%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC285+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 : n003.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 02:43:46 PM UTC 2026
% Result : Theorem 0.15s 0.73s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 106 ( 19 unt; 0 def)
% Number of atoms : 420 ( 85 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 529 ( 215 ~; 215 |; 35 &)
% ( 7 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 141 ( 0 sgn 86 !; 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] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( ! [X8] :
( ssItem(X8)
=> ( ( leq(X5,X8)
| ~ memberP(X7,X8) )
& ( leq(X8,X5)
| ~ memberP(X6,X8) ) ) )
| app(app(X6,cons(X5,nil)),X7) != X1 ) ) ) )
| ~ segmentP(X4,X3)
| 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(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(ax36,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X3,X1)
| memberP(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax36) ).
fof(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( memberP(X3,X1)
| X1 = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X1
& nil = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax4,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( cons(X2,nil) = X1
& ssItem(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax53,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X2,X3)
& segmentP(X1,X2) )
=> segmentP(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax53) ).
fof(ax58,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(ax31,axiom,
! [X1] :
( ssItem(X1)
=> leq(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax31) ).
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] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( ! [X8] :
( ssItem(X8)
=> ( ( leq(X5,X8)
| ~ memberP(X7,X8) )
& ( leq(X8,X5)
| ~ memberP(X6,X8) ) ) )
| app(app(X6,cons(X5,nil)),X7) != 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] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( ! [X8] :
( ssItem(X8)
=> ( ( leq(X5,X8)
| ~ memberP(X7,X8) )
& ( leq(X8,X5)
| ~ memberP(X6,X8) ) ) )
| app(app(X6,cons(X5,nil)),X7) != X1 ) ) ) )
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_18,negated_conjecture,
( ( ~ neq(esk4_0,nil)
| singletonP(esk3_0) )
& ( ~ leq(esk8_0,esk5_0)
| ~ leq(esk5_0,esk8_0) )
& ( ~ leq(esk8_0,esk5_0)
| memberP(esk7_0,esk8_0) )
& ( memberP(esk6_0,esk8_0)
| ~ leq(esk5_0,esk8_0) )
& ( memberP(esk6_0,esk8_0)
| memberP(esk7_0,esk8_0) )
& ssItem(esk8_0)
& app(app(esk6_0,cons(esk5_0,nil)),esk7_0) = esk1_0
& ssList(esk7_0)
& ssList(esk6_0)
& ssItem(esk5_0)
& segmentP(esk4_0,esk3_0)
& esk1_0 = esk3_0
& esk2_0 = esk4_0
& ssList(esk4_0)
& ssList(esk3_0)
& ssList(esk2_0)
& ssList(esk1_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(esk6_0,cons(esk5_0,nil)),esk7_0) = esk1_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_20,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
! [X71,X72,X73] :
( app(app(X71,X72),X73) = app(X71,app(X72,X73))
| ~ ssList(X73)
| ~ ssList(X72)
| ~ ssList(X71) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
cnf(c_0_22,negated_conjecture,
app(app(esk6_0,cons(esk5_0,nil)),esk7_0) = esk3_0,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,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_24,negated_conjecture,
ssList(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
ssList(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_26,plain,
! [X69,X70] :
( cons(X70,X69) = app(cons(X70,nil),X69)
| ~ ssItem(X70)
| ~ ssList(X69) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
fof(c_0_27,plain,
! [X48,X49,X50] :
( ( ~ ssItem(X48)
| ~ ssList(X49)
| ~ ssList(X50)
| memberP(app(X49,X50),X48)
| ~ memberP(X50,X48) )
& ( ~ ssItem(X48)
| ~ ssList(X49)
| ~ ssList(X50)
| memberP(app(X49,X50),X48)
| ~ memberP(X49,X48) )
& ( ~ ssItem(X48)
| ~ ssList(X49)
| ~ ssList(X50)
| memberP(X50,X48)
| memberP(X49,X48)
| ~ memberP(app(X49,X50),X48) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])])]) ).
fof(c_0_28,plain,
! [X51,X52,X53] :
( ( ~ ssItem(X51)
| ~ ssItem(X52)
| ~ ssList(X53)
| memberP(cons(X52,X53),X51)
| ~ memberP(X53,X51) )
& ( ~ ssItem(X51)
| ~ ssItem(X52)
| ~ ssList(X53)
| memberP(cons(X52,X53),X51)
| X51 != X52 )
& ( ~ ssItem(X51)
| ~ ssItem(X52)
| ~ ssList(X53)
| memberP(X53,X51)
| X51 = X52
| ~ memberP(cons(X52,X53),X51) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])])]) ).
cnf(c_0_29,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| app(esk6_0,app(cons(esk5_0,nil),esk7_0)) = esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_30,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
ssItem(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_32,plain,
( ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| memberP(app(X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_33,plain,
! [X57,X58] :
( ssList(app(X57,X58))
| ~ ssList(X58)
| ~ ssList(X57) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
cnf(c_0_34,plain,
( ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2
| memberP(cons(X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_35,plain,
! [X59,X60,X61] :
( cons(X61,app(X60,X59)) = app(cons(X61,X60),X59)
| ~ ssItem(X61)
| ~ ssList(X60)
| ~ ssList(X59) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).
cnf(c_0_36,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ memberP(X1,X2)
| memberP(app(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| app(esk6_0,cons(esk5_0,esk7_0)) = esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_24]),c_0_31])]) ).
fof(c_0_38,plain,
! [X77,X78] :
( ssList(cons(X78,X77))
| ~ ssItem(X78)
| ~ ssList(X77) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_39,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(app(esk6_0,cons(esk5_0,nil)))
| ~ memberP(esk7_0,X1)
| memberP(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_22]),c_0_24])]) ).
cnf(c_0_40,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| memberP(cons(X1,X2),X1) ),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_43,plain,
! [X74,X75] :
( ( ~ ssList(X74)
| ~ ssList(X75)
| nil = app(X74,X75)
| nil != X74
| nil != X75 )
& ( ~ ssList(X74)
| ~ ssList(X75)
| nil != app(X74,X75)
| nil = X74 )
& ( ~ ssList(X74)
| ~ ssList(X75)
| nil != app(X74,X75)
| nil = X75 ) ),
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])])])])]) ).
fof(c_0_44,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_45,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(cons(esk5_0,nil))
| ~ ssList(cons(esk5_0,esk7_0))
| ~ memberP(esk6_0,X1)
| memberP(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_25])]) ).
cnf(c_0_46,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(cons(esk5_0,nil))
| ~ memberP(esk7_0,X1)
| memberP(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_25])]) ).
cnf(c_0_48,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_49,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(cons(esk5_0,nil))
| ~ ssList(app(cons(esk5_0,nil),esk7_0))
| ~ memberP(app(cons(esk5_0,nil),esk7_0),X1)
| memberP(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_29]),c_0_25])]) ).
cnf(c_0_50,plain,
( ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(app(cons(X1,X2),X3),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_40]) ).
cnf(c_0_51,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != app(X2,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_53,plain,
! [X26,X28] :
( ( ~ ssList(X26)
| singletonP(X26)
| cons(X28,nil) != X26
| ~ ssItem(X28) )
& ( ~ ssList(X26)
| ~ singletonP(X26)
| cons(esk11_1(X26),nil) = X26 )
& ( ~ ssList(X26)
| ~ singletonP(X26)
| ssItem(esk11_1(X26)) ) ),
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,
! [X54] :
( ~ memberP(nil,X54)
| ~ ssItem(X54) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])]) ).
cnf(c_0_55,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(cons(esk5_0,nil))
| ~ memberP(esk6_0,X1)
| memberP(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_24]),c_0_31])]) ).
cnf(c_0_56,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk7_0,X1)
| memberP(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_46]),c_0_48]),c_0_31])]) ).
cnf(c_0_57,negated_conjecture,
( memberP(esk6_0,esk8_0)
| memberP(esk7_0,esk8_0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_58,negated_conjecture,
ssItem(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_59,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| ~ ssList(app(cons(esk5_0,nil),esk7_0))
| memberP(esk3_0,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_31]),c_0_48]),c_0_24])]) ).
cnf(c_0_60,negated_conjecture,
( ~ ssList(app(esk6_0,cons(esk5_0,nil)))
| esk3_0 != nil
| esk7_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_22]),c_0_24])]) ).
cnf(c_0_61,negated_conjecture,
( ~ ssList(app(esk6_0,cons(esk5_0,nil)))
| esk3_0 != nil
| app(esk6_0,cons(esk5_0,nil)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_22]),c_0_24])]) ).
cnf(c_0_62,plain,
( ~ ssItem(X3)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X3)
| memberP(X2,X3)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_63,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| cons(esk11_1(X1),nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_64,plain,
( ~ ssList(X1)
| ~ singletonP(X1)
| ssItem(esk11_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_65,plain,
( ~ memberP(nil,X1)
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_66,negated_conjecture,
( ~ ssItem(X1)
| ~ memberP(esk6_0,X1)
| memberP(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_46]),c_0_48]),c_0_31])]) ).
cnf(c_0_67,negated_conjecture,
( memberP(esk3_0,esk8_0)
| memberP(esk6_0,esk8_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58])]) ).
cnf(c_0_68,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| memberP(esk3_0,esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_40]),c_0_24])]) ).
fof(c_0_69,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_70,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| esk3_0 != nil
| esk7_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_40]),c_0_25])]) ).
cnf(c_0_71,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| esk3_0 != nil
| app(esk6_0,cons(esk5_0,nil)) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_40]),c_0_25])]) ).
fof(c_0_72,plain,
! [X91,X92,X93] :
( segmentP(X91,X93)
| ~ segmentP(X92,X93)
| ~ segmentP(X91,X92)
| ~ ssList(X93)
| ~ ssList(X92)
| ~ ssList(X91) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax53])])])]) ).
cnf(c_0_73,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| ~ singletonP(X1)
| esk11_1(X1) = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_48])]),c_0_64]),c_0_65]) ).
cnf(c_0_74,negated_conjecture,
memberP(esk3_0,esk8_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_58])]) ).
cnf(c_0_75,negated_conjecture,
ssList(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_76,negated_conjecture,
memberP(esk3_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_46]),c_0_48]),c_0_31])]) ).
fof(c_0_77,plain,
! [X19,X20] :
( ( ~ ssList(X19)
| ~ ssList(X20)
| neq(X19,X20)
| X19 = X20 )
& ( ~ ssList(X19)
| ~ ssList(X20)
| X19 != X20
| ~ neq(X19,X20) ) ),
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_69])])])])]) ).
cnf(c_0_78,negated_conjecture,
( esk3_0 != nil
| esk7_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_46]),c_0_48]),c_0_31])]) ).
cnf(c_0_79,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| esk3_0 != nil
| esk6_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_71]),c_0_25])]) ).
fof(c_0_80,plain,
! [X102] :
( ( ~ ssList(X102)
| segmentP(nil,X102)
| nil != X102 )
& ( ~ ssList(X102)
| nil = X102
| ~ segmentP(nil,X102) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax58])])])]) ).
cnf(c_0_81,plain,
( ~ segmentP(X2,X3)
| ~ segmentP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_82,negated_conjecture,
segmentP(esk4_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_83,negated_conjecture,
ssList(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_84,negated_conjecture,
( ~ singletonP(esk3_0)
| esk11_1(esk3_0) = esk8_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]),c_0_58])]) ).
cnf(c_0_85,negated_conjecture,
( ~ singletonP(esk3_0)
| esk11_1(esk3_0) = esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_76]),c_0_75]),c_0_31])]) ).
cnf(c_0_86,negated_conjecture,
( ~ neq(esk4_0,nil)
| singletonP(esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_87,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_88,negated_conjecture,
( esk3_0 != nil
| memberP(nil,esk8_0)
| memberP(esk6_0,esk8_0) ),
inference(spm,[status(thm)],[c_0_57,c_0_78]) ).
cnf(c_0_89,negated_conjecture,
( esk3_0 != nil
| esk6_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_46]),c_0_48]),c_0_31])]) ).
cnf(c_0_90,plain,
( ~ ssList(X1)
| ~ segmentP(nil,X1)
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_91,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(X1,esk4_0)
| segmentP(X1,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_75]),c_0_83])]) ).
cnf(c_0_92,negated_conjecture,
( ~ singletonP(esk3_0)
| esk5_0 = esk8_0 ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_93,negated_conjecture,
( singletonP(esk3_0)
| esk4_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_48]),c_0_83])]) ).
cnf(c_0_94,plain,
( ~ ssList(X1)
| nil != X1
| segmentP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_95,negated_conjecture,
( esk3_0 != nil
| memberP(nil,esk8_0) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_96,negated_conjecture,
( ~ segmentP(nil,esk4_0)
| esk3_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_75]),c_0_48])]) ).
cnf(c_0_97,negated_conjecture,
( esk5_0 = esk8_0
| esk4_0 = nil ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_98,plain,
segmentP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_94]),c_0_48])]) ).
cnf(c_0_99,negated_conjecture,
esk3_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_95]),c_0_58])]) ).
cnf(c_0_100,negated_conjecture,
( ~ leq(esk8_0,esk5_0)
| ~ leq(esk5_0,esk8_0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_101,negated_conjecture,
esk5_0 = esk8_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98])]),c_0_99]) ).
fof(c_0_102,plain,
! [X34] :
( leq(X34,X34)
| ~ ssItem(X34) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax31])])]) ).
cnf(c_0_103,negated_conjecture,
~ leq(esk8_0,esk8_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101]),c_0_101])]) ).
cnf(c_0_104,plain,
( ~ ssItem(X1)
| leq(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_105,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_58])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC285+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.53 % Computer : n003.cluster.edu
% 0.11/0.53 % Model : x86_64 x86_64
% 0.11/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.53 % Memory : 8046.5625MB
% 0.11/0.53 % OS : Linux 6.8.0-71-generic
% 0.11/0.53 % CPULimit : 300
% 0.11/0.53 % WCLimit : 300
% 0.11/0.53 % DateTime : Mon Sep 21 08:13:47 UTC 2026
% 0.11/0.53 % CPUTime :
% 0.11/0.53 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.58 Running first-order theorem proving
% 0.11/0.58 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
% 0.15/0.73 % Version: 3.5.1
% 0.15/0.73 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.73 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.73 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.73 % Starting sh5l with 300s (1) cores
% 0.15/0.73 % new_bool_3 with pid 3828062 completed with status 0
% 0.15/0.73 % Result found by new_bool_3
% 0.15/0.73 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.73 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.73 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.73 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.73 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.15/0.73 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.73 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.73 % SubtermCWHack with pid 3828065 completed with status 0
% 0.15/0.73 % Result found by SubtermCWHack
% 0.15/0.73 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.73 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.73 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.73 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.73 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.15/0.73 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.73 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.73 % Preprocessing time : 0.002 s
% 0.15/0.73
% 0.15/0.73 % Proof found!
% 0.15/0.73 % SZS status Theorem
% 0.15/0.73 % SZS output start CNFRefutation
% See solution above
% 0.15/0.73 % Parsed axioms : 96
% 0.15/0.73 % Removed by relevancy pruning/SinE : 55
% 0.15/0.73 % Initial clauses : 81
% 0.15/0.73 % Removed in clause preprocessing : 0
% 0.15/0.73 % Initial clauses in saturation : 81
% 0.15/0.73 % Processed clauses : 1351
% 0.15/0.73 % ...of these trivial : 3
% 0.15/0.73 % ...subsumed : 887
% 0.15/0.73 % ...remaining for further processing : 461
% 0.15/0.73 % Other redundant clauses eliminated : 76
% 0.15/0.73 % Clauses deleted for lack of memory : 0
% 0.15/0.73 % Backward-subsumed : 62
% 0.15/0.73 % Backward-rewritten : 39
% 0.15/0.73 % Generated clauses : 5123
% 0.15/0.73 % ...of the previous two non-redundant : 4250
% 0.15/0.73 % ...aggressively subsumed : 0
% 0.15/0.73 % Contextual simplify-reflections : 108
% 0.15/0.73 % Paramodulations : 5032
% 0.15/0.73 % Factorizations : 0
% 0.15/0.73 % NegExts : 0
% 0.15/0.73 % Equation resolutions : 92
% 0.15/0.73 % Disequality decompositions : 0
% 0.15/0.73 % Total rewrite steps : 4516
% 0.15/0.73 % ...of those cached : 4497
% 0.15/0.73 % Propositional unsat checks : 0
% 0.15/0.73 % Propositional check models : 0
% 0.15/0.73 % Propositional check unsatisfiable : 0
% 0.15/0.73 % Propositional clauses : 0
% 0.15/0.73 % Propositional clauses after purity: 0
% 0.15/0.73 % Propositional unsat core size : 0
% 0.15/0.73 % Propositional preprocessing time : 0.000
% 0.15/0.73 % Propositional encoding time : 0.000
% 0.15/0.73 % Propositional solver time : 0.000
% 0.15/0.73 % Success case prop preproc time : 0.000
% 0.15/0.73 % Success case prop encoding time : 0.000
% 0.15/0.73 % Success case prop solver time : 0.000
% 0.15/0.73 % Current number of processed clauses : 351
% 0.15/0.73 % Positive orientable unit clauses : 19
% 0.15/0.73 % Positive unorientable unit clauses: 0
% 0.15/0.73 % Negative unit clauses : 6
% 0.15/0.73 % Non-unit-clauses : 326
% 0.15/0.73 % Current number of unprocessed clauses: 2878
% 0.15/0.73 % ...number of literals in the above : 15968
% 0.15/0.73 % Current number of archived formulas : 0
% 0.15/0.73 % Current number of archived clauses : 101
% 0.15/0.73 % Clause-clause subsumption calls (NU) : 21966
% 0.15/0.73 % Rec. Clause-clause subsumption calls : 8674
% 0.15/0.73 % Non-unit clause-clause subsumptions : 938
% 0.15/0.73 % Unit Clause-clause subsumption calls : 1031
% 0.15/0.73 % Rewrite failures with RHS unbound : 0
% 0.15/0.73 % BW rewrite match attempts : 9
% 0.15/0.73 % BW rewrite match successes : 9
% 0.15/0.73 % Condensation attempts : 0
% 0.15/0.73 % Condensation successes : 0
% 0.15/0.73 % Termbank termtop insertions : 95079
% 0.15/0.73 % Search garbage collected termcells : 2095
% 0.15/0.73
% 0.15/0.73 % -------------------------------------------------
% 0.15/0.73 % User time : 0.120 s
% 0.15/0.73 % System time : 0.011 s
% 0.15/0.73 % Total time : 0.131 s
% 0.15/0.73 % Maximum resident set size: 3760 pages
% 0.15/0.73
% 0.15/0.73 % -------------------------------------------------
% 0.15/0.73 % User time : 0.125 s
% 0.15/0.73 % System time : 0.015 s
% 0.15/0.73 % Total time : 0.140 s
% 0.15/0.73 % Maximum resident set size: 4608 pages
% 0.15/0.73 % E exiting
%------------------------------------------------------------------------------