%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC304+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 02:43:51 PM UTC 2026
% Result : Theorem 0.92s 0.72s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 24 unt; 0 def)
% Number of atoms : 316 ( 71 equ)
% Maximal formula atoms : 33 ( 5 avg)
% Number of connectives : 380 ( 124 ~; 121 |; 70 &)
% ( 3 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 12 con; 0-2 aty)
% Number of variables : 133 ( 0 sgn 87 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X3
& nil != X4 )
| ! [X15] :
( ssItem(X15)
=> ! [X16] :
( ssItem(X16)
=> ! [X17] :
( ssList(X17)
=> ! [X18] :
( ssList(X18)
=> ! [X19] :
( ssList(X19)
=> ( ~ lt(X16,X15)
| app(app(app(app(X17,cons(X15,nil)),X18),cons(X16,nil)),X19) != X1 ) ) ) ) ) )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ? [X11] :
( ? [X12] :
( ? [X13] :
( ? [X14] :
( leq(X13,X11)
& app(X14,cons(X13,nil)) = X3
& ssList(X14) )
& ssItem(X13) )
& app(cons(X11,nil),X12) = X6
& ssList(X12) )
& ssItem(X11) )
| ? [X7] :
( ? [X8] :
( ? [X9] :
( ? [X10] :
( leq(X7,X9)
& app(cons(X9,nil),X10) = X3
& ssList(X10) )
& ssItem(X9) )
& app(X8,cons(X7,nil)) = X5
& ssList(X8) )
& ssItem(X7) )
| ~ totalorderedP(X3)
| app(app(X5,X3),X6) != X4 ) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax93,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
<=> ( leq(X1,X2)
& X1 != X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax93) ).
fof(ax11,axiom,
! [X1] :
( ssList(X1)
=> ( totalorderedP(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
=> leq(X2,X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax11) ).
fof(ax33,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
=> ~ lt(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax33) ).
fof(ax29,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( leq(X2,X1)
& leq(X1,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax29) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X3
& nil != X4 )
| ! [X15] :
( ssItem(X15)
=> ! [X16] :
( ssItem(X16)
=> ! [X17] :
( ssList(X17)
=> ! [X18] :
( ssList(X18)
=> ! [X19] :
( ssList(X19)
=> ( ~ lt(X16,X15)
| app(app(app(app(X17,cons(X15,nil)),X18),cons(X16,nil)),X19) != X1 ) ) ) ) ) )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ? [X11] :
( ? [X12] :
( ? [X13] :
( ? [X14] :
( leq(X13,X11)
& app(X14,cons(X13,nil)) = X3
& ssList(X14) )
& ssItem(X13) )
& app(cons(X11,nil),X12) = X6
& ssList(X12) )
& ssItem(X11) )
| ? [X7] :
( ? [X8] :
( ? [X9] :
( ? [X10] :
( leq(X7,X9)
& app(cons(X9,nil),X10) = X3
& ssList(X10) )
& ssItem(X9) )
& app(X8,cons(X7,nil)) = X5
& ssList(X8) )
& ssItem(X7) )
| ~ totalorderedP(X3)
| app(app(X5,X3),X6) != X4 ) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( nil = X3
& nil != X4 )
| ! [X15] :
( ssItem(X15)
=> ! [X16] :
( ssItem(X16)
=> ! [X17] :
( ssList(X17)
=> ! [X18] :
( ssList(X18)
=> ! [X19] :
( ssList(X19)
=> ( ~ lt(X16,X15)
| app(app(app(app(X17,cons(X15,nil)),X18),cons(X16,nil)),X19) != X1 ) ) ) ) ) )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ? [X11] :
( ? [X12] :
( ? [X13] :
( ? [X14] :
( leq(X13,X11)
& app(X14,cons(X13,nil)) = X3
& ssList(X14) )
& ssItem(X13) )
& app(cons(X11,nil),X12) = X6
& ssList(X12) )
& ssItem(X11) )
| ? [X7] :
( ? [X8] :
( ? [X9] :
( ? [X10] :
( leq(X7,X9)
& app(cons(X9,nil),X10) = X3
& ssList(X10) )
& ssItem(X9) )
& app(X8,cons(X7,nil)) = X5
& ssList(X8) )
& ssItem(X7) )
| ~ totalorderedP(X3)
| app(app(X5,X3),X6) != X4 ) ) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_12,negated_conjecture,
! [X270,X271,X272,X273,X274,X275,X276,X277] :
( ( nil != esk50_0
| nil = esk51_0 )
& lt(esk55_0,esk54_0)
& app(app(app(app(esk56_0,cons(esk54_0,nil)),esk57_0),cons(esk55_0,nil)),esk58_0) = esk48_0
& ssList(esk58_0)
& ssList(esk57_0)
& ssList(esk56_0)
& ssItem(esk55_0)
& ssItem(esk54_0)
& ( ~ leq(X276,X274)
| app(X277,cons(X276,nil)) != esk50_0
| ~ ssList(X277)
| ~ ssItem(X276)
| app(cons(X274,nil),X275) != esk53_0
| ~ ssList(X275)
| ~ ssItem(X274) )
& ( ~ leq(X270,X272)
| app(cons(X272,nil),X273) != esk50_0
| ~ ssList(X273)
| ~ ssItem(X272)
| app(X271,cons(X270,nil)) != esk52_0
| ~ ssList(X271)
| ~ ssItem(X270) )
& totalorderedP(esk50_0)
& app(app(esk52_0,esk50_0),esk53_0) = esk51_0
& ssList(esk53_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(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_11])])])])]) ).
cnf(c_0_13,negated_conjecture,
app(app(app(app(esk56_0,cons(esk54_0,nil)),esk57_0),cons(esk55_0,nil)),esk58_0) = esk48_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_14,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X235,X236,X237] :
( app(app(X235,X236),X237) = app(X235,app(X236,X237))
| ~ ssList(X237)
| ~ ssList(X236)
| ~ ssList(X235) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
cnf(c_0_16,negated_conjecture,
app(app(app(app(esk56_0,cons(esk54_0,nil)),esk57_0),cons(esk55_0,nil)),esk58_0) = esk50_0,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,negated_conjecture,
ssList(esk57_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
ssList(esk56_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_20,plain,
! [X124,X125] :
( ssList(cons(X125,X124))
| ~ ssItem(X125)
| ~ ssList(X124) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_21,negated_conjecture,
( ~ ssList(cons(esk54_0,nil))
| app(app(app(esk56_0,app(cons(esk54_0,nil),esk57_0)),cons(esk55_0,nil)),esk58_0) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19])]) ).
cnf(c_0_22,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_24,negated_conjecture,
ssItem(esk54_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_25,plain,
! [X233,X234] :
( cons(X234,X233) = app(cons(X234,nil),X233)
| ~ ssItem(X234)
| ~ ssList(X233) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_26,negated_conjecture,
app(app(app(esk56_0,app(cons(esk54_0,nil),esk57_0)),cons(esk55_0,nil)),esk58_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]) ).
cnf(c_0_27,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_28,negated_conjecture,
app(app(app(esk56_0,cons(esk54_0,esk57_0)),cons(esk55_0,nil)),esk58_0) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_18]),c_0_24])]) ).
cnf(c_0_29,negated_conjecture,
ssList(esk58_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,negated_conjecture,
( ~ ssList(cons(esk55_0,nil))
| ~ ssList(app(esk56_0,cons(esk54_0,esk57_0)))
| app(app(esk56_0,cons(esk54_0,esk57_0)),app(cons(esk55_0,nil),esk58_0)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_28]),c_0_29])]) ).
cnf(c_0_31,negated_conjecture,
ssItem(esk55_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_32,plain,
! [X143,X144] :
( ssList(app(X143,X144))
| ~ ssList(X144)
| ~ ssList(X143) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
cnf(c_0_33,negated_conjecture,
( ~ ssList(app(esk56_0,cons(esk54_0,esk57_0)))
| app(app(esk56_0,cons(esk54_0,esk57_0)),app(cons(esk55_0,nil),esk58_0)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_22]),c_0_23]),c_0_31])]) ).
cnf(c_0_34,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_35,plain,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
<=> ( leq(X1,X2)
& X1 != X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[ax93]) ).
cnf(c_0_36,negated_conjecture,
( ~ ssList(cons(esk54_0,esk57_0))
| app(app(esk56_0,cons(esk54_0,esk57_0)),app(cons(esk55_0,nil),esk58_0)) = esk50_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_19])]) ).
fof(c_0_37,plain,
! [X257,X258] :
( ( ~ ssItem(X257)
| ~ ssItem(X258)
| lt(X257,X258)
| ~ leq(X257,X258)
| X257 = X258 )
& ( ~ ssItem(X257)
| ~ ssItem(X258)
| ~ lt(X257,X258)
| leq(X257,X258) )
& ( ~ ssItem(X257)
| ~ ssItem(X258)
| ~ lt(X257,X258)
| X257 != X258 ) ),
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_35])])])])]) ).
fof(c_0_38,plain,
! [X80,X81,X82,X83,X84,X85] :
( ( ~ ssList(X80)
| totalorderedP(X80)
| ~ leq(esk25_1(X80),esk26_1(X80)) )
& ( ~ ssList(X80)
| totalorderedP(X80)
| app(app(esk27_1(X80),cons(esk25_1(X80),esk28_1(X80))),cons(esk26_1(X80),esk29_1(X80))) = X80 )
& ( ~ ssList(X80)
| totalorderedP(X80)
| ssList(esk29_1(X80)) )
& ( ~ ssList(X80)
| totalorderedP(X80)
| ssList(esk28_1(X80)) )
& ( ~ ssList(X80)
| totalorderedP(X80)
| ssList(esk27_1(X80)) )
& ( ~ ssList(X80)
| totalorderedP(X80)
| ssItem(esk26_1(X80)) )
& ( ~ ssList(X80)
| totalorderedP(X80)
| ssItem(esk25_1(X80)) )
& ( ~ ssList(X80)
| leq(X81,X82)
| app(app(X83,cons(X81,X84)),cons(X82,X85)) != X80
| ~ ssList(X85)
| ~ ssList(X84)
| ~ ssList(X83)
| ~ ssItem(X82)
| ~ ssItem(X81)
| ~ totalorderedP(X80) ) ),
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)],[ax11])])])])])]) ).
cnf(c_0_39,negated_conjecture,
app(app(esk56_0,cons(esk54_0,esk57_0)),app(cons(esk55_0,nil),esk58_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_22]),c_0_18]),c_0_24])]) ).
fof(c_0_40,plain,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( lt(X1,X2)
=> ~ lt(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[ax33]) ).
fof(c_0_41,plain,
! [X149,X150] :
( X149 = X150
| ~ leq(X150,X149)
| ~ leq(X149,X150)
| ~ ssItem(X150)
| ~ ssItem(X149) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax29])])])]) ).
cnf(c_0_42,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ lt(X1,X2)
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,negated_conjecture,
lt(esk55_0,esk54_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_44,plain,
( ~ ssList(X1)
| app(app(X4,cons(X2,X5)),cons(X3,X6)) != X1
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ totalorderedP(X1)
| leq(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,negated_conjecture,
app(app(esk56_0,cons(esk54_0,esk57_0)),cons(esk55_0,esk58_0)) = esk50_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_27]),c_0_29]),c_0_31])]) ).
cnf(c_0_46,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_47,plain,
! [X157,X158] :
( ~ lt(X158,X157)
| ~ lt(X157,X158)
| ~ ssItem(X158)
| ~ ssItem(X157) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])]) ).
cnf(c_0_48,plain,
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,negated_conjecture,
leq(esk55_0,esk54_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_24]),c_0_31])]) ).
cnf(c_0_50,negated_conjecture,
( ~ ssList(X1)
| ~ totalorderedP(X1)
| esk50_0 != X1
| leq(esk54_0,esk55_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_44,c_0_45]),c_0_29]),c_0_18]),c_0_19]),c_0_31]),c_0_24])]) ).
cnf(c_0_51,negated_conjecture,
totalorderedP(esk50_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_52,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_46,c_0_14]) ).
cnf(c_0_53,plain,
( ~ lt(X2,X1)
| ~ lt(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,negated_conjecture,
( ~ leq(esk54_0,esk55_0)
| esk55_0 = esk54_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_31]),c_0_24])]) ).
cnf(c_0_55,negated_conjecture,
leq(esk54_0,esk55_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_50]),c_0_51]),c_0_52])]) ).
cnf(c_0_56,negated_conjecture,
~ lt(esk54_0,esk55_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_43]),c_0_31]),c_0_24])]) ).
cnf(c_0_57,negated_conjecture,
esk55_0 = esk54_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
cnf(c_0_58,negated_conjecture,
~ lt(esk54_0,esk54_0),
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_57]),c_0_58]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC304+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 08:14:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.92/0.72 % Version: 3.5.1
% 0.92/0.72 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.92/0.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.92/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.92/0.72 % Starting new_bool_3 with 300s (1) cores
% 0.92/0.72 % Starting new_bool_1 with 300s (1) cores
% 0.92/0.72 % Starting sh5l with 300s (1) cores
% 0.92/0.72 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 444518 completed with status 0
% 0.92/0.72 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.92/0.72 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.92/0.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.92/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.92/0.72 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.92/0.72 % No SInE strategy applied
% 0.92/0.72 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.92/0.72 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.92/0.72 % Starting SubtermCWHack with 136s (1) cores
% 0.92/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.92/0.72 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.92/0.72 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 0.92/0.72 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 0.92/0.72 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with pid 444527 completed with status 0
% 0.92/0.72 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d
% 0.92/0.72 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.92/0.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.92/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.92/0.72 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.92/0.72 % No SInE strategy applied
% 0.92/0.72 % Search class: FGHSF-FSLM21-MFFFFFNN
% 0.92/0.72 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.92/0.72 % Starting SubtermCWHack with 136s (1) cores
% 0.92/0.72 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.92/0.72 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4d with 136s (1) cores
% 0.92/0.72 % Preprocessing time : 0.006 s
% 0.92/0.72
% 0.92/0.72 % Proof found!
% 0.92/0.72 % SZS status Theorem
% 0.92/0.72 % SZS output start CNFRefutation
% See solution above
% 0.92/0.72 % Parsed axioms : 96
% 0.92/0.72 % Removed by relevancy pruning/SinE : 0
% 0.92/0.72 % Initial clauses : 210
% 0.92/0.72 % Removed in clause preprocessing : 2
% 0.92/0.72 % Initial clauses in saturation : 208
% 0.92/0.72 % Processed clauses : 576
% 0.92/0.72 % ...of these trivial : 29
% 0.92/0.72 % ...subsumed : 15
% 0.92/0.72 % ...remaining for further processing : 531
% 0.92/0.72 % Other redundant clauses eliminated : 63
% 0.92/0.72 % Clauses deleted for lack of memory : 0
% 0.92/0.72 % Backward-subsumed : 27
% 0.92/0.72 % Backward-rewritten : 87
% 0.92/0.72 % Generated clauses : 1969
% 0.92/0.72 % ...of the previous two non-redundant : 1708
% 0.92/0.72 % ...aggressively subsumed : 0
% 0.92/0.72 % Contextual simplify-reflections : 13
% 0.92/0.72 % Paramodulations : 1882
% 0.92/0.72 % Factorizations : 0
% 0.92/0.72 % NegExts : 0
% 0.92/0.72 % Equation resolutions : 87
% 0.92/0.72 % Disequality decompositions : 0
% 0.92/0.72 % Total rewrite steps : 1901
% 0.92/0.72 % ...of those cached : 1820
% 0.92/0.72 % Propositional unsat checks : 0
% 0.92/0.72 % Propositional check models : 0
% 0.92/0.72 % Propositional check unsatisfiable : 0
% 0.92/0.72 % Propositional clauses : 0
% 0.92/0.72 % Propositional clauses after purity: 0
% 0.92/0.72 % Propositional unsat core size : 0
% 0.92/0.72 % Propositional preprocessing time : 0.000
% 0.92/0.72 % Propositional encoding time : 0.000
% 0.92/0.72 % Propositional solver time : 0.000
% 0.92/0.72 % Success case prop preproc time : 0.000
% 0.92/0.72 % Success case prop encoding time : 0.000
% 0.92/0.72 % Success case prop solver time : 0.000
% 0.92/0.72 % Current number of processed clauses : 411
% 0.92/0.72 % Positive orientable unit clauses : 94
% 0.92/0.72 % Positive unorientable unit clauses: 0
% 0.92/0.72 % Negative unit clauses : 3
% 0.92/0.72 % Non-unit-clauses : 314
% 0.92/0.72 % Current number of unprocessed clauses: 1331
% 0.92/0.72 % ...number of literals in the above : 7062
% 0.92/0.72 % Current number of archived formulas : 0
% 0.92/0.72 % Current number of archived clauses : 114
% 0.92/0.72 % Clause-clause subsumption calls (NU) : 23659
% 0.92/0.72 % Rec. Clause-clause subsumption calls : 14841
% 0.92/0.72 % Non-unit clause-clause subsumptions : 54
% 0.92/0.72 % Unit Clause-clause subsumption calls : 1289
% 0.92/0.72 % Rewrite failures with RHS unbound : 0
% 0.92/0.72 % BW rewrite match attempts : 229
% 0.92/0.72 % BW rewrite match successes : 44
% 0.92/0.72 % Condensation attempts : 0
% 0.92/0.72 % Condensation successes : 0
% 0.92/0.72 % Termbank termtop insertions : 64280
% 0.92/0.72 % Search garbage collected termcells : 4571
% 0.92/0.72
% 0.92/0.72 % -------------------------------------------------
% 0.92/0.72 % User time : 0.145 s
% 0.92/0.72 % System time : 0.013 s
% 0.92/0.72 % Total time : 0.158 s
% 0.92/0.72 % Maximum resident set size: 4236 pages
% 0.92/0.72
% 0.92/0.72 % -------------------------------------------------
% 0.92/0.72 % User time : 0.626 s
% 0.92/0.72 % System time : 0.050 s
% 0.92/0.72 % Total time : 0.676 s
% 0.92/0.72 % Maximum resident set size: 4608 pages
% 0.92/0.72 % E exiting
%------------------------------------------------------------------------------