%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC162+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 : n018.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 02:43:16 PM UTC 2026
% Result : Theorem 0.15s 5.63s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 98 ( 23 unt; 0 def)
% Number of atoms : 415 ( 83 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 525 ( 208 ~; 199 |; 43 &)
% ( 6 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-2 aty)
% Number of variables : 142 ( 0 sgn 98 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( neq(X4,nil)
& ~ singletonP(X3) )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( ( leq(X5,X6)
& ! [X10] :
( ssItem(X10)
=> ( ( leq(X10,X6)
& leq(X5,X10) )
| ~ memberP(X8,X10) ) ) )
| ~ leq(X6,X5)
| app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) != X1 ) ) ) ) ) )
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
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(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(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(ax90,axiom,
! [X1] :
( ssItem(X1)
=> ~ lt(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax90) ).
fof(ax91,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( ( lt(X2,X3)
& leq(X1,X2) )
=> lt(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax91) ).
fof(ax12,axiom,
! [X1] :
( ssList(X1)
=> ( strictorderedP(X1)
<=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X4,cons(X2,X5)),cons(X3,X6)) = X1
=> lt(X2,X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax12) ).
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(ax68,axiom,
! [X1] :
( ssItem(X1)
=> strictorderedP(cons(X1,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax68) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( cons(X2,nil) = X1
& ssItem(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(ax53,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X2,X3)
& segmentP(X1,X2) )
=> segmentP(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax53) ).
fof(ax58,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( neq(X4,nil)
& ~ singletonP(X3) )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( ( leq(X5,X6)
& ! [X10] :
( ssItem(X10)
=> ( ( leq(X10,X6)
& leq(X5,X10) )
| ~ memberP(X8,X10) ) ) )
| ~ leq(X6,X5)
| app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) != X1 ) ) ) ) ) )
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( neq(X4,nil)
& ~ singletonP(X3) )
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( ( leq(X5,X6)
& ! [X10] :
( ssItem(X10)
=> ( ( leq(X10,X6)
& leq(X5,X10) )
| ~ memberP(X8,X10) ) ) )
| ~ leq(X6,X5)
| app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) != X1 ) ) ) ) ) )
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_18,negated_conjecture,
( ( ~ neq(esk51_0,nil)
| singletonP(esk50_0) )
& ( ~ leq(esk52_0,esk53_0)
| ~ leq(esk57_0,esk53_0)
| ~ leq(esk52_0,esk57_0) )
& ( ~ leq(esk52_0,esk53_0)
| memberP(esk55_0,esk57_0) )
& ( ~ leq(esk52_0,esk53_0)
| ssItem(esk57_0) )
& leq(esk53_0,esk52_0)
& app(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)),esk56_0) = esk48_0
& ssList(esk56_0)
& ssList(esk55_0)
& ssList(esk54_0)
& ssItem(esk53_0)
& ssItem(esk52_0)
& segmentP(esk51_0,esk50_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(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])]) ).
cnf(c_0_19,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_18]) ).
cnf(c_0_20,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
! [X226,X227,X228] :
( app(app(X226,X227),X228) = app(X226,app(X227,X228))
| ~ ssList(X228)
| ~ ssList(X227)
| ~ ssList(X226) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
fof(c_0_22,plain,
! [X229,X230] :
( ( ~ ssList(X229)
| ~ ssList(X230)
| nil = app(X229,X230)
| nil != X229
| nil != X230 )
& ( ~ ssList(X229)
| ~ ssList(X230)
| nil != app(X229,X230)
| nil = X229 )
& ( ~ ssList(X229)
| ~ ssList(X230)
| nil != app(X229,X230)
| nil = X230 ) ),
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_23,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_19,c_0_20]) ).
cnf(c_0_24,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
ssList(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_27,plain,
! [X224,X225] :
( cons(X225,X224) = app(cons(X225,nil),X224)
| ~ ssItem(X225)
| ~ ssList(X224) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_28,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
ssList(esk56_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_30,plain,
! [X134,X135] :
( ssList(app(X134,X135))
| ~ ssList(X135)
| ~ ssList(X134) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
cnf(c_0_31,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| 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_23,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_32,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_34,plain,
! [X1] :
( ssItem(X1)
=> ~ lt(X1,X1) ),
inference(fof_simplification,[status(thm)],[ax90]) ).
fof(c_0_35,plain,
! [X243,X244,X245] :
( lt(X243,X245)
| ~ lt(X244,X245)
| ~ leq(X243,X244)
| ~ ssItem(X245)
| ~ ssItem(X244)
| ~ ssItem(X243) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax91])])])]) ).
cnf(c_0_36,negated_conjecture,
( ~ ssList(app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)))
| esk50_0 != nil
| app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_23]),c_0_29])]) ).
cnf(c_0_37,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_38,plain,
! [X82,X83,X84,X85,X86,X87] :
( ( ~ ssList(X82)
| strictorderedP(X82)
| ~ lt(esk30_1(X82),esk31_1(X82)) )
& ( ~ ssList(X82)
| strictorderedP(X82)
| app(app(esk32_1(X82),cons(esk30_1(X82),esk33_1(X82))),cons(esk31_1(X82),esk34_1(X82))) = X82 )
& ( ~ ssList(X82)
| strictorderedP(X82)
| ssList(esk34_1(X82)) )
& ( ~ ssList(X82)
| strictorderedP(X82)
| ssList(esk33_1(X82)) )
& ( ~ ssList(X82)
| strictorderedP(X82)
| ssList(esk32_1(X82)) )
& ( ~ ssList(X82)
| strictorderedP(X82)
| ssItem(esk31_1(X82)) )
& ( ~ ssList(X82)
| strictorderedP(X82)
| ssItem(esk30_1(X82)) )
& ( ~ ssList(X82)
| lt(X83,X84)
| app(app(X85,cons(X83,X86)),cons(X84,X87)) != X82
| ~ ssList(X87)
| ~ ssList(X86)
| ~ ssList(X85)
| ~ ssItem(X84)
| ~ ssItem(X83)
| ~ strictorderedP(X82) ) ),
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)],[ax12])])])])])]) ).
cnf(c_0_39,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| 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_31,c_0_32]),c_0_25]),c_0_33])]) ).
fof(c_0_40,plain,
! [X242] :
( ~ lt(X242,X242)
| ~ ssItem(X242) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])]) ).
cnf(c_0_41,plain,
( ~ lt(X2,X3)
| ~ leq(X1,X2)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| lt(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,negated_conjecture,
leq(esk53_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_43,negated_conjecture,
ssItem(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_44,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_45,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_46,negated_conjecture,
( ~ ssList(cons(esk53_0,nil))
| ~ ssList(app(app(esk54_0,cons(esk52_0,nil)),esk55_0))
| esk50_0 != nil
| app(app(app(esk54_0,cons(esk52_0,nil)),esk55_0),cons(esk53_0,nil)) = nil ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_47,plain,
( ~ ssList(X1)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ strictorderedP(X1)
| lt(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_48,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ ssList(cons(esk53_0,nil))
| ~ ssList(app(esk54_0,cons(esk52_0,esk55_0)))
| app(app(esk54_0,cons(esk52_0,esk55_0)),app(cons(esk53_0,nil),esk56_0)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_39]),c_0_29])]) ).
cnf(c_0_49,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_50,plain,
( ~ lt(X1,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,negated_conjecture,
( ~ ssItem(X1)
| ~ lt(esk52_0,X1)
| lt(esk53_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_33]),c_0_43])]) ).
fof(c_0_52,plain,
! [X206] :
( strictorderedP(cons(X206,nil))
| ~ ssItem(X206) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax68])])]) ).
fof(c_0_53,plain,
! [X21,X23] :
( ( ~ ssList(X21)
| singletonP(X21)
| cons(X23,nil) != X21
| ~ ssItem(X23) )
& ( ~ ssList(X21)
| ~ singletonP(X21)
| cons(esk5_1(X21),nil) = X21 )
& ( ~ ssList(X21)
| ~ singletonP(X21)
| ssItem(esk5_1(X21)) ) ),
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)],[ax4])])])])])]) ).
fof(c_0_54,plain,
! [X113,X114] :
( ( ~ ssList(X113)
| ~ ssList(X114)
| neq(X113,X114)
| X113 = X114 )
& ( ~ ssList(X113)
| ~ ssList(X114)
| X113 != X114
| ~ neq(X113,X114) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])])]) ).
cnf(c_0_55,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_56,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_57,negated_conjecture,
( ~ ssList(cons(esk53_0,nil))
| ~ ssList(app(app(esk54_0,cons(esk52_0,nil)),esk55_0))
| esk50_0 != nil
| cons(esk53_0,nil) = nil ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_58,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| ~ strictorderedP(app(app(X3,cons(X1,X4)),cons(X2,X5)))
| lt(X1,X2) ),
inference(er,[status(thm)],[c_0_47]) ).
cnf(c_0_59,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ ssList(cons(esk53_0,nil))
| ~ ssList(app(esk54_0,cons(esk52_0,esk55_0)))
| app(app(esk54_0,cons(esk52_0,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_48,c_0_32]),c_0_29]),c_0_43])]) ).
cnf(c_0_60,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_49,c_0_20]) ).
cnf(c_0_61,negated_conjecture,
~ lt(esk52_0,esk53_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_43])]) ).
cnf(c_0_62,plain,
( ~ ssItem(X1)
| strictorderedP(cons(X1,nil)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_63,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(esk5_1(X1),nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_64,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ssItem(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_65,negated_conjecture,
( ~ neq(esk51_0,nil)
| singletonP(esk50_0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_66,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_67,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_68,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_69,negated_conjecture,
( ~ ssList(cons(esk53_0,nil))
| ~ ssList(app(esk54_0,cons(esk52_0,nil)))
| esk50_0 != nil
| cons(esk53_0,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_37]),c_0_25])]) ).
fof(c_0_70,plain,
! [X115,X116] :
( ssList(cons(X116,X115))
| ~ ssItem(X116)
| ~ ssList(X115) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_71,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ ssList(cons(esk53_0,nil))
| ~ ssList(app(esk54_0,cons(esk52_0,esk55_0)))
| ~ strictorderedP(esk50_0) ),
inference(sr,[status(thm)],[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_58,c_0_59]),c_0_60]),c_0_29]),c_0_25]),c_0_26]),c_0_43]),c_0_33])]),c_0_61]) ).
cnf(c_0_72,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| strictorderedP(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_73,negated_conjecture,
( singletonP(esk50_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_68])]) ).
fof(c_0_74,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
inference(fof_simplification,[status(thm)],[ax18]) ).
cnf(c_0_75,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ ssList(cons(esk53_0,nil))
| esk50_0 != nil
| cons(esk53_0,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_37]),c_0_26])]) ).
cnf(c_0_76,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_77,negated_conjecture,
( ~ ssList(cons(esk52_0,esk55_0))
| ~ ssList(cons(esk52_0,nil))
| ~ ssList(cons(esk53_0,nil))
| ~ strictorderedP(esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_37]),c_0_26])]) ).
cnf(c_0_78,negated_conjecture,
( strictorderedP(esk50_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_60])]) ).
fof(c_0_79,plain,
! [X188,X189,X190] :
( segmentP(X188,X190)
| ~ segmentP(X189,X190)
| ~ segmentP(X188,X189)
| ~ ssList(X190)
| ~ ssList(X189)
| ~ ssList(X188) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax53])])])]) ).
fof(c_0_80,plain,
! [X117,X118] :
( cons(X118,X117) != X117
| ~ ssItem(X118)
| ~ ssList(X117) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_74])])])]) ).
cnf(c_0_81,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| esk50_0 != nil
| cons(esk53_0,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_67]),c_0_43])]) ).
cnf(c_0_82,negated_conjecture,
( ~ ssList(cons(esk52_0,esk55_0))
| ~ ssList(cons(esk52_0,nil))
| ~ ssList(cons(esk53_0,nil))
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
fof(c_0_83,plain,
! [X199] :
( ( ~ ssList(X199)
| segmentP(nil,X199)
| nil != X199 )
& ( ~ ssList(X199)
| nil = X199
| ~ segmentP(nil,X199) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax58])])])]) ).
cnf(c_0_84,plain,
( ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_85,negated_conjecture,
segmentP(esk51_0,esk50_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_86,plain,
( cons(X2,X1) != X1
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_87,negated_conjecture,
( esk50_0 != nil
| cons(esk53_0,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_76]),c_0_67]),c_0_33])]) ).
cnf(c_0_88,negated_conjecture,
( ~ ssList(cons(esk52_0,esk55_0))
| ~ ssList(cons(esk52_0,nil))
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_76]),c_0_67]),c_0_43])]) ).
cnf(c_0_89,plain,
( ~ ssList(X1)
| ~ segmentP(nil,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_90,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(X1,esk51_0)
| segmentP(X1,esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_60]),c_0_68])]) ).
cnf(c_0_91,negated_conjecture,
esk50_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_67]),c_0_43])]) ).
cnf(c_0_92,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_76]),c_0_25]),c_0_33])]) ).
cnf(c_0_93,plain,
( ~ ssList(X1)
| nil != X1
| segmentP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_94,negated_conjecture,
~ segmentP(nil,esk51_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_60]),c_0_67])]),c_0_91]) ).
cnf(c_0_95,negated_conjecture,
esk51_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_76]),c_0_67]),c_0_33])]) ).
cnf(c_0_96,plain,
segmentP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_93]),c_0_67])]) ).
cnf(c_0_97,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95]),c_0_96])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC162+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.37 % Computer : n018.cluster.edu
% 0.12/5.37 % Model : x86_64 x86_64
% 0.12/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.37 % Memory : 8046.5625MB
% 0.12/5.37 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Mon Sep 21 08:02:50 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.41 Running first-order theorem proving
% 0.15/5.41 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
% 0.15/5.63 % Version: 3.5.1
% 0.15/5.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/5.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/5.63 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.63 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.63 % Starting sh5l with 300s (1) cores
% 0.15/5.63 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1401627 completed with status 0
% 0.15/5.63 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.15/5.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/5.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/5.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.63 % No SInE strategy applied
% 0.15/5.63 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.15/5.63 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.63 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.15/5.63 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.15/5.63 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.15/5.63 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.15/5.63 % G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with pid 1401650 completed with status 0
% 0.15/5.63 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y
% 0.15/5.63 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/5.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/5.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.63 % No SInE strategy applied
% 0.15/5.63 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.15/5.63 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.63 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.63 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.15/5.63 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.15/5.63 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.15/5.63 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.15/5.63 % Preprocessing time : 0.005 s
% 0.15/5.63 % Presaturation interreduction done
% 0.15/5.63
% 0.15/5.63 % Proof found!
% 0.15/5.63 % SZS status Theorem
% 0.15/5.63 % SZS output start CNFRefutation
% See solution above
% 0.15/5.63 % Parsed axioms : 96
% 0.15/5.63 % Removed by relevancy pruning/SinE : 0
% 0.15/5.63 % Initial clauses : 208
% 0.15/5.63 % Removed in clause preprocessing : 2
% 0.15/5.63 % Initial clauses in saturation : 206
% 0.15/5.63 % Processed clauses : 801
% 0.15/5.63 % ...of these trivial : 2
% 0.15/5.63 % ...subsumed : 177
% 0.15/5.63 % ...remaining for further processing : 622
% 0.15/5.63 % Other redundant clauses eliminated : 96
% 0.15/5.63 % Clauses deleted for lack of memory : 0
% 0.15/5.63 % Backward-subsumed : 35
% 0.15/5.63 % Backward-rewritten : 35
% 0.15/5.63 % Generated clauses : 1830
% 0.15/5.63 % ...of the previous two non-redundant : 1597
% 0.15/5.63 % ...aggressively subsumed : 0
% 0.15/5.63 % Contextual simplify-reflections : 66
% 0.15/5.63 % Paramodulations : 1731
% 0.15/5.63 % Factorizations : 0
% 0.15/5.63 % NegExts : 0
% 0.15/5.63 % Equation resolutions : 101
% 0.15/5.63 % Disequality decompositions : 0
% 0.15/5.63 % Total rewrite steps : 1023
% 0.15/5.63 % ...of those cached : 998
% 0.15/5.63 % Propositional unsat checks : 0
% 0.15/5.63 % Propositional check models : 0
% 0.15/5.63 % Propositional check unsatisfiable : 0
% 0.15/5.63 % Propositional clauses : 0
% 0.15/5.63 % Propositional clauses after purity: 0
% 0.15/5.63 % Propositional unsat core size : 0
% 0.15/5.63 % Propositional preprocessing time : 0.000
% 0.15/5.63 % Propositional encoding time : 0.000
% 0.15/5.63 % Propositional solver time : 0.000
% 0.15/5.63 % Success case prop preproc time : 0.000
% 0.15/5.63 % Success case prop encoding time : 0.000
% 0.15/5.63 % Success case prop solver time : 0.000
% 0.15/5.63 % Current number of processed clauses : 329
% 0.15/5.63 % Positive orientable unit clauses : 26
% 0.15/5.63 % Positive unorientable unit clauses: 0
% 0.15/5.63 % Negative unit clauses : 5
% 0.15/5.63 % Non-unit-clauses : 298
% 0.15/5.63 % Current number of unprocessed clauses: 1169
% 0.15/5.63 % ...number of literals in the above : 7905
% 0.15/5.63 % Current number of archived formulas : 0
% 0.15/5.63 % Current number of archived clauses : 270
% 0.15/5.63 % Clause-clause subsumption calls (NU) : 36611
% 0.15/5.63 % Rec. Clause-clause subsumption calls : 10272
% 0.15/5.63 % Non-unit clause-clause subsumptions : 223
% 0.15/5.63 % Unit Clause-clause subsumption calls : 223
% 0.15/5.63 % Rewrite failures with RHS unbound : 0
% 0.15/5.63 % BW rewrite match attempts : 3
% 0.15/5.63 % BW rewrite match successes : 3
% 0.15/5.63 % Condensation attempts : 0
% 0.15/5.63 % Condensation successes : 0
% 0.15/5.63 % Termbank termtop insertions : 57991
% 0.15/5.63 % Search garbage collected termcells : 4403
% 0.15/5.63
% 0.15/5.63 % -------------------------------------------------
% 0.15/5.63 % User time : 0.161 s
% 0.15/5.63 % System time : 0.019 s
% 0.15/5.63 % Total time : 0.180 s
% 0.15/5.63 % Maximum resident set size: 4276 pages
% 0.15/5.63
% 0.15/5.63 % -------------------------------------------------
% 0.15/5.63 % User time : 0.823 s
% 0.15/5.63 % System time : 0.051 s
% 0.15/5.63 % Total time : 0.874 s
% 0.15/5.63 % Maximum resident set size: 4864 pages
% 0.15/5.63 % E exiting
%------------------------------------------------------------------------------