%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWC162+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 : n011.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 05:18:32 PM UTC 2026
% Result : Theorem 1.72s 1.84s
% Output : CNFRefutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 26
% Syntax : Number of formulae : 165 ( 32 unt; 0 def)
% Number of atoms : 555 ( 194 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 637 ( 247 ~; 270 |; 41 &)
% ( 5 <=>; 74 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-2 aty)
% Number of variables : 187 ( 0 sgn 117 !; 4 ?)
% 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)),X8),cons(X6,nil)),X9) != X1
| ~ leq(X6,X5)
| ( ! [X10] :
( ssItem(X10)
=> ( ~ memberP(X8,X10)
| ( leq(X5,X10)
& leq(X10,X6) ) ) )
& leq(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(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(ax86,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax86) ).
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(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(ax25,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> tl(cons(X2,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).
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(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
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(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
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(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(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(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(c_0_26,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)),X8),cons(X6,nil)),X9) != X1
| ~ leq(X6,X5)
| ( ! [X10] :
( ssItem(X10)
=> ( ~ memberP(X8,X10)
| ( leq(X5,X10)
& leq(X10,X6) ) ) )
& leq(X5,X6) ) ) ) ) ) ) )
| ( ~ singletonP(X3)
& neq(X4,nil) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_27,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)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk48_0
& leq(esk53_0,esk52_0)
& ( ssItem(esk57_0)
| ~ leq(esk52_0,esk53_0) )
& ( memberP(esk55_0,esk57_0)
| ~ leq(esk52_0,esk53_0) )
& ( ~ leq(esk52_0,esk57_0)
| ~ leq(esk57_0,esk53_0)
| ~ leq(esk52_0,esk53_0) )
& ( singletonP(esk50_0)
| ~ neq(esk51_0,nil) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])]) ).
cnf(c_0_28,negated_conjecture,
app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_29,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_30,plain,
! [X439,X440,X441] :
( ~ ssList(X439)
| ~ ssList(X440)
| ~ ssList(X441)
| app(app(X439,X440),X441) = app(X439,app(X440,X441)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
cnf(c_0_31,negated_conjecture,
app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk50_0,
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_33,negated_conjecture,
ssList(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_35,plain,
! [X328,X329] :
( ~ ssList(X328)
| ~ ssItem(X329)
| ssList(cons(X329,X328)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_36,negated_conjecture,
( app(app(app(esk54_0,app(cons(esk52_0,nil),esk55_0)),cons(esk53_0,nil)),esk56_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_31,c_0_32]),c_0_33]),c_0_34])]) ).
cnf(c_0_37,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_38,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_39,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_40,plain,
! [X437,X438] :
( ~ ssList(X437)
| ~ ssItem(X438)
| cons(X438,X437) = app(cons(X438,nil),X437) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_41,negated_conjecture,
app(app(app(esk54_0,app(cons(esk52_0,nil),esk55_0)),cons(esk53_0,nil)),esk56_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39])]) ).
cnf(c_0_42,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_43,negated_conjecture,
app(app(app(esk54_0,cons(esk52_0,esk55_0)),cons(esk53_0,nil)),esk56_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_33]),c_0_39])]) ).
cnf(c_0_44,negated_conjecture,
( app(app(esk54_0,app(cons(esk52_0,esk55_0),cons(esk53_0,nil))),esk56_0) = esk50_0
| ~ ssList(cons(esk53_0,nil))
| ~ ssList(cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_32]),c_0_34])]) ).
cnf(c_0_45,negated_conjecture,
ssItem(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_46,negated_conjecture,
( app(app(esk54_0,app(cons(esk52_0,esk55_0),cons(esk53_0,nil))),esk56_0) = esk50_0
| ~ ssList(cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_37]),c_0_38]),c_0_45])]) ).
cnf(c_0_47,negated_conjecture,
app(app(esk54_0,app(cons(esk52_0,esk55_0),cons(esk53_0,nil))),esk56_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_37]),c_0_33]),c_0_39])]) ).
cnf(c_0_48,negated_conjecture,
ssList(esk56_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_49,plain,
! [X347,X348] :
( ~ ssList(X347)
| ~ ssList(X348)
| ssList(app(X347,X348)) ),
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,app(app(cons(esk52_0,esk55_0),cons(esk53_0,nil)),esk56_0)) = esk50_0
| ~ ssList(app(cons(esk52_0,esk55_0),cons(esk53_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_47]),c_0_48]),c_0_34])]) ).
cnf(c_0_51,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_52,negated_conjecture,
( app(esk54_0,app(app(cons(esk52_0,esk55_0),cons(esk53_0,nil)),esk56_0)) = esk50_0
| ~ ssList(cons(esk53_0,nil))
| ~ ssList(cons(esk52_0,esk55_0)) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_53,negated_conjecture,
( app(esk54_0,app(app(cons(esk52_0,esk55_0),cons(esk53_0,nil)),esk56_0)) = esk50_0
| ~ ssList(cons(esk52_0,esk55_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_37]),c_0_38]),c_0_45])]) ).
fof(c_0_54,plain,
! [X349,X350,X351] :
( ~ ssList(X349)
| ~ ssList(X350)
| ~ ssItem(X351)
| cons(X351,app(X350,X349)) = app(cons(X351,X350),X349) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
cnf(c_0_55,negated_conjecture,
app(esk54_0,app(app(cons(esk52_0,esk55_0),cons(esk53_0,nil)),esk56_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_37]),c_0_33]),c_0_39])]) ).
cnf(c_0_56,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_57,negated_conjecture,
( app(esk54_0,app(cons(esk52_0,app(esk55_0,cons(esk53_0,nil))),esk56_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_55,c_0_56]),c_0_33]),c_0_39])]) ).
cnf(c_0_58,negated_conjecture,
app(esk54_0,app(cons(esk52_0,app(esk55_0,cons(esk53_0,nil))),esk56_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_37]),c_0_38]),c_0_45])]) ).
cnf(c_0_59,negated_conjecture,
( app(esk54_0,cons(esk52_0,app(app(esk55_0,cons(esk53_0,nil)),esk56_0))) = esk50_0
| ~ ssList(app(esk55_0,cons(esk53_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_56]),c_0_48]),c_0_39])]) ).
cnf(c_0_60,negated_conjecture,
( app(esk54_0,cons(esk52_0,app(app(esk55_0,cons(esk53_0,nil)),esk56_0))) = esk50_0
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_51]),c_0_33])]) ).
cnf(c_0_61,negated_conjecture,
app(esk54_0,cons(esk52_0,app(app(esk55_0,cons(esk53_0,nil)),esk56_0))) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_37]),c_0_38]),c_0_45])]) ).
fof(c_0_62,plain,
! [X237,X238,X240] :
( ( ssList(esk6_2(X237,X238))
| ~ frontsegP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) )
& ( app(X238,esk6_2(X237,X238)) = X237
| ~ frontsegP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) )
& ( ~ ssList(X240)
| app(X238,X240) != X237
| frontsegP(X237,X238)
| ~ ssList(X238)
| ~ ssList(X237) ) ),
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_63,negated_conjecture,
( app(esk54_0,cons(esk52_0,app(esk55_0,app(cons(esk53_0,nil),esk56_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_61,c_0_32]),c_0_48]),c_0_33])]) ).
cnf(c_0_64,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_65,negated_conjecture,
app(esk54_0,cons(esk52_0,app(esk55_0,app(cons(esk53_0,nil),esk56_0)))) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_37]),c_0_38]),c_0_45])]) ).
cnf(c_0_66,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_64]),c_0_51]) ).
cnf(c_0_67,negated_conjecture,
app(esk54_0,cons(esk52_0,app(esk55_0,cons(esk53_0,esk56_0)))) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_42]),c_0_48]),c_0_45])]) ).
cnf(c_0_68,negated_conjecture,
( frontsegP(esk50_0,esk54_0)
| ~ ssList(cons(esk52_0,app(esk55_0,cons(esk53_0,esk56_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_34])]) ).
cnf(c_0_69,negated_conjecture,
( frontsegP(esk50_0,esk54_0)
| ~ ssList(app(esk55_0,cons(esk53_0,esk56_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_37]),c_0_39])]) ).
cnf(c_0_70,negated_conjecture,
( frontsegP(esk50_0,esk54_0)
| ~ ssList(cons(esk53_0,esk56_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_51]),c_0_33])]) ).
cnf(c_0_71,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_72,plain,
! [X447,X448] :
( ~ ssList(X447)
| ~ ssList(X448)
| nil = X447
| tl(app(X447,X448)) = app(tl(X447),X448) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax86])])]) ).
cnf(c_0_73,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_74,negated_conjecture,
frontsegP(esk50_0,esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_37]),c_0_48]),c_0_45])]) ).
cnf(c_0_75,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_71,c_0_29]) ).
cnf(c_0_76,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_77,plain,
! [X434,X435,X436] :
( ~ ssList(X434)
| ~ ssList(X435)
| ~ ssList(X436)
| app(X435,X436) != app(X435,X434)
| X436 = X434 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])]) ).
fof(c_0_78,plain,
! [X444] :
( ~ ssList(X444)
| app(X444,nil) = X444 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
fof(c_0_79,plain,
! [X442,X443] :
( ( nil = X443
| nil != app(X442,X443)
| ~ ssList(X443)
| ~ ssList(X442) )
& ( nil = X442
| nil != app(X442,X443)
| ~ ssList(X443)
| ~ ssList(X442) )
& ( nil != X443
| nil != X442
| nil = app(X442,X443)
| ~ ssList(X443)
| ~ ssList(X442) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
cnf(c_0_80,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_81,negated_conjecture,
app(esk54_0,esk6_2(esk50_0,esk54_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]),c_0_34])]) ).
cnf(c_0_82,negated_conjecture,
ssList(esk6_2(esk50_0,esk54_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_74]),c_0_34]),c_0_75])]) ).
fof(c_0_83,plain,
! [X345,X346] :
( ~ ssList(X345)
| ~ ssItem(X346)
| tl(cons(X346,X345)) = X345 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])])]) ).
fof(c_0_84,plain,
! [X234,X236] :
( ( ssItem(esk5_1(X234))
| ~ singletonP(X234)
| ~ ssList(X234) )
& ( cons(esk5_1(X234),nil) = X234
| ~ singletonP(X234)
| ~ ssList(X234) )
& ( ~ ssItem(X236)
| cons(X236,nil) != X234
| singletonP(X234)
| ~ ssList(X234) ) ),
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_85,plain,
! [X326,X327] :
( ( ~ neq(X326,X327)
| X326 != X327
| ~ ssList(X327)
| ~ ssList(X326) )
& ( X326 = X327
| neq(X326,X327)
| ~ ssList(X327)
| ~ ssList(X326) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax15])])])]) ).
cnf(c_0_86,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_87,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_88,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,X3) != app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_89,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
fof(c_0_90,plain,
! [X342,X343] :
( ~ ssList(X342)
| ~ ssItem(X343)
| hd(cons(X343,X342)) = X343 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
fof(c_0_91,plain,
! [X445,X446] :
( ~ ssList(X445)
| ~ ssList(X446)
| nil = X445
| hd(app(X445,X446)) = hd(X445) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).
cnf(c_0_92,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_93,negated_conjecture,
( app(tl(esk54_0),esk6_2(esk50_0,esk54_0)) = tl(esk50_0)
| esk54_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_34])]) ).
fof(c_0_94,plain,
! [X344] :
( ~ ssList(X344)
| nil = X344
| ssList(tl(X344)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax24])]) ).
cnf(c_0_95,plain,
( tl(cons(X2,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_96,plain,
( cons(esk5_1(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_97,plain,
( ssItem(esk5_1(X1))
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_98,negated_conjecture,
( singletonP(esk50_0)
| ~ neq(esk51_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_99,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_100,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_101,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_88,c_0_89]),c_0_38])]) ).
cnf(c_0_102,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
fof(c_0_103,plain,
! [X430] :
( ~ ssList(X430)
| nil = X430
| cons(hd(X430),tl(X430)) = X430 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax78])]) ).
cnf(c_0_104,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_105,negated_conjecture,
( tl(esk54_0) = nil
| esk54_0 = nil
| tl(esk50_0) != nil
| ~ ssList(tl(esk54_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_82])]) ).
cnf(c_0_106,plain,
( nil = X1
| ssList(tl(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_107,plain,
( tl(X1) = nil
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_38])]),c_0_97]) ).
cnf(c_0_108,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_98,c_0_99]),c_0_38]),c_0_100])]) ).
cnf(c_0_109,negated_conjecture,
( cons(esk52_0,app(esk55_0,cons(esk53_0,esk56_0))) = nil
| esk54_0 != esk50_0
| ~ ssList(cons(esk52_0,app(esk55_0,cons(esk53_0,esk56_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_67]),c_0_34])]) ).
cnf(c_0_110,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_102,c_0_96]),c_0_38])]),c_0_97]) ).
cnf(c_0_111,plain,
( nil = X1
| cons(hd(X1),tl(X1)) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_112,negated_conjecture,
( hd(esk54_0) = hd(esk50_0)
| esk54_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_81]),c_0_82]),c_0_34])]) ).
cnf(c_0_113,negated_conjecture,
( tl(esk54_0) = nil
| esk54_0 = nil
| tl(esk50_0) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_34])]) ).
cnf(c_0_114,negated_conjecture,
( tl(esk50_0) = nil
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_75])]) ).
cnf(c_0_115,negated_conjecture,
( cons(esk52_0,app(esk55_0,cons(esk53_0,esk56_0))) = nil
| esk54_0 != esk50_0
| ~ ssList(app(esk55_0,cons(esk53_0,esk56_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_37]),c_0_39])]) ).
cnf(c_0_116,plain,
( cons(hd(X1),nil) = X1
| ~ singletonP(X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_110]) ).
cnf(c_0_117,negated_conjecture,
( cons(hd(esk50_0),tl(esk54_0)) = esk54_0
| esk54_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_34])]) ).
cnf(c_0_118,negated_conjecture,
( tl(esk54_0) = nil
| esk51_0 = nil
| esk54_0 = nil ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_119,negated_conjecture,
( cons(esk52_0,app(esk55_0,cons(esk53_0,esk56_0))) = nil
| esk54_0 != esk50_0
| ~ ssList(cons(esk53_0,esk56_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_51]),c_0_33])]) ).
cnf(c_0_120,negated_conjecture,
( cons(hd(esk50_0),nil) = esk50_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_108]),c_0_75])]) ).
cnf(c_0_121,negated_conjecture,
( cons(hd(esk50_0),nil) = esk54_0
| esk51_0 = nil
| esk54_0 = nil ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
fof(c_0_122,plain,
! [X339,X340] :
( ~ ssList(X339)
| ~ ssItem(X340)
| nil != cons(X340,X339) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
cnf(c_0_123,negated_conjecture,
( cons(esk52_0,app(esk55_0,cons(esk53_0,esk56_0))) = nil
| esk54_0 != esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_37]),c_0_48]),c_0_45])]) ).
cnf(c_0_124,negated_conjecture,
( esk54_0 = nil
| esk51_0 = nil
| esk54_0 = esk50_0 ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_125,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_126,negated_conjecture,
( cons(esk52_0,app(esk55_0,cons(esk53_0,esk56_0))) = nil
| esk51_0 = nil
| esk54_0 = nil ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_127,negated_conjecture,
( esk54_0 = nil
| esk51_0 = nil
| ~ ssList(app(esk55_0,cons(esk53_0,esk56_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_39])]) ).
cnf(c_0_128,negated_conjecture,
( esk51_0 = nil
| esk54_0 = nil
| ~ ssList(cons(esk53_0,esk56_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_51]),c_0_33])]) ).
fof(c_0_129,plain,
! [X352] :
( ~ ssList(X352)
| app(nil,X352) = X352 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_130,negated_conjecture,
( esk54_0 = nil
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_37]),c_0_48]),c_0_45])]) ).
cnf(c_0_131,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_132,negated_conjecture,
( app(nil,cons(esk52_0,app(esk55_0,cons(esk53_0,esk56_0)))) = esk50_0
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_67,c_0_130]) ).
cnf(c_0_133,negated_conjecture,
( cons(esk52_0,app(esk55_0,cons(esk53_0,esk56_0))) = esk50_0
| esk51_0 = nil
| ~ ssList(cons(esk52_0,app(esk55_0,cons(esk53_0,esk56_0)))) ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
fof(c_0_134,plain,
! [X332,X333,X334,X335] :
( ( X334 = X335
| cons(X334,X332) != cons(X335,X333)
| ~ ssItem(X335)
| ~ ssItem(X334)
| ~ ssList(X333)
| ~ ssList(X332) )
& ( X333 = X332
| cons(X334,X332) != cons(X335,X333)
| ~ ssItem(X335)
| ~ ssItem(X334)
| ~ ssList(X333)
| ~ ssList(X332) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])]) ).
cnf(c_0_135,negated_conjecture,
( cons(esk52_0,app(esk55_0,cons(esk53_0,esk56_0))) = esk50_0
| esk51_0 = nil
| ~ ssList(app(esk55_0,cons(esk53_0,esk56_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_37]),c_0_39])]) ).
cnf(c_0_136,plain,
( X1 = X2
| cons(X3,X2) != cons(X4,X1)
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_137,negated_conjecture,
( cons(esk52_0,app(esk55_0,cons(esk53_0,esk56_0))) = esk50_0
| esk51_0 = nil
| ~ ssList(cons(esk53_0,esk56_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_51]),c_0_33])]) ).
cnf(c_0_138,plain,
( nil = X1
| ~ singletonP(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_96]),c_0_38])])]),c_0_97]),c_0_37]) ).
cnf(c_0_139,negated_conjecture,
( cons(esk52_0,app(esk55_0,cons(esk53_0,esk56_0))) = esk50_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_37]),c_0_48]),c_0_45])]) ).
fof(c_0_140,plain,
! [X228,X229,X232,X233] :
( ( ssList(esk3_2(X228,X229))
| ~ memberP(X228,X229)
| ~ ssItem(X229)
| ~ ssList(X228) )
& ( ssList(esk4_2(X228,X229))
| ~ memberP(X228,X229)
| ~ ssItem(X229)
| ~ ssList(X228) )
& ( app(esk3_2(X228,X229),cons(X229,esk4_2(X228,X229))) = X228
| ~ memberP(X228,X229)
| ~ ssItem(X229)
| ~ ssList(X228) )
& ( ~ ssList(X232)
| ~ ssList(X233)
| app(X232,cons(X229,X233)) != X228
| memberP(X228,X229)
| ~ ssItem(X229)
| ~ ssList(X228) ) ),
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_141,negated_conjecture,
( app(esk55_0,cons(esk53_0,esk56_0)) = nil
| esk51_0 = nil
| ~ ssList(app(esk55_0,cons(esk53_0,esk56_0))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_39])]),c_0_108]) ).
cnf(c_0_142,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_140]) ).
fof(c_0_143,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_144,negated_conjecture,
( app(esk55_0,cons(esk53_0,esk56_0)) = nil
| esk51_0 = nil
| ~ ssList(cons(esk53_0,esk56_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_51]),c_0_33])]) ).
cnf(c_0_145,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_142]) ).
fof(c_0_146,plain,
! [X404,X405] :
( ~ ssList(X404)
| ~ ssList(X405)
| ~ segmentP(X404,X405)
| ~ segmentP(X405,X404)
| X404 = X405 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax54])])]) ).
fof(c_0_147,plain,
! [X374] :
( ~ ssItem(X374)
| ~ memberP(nil,X374) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_143])]) ).
cnf(c_0_148,negated_conjecture,
( app(esk55_0,cons(esk53_0,esk56_0)) = nil
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_37]),c_0_48]),c_0_45])]) ).
cnf(c_0_149,negated_conjecture,
( memberP(esk50_0,esk52_0)
| ~ ssList(app(app(esk55_0,cons(esk53_0,nil)),esk56_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_61]),c_0_75]),c_0_34]),c_0_39])]) ).
cnf(c_0_150,plain,
( X1 = X2
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_146]) ).
cnf(c_0_151,negated_conjecture,
segmentP(esk51_0,esk50_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_152,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_147]) ).
cnf(c_0_153,negated_conjecture,
( esk51_0 = nil
| memberP(nil,esk53_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_148]),c_0_38]),c_0_48]),c_0_33]),c_0_45])]) ).
cnf(c_0_154,negated_conjecture,
( memberP(esk50_0,esk52_0)
| ~ ssList(app(esk55_0,cons(esk53_0,nil))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_51]),c_0_48])]) ).
cnf(c_0_155,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_150,c_0_151]),c_0_100]),c_0_75])]) ).
cnf(c_0_156,negated_conjecture,
esk51_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_45])]) ).
fof(c_0_157,plain,
! [X411] :
( ~ ssList(X411)
| segmentP(X411,nil) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])]) ).
cnf(c_0_158,negated_conjecture,
( memberP(esk50_0,esk52_0)
| ~ ssList(cons(esk53_0,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_51]),c_0_33])]) ).
cnf(c_0_159,negated_conjecture,
( esk50_0 = nil
| ~ segmentP(esk50_0,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_156]),c_0_156]) ).
cnf(c_0_160,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_157]) ).
cnf(c_0_161,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_158,c_0_37]),c_0_38]),c_0_45])]) ).
cnf(c_0_162,negated_conjecture,
esk50_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_75])]) ).
cnf(c_0_163,negated_conjecture,
memberP(nil,esk52_0),
inference(rw,[status(thm)],[c_0_161,c_0_162]) ).
cnf(c_0_164,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_163]),c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC162+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
% 0.15/0.32 % Computer : n011.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 04:30:32 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.72/1.84 % Version : CSE_E---1.7
% 1.72/1.84 % Problem : theBenchmark.p
% 1.72/1.84 % SZS status Theorem for theBenchmark.p
% 1.72/1.84 % SZS output start CNFRefutation
% See solution above
% 1.72/1.84 % Total time : 1.373s
%------------------------------------------------------------------------------