%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC173+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 02:43:19 PM UTC 2026
% Result : Theorem 0.21s 5.79s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 17 unt; 0 def)
% Number of atoms : 340 ( 104 equ)
% Maximal formula atoms : 48 ( 5 avg)
% Number of connectives : 421 ( 146 ~; 152 |; 51 &)
% ( 5 <=>; 67 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 12 con; 0-2 aty)
% Number of variables : 123 ( 0 sgn 89 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ssList(X11)
=> ( ? [X13] :
( lt(X13,X9)
& memberP(X11,X13)
& ssItem(X13) )
| ? [X12] :
( lt(X9,X12)
& memberP(X10,X12)
& ssItem(X12) )
| app(app(X10,X3),X11) != X4
| cons(X9,nil) != 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 ) ) ) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
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(ax1,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax1) ).
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(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(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(c_0_11,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ssList(X11)
=> ( ? [X13] :
( lt(X13,X9)
& memberP(X11,X13)
& ssItem(X13) )
| ? [X12] :
( lt(X9,X12)
& memberP(X10,X12)
& ssItem(X12) )
| app(app(X10,X3),X11) != X4
| cons(X9,nil) != 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 ) ) ) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssList(X10)
=> ! [X11] :
( ssList(X11)
=> ( ? [X13] :
( lt(X13,X9)
& memberP(X11,X13)
& ssItem(X13) )
| ? [X12] :
( lt(X9,X12)
& memberP(X10,X12)
& ssItem(X12) )
| app(app(X10,X3),X11) != X4
| cons(X9,nil) != 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 ) ) ) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_13,negated_conjecture,
! [X269,X270] :
( ( ~ lt(X270,esk56_0)
| ~ memberP(esk58_0,X270)
| ~ ssItem(X270)
| nil = esk50_0 )
& ( ~ lt(X270,esk56_0)
| ~ memberP(esk58_0,X270)
| ~ ssItem(X270)
| nil = esk51_0 )
& ( ~ lt(esk56_0,X269)
| ~ memberP(esk57_0,X269)
| ~ ssItem(X269)
| nil = esk50_0 )
& ( ~ lt(esk56_0,X269)
| ~ memberP(esk57_0,X269)
| ~ ssItem(X269)
| nil = esk51_0 )
& ( app(app(esk57_0,esk50_0),esk58_0) = esk51_0
| nil = esk50_0 )
& ( app(app(esk57_0,esk50_0),esk58_0) = esk51_0
| nil = esk51_0 )
& ( cons(esk56_0,nil) = esk50_0
| nil = esk50_0 )
& ( cons(esk56_0,nil) = esk50_0
| nil = esk51_0 )
& ( ssList(esk58_0)
| nil = esk50_0 )
& ( ssList(esk58_0)
| nil = esk51_0 )
& ( ssList(esk57_0)
| nil = esk50_0 )
& ( ssList(esk57_0)
| nil = esk51_0 )
& ( ssItem(esk56_0)
| nil = esk50_0 )
& ( ssItem(esk56_0)
| nil = esk51_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)
& 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_12])])])])])]) ).
fof(c_0_14,plain,
! [X232,X233] :
( ( ~ ssList(X232)
| ~ ssList(X233)
| nil = app(X232,X233)
| nil != X232
| nil != X233 )
& ( ~ ssList(X232)
| ~ ssList(X233)
| nil != app(X232,X233)
| nil = X232 )
& ( ~ ssList(X232)
| ~ ssList(X233)
| nil != app(X232,X233)
| nil = X233 ) ),
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_15,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_13]) ).
cnf(c_0_16,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,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_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
ssList(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,plain,
! [X137,X138] :
( ssList(app(X137,X138))
| ~ ssList(X138)
| ~ ssList(X137) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
cnf(c_0_21,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_17,c_0_18]),c_0_19])]) ).
cnf(c_0_22,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,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_21,c_0_22]) ).
fof(c_0_25,plain,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax1]) ).
cnf(c_0_26,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_23,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
ssList(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_28,plain,
! [X118,X119] :
( ssList(cons(X119,X118))
| ~ ssItem(X119)
| ~ ssList(X118) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_29,plain,
! [X14,X15] :
( ( ~ ssItem(X14)
| ~ ssItem(X15)
| neq(X14,X15)
| X14 = X15 )
& ( ~ ssItem(X14)
| ~ ssItem(X15)
| X14 != X15
| ~ neq(X14,X15) ) ),
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_25])])])])]) ).
fof(c_0_30,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
inference(fof_simplification,[status(thm)],[ax18]) ).
cnf(c_0_31,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_26,c_0_22]),c_0_27])]) ).
cnf(c_0_32,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_34,negated_conjecture,
ssItem(esk53_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_35,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]) ).
fof(c_0_36,plain,
! [X229,X230,X231] :
( app(app(X229,X230),X231) = app(X229,app(X230,X231))
| ~ ssList(X231)
| ~ ssList(X230)
| ~ ssList(X229) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
cnf(c_0_37,negated_conjecture,
~ neq(esk52_0,esk53_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_38,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_40,plain,
! [X212] :
( duplicatefreeP(cons(X212,nil))
| ~ ssItem(X212) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax71])])]) ).
fof(c_0_41,plain,
! [X120,X121] :
( cons(X121,X120) != X120
| ~ ssItem(X121)
| ~ ssList(X120) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])]) ).
cnf(c_0_42,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_31,c_0_32]),c_0_33]),c_0_34])]) ).
fof(c_0_43,plain,
! [X96,X97,X98,X99,X100,X101] :
( ( ~ ssList(X96)
| duplicatefreeP(X96)
| esk35_1(X96) = esk36_1(X96) )
& ( ~ ssList(X96)
| duplicatefreeP(X96)
| app(app(esk37_1(X96),cons(esk35_1(X96),esk38_1(X96))),cons(esk36_1(X96),esk39_1(X96))) = X96 )
& ( ~ ssList(X96)
| duplicatefreeP(X96)
| ssList(esk39_1(X96)) )
& ( ~ ssList(X96)
| duplicatefreeP(X96)
| ssList(esk38_1(X96)) )
& ( ~ ssList(X96)
| duplicatefreeP(X96)
| ssList(esk37_1(X96)) )
& ( ~ ssList(X96)
| duplicatefreeP(X96)
| ssItem(esk36_1(X96)) )
& ( ~ ssList(X96)
| duplicatefreeP(X96)
| ssItem(esk35_1(X96)) )
& ( ~ ssList(X96)
| X97 != X98
| app(app(X99,cons(X97,X100)),cons(X98,X101)) != X96
| ~ ssList(X101)
| ~ ssList(X100)
| ~ ssList(X99)
| ~ ssItem(X98)
| ~ ssItem(X97)
| ~ duplicatefreeP(X96) ) ),
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_35])])])])])]) ).
cnf(c_0_44,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,negated_conjecture,
esk53_0 = esk52_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_34]),c_0_39])]) ).
fof(c_0_46,plain,
! [X227,X228] :
( cons(X228,X227) = app(cons(X228,nil),X227)
| ~ ssItem(X228)
| ~ ssList(X227) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_47,plain,
( ~ ssItem(X1)
| duplicatefreeP(cons(X1,nil)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_48,negated_conjecture,
( cons(esk56_0,nil) = esk50_0
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_49,negated_conjecture,
( ssItem(esk56_0)
| nil = esk50_0 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_50,plain,
( cons(X2,X1) != X1
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_51,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_42,c_0_32]),c_0_33]),c_0_39])]) ).
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_43]) ).
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_44]),c_0_45]),c_0_19]),c_0_45])]) ).
cnf(c_0_54,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,negated_conjecture,
( duplicatefreeP(esk50_0)
| esk50_0 = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_56,negated_conjecture,
esk50_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_33]),c_0_34])]) ).
cnf(c_0_57,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_58,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_59,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_19]),c_0_39])]) ).
cnf(c_0_60,negated_conjecture,
duplicatefreeP(esk50_0),
inference(sr,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_61,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_57,c_0_16]) ).
cnf(c_0_62,negated_conjecture,
( ~ ssList(cons(esk52_0,nil))
| ~ ssList(app(esk54_0,cons(esk52_0,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_58,c_0_59]),c_0_60]),c_0_61]),c_0_19]),c_0_33]),c_0_27]),c_0_39])]) ).
cnf(c_0_63,negated_conjecture,
~ ssList(cons(esk52_0,nil)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_22]),c_0_27])]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_32]),c_0_33]),c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC173+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/5.43 % Computer : n015.cluster.edu
% 0.17/5.43 % Model : x86_64 x86_64
% 0.17/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.43 % Memory : 8046.5625MB
% 0.17/5.43 % OS : Linux 6.8.0-71-generic
% 0.17/5.43 % CPULimit : 300
% 0.17/5.43 % WCLimit : 300
% 0.17/5.43 % DateTime : Mon Sep 21 08:04:11 UTC 2026
% 0.17/5.44 % CPUTime :
% 0.17/5.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/5.51 Running first-order theorem proving
% 0.21/5.51 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
% 0.21/5.79 % Version: 3.5.1
% 0.21/5.79 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/5.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/5.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/5.79 % Starting new_bool_3 with 300s (1) cores
% 0.21/5.79 % Starting new_bool_1 with 300s (1) cores
% 0.21/5.79 % Starting sh5l with 300s (1) cores
% 0.21/5.79 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 989999 completed with status 0
% 0.21/5.79 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.21/5.79 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/5.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/5.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/5.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/5.79 % No SInE strategy applied
% 0.21/5.79 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.21/5.79 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/5.79 % Starting SubtermCWHack with 136s (1) cores
% 0.21/5.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.21/5.79 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.21/5.79 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.21/5.79 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.21/5.79 % G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with pid 990010 completed with status 0
% 0.21/5.79 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y
% 0.21/5.79 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.21/5.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/5.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.21/5.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/5.79 % No SInE strategy applied
% 0.21/5.79 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.21/5.79 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/5.79 % Starting SubtermCWHack with 136s (1) cores
% 0.21/5.79 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.21/5.79 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.21/5.79 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.21/5.79 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.21/5.79 % Preprocessing time : 0.006 s
% 0.21/5.79 % Presaturation interreduction done
% 0.21/5.79
% 0.21/5.79 % Proof found!
% 0.21/5.79 % SZS status Theorem
% 0.21/5.79 % SZS output start CNFRefutation
% See solution above
% 0.21/5.79 % Parsed axioms : 96
% 0.21/5.79 % Removed by relevancy pruning/SinE : 0
% 0.21/5.79 % Initial clauses : 216
% 0.21/5.79 % Removed in clause preprocessing : 2
% 0.21/5.79 % Initial clauses in saturation : 214
% 0.21/5.79 % Processed clauses : 895
% 0.21/5.79 % ...of these trivial : 21
% 0.21/5.79 % ...subsumed : 176
% 0.21/5.79 % ...remaining for further processing : 698
% 0.21/5.79 % Other redundant clauses eliminated : 101
% 0.21/5.79 % Clauses deleted for lack of memory : 0
% 0.21/5.79 % Backward-subsumed : 90
% 0.21/5.79 % Backward-rewritten : 10
% 0.21/5.79 % Generated clauses : 2218
% 0.21/5.79 % ...of the previous two non-redundant : 1908
% 0.21/5.79 % ...aggressively subsumed : 0
% 0.21/5.79 % Contextual simplify-reflections : 71
% 0.21/5.79 % Paramodulations : 2095
% 0.21/5.79 % Factorizations : 0
% 0.21/5.79 % NegExts : 0
% 0.21/5.79 % Equation resolutions : 106
% 0.21/5.79 % Disequality decompositions : 0
% 0.21/5.79 % Total rewrite steps : 1749
% 0.21/5.79 % ...of those cached : 1701
% 0.21/5.79 % Propositional unsat checks : 0
% 0.21/5.79 % Propositional check models : 0
% 0.21/5.79 % Propositional check unsatisfiable : 0
% 0.21/5.79 % Propositional clauses : 0
% 0.21/5.79 % Propositional clauses after purity: 0
% 0.21/5.79 % Propositional unsat core size : 0
% 0.21/5.79 % Propositional preprocessing time : 0.000
% 0.21/5.79 % Propositional encoding time : 0.000
% 0.21/5.79 % Propositional solver time : 0.000
% 0.21/5.79 % Success case prop preproc time : 0.000
% 0.21/5.79 % Success case prop encoding time : 0.000
% 0.21/5.79 % Success case prop solver time : 0.000
% 0.21/5.79 % Current number of processed clauses : 348
% 0.21/5.79 % Positive orientable unit clauses : 54
% 0.21/5.79 % Positive unorientable unit clauses: 0
% 0.21/5.79 % Negative unit clauses : 12
% 0.21/5.79 % Non-unit-clauses : 282
% 0.21/5.79 % Current number of unprocessed clauses: 1353
% 0.21/5.79 % ...number of literals in the above : 8534
% 0.21/5.79 % Current number of archived formulas : 0
% 0.21/5.79 % Current number of archived clauses : 327
% 0.21/5.79 % Clause-clause subsumption calls (NU) : 27175
% 0.21/5.79 % Rec. Clause-clause subsumption calls : 8576
% 0.21/5.79 % Non-unit clause-clause subsumptions : 223
% 0.21/5.79 % Unit Clause-clause subsumption calls : 1298
% 0.21/5.79 % Rewrite failures with RHS unbound : 0
% 0.21/5.79 % BW rewrite match attempts : 14
% 0.21/5.79 % BW rewrite match successes : 13
% 0.21/5.79 % Condensation attempts : 0
% 0.21/5.79 % Condensation successes : 0
% 0.21/5.79 % Termbank termtop insertions : 62400
% 0.21/5.79 % Search garbage collected termcells : 4503
% 0.21/5.79
% 0.21/5.79 % -------------------------------------------------
% 0.21/5.79 % User time : 0.172 s
% 0.21/5.79 % System time : 0.015 s
% 0.21/5.79 % Total time : 0.187 s
% 0.21/5.79 % Maximum resident set size: 4024 pages
% 0.21/5.79
% 0.21/5.79 % -------------------------------------------------
% 0.21/5.79 % User time : 0.751 s
% 0.21/5.79 % System time : 0.053 s
% 0.21/5.79 % Total time : 0.804 s
% 0.21/5.79 % Maximum resident set size: 4608 pages
% 0.21/5.79 % E exiting
%------------------------------------------------------------------------------