%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC073+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 : n007.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 02:42:52 PM UTC 2026
% Result : Theorem 246.34s 32.21s
% Output : CNFRefutation 246.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 98 ( 16 unt; 0 def)
% Number of atoms : 393 ( 130 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 474 ( 179 ~; 185 |; 65 &)
% ( 4 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 118 ( 0 sgn 60 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ? [X6] :
( ? [X7] :
( ? [X8] :
( neq(nil,X3)
& ? [X9] :
( neq(nil,X3)
& hd(X3) = X9
& cons(X9,nil) = X8
& ssItem(X9) )
& app(X7,X8) = X6
& tl(X3) = X7
& ssList(X8) )
& ssList(X7) )
& X4 != X6
& ssList(X6) )
| ~ neq(X3,nil) )
& neq(X4,nil) )
| ( nil = X1
& nil = X2 )
| ( nil = X4
& nil != X3 )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ? [X4] :
( app(app(X3,X2),X4) = X1
& ssList(X4) )
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
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(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
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(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax58,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ? [X6] :
( ? [X7] :
( ? [X8] :
( neq(nil,X3)
& ? [X9] :
( neq(nil,X3)
& hd(X3) = X9
& cons(X9,nil) = X8
& ssItem(X9) )
& app(X7,X8) = X6
& tl(X3) = X7
& ssList(X8) )
& ssList(X7) )
& X4 != X6
& ssList(X6) )
| ~ neq(X3,nil) )
& neq(X4,nil) )
| ( nil = X1
& nil = X2 )
| ( nil = X4
& nil != X3 )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| 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)
=> ( ( ( ? [X6] :
( ? [X7] :
( ? [X8] :
( neq(nil,X3)
& ? [X9] :
( neq(nil,X3)
& hd(X3) = X9
& cons(X9,nil) = X8
& ssItem(X9) )
& app(X7,X8) = X6
& tl(X3) = X7
& ssList(X8) )
& ssList(X7) )
& X4 != X6
& ssList(X6) )
| ~ neq(X3,nil) )
& neq(X4,nil) )
| ( nil = X1
& nil = X2 )
| ( nil = X4
& nil != X3 )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_17,plain,
! [X75,X76,X79,X80] :
( ( ~ ssList(X75)
| ~ ssList(X76)
| segmentP(X75,X76)
| app(app(X79,X76),X80) != X75
| ~ ssList(X80)
| ~ ssList(X79) )
& ( ~ ssList(X75)
| ~ ssList(X76)
| ~ segmentP(X75,X76)
| app(app(esk11_2(X75,X76),X76),esk12_2(X75,X76)) = X75 )
& ( ~ ssList(X75)
| ~ ssList(X76)
| ~ segmentP(X75,X76)
| ssList(esk12_2(X75,X76)) )
& ( ~ ssList(X75)
| ~ ssList(X76)
| ~ segmentP(X75,X76)
| ssList(esk11_2(X75,X76)) ) ),
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)],[ax7])])])])])]) ).
fof(c_0_18,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_19,negated_conjecture,
! [X14,X15,X16,X17,X18] :
( ( ~ neq(esk4_0,nil)
| ~ neq(nil,esk3_0)
| ~ neq(nil,esk3_0)
| hd(esk3_0) != X18
| cons(X18,nil) != X17
| ~ ssItem(X18)
| app(X16,X17) != X15
| tl(esk3_0) != X16
| ~ ssList(X17)
| ~ ssList(X16)
| esk4_0 = X15
| ~ ssList(X15) )
& ( ~ neq(esk4_0,nil)
| neq(esk3_0,nil) )
& ( nil != esk1_0
| nil != esk2_0 )
& ( nil != esk4_0
| nil = esk3_0 )
& ( ~ segmentP(esk1_0,X14)
| ~ segmentP(esk2_0,X14)
| ~ neq(X14,nil)
| ~ ssList(X14) )
& 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(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])])]) ).
fof(c_0_20,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
cnf(c_0_21,plain,
( ~ ssList(X4)
| ~ ssList(X3)
| app(app(X1,X3),X2) != X4
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,plain,
! [X67] :
( app(X67,nil) = X67
| ~ ssList(X67) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
fof(c_0_23,plain,
! [X53,X54] :
( ssList(app(X53,X54))
| ~ ssList(X54)
| ~ ssList(X53) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_24,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
fof(c_0_25,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
fof(c_0_26,plain,
! [X21,X22] :
( ( ~ ssList(X21)
| ~ ssList(X22)
| neq(X21,X22)
| X21 = X22 )
& ( ~ ssList(X21)
| ~ ssList(X22)
| X21 != X22
| ~ neq(X21,X22) ) ),
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_27,negated_conjecture,
( nil != esk1_0
| nil != esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_30,plain,
! [X68] :
( ssList(tl(X68))
| nil = X68
| ~ ssList(X68) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
cnf(c_0_31,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_32,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(app(app(X1,X2),X3))
| segmentP(app(app(X1,X2),X3),X2) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_33,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_34,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_35,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_36,plain,
! [X49,X50] :
( cons(X50,X49) = app(cons(X50,nil),X49)
| ~ ssItem(X50)
| ~ ssList(X49) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
fof(c_0_37,plain,
! [X35] :
( cons(hd(X35),tl(X35)) = X35
| nil = X35
| ~ ssList(X35) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
fof(c_0_38,plain,
! [X28] :
( ssItem(hd(X28))
| nil = X28
| ~ ssList(X28) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
cnf(c_0_39,negated_conjecture,
( ~ neq(esk4_0,nil)
| ~ neq(nil,esk3_0)
| ~ neq(nil,esk3_0)
| hd(esk3_0) != X4
| cons(X4,nil) != X3
| ~ ssItem(X4)
| app(X2,X3) != X1
| tl(esk3_0) != X2
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| esk4_0 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_40,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_41,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_42,negated_conjecture,
( nil != esk4_0
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_43,negated_conjecture,
( esk4_0 != nil
| esk3_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_44,plain,
( ~ ssList(X1)
| ssList(tl(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_45,negated_conjecture,
ssList(esk3_0),
inference(rw,[status(thm)],[c_0_31,c_0_28]) ).
cnf(c_0_46,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| segmentP(app(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_47,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_48,plain,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_49,plain,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_50,plain,
! [X55] :
( app(nil,X55) = X55
| ~ ssList(X55) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_51,negated_conjecture,
( ~ neq(esk4_0,nil)
| ~ neq(nil,esk3_0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X4)
| cons(X4,nil) != X3
| app(X2,X3) != X1
| tl(esk3_0) != X2
| hd(esk3_0) != X4
| esk4_0 = X1 ),
inference(cn,[status(thm)],[c_0_39]) ).
cnf(c_0_52,plain,
( ~ ssList(X1)
| neq(X1,nil)
| X1 = nil ),
inference(spm,[status(thm)],[c_0_40,c_0_34]) ).
cnf(c_0_53,negated_conjecture,
ssList(esk4_0),
inference(rw,[status(thm)],[c_0_41,c_0_29]) ).
cnf(c_0_54,negated_conjecture,
esk4_0 != nil,
inference(csr,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_55,negated_conjecture,
( ~ segmentP(esk1_0,X1)
| ~ segmentP(esk2_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_56,negated_conjecture,
( ssList(tl(esk3_0))
| esk3_0 = nil ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_57,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| segmentP(cons(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_58,negated_conjecture,
( esk3_0 = nil
| cons(hd(esk3_0),tl(esk3_0)) = esk3_0 ),
inference(spm,[status(thm)],[c_0_48,c_0_45]) ).
cnf(c_0_59,negated_conjecture,
( ssItem(hd(esk3_0))
| esk3_0 = nil ),
inference(spm,[status(thm)],[c_0_49,c_0_45]) ).
fof(c_0_60,plain,
! [X38,X39] :
( ssList(cons(X39,X38))
| ~ ssItem(X39)
| ~ ssList(X38) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_61,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_62,negated_conjecture,
( ~ ssItem(hd(esk3_0))
| ~ neq(esk4_0,nil)
| ~ neq(nil,esk3_0)
| ~ ssList(tl(esk3_0))
| ~ ssList(cons(hd(esk3_0),nil))
| app(tl(esk3_0),cons(hd(esk3_0),nil)) = esk4_0 ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_51])])])]),c_0_35]) ).
cnf(c_0_63,negated_conjecture,
neq(esk4_0,nil),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_64,negated_conjecture,
( ~ neq(X1,nil)
| ~ ssList(X1)
| ~ segmentP(esk4_0,X1)
| ~ segmentP(esk3_0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_28]),c_0_29]) ).
cnf(c_0_65,negated_conjecture,
( neq(tl(esk3_0),nil)
| esk3_0 = nil
| tl(esk3_0) = nil ),
inference(spm,[status(thm)],[c_0_52,c_0_56]) ).
cnf(c_0_66,negated_conjecture,
( ~ ssList(cons(hd(esk3_0),nil))
| segmentP(esk3_0,tl(esk3_0))
| esk3_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_56]) ).
cnf(c_0_67,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_68,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| segmentP(app(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_61]),c_0_34])]),c_0_35]) ).
cnf(c_0_69,negated_conjecture,
( ~ ssItem(hd(esk3_0))
| ~ neq(nil,esk3_0)
| ~ ssList(tl(esk3_0))
| ~ ssList(cons(hd(esk3_0),nil))
| app(tl(esk3_0),cons(hd(esk3_0),nil)) = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]) ).
cnf(c_0_70,negated_conjecture,
( ~ segmentP(esk4_0,tl(esk3_0))
| ~ segmentP(esk3_0,tl(esk3_0))
| esk3_0 = nil
| tl(esk3_0) = nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_56]) ).
cnf(c_0_71,negated_conjecture,
( segmentP(esk3_0,tl(esk3_0))
| esk3_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_34])]),c_0_59]) ).
cnf(c_0_72,negated_conjecture,
( ~ ssItem(hd(esk3_0))
| ~ neq(nil,esk3_0)
| ~ ssList(tl(esk3_0))
| ~ ssList(cons(hd(esk3_0),nil))
| segmentP(esk4_0,tl(esk3_0)) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_73,negated_conjecture,
( ~ ssList(X1)
| neq(X1,esk3_0)
| X1 = esk3_0 ),
inference(spm,[status(thm)],[c_0_40,c_0_45]) ).
cnf(c_0_74,negated_conjecture,
( ~ segmentP(esk4_0,tl(esk3_0))
| esk3_0 = nil
| tl(esk3_0) = nil ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_75,negated_conjecture,
( ~ ssItem(hd(esk3_0))
| ~ neq(nil,esk3_0)
| ~ ssList(tl(esk3_0))
| segmentP(esk4_0,tl(esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_67]),c_0_34])]) ).
cnf(c_0_76,negated_conjecture,
( neq(nil,esk3_0)
| esk3_0 = nil ),
inference(spm,[status(thm)],[c_0_73,c_0_34]) ).
cnf(c_0_77,negated_conjecture,
( esk3_0 = nil
| tl(esk3_0) = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_59]),c_0_76]),c_0_56]) ).
cnf(c_0_78,negated_conjecture,
( esk3_0 = nil
| cons(hd(esk3_0),nil) = esk3_0 ),
inference(spm,[status(thm)],[c_0_58,c_0_77]) ).
fof(c_0_79,plain,
! [X86] :
( segmentP(X86,X86)
| ~ ssList(X86) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
cnf(c_0_80,negated_conjecture,
( esk3_0 = nil
| app(tl(esk3_0),esk3_0) = esk4_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_78]),c_0_45])]),c_0_59]),c_0_76]),c_0_56]) ).
cnf(c_0_81,negated_conjecture,
( ~ segmentP(esk4_0,esk4_0)
| ~ segmentP(esk3_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_63]),c_0_53])]) ).
cnf(c_0_82,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_83,negated_conjecture,
( esk3_0 = nil
| app(nil,esk3_0) = esk4_0 ),
inference(spm,[status(thm)],[c_0_80,c_0_77]) ).
cnf(c_0_84,negated_conjecture,
( ~ neq(esk4_0,nil)
| neq(esk3_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_85,negated_conjecture,
~ segmentP(esk3_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_53])]) ).
cnf(c_0_86,negated_conjecture,
( esk4_0 = esk3_0
| esk3_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_83]),c_0_45])]) ).
fof(c_0_87,plain,
! [X92] :
( ( ~ ssList(X92)
| segmentP(nil,X92)
| nil != X92 )
& ( ~ ssList(X92)
| nil = X92
| ~ segmentP(nil,X92) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax58])])])]) ).
cnf(c_0_88,negated_conjecture,
neq(esk3_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_63])]) ).
cnf(c_0_89,negated_conjecture,
( ~ segmentP(esk3_0,esk3_0)
| esk3_0 = nil ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_90,plain,
( ~ ssList(X1)
| nil != X1
| segmentP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_91,negated_conjecture,
( ~ segmentP(esk4_0,esk3_0)
| ~ segmentP(esk3_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_88]),c_0_45])]) ).
cnf(c_0_92,negated_conjecture,
esk3_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_82]),c_0_45])]) ).
cnf(c_0_93,plain,
segmentP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_90]),c_0_34])]) ).
fof(c_0_94,plain,
! [X91] :
( segmentP(X91,nil)
| ~ ssList(X91) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])])]) ).
cnf(c_0_95,negated_conjecture,
~ segmentP(esk4_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92]),c_0_92]),c_0_93]),c_0_92])]) ).
cnf(c_0_96,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_97,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_53])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC073+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n007.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 07:51:36 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.51 Running first-order theorem proving
% 0.26/0.51 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
% 246.34/32.21 % Version: 3.5.1
% 246.34/32.21 % Preprocessing class: FSLSSMSSSSSNFFN.
% 246.34/32.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 246.34/32.21 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 246.34/32.21 % Starting new_bool_3 with 300s (1) cores
% 246.34/32.21 % Starting new_bool_1 with 300s (1) cores
% 246.34/32.21 % Starting sh5l with 300s (1) cores
% 246.34/32.21 % new_bool_3 with pid 577714 completed with status 0
% 246.34/32.21 % Result found by new_bool_3
% 246.34/32.21 % Preprocessing class: FSLSSMSSSSSNFFN.
% 246.34/32.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 246.34/32.21 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 246.34/32.21 % Starting new_bool_3 with 300s (1) cores
% 246.34/32.21 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 246.34/32.21 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 246.34/32.21 % Search class: FGHSF-FFMM21-MFFFFFNN
% 246.34/32.21 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 246.34/32.21 % Starting SubtermCWHack with 31s (1) cores
% 246.34/32.21 % SubtermCWHack with pid 577717 completed with status 8
% 246.34/32.21 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 246.34/32.21 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 577729 completed with status 0
% 246.34/32.21 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 246.34/32.21 % Preprocessing class: FSLSSMSSSSSNFFN.
% 246.34/32.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 246.34/32.21 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 246.34/32.21 % Starting new_bool_3 with 300s (1) cores
% 246.34/32.21 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 246.34/32.21 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 246.34/32.21 % Search class: FGHSF-FFMM21-MFFFFFNN
% 246.34/32.21 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 246.34/32.21 % Starting SubtermCWHack with 31s (1) cores
% 246.34/32.21 % SubtermCWHack with pid 577717 completed with status 8
% 246.34/32.21 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 246.34/32.21 % Preprocessing time : 0.002 s
% 246.34/32.21 % Presaturation interreduction done
% 246.34/32.21
% 246.34/32.21 % Proof found!
% 246.34/32.21 % SZS status Theorem
% 246.34/32.21 % SZS output start CNFRefutation
% See solution above
% 246.34/32.21 % Parsed axioms : 96
% 246.34/32.21 % Removed by relevancy pruning/SinE : 60
% 246.34/32.21 % Initial clauses : 61
% 246.34/32.21 % Removed in clause preprocessing : 0
% 246.34/32.21 % Initial clauses in saturation : 61
% 246.34/32.21 % Processed clauses : 748
% 246.34/32.21 % ...of these trivial : 13
% 246.34/32.21 % ...subsumed : 264
% 246.34/32.21 % ...remaining for further processing : 471
% 246.34/32.21 % Other redundant clauses eliminated : 16
% 246.34/32.21 % Clauses deleted for lack of memory : 0
% 246.34/32.21 % Backward-subsumed : 60
% 246.34/32.21 % Backward-rewritten : 126
% 246.34/32.21 % Generated clauses : 2727
% 246.34/32.21 % ...of the previous two non-redundant : 2598
% 246.34/32.21 % ...aggressively subsumed : 0
% 246.34/32.21 % Contextual simplify-reflections : 119
% 246.34/32.21 % Paramodulations : 2710
% 246.34/32.21 % Factorizations : 0
% 246.34/32.21 % NegExts : 0
% 246.34/32.21 % Equation resolutions : 21
% 246.34/32.21 % Disequality decompositions : 0
% 246.34/32.21 % Total rewrite steps : 1001
% 246.34/32.21 % ...of those cached : 977
% 246.34/32.21 % Propositional unsat checks : 0
% 246.34/32.21 % Propositional check models : 0
% 246.34/32.21 % Propositional check unsatisfiable : 0
% 246.34/32.21 % Propositional clauses : 0
% 246.34/32.21 % Propositional clauses after purity: 0
% 246.34/32.21 % Propositional unsat core size : 0
% 246.34/32.21 % Propositional preprocessing time : 0.000
% 246.34/32.21 % Propositional encoding time : 0.000
% 246.34/32.21 % Propositional solver time : 0.000
% 246.34/32.21 % Success case prop preproc time : 0.000
% 246.34/32.21 % Success case prop encoding time : 0.000
% 246.34/32.21 % Success case prop solver time : 0.000
% 246.34/32.21 % Current number of processed clauses : 221
% 246.34/32.21 % Positive orientable unit clauses : 31
% 246.34/32.21 % Positive unorientable unit clauses: 0
% 246.34/32.21 % Negative unit clauses : 12
% 246.34/32.21 % Non-unit-clauses : 178
% 246.34/32.21 % Current number of unprocessed clauses: 1922
% 246.34/32.21 % ...number of literals in the above : 9137
% 246.34/32.21 % Current number of archived formulas : 0
% 246.34/32.21 % Current number of archived clauses : 244
% 246.34/32.21 % Clause-clause subsumption calls (NU) : 20157
% 246.34/32.21 % Rec. Clause-clause subsumption calls : 5689
% 246.34/32.21 % Non-unit clause-clause subsumptions : 395
% 246.34/32.21 % Unit Clause-clause subsumption calls : 836
% 246.34/32.21 % Rewrite failures with RHS unbound : 0
% 246.34/32.21 % BW rewrite match attempts : 6
% 246.34/32.21 % BW rewrite match successes : 6
% 246.34/32.21 % Condensation attempts : 0
% 246.34/32.21 % Condensation successes : 0
% 246.34/32.21 % Termbank termtop insertions : 51460
% 246.34/32.21 % Search garbage collected termcells : 1851
% 246.34/32.21
% 246.34/32.21 % -------------------------------------------------
% 246.34/32.21 % User time : 30.047 s
% 246.34/32.21 % System time : 1.238 s
% 246.34/32.21 % Total time : 31.285 s
% 246.34/32.21 % Maximum resident set size: 3764 pages
% 246.34/32.21
% 246.34/32.21 % -------------------------------------------------
% 246.34/32.21 % User time : 30.055 s
% 246.34/32.21 % System time : 1.246 s
% 246.34/32.21 % Total time : 31.301 s
% 246.34/32.21 % Maximum resident set size: 4608 pages
% 246.34/32.21 % E exiting
%------------------------------------------------------------------------------