TSTP Solution File: SWC110+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWC110+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 : n013.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 20:19:54 EDT 2023
% Result : Theorem 0.54s 0.82s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 91
% Syntax : Number of formulae : 177 ( 27 unt; 76 typ; 0 def)
% Number of atoms : 388 ( 103 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 488 ( 201 ~; 198 |; 44 &)
% ( 5 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 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 : 57 ( 57 usr; 8 con; 0-2 aty)
% Number of variables : 148 ( 0 sgn; 71 !; 10 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ssItem: $i > $o ).
tff(decl_23,type,
neq: ( $i * $i ) > $o ).
tff(decl_24,type,
ssList: $i > $o ).
tff(decl_25,type,
memberP: ( $i * $i ) > $o ).
tff(decl_26,type,
cons: ( $i * $i ) > $i ).
tff(decl_27,type,
app: ( $i * $i ) > $i ).
tff(decl_28,type,
singletonP: $i > $o ).
tff(decl_29,type,
nil: $i ).
tff(decl_30,type,
frontsegP: ( $i * $i ) > $o ).
tff(decl_31,type,
rearsegP: ( $i * $i ) > $o ).
tff(decl_32,type,
segmentP: ( $i * $i ) > $o ).
tff(decl_33,type,
cyclefreeP: $i > $o ).
tff(decl_34,type,
leq: ( $i * $i ) > $o ).
tff(decl_35,type,
totalorderP: $i > $o ).
tff(decl_36,type,
strictorderP: $i > $o ).
tff(decl_37,type,
lt: ( $i * $i ) > $o ).
tff(decl_38,type,
totalorderedP: $i > $o ).
tff(decl_39,type,
strictorderedP: $i > $o ).
tff(decl_40,type,
duplicatefreeP: $i > $o ).
tff(decl_41,type,
equalelemsP: $i > $o ).
tff(decl_42,type,
hd: $i > $i ).
tff(decl_43,type,
tl: $i > $i ).
tff(decl_44,type,
geq: ( $i * $i ) > $o ).
tff(decl_45,type,
gt: ( $i * $i ) > $o ).
tff(decl_46,type,
esk1_0: $i ).
tff(decl_47,type,
esk2_0: $i ).
tff(decl_48,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk5_1: $i > $i ).
tff(decl_51,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk10_1: $i > $i ).
tff(decl_56,type,
esk11_1: $i > $i ).
tff(decl_57,type,
esk12_1: $i > $i ).
tff(decl_58,type,
esk13_1: $i > $i ).
tff(decl_59,type,
esk14_1: $i > $i ).
tff(decl_60,type,
esk15_1: $i > $i ).
tff(decl_61,type,
esk16_1: $i > $i ).
tff(decl_62,type,
esk17_1: $i > $i ).
tff(decl_63,type,
esk18_1: $i > $i ).
tff(decl_64,type,
esk19_1: $i > $i ).
tff(decl_65,type,
esk20_1: $i > $i ).
tff(decl_66,type,
esk21_1: $i > $i ).
tff(decl_67,type,
esk22_1: $i > $i ).
tff(decl_68,type,
esk23_1: $i > $i ).
tff(decl_69,type,
esk24_1: $i > $i ).
tff(decl_70,type,
esk25_1: $i > $i ).
tff(decl_71,type,
esk26_1: $i > $i ).
tff(decl_72,type,
esk27_1: $i > $i ).
tff(decl_73,type,
esk28_1: $i > $i ).
tff(decl_74,type,
esk29_1: $i > $i ).
tff(decl_75,type,
esk30_1: $i > $i ).
tff(decl_76,type,
esk31_1: $i > $i ).
tff(decl_77,type,
esk32_1: $i > $i ).
tff(decl_78,type,
esk33_1: $i > $i ).
tff(decl_79,type,
esk34_1: $i > $i ).
tff(decl_80,type,
esk35_1: $i > $i ).
tff(decl_81,type,
esk36_1: $i > $i ).
tff(decl_82,type,
esk37_1: $i > $i ).
tff(decl_83,type,
esk38_1: $i > $i ).
tff(decl_84,type,
esk39_1: $i > $i ).
tff(decl_85,type,
esk40_1: $i > $i ).
tff(decl_86,type,
esk41_1: $i > $i ).
tff(decl_87,type,
esk42_1: $i > $i ).
tff(decl_88,type,
esk43_1: $i > $i ).
tff(decl_89,type,
esk44_1: $i > $i ).
tff(decl_90,type,
esk45_1: $i > $i ).
tff(decl_91,type,
esk46_1: $i > $i ).
tff(decl_92,type,
esk47_1: $i > $i ).
tff(decl_93,type,
esk48_0: $i ).
tff(decl_94,type,
esk49_0: $i ).
tff(decl_95,type,
esk50_0: $i ).
tff(decl_96,type,
esk51_0: $i ).
tff(decl_97,type,
esk52_0: $i ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ( app(X3,X5) != X4
| ~ equalelemsP(X3)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X5
& ? [X8] :
( ssList(X8)
& app(X8,cons(X6,nil)) = X3 ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
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(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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
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(ax47,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( rearsegP(X1,X2)
& rearsegP(X2,X3) )
=> rearsegP(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax47) ).
fof(ax51,axiom,
! [X1] :
( ssList(X1)
=> rearsegP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax51) ).
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(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(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(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(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(c_0_15,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
| ~ equalelemsP(X3)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X5
& ? [X8] :
( ssList(X8)
& app(X8,cons(X6,nil)) = X3 ) ) ) ) )
| ( nil != X4
& nil = X3 )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ( neq(X1,nil)
& segmentP(X2,X1) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_16,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
& ssList(esk52_0)
& app(esk50_0,esk52_0) = esk51_0
& equalelemsP(esk50_0)
& ( ~ ssItem(X258)
| ~ ssList(X259)
| app(cons(X258,nil),X259) != esk52_0
| ~ ssList(X260)
| app(X260,cons(X258,nil)) != esk50_0 )
& ( nil = esk51_0
| nil != esk50_0 )
& ( neq(esk49_0,nil)
| nil = esk49_0 )
& ( ~ neq(esk48_0,nil)
| ~ segmentP(esk49_0,esk48_0)
| nil = esk49_0 )
& ( neq(esk49_0,nil)
| nil != esk48_0 )
& ( ~ neq(esk48_0,nil)
| ~ segmentP(esk49_0,esk48_0)
| nil != 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_15])])])])]) ).
fof(c_0_17,plain,
! [X224,X225,X226] :
( ~ ssList(X224)
| ~ ssList(X225)
| ~ ssList(X226)
| app(app(X224,X225),X226) = app(X224,app(X225,X226)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_18,negated_conjecture,
app(esk50_0,esk52_0) = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,plain,
! [X26,X27,X29] :
( ( ssList(esk7_2(X26,X27))
| ~ rearsegP(X26,X27)
| ~ ssList(X27)
| ~ ssList(X26) )
& ( app(esk7_2(X26,X27),X27) = X26
| ~ rearsegP(X26,X27)
| ~ ssList(X27)
| ~ ssList(X26) )
& ( ~ ssList(X29)
| app(X29,X27) != X26
| rearsegP(X26,X27)
| ~ ssList(X27)
| ~ ssList(X26) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])])])])]) ).
fof(c_0_22,plain,
! [X132,X133] :
( ~ ssList(X132)
| ~ ssList(X133)
| ssList(app(X132,X133)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_23,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
app(esk48_0,esk52_0) = esk49_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_25,negated_conjecture,
ssList(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_27,plain,
! [X229] :
( ~ ssList(X229)
| app(X229,nil) = X229 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_28,plain,
( rearsegP(X3,X2)
| ~ ssList(X1)
| app(X1,X2) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_30,plain,
! [X181,X182,X183] :
( ~ ssList(X181)
| ~ ssList(X182)
| ~ ssList(X183)
| ~ rearsegP(X181,X182)
| rearsegP(app(X183,X181),X182) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax50])])]) ).
cnf(c_0_31,negated_conjecture,
( app(esk48_0,app(esk52_0,X1)) = app(esk49_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_32,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_34,plain,
! [X175,X176,X177] :
( ~ ssList(X175)
| ~ ssList(X176)
| ~ ssList(X177)
| ~ rearsegP(X175,X176)
| ~ rearsegP(X176,X177)
| rearsegP(X175,X177) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax47])])]) ).
cnf(c_0_35,plain,
( rearsegP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_28]),c_0_29]) ).
cnf(c_0_36,plain,
( rearsegP(app(X3,X1),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,negated_conjecture,
app(esk49_0,nil) = esk49_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_24]),c_0_33]),c_0_25])]) ).
cnf(c_0_38,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_39,plain,
( rearsegP(X1,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,negated_conjecture,
rearsegP(esk49_0,esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_41,plain,
( rearsegP(app(X1,app(X2,X3)),X3)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_35]),c_0_29]) ).
cnf(c_0_42,negated_conjecture,
( app(esk49_0,app(nil,X1)) = app(esk49_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_37]),c_0_33]),c_0_38])]) ).
cnf(c_0_43,negated_conjecture,
( rearsegP(X1,esk52_0)
| ~ rearsegP(X1,esk49_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_25]),c_0_38])]) ).
cnf(c_0_44,negated_conjecture,
( rearsegP(app(esk49_0,X1),X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_38]),c_0_33])]) ).
cnf(c_0_45,negated_conjecture,
( rearsegP(app(esk49_0,esk49_0),esk52_0)
| ~ ssList(app(esk49_0,esk49_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_38])]) ).
fof(c_0_46,plain,
! [X184] :
( ~ ssList(X184)
| rearsegP(X184,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax51])]) ).
cnf(c_0_47,plain,
( app(esk7_2(X1,X2),X2) = X1
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_48,negated_conjecture,
rearsegP(app(esk49_0,esk49_0),esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_29]),c_0_38])]) ).
cnf(c_0_49,plain,
( ssList(esk7_2(X1,X2))
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_50,plain,
( rearsegP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_51,negated_conjecture,
( app(esk7_2(app(esk49_0,esk49_0),esk52_0),esk52_0) = app(esk49_0,esk49_0)
| ~ ssList(app(esk49_0,esk49_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_25])]) ).
cnf(c_0_52,negated_conjecture,
( ssList(esk7_2(app(esk49_0,esk49_0),esk52_0))
| ~ ssList(app(esk49_0,esk49_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_48]),c_0_25])]) ).
fof(c_0_53,plain,
! [X22,X23,X25] :
( ( ssList(esk6_2(X22,X23))
| ~ frontsegP(X22,X23)
| ~ ssList(X23)
| ~ ssList(X22) )
& ( app(X23,esk6_2(X22,X23)) = X22
| ~ frontsegP(X22,X23)
| ~ ssList(X23)
| ~ ssList(X22) )
& ( ~ ssList(X25)
| app(X23,X25) != X22
| frontsegP(X22,X23)
| ~ ssList(X23)
| ~ ssList(X22) ) ),
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_54,plain,
( rearsegP(app(X1,X2),nil)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_50]),c_0_33])]) ).
cnf(c_0_55,negated_conjecture,
app(esk7_2(app(esk49_0,esk49_0),esk52_0),esk52_0) = app(esk49_0,esk49_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_29]),c_0_38])]) ).
cnf(c_0_56,negated_conjecture,
ssList(esk7_2(app(esk49_0,esk49_0),esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_29]),c_0_38])]) ).
fof(c_0_57,plain,
! [X30,X31,X34,X35] :
( ( ssList(esk8_2(X30,X31))
| ~ segmentP(X30,X31)
| ~ ssList(X31)
| ~ ssList(X30) )
& ( ssList(esk9_2(X30,X31))
| ~ segmentP(X30,X31)
| ~ ssList(X31)
| ~ ssList(X30) )
& ( app(app(esk8_2(X30,X31),X31),esk9_2(X30,X31)) = X30
| ~ segmentP(X30,X31)
| ~ ssList(X31)
| ~ ssList(X30) )
& ( ~ ssList(X34)
| ~ ssList(X35)
| app(app(X34,X31),X35) != X30
| segmentP(X30,X31)
| ~ ssList(X31)
| ~ ssList(X30) ) ),
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_58,plain,
! [X166,X167,X168] :
( ~ ssList(X166)
| ~ ssList(X167)
| ~ ssList(X168)
| ~ frontsegP(X166,X167)
| frontsegP(app(X166,X168),X167) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax43])])]) ).
cnf(c_0_59,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,negated_conjecture,
rearsegP(app(esk49_0,esk49_0),nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_25])]) ).
cnf(c_0_61,negated_conjecture,
ssList(app(esk49_0,esk49_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_55]),c_0_25]),c_0_56])]) ).
cnf(c_0_62,plain,
( app(esk7_2(X1,nil),nil) = X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_50]),c_0_33])]) ).
cnf(c_0_63,plain,
( ssList(esk7_2(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_33])]) ).
cnf(c_0_64,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_57]) ).
fof(c_0_65,plain,
! [X137] :
( ~ ssList(X137)
| app(nil,X137) = X137 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
fof(c_0_66,plain,
! [X227,X228] :
( ( nil = X228
| nil != app(X227,X228)
| ~ ssList(X228)
| ~ ssList(X227) )
& ( nil = X227
| nil != app(X227,X228)
| ~ ssList(X228)
| ~ ssList(X227) )
& ( nil != X228
| nil != X227
| nil = app(X227,X228)
| ~ ssList(X228)
| ~ ssList(X227) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_67,plain,
( frontsegP(app(X1,X3),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_68,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_59]),c_0_29]) ).
cnf(c_0_69,negated_conjecture,
app(esk7_2(app(esk49_0,esk49_0),nil),nil) = app(esk49_0,esk49_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_60]),c_0_33]),c_0_61])]) ).
cnf(c_0_70,plain,
( esk7_2(X1,nil) = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_62]),c_0_63]) ).
cnf(c_0_71,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_64]) ).
cnf(c_0_72,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_73,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_74,plain,
( frontsegP(app(app(X1,X2),X3),X1)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_29]) ).
cnf(c_0_75,negated_conjecture,
app(app(esk49_0,esk49_0),nil) = app(esk49_0,esk49_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_61])]) ).
cnf(c_0_76,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_71,c_0_72]),c_0_33])]),c_0_29]) ).
cnf(c_0_77,negated_conjecture,
( esk48_0 = nil
| app(esk49_0,X1) != nil
| ~ ssList(app(esk52_0,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_31]),c_0_26])]) ).
cnf(c_0_78,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_79,negated_conjecture,
frontsegP(app(esk49_0,esk49_0),esk49_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_33]),c_0_38])]) ).
cnf(c_0_80,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_81,negated_conjecture,
( nil = esk49_0
| ~ neq(esk48_0,nil)
| ~ segmentP(esk49_0,esk48_0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_82,negated_conjecture,
segmentP(esk49_0,esk48_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_24]),c_0_26]),c_0_25])]) ).
fof(c_0_83,plain,
! [X111,X112] :
( ( ~ neq(X111,X112)
| X111 != X112
| ~ ssList(X112)
| ~ ssList(X111) )
& ( X111 = X112
| neq(X111,X112)
| ~ ssList(X112)
| ~ ssList(X111) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_84,negated_conjecture,
( nil = esk51_0
| nil != esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_85,negated_conjecture,
( esk48_0 = nil
| app(esk49_0,X1) != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_29]),c_0_25])]) ).
cnf(c_0_86,negated_conjecture,
app(esk49_0,esk6_2(app(esk49_0,esk49_0),esk49_0)) = app(esk49_0,esk49_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_61]),c_0_38])]) ).
cnf(c_0_87,negated_conjecture,
ssList(esk6_2(app(esk49_0,esk49_0),esk49_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_79]),c_0_38]),c_0_61])]) ).
cnf(c_0_88,negated_conjecture,
( esk49_0 = nil
| ~ neq(esk48_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82])]) ).
cnf(c_0_89,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_90,negated_conjecture,
( esk49_0 = nil
| esk48_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_20]),c_0_19]) ).
cnf(c_0_91,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_92,negated_conjecture,
( ~ neq(esk48_0,nil)
| ~ segmentP(esk49_0,esk48_0)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_93,negated_conjecture,
( esk48_0 = nil
| app(esk49_0,esk49_0) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87])]) ).
cnf(c_0_94,negated_conjecture,
esk49_0 = nil,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_33]),c_0_26])]),c_0_90]) ).
cnf(c_0_95,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_91])]),c_0_33])]) ).
cnf(c_0_96,negated_conjecture,
( esk48_0 != nil
| ~ neq(esk48_0,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_82])]) ).
cnf(c_0_97,negated_conjecture,
esk48_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94]),c_0_94]),c_0_95])]) ).
cnf(c_0_98,negated_conjecture,
( neq(esk49_0,nil)
| nil != esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_99,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97]),c_0_97])]) ).
cnf(c_0_100,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_94]),c_0_97])]),c_0_99]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC110+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 18:33:16 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.54/0.82 % Version : CSE_E---1.5
% 0.54/0.82 % Problem : theBenchmark.p
% 0.54/0.82 % Proof found
% 0.54/0.82 % SZS status Theorem for theBenchmark.p
% 0.54/0.82 % SZS output start Proof
% See solution above
% 0.81/0.83 % Total time : 0.249000 s
% 0.81/0.83 % SZS output end Proof
% 0.81/0.83 % Total time : 0.255000 s
%------------------------------------------------------------------------------