%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC343+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:44:00 PM UTC 2026
% Result : Theorem 11.05s 2.43s
% Output : CNFRefutation 11.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 84 ( 19 unt; 0 def)
% Number of atoms : 441 ( 184 equ)
% Maximal formula atoms : 88 ( 5 avg)
% Number of connectives : 587 ( 230 ~; 248 |; 64 &)
% ( 3 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 130 ( 0 sgn 61 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil = X2
| nil != X1 )
& ? [X10] :
( strictorderedP(X1)
& ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ( ! [X13] :
( ssItem(X13)
=> ! [X14] :
( ssList(X14)
=> ( ~ lt(X13,X11)
| app(X14,cons(X13,nil)) != X1 ) ) )
| app(cons(X11,nil),X12) != X10 ) ) )
& app(X1,X10) = X2
& ssList(X10) ) )
| ( nil = X3
& nil != X4 )
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( lt(X8,X6)
& app(X9,cons(X8,nil)) = X3
& ssList(X9) )
& ssItem(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ strictorderedP(X3)
| app(X3,X5) != X4 ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax46,axiom,
! [X1] :
( ssList(X1)
=> ( frontsegP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax46) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( app(X2,X3) = X1
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax42,axiom,
! [X1] :
( ssList(X1)
=> frontsegP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax42) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X1
& nil = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil = X2
| nil != X1 )
& ? [X10] :
( strictorderedP(X1)
& ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ( ! [X13] :
( ssItem(X13)
=> ! [X14] :
( ssList(X14)
=> ( ~ lt(X13,X11)
| app(X14,cons(X13,nil)) != X1 ) ) )
| app(cons(X11,nil),X12) != X10 ) ) )
& app(X1,X10) = X2
& ssList(X10) ) )
| ( nil = X3
& nil != X4 )
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( lt(X8,X6)
& app(X9,cons(X8,nil)) = X3
& ssList(X9) )
& ssItem(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ strictorderedP(X3)
| app(X3,X5) != X4 ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil = X2
| nil != X1 )
& ? [X10] :
( strictorderedP(X1)
& ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ( ! [X13] :
( ssItem(X13)
=> ! [X14] :
( ssList(X14)
=> ( ~ lt(X13,X11)
| app(X14,cons(X13,nil)) != X1 ) ) )
| app(cons(X11,nil),X12) != X10 ) ) )
& app(X1,X10) = X2
& ssList(X10) ) )
| ( nil = X3
& nil != X4 )
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( lt(X8,X6)
& app(X9,cons(X8,nil)) = X3
& ssList(X9) )
& ssItem(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ strictorderedP(X3)
| app(X3,X5) != X4 ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_11,negated_conjecture,
! [X264,X265,X266,X267,X268] :
( ( ~ strictorderedP(esk48_0)
| app(esk48_0,X268) != esk49_0
| ~ ssList(X268)
| lt(esk55_1(X268),esk53_1(X268))
| nil != esk49_0 )
& ( ~ strictorderedP(esk48_0)
| app(esk48_0,X268) != esk49_0
| ~ ssList(X268)
| lt(esk55_1(X268),esk53_1(X268))
| nil = esk48_0 )
& ( ~ strictorderedP(esk48_0)
| app(esk48_0,X268) != esk49_0
| ~ ssList(X268)
| app(esk56_1(X268),cons(esk55_1(X268),nil)) = esk48_0
| nil != esk49_0 )
& ( ~ strictorderedP(esk48_0)
| app(esk48_0,X268) != esk49_0
| ~ ssList(X268)
| app(esk56_1(X268),cons(esk55_1(X268),nil)) = esk48_0
| nil = esk48_0 )
& ( ~ strictorderedP(esk48_0)
| app(esk48_0,X268) != esk49_0
| ~ ssList(X268)
| ssList(esk56_1(X268))
| nil != esk49_0 )
& ( ~ strictorderedP(esk48_0)
| app(esk48_0,X268) != esk49_0
| ~ ssList(X268)
| ssList(esk56_1(X268))
| nil = esk48_0 )
& ( ~ strictorderedP(esk48_0)
| app(esk48_0,X268) != esk49_0
| ~ ssList(X268)
| ssItem(esk55_1(X268))
| nil != esk49_0 )
& ( ~ strictorderedP(esk48_0)
| app(esk48_0,X268) != esk49_0
| ~ ssList(X268)
| ssItem(esk55_1(X268))
| nil = esk48_0 )
& ( ~ strictorderedP(esk48_0)
| app(esk48_0,X268) != esk49_0
| ~ ssList(X268)
| app(cons(esk53_1(X268),nil),esk54_1(X268)) = X268
| nil != esk49_0 )
& ( ~ strictorderedP(esk48_0)
| app(esk48_0,X268) != esk49_0
| ~ ssList(X268)
| app(cons(esk53_1(X268),nil),esk54_1(X268)) = X268
| nil = esk48_0 )
& ( ~ strictorderedP(esk48_0)
| app(esk48_0,X268) != esk49_0
| ~ ssList(X268)
| ssList(esk54_1(X268))
| nil != esk49_0 )
& ( ~ strictorderedP(esk48_0)
| app(esk48_0,X268) != esk49_0
| ~ ssList(X268)
| ssList(esk54_1(X268))
| nil = esk48_0 )
& ( ~ strictorderedP(esk48_0)
| app(esk48_0,X268) != esk49_0
| ~ ssList(X268)
| ssItem(esk53_1(X268))
| nil != esk49_0 )
& ( ~ strictorderedP(esk48_0)
| app(esk48_0,X268) != esk49_0
| ~ ssList(X268)
| ssItem(esk53_1(X268))
| nil = esk48_0 )
& ( nil != esk50_0
| nil = esk51_0 )
& ( ~ lt(X266,X264)
| app(X267,cons(X266,nil)) != esk50_0
| ~ ssList(X267)
| ~ ssItem(X266)
| app(cons(X264,nil),X265) != esk52_0
| ~ ssList(X265)
| ~ ssItem(X264) )
& strictorderedP(esk50_0)
& app(esk50_0,esk52_0) = esk51_0
& ssList(esk52_0)
& esk48_0 = esk50_0
& esk49_0 = esk51_0
& ssList(esk51_0)
& ssList(esk50_0)
& ssList(esk49_0)
& ssList(esk48_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])])]) ).
cnf(c_0_12,negated_conjecture,
strictorderedP(esk50_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_13,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,negated_conjecture,
( ~ strictorderedP(esk48_0)
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1)
| app(esk56_1(X1),cons(esk55_1(X1),nil)) = esk48_0
| nil = esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
strictorderedP(esk48_0),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
app(esk50_0,esk52_0) = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( ~ strictorderedP(esk48_0)
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1)
| ssItem(esk55_1(X1))
| nil = esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
( ~ strictorderedP(esk48_0)
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1)
| ssList(esk56_1(X1))
| nil = esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
( ~ lt(X3,X1)
| app(X4,cons(X3,nil)) != esk50_0
| ~ ssList(X4)
| ~ ssItem(X3)
| app(cons(X1,nil),X2) != esk52_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,negated_conjecture,
( ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| esk48_0 = nil
| app(esk56_1(X1),cons(esk55_1(X1),nil)) = esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
cnf(c_0_22,negated_conjecture,
app(esk48_0,esk52_0) = esk49_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_13]),c_0_17]) ).
cnf(c_0_23,negated_conjecture,
ssList(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,negated_conjecture,
( ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ssItem(esk55_1(X1))
| esk48_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_15])]) ).
cnf(c_0_25,negated_conjecture,
( ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ssList(esk56_1(X1))
| esk48_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_15])]) ).
cnf(c_0_26,negated_conjecture,
( ~ strictorderedP(esk48_0)
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1)
| lt(esk55_1(X1),esk53_1(X1))
| nil = esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_27,negated_conjecture,
( ~ strictorderedP(esk48_0)
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1)
| ssItem(esk53_1(X1))
| nil = esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_28,negated_conjecture,
( ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X4)
| ~ ssList(X1)
| ~ lt(X2,X3)
| app(cons(X3,nil),X4) != esk52_0
| app(X1,cons(X2,nil)) != esk48_0 ),
inference(rw,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_29,negated_conjecture,
( esk48_0 = nil
| app(esk56_1(esk52_0),cons(esk55_1(esk52_0),nil)) = esk48_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_30,negated_conjecture,
( ssItem(esk55_1(esk52_0))
| esk48_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_23])]) ).
cnf(c_0_31,negated_conjecture,
( ssList(esk56_1(esk52_0))
| esk48_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_22]),c_0_23])]) ).
cnf(c_0_32,negated_conjecture,
( ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| lt(esk55_1(X1),esk53_1(X1))
| esk48_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_15])]) ).
cnf(c_0_33,negated_conjecture,
( ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ssItem(esk53_1(X1))
| esk48_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_15])]) ).
cnf(c_0_34,negated_conjecture,
( ~ strictorderedP(esk48_0)
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1)
| app(cons(esk53_1(X1),nil),esk54_1(X1)) = X1
| nil = esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_35,negated_conjecture,
( ~ strictorderedP(esk48_0)
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1)
| ssList(esk54_1(X1))
| nil = esk48_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_36,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ lt(esk55_1(esk52_0),X1)
| app(cons(X1,nil),X2) != esk52_0
| esk48_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31]) ).
cnf(c_0_37,negated_conjecture,
( lt(esk55_1(esk52_0),esk53_1(esk52_0))
| esk48_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_22]),c_0_23])]) ).
cnf(c_0_38,negated_conjecture,
( ssItem(esk53_1(esk52_0))
| esk48_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_22]),c_0_23])]) ).
cnf(c_0_39,negated_conjecture,
( ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| esk48_0 = nil
| app(cons(esk53_1(X1),nil),esk54_1(X1)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_15])]) ).
cnf(c_0_40,negated_conjecture,
( ~ ssList(X1)
| app(esk48_0,X1) != esk49_0
| ssList(esk54_1(X1))
| esk48_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_15])]) ).
fof(c_0_41,plain,
! [X180] :
( ( ~ ssList(X180)
| frontsegP(nil,X180)
| nil != X180 )
& ( ~ ssList(X180)
| nil = X180
| ~ frontsegP(nil,X180) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax46])])])]) ).
cnf(c_0_42,negated_conjecture,
( nil != esk50_0
| nil = esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_43,negated_conjecture,
( ~ ssList(X1)
| app(cons(esk53_1(esk52_0),nil),X1) != esk52_0
| esk48_0 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( esk48_0 = nil
| app(cons(esk53_1(esk52_0),nil),esk54_1(esk52_0)) = esk52_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_22]),c_0_23])]) ).
cnf(c_0_45,negated_conjecture,
( ssList(esk54_1(esk52_0))
| esk48_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_22]),c_0_23])]) ).
fof(c_0_46,plain,
! [X28,X29,X31] :
( ( ~ ssList(X28)
| ~ ssList(X29)
| frontsegP(X28,X29)
| app(X29,X31) != X28
| ~ ssList(X31) )
& ( ~ ssList(X28)
| ~ ssList(X29)
| ~ frontsegP(X28,X29)
| app(X29,esk6_2(X28,X29)) = X28 )
& ( ~ ssList(X28)
| ~ ssList(X29)
| ~ frontsegP(X28,X29)
| ssList(esk6_2(X28,X29)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_47,plain,
( ~ ssList(X1)
| nil != X1
| frontsegP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_49,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_50,negated_conjecture,
( ~ strictorderedP(esk48_0)
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1)
| nil != esk49_0
| app(cons(esk53_1(X1),nil),esk54_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_51,negated_conjecture,
( esk48_0 != nil
| esk49_0 = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_17]),c_0_13]) ).
cnf(c_0_52,negated_conjecture,
esk48_0 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
fof(c_0_53,plain,
! [X171] :
( frontsegP(X171,X171)
| ~ ssList(X171) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax42])])]) ).
fof(c_0_54,plain,
! [X233,X234] :
( ( ~ ssList(X233)
| ~ ssList(X234)
| nil = app(X233,X234)
| nil != X233
| nil != X234 )
& ( ~ ssList(X233)
| ~ ssList(X234)
| nil != app(X233,X234)
| nil = X233 )
& ( ~ ssList(X233)
| ~ ssList(X234)
| nil != app(X233,X234)
| nil = X234 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])])]) ).
cnf(c_0_55,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| app(X1,esk6_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_56,plain,
frontsegP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_47]),c_0_48])]) ).
cnf(c_0_57,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ssList(esk6_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_58,negated_conjecture,
( ~ strictorderedP(esk48_0)
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1)
| nil != esk49_0
| ssList(esk54_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_59,negated_conjecture,
( ~ strictorderedP(esk48_0)
| app(esk48_0,X1) != esk49_0
| ~ ssList(X1)
| nil != esk49_0
| ssItem(esk53_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_60,plain,
! [X130,X131] :
( nil != cons(X131,X130)
| ~ ssItem(X131)
| ~ ssList(X130) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])]) ).
fof(c_0_61,plain,
! [X140,X141,X142] :
( cons(X142,app(X141,X140)) = app(cons(X142,X141),X140)
| ~ ssItem(X142)
| ~ ssList(X141)
| ~ ssList(X140) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).
fof(c_0_62,plain,
! [X138,X139] :
( ssList(app(X138,X139))
| ~ ssList(X139)
| ~ ssList(X138) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
cnf(c_0_63,negated_conjecture,
( ~ ssList(X1)
| esk49_0 != nil
| app(esk48_0,X1) != esk49_0
| app(cons(esk53_1(X1),nil),esk54_1(X1)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_15])]) ).
cnf(c_0_64,negated_conjecture,
esk49_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
cnf(c_0_65,plain,
( ~ ssList(X1)
| frontsegP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_66,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_67,plain,
app(nil,esk6_2(nil,nil)) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_48])]) ).
cnf(c_0_68,plain,
ssList(esk6_2(nil,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_56]),c_0_48])]) ).
cnf(c_0_69,negated_conjecture,
( ~ ssList(X1)
| esk49_0 != nil
| app(esk48_0,X1) != esk49_0
| ssList(esk54_1(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_15])]) ).
cnf(c_0_70,negated_conjecture,
( ~ ssList(X1)
| esk49_0 != nil
| app(esk48_0,X1) != esk49_0
| ssItem(esk53_1(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_15])]) ).
cnf(c_0_71,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_72,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_73,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_74,negated_conjecture,
( ~ ssList(X1)
| app(nil,X1) != nil
| app(cons(esk53_1(X1),nil),esk54_1(X1)) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_52]),c_0_64]),c_0_64])]) ).
cnf(c_0_75,plain,
( ~ ssList(X1)
| app(X1,esk6_2(X1,X1)) = X1 ),
inference(spm,[status(thm)],[c_0_55,c_0_65]) ).
cnf(c_0_76,plain,
esk6_2(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_48]),c_0_68])]) ).
cnf(c_0_77,negated_conjecture,
( ~ ssList(X1)
| app(nil,X1) != nil
| ssList(esk54_1(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_52]),c_0_64]),c_0_64])]) ).
cnf(c_0_78,negated_conjecture,
( ~ ssList(X1)
| app(nil,X1) != nil
| ssItem(esk53_1(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_52]),c_0_64]),c_0_64])]) ).
cnf(c_0_79,plain,
( ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| app(cons(X1,X2),X3) != nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_80,negated_conjecture,
app(cons(esk53_1(nil),nil),esk54_1(nil)) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_76]),c_0_76]),c_0_76]),c_0_48]),c_0_48])]) ).
cnf(c_0_81,negated_conjecture,
ssList(esk54_1(nil)),
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_77,c_0_75]),c_0_76]),c_0_76]),c_0_48]),c_0_48])]) ).
cnf(c_0_82,negated_conjecture,
ssItem(esk53_1(nil)),
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_78,c_0_75]),c_0_76]),c_0_76]),c_0_48]),c_0_48])]) ).
cnf(c_0_83,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_48]),c_0_81]),c_0_82])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC343+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.40 % Computer : n009.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.16/0.40 % DateTime : Mon Sep 21 08:17:27 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.48 Running first-order theorem proving
% 0.19/0.49 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.05/2.43 % Version: 3.5.1
% 11.05/2.43 % Preprocessing class: FSLSSMSSSSSNFFN.
% 11.05/2.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.05/2.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 11.05/2.43 % Starting new_bool_3 with 300s (1) cores
% 11.05/2.43 % Starting new_bool_1 with 300s (1) cores
% 11.05/2.43 % Starting sh5l with 300s (1) cores
% 11.05/2.43 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1292636 completed with status 0
% 11.05/2.43 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 11.05/2.43 % Preprocessing class: FSLSSMSSSSSNFFN.
% 11.05/2.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.05/2.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 11.05/2.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 11.05/2.43 % No SInE strategy applied
% 11.05/2.43 % Search class: FGHSF-FSLM21-MFFFFFNN
% 11.05/2.43 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 11.05/2.43 % Starting SubtermCWHack with 136s (1) cores
% 11.05/2.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 11.05/2.43 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 11.05/2.43 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 11.05/2.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 11.05/2.43 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1292643 completed with status 0
% 11.05/2.43 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 11.05/2.43 % Preprocessing class: FSLSSMSSSSSNFFN.
% 11.05/2.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.05/2.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 11.05/2.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 11.05/2.43 % No SInE strategy applied
% 11.05/2.43 % Search class: FGHSF-FSLM21-MFFFFFNN
% 11.05/2.43 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 11.05/2.43 % Starting SubtermCWHack with 136s (1) cores
% 11.05/2.43 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 11.05/2.43 % Preprocessing time : 0.007 s
% 11.05/2.43 % Presaturation interreduction done
% 11.05/2.43
% 11.05/2.43 % Proof found!
% 11.05/2.43 % SZS status Theorem
% 11.05/2.43 % SZS output start CNFRefutation
% See solution above
% 11.05/2.43 % Parsed axioms : 96
% 11.05/2.43 % Removed by relevancy pruning/SinE : 0
% 11.05/2.43 % Initial clauses : 215
% 11.05/2.43 % Removed in clause preprocessing : 2
% 11.05/2.43 % Initial clauses in saturation : 213
% 11.05/2.43 % Processed clauses : 5914
% 11.05/2.43 % ...of these trivial : 115
% 11.05/2.43 % ...subsumed : 3754
% 11.05/2.43 % ...remaining for further processing : 2045
% 11.05/2.43 % Other redundant clauses eliminated : 224
% 11.05/2.43 % Clauses deleted for lack of memory : 0
% 11.05/2.43 % Backward-subsumed : 186
% 11.05/2.43 % Backward-rewritten : 890
% 11.05/2.43 % Generated clauses : 28486
% 11.05/2.43 % ...of the previous two non-redundant : 26960
% 11.05/2.43 % ...aggressively subsumed : 0
% 11.05/2.43 % Contextual simplify-reflections : 1144
% 11.05/2.43 % Paramodulations : 28252
% 11.05/2.43 % Factorizations : 1
% 11.05/2.43 % NegExts : 0
% 11.05/2.43 % Equation resolutions : 235
% 11.05/2.43 % Disequality decompositions : 0
% 11.05/2.43 % Total rewrite steps : 18543
% 11.05/2.43 % ...of those cached : 18456
% 11.05/2.43 % Propositional unsat checks : 0
% 11.05/2.43 % Propositional check models : 0
% 11.05/2.43 % Propositional check unsatisfiable : 0
% 11.05/2.43 % Propositional clauses : 0
% 11.05/2.43 % Propositional clauses after purity: 0
% 11.05/2.43 % Propositional unsat core size : 0
% 11.05/2.43 % Propositional preprocessing time : 0.000
% 11.05/2.43 % Propositional encoding time : 0.000
% 11.05/2.43 % Propositional solver time : 0.000
% 11.05/2.43 % Success case prop preproc time : 0.000
% 11.05/2.43 % Success case prop encoding time : 0.000
% 11.05/2.43 % Success case prop solver time : 0.000
% 11.05/2.43 % Current number of processed clauses : 739
% 11.05/2.43 % Positive orientable unit clauses : 40
% 11.05/2.43 % Positive unorientable unit clauses: 0
% 11.05/2.43 % Negative unit clauses : 2
% 11.05/2.43 % Non-unit-clauses : 697
% 11.05/2.43 % Current number of unprocessed clauses: 20185
% 11.05/2.43 % ...number of literals in the above : 143809
% 11.05/2.43 % Current number of archived formulas : 0
% 11.05/2.43 % Current number of archived clauses : 1283
% 11.05/2.43 % Clause-clause subsumption calls (NU) : 392642
% 11.05/2.43 % Rec. Clause-clause subsumption calls : 98072
% 11.05/2.43 % Non-unit clause-clause subsumptions : 4513
% 11.05/2.43 % Unit Clause-clause subsumption calls : 4147
% 11.05/2.43 % Rewrite failures with RHS unbound : 0
% 11.05/2.43 % BW rewrite match attempts : 39
% 11.05/2.43 % BW rewrite match successes : 39
% 11.05/2.43 % Condensation attempts : 0
% 11.05/2.43 % Condensation successes : 0
% 11.05/2.43 % Termbank termtop insertions : 683505
% 11.05/2.43 % Search garbage collected termcells : 4584
% 11.05/2.43
% 11.05/2.43 % -------------------------------------------------
% 11.05/2.43 % User time : 1.789 s
% 11.05/2.43 % System time : 0.049 s
% 11.05/2.43 % Total time : 1.838 s
% 11.05/2.43 % Maximum resident set size: 4024 pages
% 11.05/2.43
% 11.05/2.43 % -------------------------------------------------
% 11.05/2.43 % User time : 7.112 s
% 11.05/2.43 % System time : 0.215 s
% 11.05/2.43 % Total time : 7.328 s
% 11.05/2.43 % Maximum resident set size: 4608 pages
% 11.05/2.43 % E exiting
%------------------------------------------------------------------------------