%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWC178+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 : n015.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 02:45:16 PM UTC 2026
% Result : Theorem 0.77s 0.54s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 90 ( 23 unt; 0 def)
% Number of atoms : 368 ( 90 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 456 ( 178 ~; 168 |; 33 &)
% ( 9 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 135 ( 0 sgn 95 !; 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)
=> ( neq(X5,X6)
| ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> app(app(app(X7,cons(X5,nil)),cons(X6,nil)),X8) != X1 ) ) ) ) )
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax1,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax1) ).
fof(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(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax13,axiom,
! [X1] :
( ssList(X1)
=> ( duplicatefreeP(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
=> X2 != X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax13) ).
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(ax71,axiom,
! [X1] :
( ssItem(X1)
=> duplicatefreeP(cons(X1,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax71) ).
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(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(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
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_15,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)
=> ( neq(X5,X6)
| ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> app(app(app(X7,cons(X5,nil)),cons(X6,nil)),X8) != X1 ) ) ) ) )
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
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)
=> ( neq(X5,X6)
| ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> app(app(app(X7,cons(X5,nil)),cons(X6,nil)),X8) != X1 ) ) ) ) )
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_17,negated_conjecture,
( ( ~ neq(esk51_0,nil)
| singletonP(esk50_0) )
& ~ neq(esk52_0,esk53_0)
& app(app(app(esk54_0,cons(esk52_0,nil)),cons(esk53_0,nil)),esk55_0) = esk48_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(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
fof(c_0_18,plain,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax1]) ).
fof(c_0_19,plain,
! [X227,X228] :
( ( ~ ssList(X227)
| ~ ssList(X228)
| nil = app(X227,X228)
| nil != X227
| nil != X228 )
& ( ~ ssList(X227)
| ~ ssList(X228)
| nil != app(X227,X228)
| nil = X227 )
& ( ~ ssList(X227)
| ~ ssList(X228)
| nil != app(X227,X228)
| nil = X228 ) ),
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_20,negated_conjecture,
app(app(app(esk54_0,cons(esk52_0,nil)),cons(esk53_0,nil)),esk55_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,plain,
! [X9,X10] :
( ( ~ ssItem(X9)
| ~ ssItem(X10)
| neq(X9,X10)
| X9 = X10 )
& ( ~ ssItem(X9)
| ~ ssItem(X10)
| X9 != X10
| ~ neq(X9,X10) ) ),
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_18])])])])]) ).
cnf(c_0_23,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
app(app(app(esk54_0,cons(esk52_0,nil)),cons(esk53_0,nil)),esk55_0) = esk50_0,
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
ssList(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_26,plain,
! [X132,X133] :
( ssList(app(X132,X133))
| ~ ssList(X133)
| ~ ssList(X132) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
cnf(c_0_27,negated_conjecture,
~ neq(esk52_0,esk53_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_28,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
ssItem(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_31,negated_conjecture,
( ~ ssList(app(app(esk54_0,cons(esk52_0,nil)),cons(esk53_0,nil)))
| esk50_0 != nil
| app(app(esk54_0,cons(esk52_0,nil)),cons(esk53_0,nil)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_32,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_33,plain,
! [X1] :
( ssList(X1)
=> ( duplicatefreeP(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
=> X2 != X3 ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ax13]) ).
cnf(c_0_34,negated_conjecture,
esk53_0 = esk52_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])]) ).
fof(c_0_35,plain,
! [X224,X225,X226] :
( app(app(X224,X225),X226) = app(X224,app(X225,X226))
| ~ ssList(X226)
| ~ ssList(X225)
| ~ ssList(X224) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
fof(c_0_36,plain,
! [X207] :
( duplicatefreeP(cons(X207,nil))
| ~ ssItem(X207) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax71])])]) ).
fof(c_0_37,plain,
! [X19,X21] :
( ( ~ ssList(X19)
| singletonP(X19)
| cons(X21,nil) != X19
| ~ ssItem(X21) )
& ( ~ ssList(X19)
| ~ singletonP(X19)
| cons(esk5_1(X19),nil) = X19 )
& ( ~ ssList(X19)
| ~ singletonP(X19)
| ssItem(esk5_1(X19)) ) ),
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])])])])])]) ).
cnf(c_0_38,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_39,negated_conjecture,
( ~ ssList(cons(esk53_0,nil))
| ~ ssList(app(esk54_0,cons(esk52_0,nil)))
| esk50_0 != nil
| app(app(esk54_0,cons(esk52_0,nil)),cons(esk53_0,nil)) = nil ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_40,plain,
! [X91,X92,X93,X94,X95,X96] :
( ( ~ ssList(X91)
| duplicatefreeP(X91)
| esk35_1(X91) = esk36_1(X91) )
& ( ~ ssList(X91)
| duplicatefreeP(X91)
| app(app(esk37_1(X91),cons(esk35_1(X91),esk38_1(X91))),cons(esk36_1(X91),esk39_1(X91))) = X91 )
& ( ~ ssList(X91)
| duplicatefreeP(X91)
| ssList(esk39_1(X91)) )
& ( ~ ssList(X91)
| duplicatefreeP(X91)
| ssList(esk38_1(X91)) )
& ( ~ ssList(X91)
| duplicatefreeP(X91)
| ssList(esk37_1(X91)) )
& ( ~ ssList(X91)
| duplicatefreeP(X91)
| ssItem(esk36_1(X91)) )
& ( ~ ssList(X91)
| duplicatefreeP(X91)
| ssItem(esk35_1(X91)) )
& ( ~ ssList(X91)
| X92 != X93
| app(app(X94,cons(X92,X95)),cons(X93,X96)) != X91
| ~ ssList(X96)
| ~ ssList(X95)
| ~ ssList(X94)
| ~ ssItem(X93)
| ~ ssItem(X92)
| ~ duplicatefreeP(X91) ) ),
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_33])])])])])]) ).
cnf(c_0_41,negated_conjecture,
app(app(app(esk54_0,cons(esk52_0,nil)),cons(esk52_0,nil)),esk55_0) = esk50_0,
inference(spm,[status(thm)],[c_0_24,c_0_34]) ).
cnf(c_0_42,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_43,plain,
! [X222,X223] :
( cons(X223,X222) = app(cons(X223,nil),X222)
| ~ ssItem(X223)
| ~ ssList(X222) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_44,plain,
( ~ ssItem(X1)
| duplicatefreeP(cons(X1,nil)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(esk5_1(X1),nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ssItem(esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_47,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_48,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_49,negated_conjecture,
( ~ ssList(cons(esk53_0,nil))
| ~ ssList(app(esk54_0,cons(esk52_0,nil)))
| esk50_0 != nil
| cons(esk53_0,nil) = nil ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_50,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_51,plain,
! [X113,X114] :
( ssList(cons(X114,X113))
| ~ ssItem(X114)
| ~ ssList(X113) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_52,plain,
( ~ ssList(X1)
| X2 != X3
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ duplicatefreeP(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_53,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ ssList(app(esk54_0,cons(esk52_0,nil)))
| app(app(esk54_0,cons(esk52_0,nil)),app(cons(esk52_0,nil),esk55_0)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_25])]) ).
cnf(c_0_54,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_55,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| duplicatefreeP(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_56,negated_conjecture,
( ~ neq(esk51_0,nil)
| singletonP(esk50_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_57,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_47,c_0_21]) ).
fof(c_0_58,plain,
! [X111,X112] :
( ( ~ ssList(X111)
| ~ ssList(X112)
| neq(X111,X112)
| X111 = X112 )
& ( ~ ssList(X111)
| ~ ssList(X112)
| X111 != X112
| ~ neq(X111,X112) ) ),
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_48])])])])]) ).
cnf(c_0_59,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_60,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_61,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
inference(fof_simplification,[status(thm)],[ax18]) ).
cnf(c_0_62,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_49,c_0_32]),c_0_50])]) ).
cnf(c_0_63,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_64,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_65,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ ssList(app(app(X1,cons(X2,X3)),cons(X2,X4)))
| ~ duplicatefreeP(app(app(X1,cons(X2,X3)),cons(X2,X4))) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_52])]) ).
cnf(c_0_66,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ ssList(app(esk54_0,cons(esk52_0,nil)))
| app(app(esk54_0,cons(esk52_0,nil)),cons(esk52_0,esk55_0)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_25]),c_0_30])]) ).
cnf(c_0_67,negated_conjecture,
( ~ neq(esk51_0,nil)
| duplicatefreeP(esk50_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).
cnf(c_0_68,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_69,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_59,c_0_60]) ).
fof(c_0_70,plain,
! [X186,X187,X188] :
( segmentP(X186,X188)
| ~ segmentP(X187,X188)
| ~ segmentP(X186,X187)
| ~ ssList(X188)
| ~ ssList(X187)
| ~ ssList(X186) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax53])])])]) ).
fof(c_0_71,plain,
! [X115,X116] :
( cons(X116,X115) != 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)],[c_0_61])])])]) ).
cnf(c_0_72,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_62,c_0_63]),c_0_64]),c_0_29])]) ).
cnf(c_0_73,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ ssList(app(esk54_0,cons(esk52_0,nil)))
| ~ duplicatefreeP(esk50_0) ),
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(spm,[status(thm)],[c_0_65,c_0_66]),c_0_57]),c_0_25]),c_0_64]),c_0_50]),c_0_30])]) ).
cnf(c_0_74,negated_conjecture,
( duplicatefreeP(esk50_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_64]),c_0_69])]) ).
fof(c_0_75,plain,
! [X197] :
( ( ~ ssList(X197)
| segmentP(nil,X197)
| nil != X197 )
& ( ~ ssList(X197)
| nil = X197
| ~ segmentP(nil,X197) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax58])])])]) ).
cnf(c_0_76,plain,
( ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_77,negated_conjecture,
segmentP(esk51_0,esk50_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_78,plain,
( cons(X2,X1) != X1
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_79,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_72,c_0_63]),c_0_64]),c_0_30])]) ).
cnf(c_0_80,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ ssList(app(esk54_0,cons(esk52_0,nil)))
| esk51_0 = nil ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,plain,
( ~ ssList(X1)
| ~ segmentP(nil,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_82,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_76,c_0_77]),c_0_57]),c_0_69])]) ).
cnf(c_0_83,negated_conjecture,
esk50_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_64]),c_0_29])]) ).
cnf(c_0_84,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_32]),c_0_50])]) ).
cnf(c_0_85,plain,
( ~ ssList(X1)
| nil != X1
| segmentP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_86,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_81,c_0_82]),c_0_57]),c_0_64])]),c_0_83]) ).
cnf(c_0_87,negated_conjecture,
esk51_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_63]),c_0_64]),c_0_30])]) ).
cnf(c_0_88,plain,
segmentP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_85]),c_0_64])]) ).
cnf(c_0_89,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87]),c_0_88])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC178+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 08:05:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.77/0.54 % Version: 3.5.1
% 0.77/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.77/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.77/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.77/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.77/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.77/0.54 % Starting sh5l with 300s (1) cores
% 0.77/0.54 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 992824 completed with status 0
% 0.77/0.54 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.77/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.77/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.77/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.77/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.77/0.54 % No SInE strategy applied
% 0.77/0.54 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.77/0.54 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.77/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.77/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.77/0.54 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.77/0.54 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.77/0.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.77/0.54 % G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with pid 992835 completed with status 0
% 0.77/0.54 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y
% 0.77/0.54 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.77/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.77/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.77/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.77/0.54 % No SInE strategy applied
% 0.77/0.54 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.77/0.54 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.77/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.77/0.54 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.77/0.54 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.77/0.54 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.77/0.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.77/0.54 % Preprocessing time : 0.004 s
% 0.77/0.54 % Presaturation interreduction done
% 0.77/0.54
% 0.77/0.54 % Proof found!
% 0.77/0.54 % SZS status Theorem
% 0.77/0.54 % SZS output start CNFRefutation
% See solution above
% 0.77/0.54 % Parsed axioms : 96
% 0.77/0.54 % Removed by relevancy pruning/SinE : 0
% 0.77/0.54 % Initial clauses : 204
% 0.77/0.54 % Removed in clause preprocessing : 2
% 0.77/0.54 % Initial clauses in saturation : 202
% 0.77/0.54 % Processed clauses : 895
% 0.77/0.54 % ...of these trivial : 7
% 0.77/0.54 % ...subsumed : 252
% 0.77/0.54 % ...remaining for further processing : 636
% 0.77/0.54 % Other redundant clauses eliminated : 96
% 0.77/0.54 % Clauses deleted for lack of memory : 0
% 0.77/0.54 % Backward-subsumed : 39
% 0.77/0.54 % Backward-rewritten : 69
% 0.77/0.54 % Generated clauses : 2145
% 0.77/0.54 % ...of the previous two non-redundant : 1912
% 0.77/0.54 % ...aggressively subsumed : 0
% 0.77/0.54 % Contextual simplify-reflections : 73
% 0.77/0.54 % Paramodulations : 2046
% 0.77/0.54 % Factorizations : 0
% 0.77/0.54 % NegExts : 0
% 0.77/0.54 % Equation resolutions : 101
% 0.77/0.54 % Disequality decompositions : 0
% 0.77/0.54 % Total rewrite steps : 1351
% 0.77/0.54 % ...of those cached : 1327
% 0.77/0.54 % Propositional unsat checks : 0
% 0.77/0.54 % Propositional check models : 0
% 0.77/0.54 % Propositional check unsatisfiable : 0
% 0.77/0.54 % Propositional clauses : 0
% 0.77/0.54 % Propositional clauses after purity: 0
% 0.77/0.54 % Propositional unsat core size : 0
% 0.77/0.54 % Propositional preprocessing time : 0.000
% 0.77/0.54 % Propositional encoding time : 0.000
% 0.77/0.54 % Propositional solver time : 0.000
% 0.77/0.54 % Success case prop preproc time : 0.000
% 0.77/0.54 % Success case prop encoding time : 0.000
% 0.77/0.54 % Success case prop solver time : 0.000
% 0.77/0.54 % Current number of processed clauses : 309
% 0.77/0.54 % Positive orientable unit clauses : 25
% 0.77/0.54 % Positive unorientable unit clauses: 0
% 0.77/0.54 % Negative unit clauses : 6
% 0.77/0.54 % Non-unit-clauses : 278
% 0.77/0.54 % Current number of unprocessed clauses: 1362
% 0.77/0.54 % ...number of literals in the above : 9001
% 0.77/0.54 % Current number of archived formulas : 0
% 0.77/0.54 % Current number of archived clauses : 304
% 0.77/0.54 % Clause-clause subsumption calls (NU) : 32870
% 0.77/0.54 % Rec. Clause-clause subsumption calls : 10724
% 0.77/0.54 % Non-unit clause-clause subsumptions : 281
% 0.77/0.54 % Unit Clause-clause subsumption calls : 269
% 0.77/0.54 % Rewrite failures with RHS unbound : 0
% 0.77/0.54 % BW rewrite match attempts : 5
% 0.77/0.54 % BW rewrite match successes : 4
% 0.77/0.54 % Condensation attempts : 0
% 0.77/0.54 % Condensation successes : 0
% 0.77/0.54 % Termbank termtop insertions : 62604
% 0.77/0.54 % Search garbage collected termcells : 4306
% 0.77/0.54
% 0.77/0.54 % -------------------------------------------------
% 0.77/0.54 % User time : 0.109 s
% 0.77/0.54 % System time : 0.010 s
% 0.77/0.54 % Total time : 0.120 s
% 0.77/0.54 % Maximum resident set size: 4272 pages
% 0.77/0.54
% 0.77/0.54 % -------------------------------------------------
% 0.77/0.54 % User time : 0.500 s
% 0.77/0.54 % System time : 0.038 s
% 0.77/0.54 % Total time : 0.538 s
% 0.77/0.54 % Maximum resident set size: 4864 pages
% 0.77/0.54 % E exiting
%------------------------------------------------------------------------------