssList(esk54_1(X268))
| ~ ssList(X268)
| app(esk48_0,X268) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil = esk48_0
| app(cons(esk53_1(X268),nil),esk54_1(X268)) = X268
| ~ ssList(X268)
| app(esk48_0,X268) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil != esk49_0
| app(cons(esk53_1(X268),nil),esk54_1(X268)) = X268
| ~ ssList(X268)
| app(esk48_0,X268) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil = esk48_0
| ssItem(esk55_1(X268))
| ~ ssList(X268)
| app(esk48_0,X268) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil != esk49_0
| ssItem(esk55_1(X268))
| ~ ssList(X268)
| app(esk48_0,X268) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil = esk48_0
| ssList(esk56_1(X268))
| ~ ssList(X268)
| app(esk48_0,X268) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil != esk49_0
| ssList(esk56_1(X268))
| ~ ssList(X268)
| app(esk48_0,X268) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil = esk48_0
| app(esk56_1(X268),cons(esk55_1(X268),nil)) = esk48_0
| ~ ssList(X268)
| app(esk48_0,X268) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil != esk49_0
| app(esk56_1(X268),cons(esk55_1(X268),nil)) = esk48_0
| ~ ssList(X268)
| app(esk48_0,X268) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil = esk48_0
| lt(esk55_1(X268),esk53_1(X268))
| ~ ssList(X268)
| app(esk48_0,X268) != esk49_0
| ~ strictorderedP(esk48_0) )
& ( nil != esk49_0
| lt(esk55_1(X268),esk53_1(X268))
| ~ ssList(X268)
| app(esk48_0,X268) != esk49_0
| ~ strictorderedP(esk48_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_10])])])])]) ).
cnf(c_0_12,negated_conjecture,
strictorderedP(esk50_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_13,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,negated_conjecture,
( nil = esk48_0
| app(esk56_1(X1),cons(esk55_1(X1),nil)) = esk48_0
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
strictorderedP(esk48_0),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
app(esk50_0,esk52_0) = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( nil = esk48_0
| ssItem(esk55_1(X1))
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
( nil = esk48_0
| ssList(esk56_1(X1))
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,nil),X2) != esk52_0
| ~ ssItem(X3)
| ~ ssList(X4)
| app(X4,cons(X3,nil)) != esk50_0
| ~ lt(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,negated_conjecture,
( app(esk56_1(X1),cons(esk55_1(X1),nil)) = esk48_0
| esk48_0 = nil
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
cnf(c_0_22,negated_conjecture,
app(esk48_0,esk52_0) = esk49_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_13]),c_0_17]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,negated_conjecture,
( esk48_0 = nil
| ssItem(esk55_1(X1))
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_15])]) ).
cnf(c_0_25,negated_conjecture,
( esk48_0 = nil
| ssList(esk56_1(X1))
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_15])]) ).
cnf(c_0_26,negated_conjecture,
( nil = esk48_0
| app(cons(esk53_1(X1),nil),esk54_1(X1)) = X1
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_27,negated_conjecture,
( nil = esk48_0
| ssItem(esk53_1(X1))
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_28,negated_conjecture,
( nil = esk48_0
| ssList(esk54_1(X1))
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,negated_conjecture,
( nil = esk48_0
| lt(esk55_1(X1),esk53_1(X1))
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_30,plain,
! [X28,X29,X31] :
( ( ssList(esk6_2(X28,X29))
| ~ frontsegP(X28,X29)
| ~ ssList(X29)
| ~ ssList(X28) )
& ( app(X29,esk6_2(X28,X29)) = X28
| ~ frontsegP(X28,X29)
| ~ ssList(X29)
| ~ ssList(X28) )
& ( ~ ssList(X31)
| app(X29,X31) != X28
| frontsegP(X28,X29)
| ~ ssList(X29)
| ~ ssList(X28) ) ),
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_31,plain,
! [X171] :
( ~ ssList(X171)
| frontsegP(X171,X171) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax42])]) ).
fof(c_0_32,plain,
! [X180] :
( ( ~ frontsegP(nil,X180)
| nil = X180
| ~ ssList(X180) )
& ( nil != X180
| frontsegP(nil,X180)
| ~ ssList(X180) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax46])])]) ).
cnf(c_0_33,negated_conjecture,
( app(X1,cons(X2,nil)) != esk48_0
| app(cons(X3,nil),X4) != esk52_0
| ~ lt(X2,X3)
| ~ ssList(X1)
| ~ ssList(X4)
| ~ ssItem(X2)
| ~ ssItem(X3) ),
inference(rw,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_34,negated_conjecture,
( app(esk56_1(esk52_0),cons(esk55_1(esk52_0),nil)) = esk48_0
| esk48_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_35,negated_conjecture,
( esk48_0 = nil
| ssItem(esk55_1(esk52_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_23])]) ).
cnf(c_0_36,negated_conjecture,
( esk48_0 = nil
| ssList(esk56_1(esk52_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_22]),c_0_23])]) ).
cnf(c_0_37,negated_conjecture,
( app(cons(esk53_1(X1),nil),esk54_1(X1)) = X1
| esk48_0 = nil
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_15])]) ).
cnf(c_0_38,negated_conjecture,
( esk48_0 = nil
| ssItem(esk53_1(X1))
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_15])]) ).
cnf(c_0_39,negated_conjecture,
( esk48_0 = nil
| ssList(esk54_1(X1))
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_15])]) ).
cnf(c_0_40,negated_conjecture,
( esk48_0 = nil
| lt(esk55_1(X1),esk53_1(X1))
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_15])]) ).
cnf(c_0_41,negated_conjecture,
( ssList(esk54_1(X1))
| nil != esk49_0
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_42,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_43,plain,
( frontsegP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_44,plain,
( frontsegP(nil,X1)
| nil != X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_45,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_46,negated_conjecture,
( ssItem(esk53_1(X1))
| nil != esk49_0
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_47,negated_conjecture,
( app(cons(esk53_1(X1),nil),esk54_1(X1)) = X1
| nil != esk49_0
| ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ~ strictorderedP(esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_48,plain,
! [X235] :
( ~ ssList(X235)
| app(X235,nil) = X235 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_49,negated_conjecture,
( nil = esk51_0
| nil != esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_50,negated_conjecture,
( esk48_0 = nil
| app(cons(X1,nil),X2) != esk52_0
| ~ lt(esk55_1(esk52_0),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36]) ).
cnf(c_0_51,negated_conjecture,
( app(cons(esk53_1(esk52_0),nil),esk54_1(esk52_0)) = esk52_0
| esk48_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_22]),c_0_23])]) ).
cnf(c_0_52,negated_conjecture,
( esk48_0 = nil
| ssItem(esk53_1(esk52_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_22]),c_0_23])]) ).
cnf(c_0_53,negated_conjecture,
( esk48_0 = nil
| ssList(esk54_1(esk52_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_22]),c_0_23])]) ).
cnf(c_0_54,negated_conjecture,
( esk48_0 = nil
| lt(esk55_1(esk52_0),esk53_1(esk52_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_22]),c_0_23])]) ).
cnf(c_0_55,negated_conjecture,
( ssList(esk54_1(X1))
| app(esk48_0,X1) != esk49_0
| esk49_0 != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_15])]) ).
cnf(c_0_56,plain,
( app(X1,esk6_2(X1,X1)) = X1
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_57,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_58,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_59,plain,
! [X233,X234] :
( ( nil = X234
| nil != app(X233,X234)
| ~ ssList(X234)
| ~ ssList(X233) )
& ( nil = X233
| nil != app(X233,X234)
| ~ ssList(X234)
| ~ ssList(X233) )
& ( nil != X234
| nil != X233
| nil = app(X233,X234)
| ~ ssList(X234)
| ~ ssList(X233) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_60,plain,
frontsegP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_44]),c_0_45])]) ).
cnf(c_0_61,negated_conjecture,
( ssItem(esk53_1(X1))
| app(esk48_0,X1) != esk49_0
| esk49_0 != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_15])]) ).
fof(c_0_62,plain,
! [X130,X131] :
( ~ ssList(X130)
| ~ ssItem(X131)
| nil != cons(X131,X130) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
fof(c_0_63,plain,
! [X140,X141,X142] :
( ~ ssList(X140)
| ~ ssList(X141)
| ~ ssItem(X142)
| cons(X142,app(X141,X140)) = app(cons(X142,X141),X140) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
fof(c_0_64,plain,
! [X138,X139] :
( ~ ssList(X138)
| ~ ssList(X139)
| ssList(app(X138,X139)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_65,negated_conjecture,
( app(cons(esk53_1(X1),nil),esk54_1(X1)) = X1
| app(esk48_0,X1) != esk49_0
| esk49_0 != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_15])]) ).
cnf(c_0_66,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_67,negated_conjecture,
( esk49_0 = nil
| esk48_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_17]),c_0_13]) ).
cnf(c_0_68,negated_conjecture,
esk48_0 = nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_53]),c_0_54]) ).
cnf(c_0_69,negated_conjecture,
( ssList(esk54_1(esk6_2(esk48_0,esk48_0)))
| esk49_0 != esk48_0
| esk49_0 != nil
| ~ ssList(esk6_2(esk48_0,esk48_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).
cnf(c_0_70,plain,
( ssList(esk6_2(X1,X1))
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_43]) ).
cnf(c_0_71,plain,
( nil = X1
| nil != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_72,plain,
app(nil,esk6_2(nil,nil)) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_60]),c_0_45])]) ).
cnf(c_0_73,plain,
ssList(esk6_2(nil,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_60]),c_0_45])]) ).
cnf(c_0_74,negated_conjecture,
( ssItem(esk53_1(esk6_2(esk48_0,esk48_0)))
| esk49_0 != esk48_0
| esk49_0 != nil
| ~ ssList(esk6_2(esk48_0,esk48_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_56]),c_0_57])]) ).
cnf(c_0_75,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_76,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_77,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_78,negated_conjecture,
( app(cons(esk53_1(nil),nil),esk54_1(nil)) = nil
| esk49_0 != esk48_0
| esk49_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_45]),c_0_57])]) ).
cnf(c_0_79,negated_conjecture,
esk49_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
cnf(c_0_80,negated_conjecture,
( ssList(esk54_1(esk6_2(esk48_0,esk48_0)))
| esk49_0 != esk48_0
| esk49_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_57])]) ).
cnf(c_0_81,plain,
esk6_2(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_45]),c_0_73])]) ).
cnf(c_0_82,negated_conjecture,
( ssItem(esk53_1(esk6_2(esk48_0,esk48_0)))
| esk49_0 != esk48_0
| esk49_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_70]),c_0_57])]) ).
cnf(c_0_83,plain,
( app(cons(X1,X2),X3) != nil
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]) ).
cnf(c_0_84,negated_conjecture,
app(cons(esk53_1(nil),nil),esk54_1(nil)) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_68])]),c_0_79])]) ).
cnf(c_0_85,negated_conjecture,
ssList(esk54_1(nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_68]),c_0_68]),c_0_81]),c_0_68])]),c_0_79])]) ).
cnf(c_0_86,negated_conjecture,
ssItem(esk53_1(nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_68]),c_0_68]),c_0_81]),c_0_68])]),c_0_79])]) ).
cnf(c_0_87,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_45]),c_0_85]),c_0_86])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC343+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n031.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 18:58:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.54 start to proof: theBenchmark
% 0.73/0.79 % Version : CSE_E---1.5
% 0.73/0.79 % Problem : theBenchmark.p
% 0.73/0.79 % Proof found
% 0.73/0.79 % SZS status Theorem for theBenchmark.p
% 0.73/0.79 % SZS output start Proof
% See solution above
% 0.73/0.80 % Total time : 0.241000 s
% 0.73/0.80 % SZS output end Proof
% 0.73/0.80 % Total time : 0.247000 s
%------------------------------------------------------------------------------