%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC197+1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 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 : Tue May 5 05:18:41 PM UTC 2026
% Result : Theorem 2.09s 1.93s
% Output : CNFRefutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 16
% Syntax : Number of formulae : 118 ( 34 unt; 0 def)
% Number of atoms : 380 ( 117 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 444 ( 182 ~; 178 |; 31 &)
% ( 5 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 117 ( 0 sgn 78 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ segmentP(X4,X3)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(app(app(app(X7,cons(X5,nil)),X9),cons(X6,nil)),X8) != X1
| X5 = X6 ) ) ) ) ) )
| ( ~ singletonP(X3)
& neq(X4,nil) ) ) ) ) ) ),
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(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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
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(ax3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
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(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
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(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax54,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X1) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax54) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ segmentP(X4,X3)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(app(app(app(X7,cons(X5,nil)),X9),cons(X6,nil)),X8) != X1
| X5 = X6 ) ) ) ) ) )
| ( ~ singletonP(X3)
& neq(X4,nil) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_17,negated_conjecture,
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& segmentP(esk51_0,esk50_0)
& ssItem(esk52_0)
& ssItem(esk53_0)
& ssList(esk54_0)
& ssList(esk55_0)
& ssList(esk56_0)
& app(app(app(app(esk54_0,cons(esk52_0,nil)),esk56_0),cons(esk53_0,nil)),esk55_0) = esk48_0
& esk52_0 != esk53_0
& ( singletonP(esk50_0)
| ~ neq(esk51_0,nil) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
cnf(c_0_18,negated_conjecture,
app(app(app(app(esk54_0,cons(esk52_0,nil)),esk56_0),cons(esk53_0,nil)),esk55_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_19,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,plain,
! [X437,X438,X439] :
( ~ ssList(X437)
| ~ ssList(X438)
| ~ ssList(X439)
| app(app(X437,X438),X439) = app(X437,app(X438,X439)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_21,negated_conjecture,
app(app(app(app(esk54_0,cons(esk52_0,nil)),esk56_0),cons(esk53_0,nil)),esk55_0) = esk50_0,
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk56_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_25,plain,
! [X326,X327] :
( ~ ssList(X326)
| ~ ssItem(X327)
| ssList(cons(X327,X326)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_26,negated_conjecture,
( app(app(app(esk54_0,app(cons(esk52_0,nil),esk56_0)),cons(esk53_0,nil)),esk55_0) = esk50_0
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]) ).
cnf(c_0_27,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_28,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_29,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_30,plain,
! [X435,X436] :
( ~ ssList(X435)
| ~ ssItem(X436)
| cons(X436,X435) = app(cons(X436,nil),X435) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_31,negated_conjecture,
app(app(app(esk54_0,app(cons(esk52_0,nil),esk56_0)),cons(esk53_0,nil)),esk55_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29])]) ).
cnf(c_0_32,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_33,negated_conjecture,
app(app(app(esk54_0,cons(esk52_0,esk56_0)),cons(esk53_0,nil)),esk55_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_23]),c_0_29])]) ).
cnf(c_0_34,negated_conjecture,
( app(app(esk54_0,app(cons(esk52_0,esk56_0),cons(esk53_0,nil))),esk55_0) = esk50_0
| ~ ssList(cons(esk53_0,nil))
| ~ ssList(cons(esk52_0,esk56_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_22]),c_0_24])]) ).
cnf(c_0_35,negated_conjecture,
ssItem(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_36,negated_conjecture,
( app(app(esk54_0,app(cons(esk52_0,esk56_0),cons(esk53_0,nil))),esk55_0) = esk50_0
| ~ ssList(cons(esk52_0,esk56_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_27]),c_0_28]),c_0_35])]) ).
cnf(c_0_37,negated_conjecture,
app(app(esk54_0,app(cons(esk52_0,esk56_0),cons(esk53_0,nil))),esk55_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_27]),c_0_23]),c_0_29])]) ).
cnf(c_0_38,negated_conjecture,
ssList(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_39,plain,
! [X345,X346] :
( ~ ssList(X345)
| ~ ssList(X346)
| ssList(app(X345,X346)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
cnf(c_0_40,negated_conjecture,
( app(esk54_0,app(app(cons(esk52_0,esk56_0),cons(esk53_0,nil)),esk55_0)) = esk50_0
| ~ ssList(app(cons(esk52_0,esk56_0),cons(esk53_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_37]),c_0_38]),c_0_24])]) ).
cnf(c_0_41,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( app(esk54_0,app(app(cons(esk52_0,esk56_0),cons(esk53_0,nil)),esk55_0)) = esk50_0
| ~ ssList(cons(esk53_0,nil))
| ~ ssList(cons(esk52_0,esk56_0)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_43,negated_conjecture,
( app(esk54_0,app(app(cons(esk52_0,esk56_0),cons(esk53_0,nil)),esk55_0)) = esk50_0
| ~ ssList(cons(esk52_0,esk56_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_27]),c_0_28]),c_0_35])]) ).
fof(c_0_44,plain,
! [X347,X348,X349] :
( ~ ssList(X347)
| ~ ssList(X348)
| ~ ssItem(X349)
| cons(X349,app(X348,X347)) = app(cons(X349,X348),X347) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
cnf(c_0_45,negated_conjecture,
app(esk54_0,app(app(cons(esk52_0,esk56_0),cons(esk53_0,nil)),esk55_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_27]),c_0_23]),c_0_29])]) ).
cnf(c_0_46,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_47,negated_conjecture,
( app(esk54_0,app(cons(esk52_0,app(esk56_0,cons(esk53_0,nil))),esk55_0)) = esk50_0
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_23]),c_0_29])]) ).
cnf(c_0_48,negated_conjecture,
app(esk54_0,app(cons(esk52_0,app(esk56_0,cons(esk53_0,nil))),esk55_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_27]),c_0_28]),c_0_35])]) ).
cnf(c_0_49,negated_conjecture,
( app(esk54_0,cons(esk52_0,app(app(esk56_0,cons(esk53_0,nil)),esk55_0))) = esk50_0
| ~ ssList(app(esk56_0,cons(esk53_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_46]),c_0_38]),c_0_29])]) ).
cnf(c_0_50,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,esk56_0)),app(cons(esk53_0,nil),esk55_0)) = esk50_0
| ~ ssList(app(esk54_0,cons(esk52_0,esk56_0)))
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_33]),c_0_38])]) ).
cnf(c_0_51,negated_conjecture,
( app(esk54_0,cons(esk52_0,app(app(esk56_0,cons(esk53_0,nil)),esk55_0))) = esk50_0
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_41]),c_0_23])]) ).
cnf(c_0_52,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,esk56_0)),app(cons(esk53_0,nil),esk55_0)) = esk50_0
| ~ ssList(app(esk54_0,cons(esk52_0,esk56_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_27]),c_0_28]),c_0_35])]) ).
cnf(c_0_53,negated_conjecture,
app(esk54_0,cons(esk52_0,app(app(esk56_0,cons(esk53_0,nil)),esk55_0))) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_27]),c_0_28]),c_0_35])]) ).
fof(c_0_54,plain,
! [X226,X227,X230,X231] :
( ( ssList(esk3_2(X226,X227))
| ~ memberP(X226,X227)
| ~ ssItem(X227)
| ~ ssList(X226) )
& ( ssList(esk4_2(X226,X227))
| ~ memberP(X226,X227)
| ~ ssItem(X227)
| ~ ssList(X226) )
& ( app(esk3_2(X226,X227),cons(X227,esk4_2(X226,X227))) = X226
| ~ memberP(X226,X227)
| ~ ssItem(X227)
| ~ ssList(X226) )
& ( ~ ssList(X230)
| ~ ssList(X231)
| app(X230,cons(X227,X231)) != X226
| memberP(X226,X227)
| ~ ssItem(X227)
| ~ ssList(X226) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])]) ).
cnf(c_0_55,negated_conjecture,
( app(app(esk54_0,cons(esk52_0,esk56_0)),app(cons(esk53_0,nil),esk55_0)) = esk50_0
| ~ ssList(cons(esk52_0,esk56_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_41]),c_0_24])]) ).
cnf(c_0_56,negated_conjecture,
( app(esk54_0,cons(esk52_0,app(esk56_0,app(cons(esk53_0,nil),esk55_0)))) = esk50_0
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_22]),c_0_38]),c_0_23])]) ).
cnf(c_0_57,plain,
( memberP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,cons(X3,X2)) != X4
| ~ ssItem(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_58,negated_conjecture,
app(app(esk54_0,cons(esk52_0,esk56_0)),app(cons(esk53_0,nil),esk55_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_27]),c_0_23]),c_0_29])]) ).
cnf(c_0_59,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_60,negated_conjecture,
app(esk54_0,cons(esk52_0,app(esk56_0,app(cons(esk53_0,nil),esk55_0)))) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_27]),c_0_28]),c_0_35])]) ).
fof(c_0_61,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_62,plain,
( memberP(app(X1,cons(X2,X3)),X2)
| ~ ssList(app(X1,cons(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(er,[status(thm)],[c_0_57]) ).
cnf(c_0_63,negated_conjecture,
app(app(esk54_0,cons(esk52_0,esk56_0)),cons(esk53_0,esk55_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_32]),c_0_38]),c_0_35])]) ).
cnf(c_0_64,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_59,c_0_19]) ).
cnf(c_0_65,negated_conjecture,
app(esk54_0,cons(esk52_0,app(esk56_0,cons(esk53_0,esk55_0)))) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_32]),c_0_38]),c_0_35])]) ).
fof(c_0_66,plain,
! [X440,X441] :
( ( nil = X441
| nil != app(X440,X441)
| ~ ssList(X441)
| ~ ssList(X440) )
& ( nil = X440
| nil != app(X440,X441)
| ~ ssList(X441)
| ~ ssList(X440) )
& ( nil != X441
| nil != X440
| nil = app(X440,X441)
| ~ ssList(X441)
| ~ ssList(X440) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
fof(c_0_67,plain,
! [X369,X370,X371] :
( ( ~ memberP(cons(X370,X371),X369)
| X369 = X370
| memberP(X371,X369)
| ~ ssList(X371)
| ~ ssItem(X370)
| ~ ssItem(X369) )
& ( X369 != X370
| memberP(cons(X370,X371),X369)
| ~ ssList(X371)
| ~ ssItem(X370)
| ~ ssItem(X369) )
& ( ~ memberP(X371,X369)
| memberP(cons(X370,X371),X369)
| ~ ssList(X371)
| ~ ssItem(X370)
| ~ ssItem(X369) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).
fof(c_0_68,plain,
! [X232,X234] :
( ( ssItem(esk5_1(X232))
| ~ singletonP(X232)
| ~ ssList(X232) )
& ( cons(esk5_1(X232),nil) = X232
| ~ singletonP(X232)
| ~ ssList(X232) )
& ( ~ ssItem(X234)
| cons(X234,nil) != X232
| singletonP(X232)
| ~ ssList(X232) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])])]) ).
fof(c_0_69,plain,
! [X372] :
( ~ ssItem(X372)
| ~ memberP(nil,X372) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])]) ).
cnf(c_0_70,negated_conjecture,
( memberP(esk50_0,esk53_0)
| ~ ssList(app(esk54_0,cons(esk52_0,esk56_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_38]),c_0_35])]) ).
cnf(c_0_71,negated_conjecture,
( memberP(esk50_0,esk52_0)
| ~ ssList(app(esk56_0,cons(esk53_0,esk55_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_65]),c_0_64]),c_0_24]),c_0_29])]) ).
cnf(c_0_72,plain,
( nil = X1
| nil != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_73,plain,
( X3 = X1
| memberP(X2,X3)
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_74,plain,
( cons(esk5_1(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_75,plain,
( ssItem(esk5_1(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_76,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_77,negated_conjecture,
( memberP(esk50_0,esk53_0)
| ~ ssList(cons(esk52_0,esk56_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_41]),c_0_24])]) ).
fof(c_0_78,plain,
! [X324,X325] :
( ( ~ neq(X324,X325)
| X324 != X325
| ~ ssList(X325)
| ~ ssList(X324) )
& ( X324 = X325
| neq(X324,X325)
| ~ ssList(X325)
| ~ ssList(X324) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_79,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_80,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_81,negated_conjecture,
( memberP(esk50_0,esk52_0)
| ~ ssList(cons(esk53_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_41]),c_0_23])]) ).
cnf(c_0_82,negated_conjecture,
( esk55_0 = nil
| esk50_0 != nil
| ~ ssList(app(app(app(esk54_0,cons(esk52_0,nil)),esk56_0),cons(esk53_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_21]),c_0_38])]) ).
cnf(c_0_83,plain,
( esk5_1(X1) = X2
| ~ singletonP(X1)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_28])]),c_0_75]),c_0_76]) ).
cnf(c_0_84,negated_conjecture,
memberP(esk50_0,esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_27]),c_0_23]),c_0_29])]) ).
cnf(c_0_85,negated_conjecture,
( singletonP(esk50_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_86,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_87,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_88,negated_conjecture,
memberP(esk50_0,esk52_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_27]),c_0_38]),c_0_35])]) ).
cnf(c_0_89,negated_conjecture,
( esk55_0 = nil
| esk50_0 != nil
| ~ ssList(app(app(esk54_0,cons(esk52_0,nil)),esk56_0))
| ~ ssList(cons(esk53_0,nil)) ),
inference(spm,[status(thm)],[c_0_82,c_0_41]) ).
fof(c_0_90,plain,
! [X402,X403] :
( ~ ssList(X402)
| ~ ssList(X403)
| ~ segmentP(X402,X403)
| ~ segmentP(X403,X402)
| X402 = X403 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax54])])]) ).
cnf(c_0_91,negated_conjecture,
( esk5_1(esk50_0) = esk53_0
| ~ singletonP(esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_64]),c_0_35])]) ).
cnf(c_0_92,negated_conjecture,
( esk51_0 = nil
| singletonP(esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_28]),c_0_87])]) ).
cnf(c_0_93,negated_conjecture,
( esk5_1(esk50_0) = esk52_0
| ~ singletonP(esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_88]),c_0_64]),c_0_29])]) ).
cnf(c_0_94,negated_conjecture,
( esk55_0 = nil
| esk50_0 != nil
| ~ ssList(app(app(esk54_0,cons(esk52_0,nil)),esk56_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_27]),c_0_28]),c_0_35])]) ).
cnf(c_0_95,plain,
( X1 = X2
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_96,negated_conjecture,
segmentP(esk51_0,esk50_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_97,negated_conjecture,
( esk5_1(esk50_0) = esk53_0
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_98,negated_conjecture,
( esk5_1(esk50_0) = esk52_0
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_93,c_0_92]) ).
cnf(c_0_99,negated_conjecture,
esk52_0 != esk53_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_100,negated_conjecture,
( cons(esk53_0,esk55_0) = nil
| esk50_0 != nil
| ~ ssList(app(esk54_0,cons(esk52_0,esk56_0)))
| ~ ssList(cons(esk53_0,esk55_0)) ),
inference(spm,[status(thm)],[c_0_72,c_0_63]) ).
cnf(c_0_101,negated_conjecture,
( esk55_0 = nil
| esk50_0 != nil
| ~ ssList(app(esk54_0,cons(esk52_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_41]),c_0_23])]) ).
cnf(c_0_102,negated_conjecture,
( esk50_0 = esk51_0
| ~ segmentP(esk50_0,esk51_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_87]),c_0_64])]) ).
cnf(c_0_103,negated_conjecture,
esk51_0 = nil,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]) ).
fof(c_0_104,plain,
! [X409] :
( ~ ssList(X409)
| segmentP(X409,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])]) ).
cnf(c_0_105,negated_conjecture,
( cons(esk53_0,esk55_0) = nil
| esk50_0 != nil
| ~ ssList(app(esk54_0,cons(esk52_0,esk56_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_27]),c_0_38]),c_0_35])]) ).
cnf(c_0_106,negated_conjecture,
( esk55_0 = nil
| esk50_0 != nil
| ~ ssList(cons(esk52_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_41]),c_0_24])]) ).
cnf(c_0_107,negated_conjecture,
( esk50_0 = nil
| ~ segmentP(esk50_0,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_103]),c_0_103]) ).
cnf(c_0_108,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_109,negated_conjecture,
( cons(esk53_0,esk55_0) = nil
| esk50_0 != nil
| ~ ssList(cons(esk52_0,esk56_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_41]),c_0_24])]) ).
cnf(c_0_110,negated_conjecture,
( esk55_0 = nil
| esk50_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_27]),c_0_28]),c_0_29])]) ).
cnf(c_0_111,negated_conjecture,
esk50_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_64])]) ).
fof(c_0_112,plain,
! [X328,X329] :
( ~ ssList(X328)
| ~ ssItem(X329)
| cons(X329,X328) != X328 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax18])])]) ).
cnf(c_0_113,negated_conjecture,
( cons(esk53_0,esk55_0) = nil
| esk50_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_27]),c_0_23]),c_0_29])]) ).
cnf(c_0_114,negated_conjecture,
esk55_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_111])]) ).
cnf(c_0_115,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_116,negated_conjecture,
cons(esk53_0,nil) = nil,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_111])]),c_0_114]) ).
cnf(c_0_117,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_28]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC197+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n031.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:35:08 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.09/1.93 % Version : CSE_E---1.7
% 2.09/1.93 % Problem : theBenchmark.p
% 2.09/1.93 % SZS status Theorem for theBenchmark.p
% 2.09/1.93 % SZS output start CNFRefutation
% See solution above
% 2.09/1.94 % Total time : 1.371s
%------------------------------------------------------------------------------