TSTP Solution File: SWC120+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWC120+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n021.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 20:19:59 EDT 2023
% Result : Theorem 0.63s 0.76s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 94
% Syntax : Number of formulae : 178 ( 12 unt; 75 typ; 0 def)
% Number of atoms : 402 ( 120 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 490 ( 191 ~; 211 |; 40 &)
% ( 5 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 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 : 56 ( 56 usr; 7 con; 0-2 aty)
% Number of variables : 132 ( 0 sgn; 72 !; 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 ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X4 != X5
& ? [X6] :
( ssList(X6)
& tl(X4) = X6
& app(X3,X6) = X5
& neq(nil,X4) ) )
| ( neq(X1,nil)
& segmentP(X2,X1) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax43,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(X1,X2)
=> frontsegP(app(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax43) ).
fof(ax45,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax45) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax50,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( rearsegP(X1,X2)
=> rearsegP(app(X3,X1),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax50) ).
fof(ax51,axiom,
! [X1] :
( ssList(X1)
=> rearsegP(X1,nil) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax6) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax86,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax86) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(c_0_19,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& X4 != X5
& ? [X6] :
( ssList(X6)
& tl(X4) = X6
& app(X3,X6) = X5
& neq(nil,X4) ) )
| ( neq(X1,nil)
& segmentP(X2,X1) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_20,negated_conjecture,
! [X255,X256] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( neq(esk49_0,nil)
| neq(esk49_0,nil) )
& ( ~ neq(esk51_0,nil)
| neq(esk49_0,nil) )
& ( neq(esk49_0,nil)
| ~ ssList(X255)
| esk51_0 = X255
| ~ ssList(X256)
| tl(esk51_0) != X256
| app(esk50_0,X256) != X255
| ~ neq(nil,esk51_0) )
& ( ~ neq(esk51_0,nil)
| ~ ssList(X255)
| esk51_0 = X255
| ~ ssList(X256)
| tl(esk51_0) != X256
| app(esk50_0,X256) != X255
| ~ neq(nil,esk51_0) )
& ( neq(esk49_0,nil)
| ~ neq(esk48_0,nil)
| ~ segmentP(esk49_0,esk48_0) )
& ( ~ neq(esk51_0,nil)
| ~ neq(esk48_0,nil)
| ~ segmentP(esk49_0,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_19])])])])]) ).
cnf(c_0_21,negated_conjecture,
( neq(esk49_0,nil)
| neq(esk49_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_22,negated_conjecture,
neq(esk49_0,nil),
inference(cn,[status(thm)],[c_0_21]) ).
cnf(c_0_23,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( esk51_0 = X1
| ~ neq(esk51_0,nil)
| ~ ssList(X1)
| ~ ssList(X2)
| tl(esk51_0) != X2
| app(esk50_0,X2) != X1
| ~ neq(nil,esk51_0) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
neq(esk51_0,nil),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_27,plain,
! [X127] :
( ~ ssList(X127)
| nil = X127
| ssList(tl(X127)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_28,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,negated_conjecture,
( app(esk48_0,tl(esk51_0)) = esk51_0
| ~ ssList(app(esk48_0,tl(esk51_0)))
| ~ ssList(tl(esk51_0))
| ~ neq(nil,esk51_0) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_26])])])]) ).
cnf(c_0_30,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_28,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,
( app(esk48_0,tl(esk51_0)) = esk51_0
| esk51_0 = nil
| ~ ssList(app(esk48_0,tl(esk51_0)))
| ~ neq(nil,esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_34,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_35,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_36,plain,
! [X164,X165,X166] :
( ~ ssList(X164)
| ~ ssList(X165)
| ~ ssList(X166)
| ~ frontsegP(X164,X165)
| frontsegP(app(X164,X166),X165) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).
fof(c_0_37,plain,
! [X171] :
( ~ ssList(X171)
| frontsegP(X171,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
cnf(c_0_38,negated_conjecture,
( app(esk48_0,tl(esk51_0)) = esk51_0
| esk51_0 = nil
| ~ ssList(tl(esk51_0))
| ~ neq(nil,esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
fof(c_0_39,plain,
! [X109,X110] :
( ( ~ neq(X109,X110)
| X109 != X110
| ~ ssList(X110)
| ~ ssList(X109) )
& ( X109 = X110
| neq(X109,X110)
| ~ ssList(X110)
| ~ ssList(X109) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_40,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,plain,
( frontsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_43,negated_conjecture,
( app(esk48_0,tl(esk51_0)) = esk51_0
| esk51_0 = nil
| ~ neq(nil,esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_30]),c_0_31])]) ).
cnf(c_0_44,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,plain,
( frontsegP(app(X1,X2),nil)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_46,negated_conjecture,
( app(esk48_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_43,c_0_44]),c_0_31]),c_0_42])]) ).
fof(c_0_47,plain,
! [X20,X21,X23] :
( ( ssList(esk6_2(X20,X21))
| ~ frontsegP(X20,X21)
| ~ ssList(X21)
| ~ ssList(X20) )
& ( app(X21,esk6_2(X20,X21)) = X20
| ~ frontsegP(X20,X21)
| ~ ssList(X21)
| ~ ssList(X20) )
& ( ~ ssList(X23)
| app(X21,X23) != X20
| frontsegP(X20,X21)
| ~ ssList(X21)
| ~ ssList(X20) ) ),
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_48,negated_conjecture,
( esk51_0 = nil
| frontsegP(esk51_0,nil)
| ~ ssList(tl(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_35])]) ).
fof(c_0_49,plain,
! [X135] :
( ~ ssList(X135)
| app(nil,X135) = X135 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_50,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_51,negated_conjecture,
( esk51_0 = nil
| frontsegP(esk51_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_30]),c_0_31])]) ).
cnf(c_0_52,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_53,plain,
! [X179,X180,X181] :
( ~ ssList(X179)
| ~ ssList(X180)
| ~ ssList(X181)
| ~ rearsegP(X179,X180)
| rearsegP(app(X181,X179),X180) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).
fof(c_0_54,plain,
! [X182] :
( ~ ssList(X182)
| rearsegP(X182,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).
cnf(c_0_55,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,negated_conjecture,
( app(nil,esk6_2(esk51_0,nil)) = esk51_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_31]),c_0_42])]) ).
cnf(c_0_57,negated_conjecture,
( esk51_0 = nil
| ssList(esk6_2(esk51_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_51]),c_0_42]),c_0_31])]) ).
cnf(c_0_58,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_59,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_60,negated_conjecture,
( esk6_2(esk51_0,nil) = esk51_0
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).
fof(c_0_61,plain,
! [X24,X25,X27] :
( ( ssList(esk7_2(X24,X25))
| ~ rearsegP(X24,X25)
| ~ ssList(X25)
| ~ ssList(X24) )
& ( app(esk7_2(X24,X25),X25) = X24
| ~ rearsegP(X24,X25)
| ~ ssList(X25)
| ~ ssList(X24) )
& ( ~ ssList(X27)
| app(X27,X25) != X24
| rearsegP(X24,X25)
| ~ ssList(X25)
| ~ ssList(X24) ) ),
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_62,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_42])]) ).
cnf(c_0_63,negated_conjecture,
( app(nil,esk51_0) = esk51_0
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_56,c_0_60]) ).
fof(c_0_64,plain,
! [X227] :
( ~ ssList(X227)
| app(X227,nil) = X227 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_65,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_66,negated_conjecture,
( esk51_0 = nil
| rearsegP(esk51_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_42]),c_0_31])]) ).
cnf(c_0_67,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_68,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_69,negated_conjecture,
( app(esk7_2(esk51_0,nil),nil) = esk51_0
| esk51_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_42]),c_0_31])]) ).
cnf(c_0_70,negated_conjecture,
( esk51_0 = nil
| ssList(esk7_2(esk51_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_66]),c_0_42]),c_0_31])]) ).
fof(c_0_71,plain,
! [X28,X29,X32,X33] :
( ( ssList(esk8_2(X28,X29))
| ~ segmentP(X28,X29)
| ~ ssList(X29)
| ~ ssList(X28) )
& ( ssList(esk9_2(X28,X29))
| ~ segmentP(X28,X29)
| ~ ssList(X29)
| ~ ssList(X28) )
& ( app(app(esk8_2(X28,X29),X29),esk9_2(X28,X29)) = X28
| ~ segmentP(X28,X29)
| ~ ssList(X29)
| ~ ssList(X28) )
& ( ~ ssList(X32)
| ~ ssList(X33)
| app(app(X32,X29),X33) != X28
| segmentP(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)],[ax7])])])])]) ).
fof(c_0_72,plain,
! [X230,X231] :
( ~ ssList(X230)
| ~ ssList(X231)
| nil = X230
| tl(app(X230,X231)) = app(tl(X230),X231) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
fof(c_0_73,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_74,negated_conjecture,
( esk7_2(esk51_0,nil) = esk51_0
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).
cnf(c_0_75,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_71]) ).
cnf(c_0_76,plain,
( nil = X1
| tl(app(X1,X2)) = app(tl(X1),X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_77,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_78,negated_conjecture,
( app(esk51_0,nil) = esk51_0
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_69,c_0_74]) ).
cnf(c_0_79,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_75]) ).
cnf(c_0_80,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_30,c_0_76]),c_0_34]),c_0_77]) ).
cnf(c_0_81,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_76,c_0_78]),c_0_42]),c_0_31])]) ).
cnf(c_0_82,negated_conjecture,
( ~ neq(esk51_0,nil)
| ~ neq(esk48_0,nil)
| ~ segmentP(esk49_0,esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_83,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_55]),c_0_42])]),c_0_34]) ).
cnf(c_0_84,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_80,c_0_81]),c_0_42]),c_0_31])]) ).
cnf(c_0_85,negated_conjecture,
( ~ segmentP(esk51_0,esk48_0)
| ~ neq(esk48_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_26]),c_0_23])]) ).
cnf(c_0_86,negated_conjecture,
( esk51_0 = nil
| segmentP(esk51_0,esk48_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_46]),c_0_35])]),c_0_84]) ).
cnf(c_0_87,negated_conjecture,
( esk51_0 = nil
| ~ neq(esk48_0,nil) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
fof(c_0_88,plain,
! [X113,X114] :
( ~ ssList(X113)
| ~ ssItem(X114)
| cons(X114,X113) != X113 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).
fof(c_0_89,plain,
! [X213] :
( ~ ssList(X213)
| nil = X213
| cons(hd(X213),tl(X213)) = X213 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
fof(c_0_90,plain,
! [X124] :
( ~ ssList(X124)
| nil = X124
| ssItem(hd(X124)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
cnf(c_0_91,negated_conjecture,
( esk48_0 = nil
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_44]),c_0_42]),c_0_35])]) ).
cnf(c_0_92,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_93,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_94,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_95,negated_conjecture,
( app(nil,tl(esk51_0)) = esk51_0
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_46,c_0_91]) ).
cnf(c_0_96,plain,
( nil = X1
| tl(X1) != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]),c_0_30]) ).
cnf(c_0_97,negated_conjecture,
( tl(esk51_0) = esk51_0
| esk51_0 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_95]),c_0_84]) ).
cnf(c_0_98,plain,
( ~ neq(X1,X2)
| X1 != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_99,negated_conjecture,
esk51_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_31])]) ).
cnf(c_0_100,plain,
( ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(er,[status(thm)],[c_0_98]) ).
cnf(c_0_101,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_26,c_0_99]) ).
cnf(c_0_102,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWC120+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n021.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 18:42:29 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.41/0.62 start to proof: theBenchmark
% 0.63/0.76 % Version : CSE_E---1.5
% 0.63/0.76 % Problem : theBenchmark.p
% 0.63/0.76 % Proof found
% 0.63/0.76 % SZS status Theorem for theBenchmark.p
% 0.63/0.76 % SZS output start Proof
% See solution above
% 0.64/0.77 % Total time : 0.121000 s
% 0.64/0.77 % SZS output end Proof
% 0.64/0.77 % Total time : 0.129000 s
%------------------------------------------------------------------------------