TSTP Solution File: SWC174+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWC174+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 : n002.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 20:20:26 EDT 2023
% Result : Theorem 0.20s 0.69s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 100
% Syntax : Number of formulae : 199 ( 28 unt; 79 typ; 0 def)
% Number of atoms : 401 ( 129 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 467 ( 186 ~; 191 |; 25 &)
% ( 5 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 5 ( 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 : 60 ( 60 usr; 11 con; 0-2 aty)
% Number of variables : 154 ( 0 sgn; 96 !; 2 ?; 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_0: $i ).
tff(decl_99,type,
esk54_0: $i ).
tff(decl_100,type,
esk55_0: $i ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ singletonP(X3)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ( ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> app(app(app(X7,cons(X5,nil)),cons(X6,nil)),X8) != X1 ) )
| neq(X5,X6) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax1,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax1) ).
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(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
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(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(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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax85) ).
fof(ax44,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( frontsegP(cons(X1,X3),cons(X2,X4))
<=> ( X1 = X2
& frontsegP(X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax44) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
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(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax46,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax46) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax19,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ( cons(X3,X1) = cons(X4,X2)
=> ( X3 = X4
& X2 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax19) ).
fof(c_0_21,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ singletonP(X3)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ( ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> app(app(app(X7,cons(X5,nil)),cons(X6,nil)),X8) != X1 ) )
| neq(X5,X6) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_22,negated_conjecture,
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& singletonP(esk50_0)
& ssItem(esk52_0)
& ssItem(esk53_0)
& ssList(esk54_0)
& ssList(esk55_0)
& app(app(app(esk54_0,cons(esk52_0,nil)),cons(esk53_0,nil)),esk55_0) = esk48_0
& ~ neq(esk52_0,esk53_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
fof(c_0_23,plain,
! [X9,X10] :
( ( ~ neq(X9,X10)
| X9 != X10
| ~ ssItem(X10)
| ~ ssItem(X9) )
& ( X9 = X10
| neq(X9,X10)
| ~ ssItem(X10)
| ~ ssItem(X9) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax1])])])]) ).
fof(c_0_24,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_25,negated_conjecture,
~ neq(esk52_0,esk53_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,negated_conjecture,
ssItem(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
app(app(app(esk54_0,cons(esk52_0,nil)),cons(esk53_0,nil)),esk55_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
esk53_0 = esk52_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_32,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_33,plain,
! [X113,X114] :
( ~ ssList(X113)
| ~ ssItem(X114)
| ssList(cons(X114,X113)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_34,negated_conjecture,
( app(app(esk54_0,app(cons(esk52_0,nil),cons(esk52_0,nil))),esk55_0) = esk48_0
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_31]),c_0_32])]) ).
cnf(c_0_35,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_36,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_37,plain,
! [X222,X223] :
( ~ ssList(X222)
| ~ ssItem(X223)
| cons(X223,X222) = app(cons(X223,nil),X222) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_38,negated_conjecture,
app(app(esk54_0,app(cons(esk52_0,nil),cons(esk52_0,nil))),esk55_0) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_28])]) ).
cnf(c_0_39,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,cons(esk52_0,nil))),esk55_0) = esk48_0
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_28])]) ).
cnf(c_0_41,negated_conjecture,
app(app(esk54_0,cons(esk52_0,cons(esk52_0,nil))),esk55_0) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_35]),c_0_36]),c_0_28])]) ).
cnf(c_0_42,negated_conjecture,
ssList(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_43,negated_conjecture,
( app(esk54_0,app(cons(esk52_0,cons(esk52_0,nil)),esk55_0)) = esk48_0
| ~ ssList(cons(esk52_0,cons(esk52_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_41]),c_0_42]),c_0_32])]) ).
cnf(c_0_44,negated_conjecture,
( app(esk54_0,app(cons(esk52_0,cons(esk52_0,nil)),esk55_0)) = esk48_0
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_35]),c_0_28])]) ).
fof(c_0_45,plain,
! [X134,X135,X136] :
( ~ ssList(X134)
| ~ ssList(X135)
| ~ ssItem(X136)
| cons(X136,app(X135,X134)) = app(cons(X136,X135),X134) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
cnf(c_0_46,negated_conjecture,
app(esk54_0,app(cons(esk52_0,cons(esk52_0,nil)),esk55_0)) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_35]),c_0_36]),c_0_28])]) ).
cnf(c_0_47,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_48,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])])])])]) ).
fof(c_0_49,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_50,negated_conjecture,
( app(esk54_0,cons(esk52_0,app(cons(esk52_0,nil),esk55_0))) = esk48_0
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_42]),c_0_28])]) ).
cnf(c_0_51,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_52,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,negated_conjecture,
app(esk54_0,cons(esk52_0,app(cons(esk52_0,nil),esk55_0))) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_35]),c_0_36]),c_0_28])]) ).
cnf(c_0_54,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_51]),c_0_52]) ).
cnf(c_0_55,negated_conjecture,
app(esk54_0,cons(esk52_0,cons(esk52_0,esk55_0))) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_39]),c_0_42]),c_0_28])]) ).
fof(c_0_56,plain,
! [X127,X128] :
( ~ ssList(X127)
| ~ ssItem(X128)
| hd(cons(X128,X127)) = X128 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
fof(c_0_57,plain,
! [X19,X21] :
( ( ssItem(esk5_1(X19))
| ~ singletonP(X19)
| ~ ssList(X19) )
& ( cons(esk5_1(X19),nil) = X19
| ~ singletonP(X19)
| ~ ssList(X19) )
& ( ~ ssItem(X21)
| cons(X21,nil) != X19
| singletonP(X19)
| ~ ssList(X19) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])]) ).
cnf(c_0_58,negated_conjecture,
( frontsegP(esk48_0,esk54_0)
| ~ ssList(cons(esk52_0,cons(esk52_0,esk55_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_32])]) ).
cnf(c_0_59,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_60,plain,
( cons(esk5_1(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_61,plain,
( ssItem(esk5_1(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_62,negated_conjecture,
( frontsegP(esk48_0,esk54_0)
| ~ ssList(cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_35]),c_0_28])]) ).
cnf(c_0_63,plain,
( esk5_1(X1) = hd(X1)
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_36])]),c_0_61]) ).
cnf(c_0_64,negated_conjecture,
singletonP(esk50_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_65,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_66,plain,
! [X230,X231] :
( ~ ssList(X230)
| ~ ssList(X231)
| nil = X230
| hd(app(X230,X231)) = hd(X230) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).
cnf(c_0_67,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_68,negated_conjecture,
frontsegP(esk48_0,esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_35]),c_0_42]),c_0_28])]) ).
cnf(c_0_69,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_70,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_71,plain,
! [X169,X170,X171,X172] :
( ( X169 = X170
| ~ frontsegP(cons(X169,X171),cons(X170,X172))
| ~ ssList(X172)
| ~ ssList(X171)
| ~ ssItem(X170)
| ~ ssItem(X169) )
& ( frontsegP(X171,X172)
| ~ frontsegP(cons(X169,X171),cons(X170,X172))
| ~ ssList(X172)
| ~ ssList(X171)
| ~ ssItem(X170)
| ~ ssItem(X169) )
& ( X169 != X170
| ~ frontsegP(X171,X172)
| frontsegP(cons(X169,X171),cons(X170,X172))
| ~ ssList(X172)
| ~ ssList(X171)
| ~ ssItem(X170)
| ~ ssItem(X169) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])])])]) ).
cnf(c_0_72,plain,
( cons(hd(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_63]) ).
cnf(c_0_73,negated_conjecture,
singletonP(esk48_0),
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_74,plain,
( ssItem(hd(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_63]) ).
fof(c_0_75,plain,
! [X215] :
( ~ ssList(X215)
| nil = X215
| cons(hd(X215),tl(X215)) = X215 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
cnf(c_0_76,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_77,negated_conjecture,
app(esk54_0,esk6_2(esk48_0,esk54_0)) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_32])]) ).
cnf(c_0_78,negated_conjecture,
ssList(esk6_2(esk48_0,esk54_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_68]),c_0_32]),c_0_69])]) ).
cnf(c_0_79,plain,
( frontsegP(X1,X2)
| ~ frontsegP(cons(X3,X1),cons(X4,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X4)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_80,negated_conjecture,
cons(hd(esk48_0),nil) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_69])]) ).
cnf(c_0_81,negated_conjecture,
ssItem(hd(esk48_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_73]),c_0_69])]) ).
cnf(c_0_82,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_83,negated_conjecture,
( hd(esk54_0) = hd(esk48_0)
| esk54_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_32])]) ).
fof(c_0_84,plain,
! [X219,X220,X221] :
( ~ ssList(X219)
| ~ ssList(X220)
| ~ ssList(X221)
| app(X220,X221) != app(X220,X219)
| X221 = X219 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])]) ).
fof(c_0_85,plain,
! [X229] :
( ~ ssList(X229)
| app(X229,nil) = X229 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_86,negated_conjecture,
( frontsegP(nil,X1)
| ~ frontsegP(esk48_0,cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_36]),c_0_81])]) ).
cnf(c_0_87,negated_conjecture,
( cons(hd(esk48_0),tl(esk54_0)) = esk54_0
| esk54_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_32])]) ).
fof(c_0_88,plain,
! [X129] :
( ~ ssList(X129)
| nil = X129
| ssList(tl(X129)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_89,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,X3) != app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_90,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
fof(c_0_91,plain,
! [X174] :
( ( ~ frontsegP(nil,X174)
| nil = X174
| ~ ssList(X174) )
& ( nil != X174
| frontsegP(nil,X174)
| ~ ssList(X174) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax46])])]) ).
cnf(c_0_92,negated_conjecture,
( esk54_0 = nil
| frontsegP(nil,tl(esk54_0))
| ~ ssList(tl(esk54_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_68]),c_0_81])]) ).
cnf(c_0_93,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_94,plain,
( X1 = nil
| app(X2,X1) != X2
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_36])]) ).
cnf(c_0_95,plain,
( nil = X1
| ~ frontsegP(nil,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_96,negated_conjecture,
( esk54_0 = nil
| frontsegP(nil,tl(esk54_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_32])]) ).
cnf(c_0_97,negated_conjecture,
( cons(esk52_0,cons(esk52_0,esk55_0)) = nil
| esk54_0 != esk48_0
| ~ ssList(cons(esk52_0,cons(esk52_0,esk55_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_55]),c_0_32])]) ).
cnf(c_0_98,negated_conjecture,
( tl(esk54_0) = nil
| esk54_0 = nil
| ~ ssList(tl(esk54_0)) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_99,negated_conjecture,
( cons(esk52_0,cons(esk52_0,esk55_0)) = nil
| esk54_0 != esk48_0
| ~ ssList(cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_35]),c_0_28])]) ).
cnf(c_0_100,negated_conjecture,
( tl(esk54_0) = nil
| esk54_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_93]),c_0_32])]) ).
fof(c_0_101,plain,
! [X124,X125] :
( ~ ssList(X124)
| ~ ssItem(X125)
| nil != cons(X125,X124) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
cnf(c_0_102,negated_conjecture,
( cons(esk52_0,cons(esk52_0,esk55_0)) = nil
| esk54_0 != esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_35]),c_0_42]),c_0_28])]) ).
cnf(c_0_103,negated_conjecture,
( esk54_0 = nil
| esk54_0 = esk48_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_100]),c_0_80]) ).
cnf(c_0_104,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_105,negated_conjecture,
( cons(esk52_0,cons(esk52_0,esk55_0)) = nil
| esk54_0 = nil ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_106,negated_conjecture,
( esk54_0 = nil
| ~ ssList(cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_28])]) ).
fof(c_0_107,plain,
! [X137] :
( ~ ssList(X137)
| app(nil,X137) = X137 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_108,negated_conjecture,
esk54_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_35]),c_0_42]),c_0_28])]) ).
cnf(c_0_109,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_110,negated_conjecture,
app(nil,cons(esk52_0,cons(esk52_0,esk55_0))) = esk48_0,
inference(rw,[status(thm)],[c_0_55,c_0_108]) ).
fof(c_0_111,plain,
! [X117,X118,X119,X120] :
( ( X119 = X120
| cons(X119,X117) != cons(X120,X118)
| ~ ssItem(X120)
| ~ ssItem(X119)
| ~ ssList(X118)
| ~ ssList(X117) )
& ( X118 = X117
| cons(X119,X117) != cons(X120,X118)
| ~ ssItem(X120)
| ~ ssItem(X119)
| ~ ssList(X118)
| ~ ssList(X117) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])]) ).
cnf(c_0_112,negated_conjecture,
( cons(esk52_0,cons(esk52_0,esk55_0)) = esk48_0
| ~ ssList(cons(esk52_0,cons(esk52_0,esk55_0))) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_113,plain,
( X1 = X2
| cons(X3,X2) != cons(X4,X1)
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_114,negated_conjecture,
( cons(esk52_0,cons(esk52_0,esk55_0)) = esk48_0
| ~ ssList(cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_35]),c_0_28])]) ).
cnf(c_0_115,negated_conjecture,
( X1 = nil
| cons(X2,X1) != esk48_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_80]),c_0_36]),c_0_81])]) ).
cnf(c_0_116,negated_conjecture,
cons(esk52_0,cons(esk52_0,esk55_0)) = esk48_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_35]),c_0_42]),c_0_28])]) ).
cnf(c_0_117,negated_conjecture,
( cons(esk52_0,esk55_0) = nil
| ~ ssList(cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_28])]) ).
cnf(c_0_118,negated_conjecture,
cons(esk52_0,esk55_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_35]),c_0_42]),c_0_28])]) ).
cnf(c_0_119,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_118]),c_0_42]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC174+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 : n002.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 18:03:34 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.69 % Version : CSE_E---1.5
% 0.20/0.69 % Problem : theBenchmark.p
% 0.20/0.69 % Proof found
% 0.20/0.69 % SZS status Theorem for theBenchmark.p
% 0.20/0.69 % SZS output start Proof
% See solution above
% 0.20/0.71 % Total time : 0.108000 s
% 0.20/0.71 % SZS output end Proof
% 0.20/0.71 % Total time : 0.113000 s
%------------------------------------------------------------------------------