%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC089+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 : n006.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 02:42:57 PM UTC 2026
% Result : Theorem 216.58s 32.86s
% Output : CNFRefutation 216.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 84 ( 12 unt; 0 def)
% Number of atoms : 360 ( 106 equ)
% Maximal formula atoms : 27 ( 4 avg)
% Number of connectives : 443 ( 167 ~; 173 |; 61 &)
% ( 3 <=>; 39 =>; 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 : 115 ( 0 sgn 56 !; 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 = X4
& nil != X3 )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax24,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax78,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(c_0_13,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 = X4
& nil != X3 )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_14,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 = X4
& nil != X3 )
| ? [X5] :
( segmentP(X1,X5)
& segmentP(X2,X5)
& neq(X5,nil)
& ssList(X5) )
| ~ neq(X2,nil)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_15,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_16,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_17,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssList(tl(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax24]) ).
fof(c_0_18,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 != esk4_0
| nil = esk3_0 )
& ( ~ segmentP(esk1_0,X14)
| ~ segmentP(esk2_0,X14)
| ~ neq(X14,nil)
| ~ ssList(X14) )
& neq(esk2_0,nil)
& 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_14])])])])])]) ).
cnf(c_0_19,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_15]) ).
fof(c_0_20,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_21,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_22,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> cons(hd(X1),tl(X1)) = X1 ) ),
inference(fof_simplification,[status(thm)],[ax78]) ).
fof(c_0_23,plain,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
inference(fof_simplification,[status(thm)],[ax22]) ).
fof(c_0_24,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_16])])])])]) ).
fof(c_0_25,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_17])])]) ).
cnf(c_0_26,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,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_19]) ).
cnf(c_0_29,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_31,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_32,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_33,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_22])])]) ).
fof(c_0_34,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_23])])]) ).
cnf(c_0_35,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_36,plain,
( ~ ssList(X1)
| ssList(tl(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,negated_conjecture,
ssList(esk3_0),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_38,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_28,c_0_29]),c_0_30])]),c_0_31]) ).
cnf(c_0_39,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,plain,
( ~ ssList(X1)
| cons(hd(X1),tl(X1)) = X1
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
( ~ ssList(X1)
| ssItem(hd(X1))
| nil = X1 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_42,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_43,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_18]) ).
cnf(c_0_44,negated_conjecture,
neq(esk2_0,nil),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_45,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_46,negated_conjecture,
( ~ segmentP(esk1_0,X1)
| ~ segmentP(esk2_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_47,plain,
( ~ ssList(X1)
| neq(X1,nil)
| X1 = nil ),
inference(spm,[status(thm)],[c_0_35,c_0_30]) ).
cnf(c_0_48,negated_conjecture,
( ssList(tl(esk3_0))
| esk3_0 = nil ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_49,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(cons(X1,nil))
| segmentP(cons(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_50,negated_conjecture,
( esk3_0 = nil
| cons(hd(esk3_0),tl(esk3_0)) = esk3_0 ),
inference(spm,[status(thm)],[c_0_40,c_0_37]) ).
cnf(c_0_51,negated_conjecture,
( ssItem(hd(esk3_0))
| esk3_0 = nil ),
inference(spm,[status(thm)],[c_0_41,c_0_37]) ).
fof(c_0_52,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_53,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_54,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_43]) ).
cnf(c_0_55,negated_conjecture,
neq(esk4_0,nil),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_56,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_46,c_0_27]),c_0_45]) ).
cnf(c_0_57,negated_conjecture,
( neq(tl(esk3_0),nil)
| esk3_0 = nil
| tl(esk3_0) = nil ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_58,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_49,c_0_50]),c_0_51]),c_0_48]) ).
cnf(c_0_59,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_60,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_28,c_0_53]),c_0_30])]),c_0_31]) ).
cnf(c_0_61,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(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])])])])])]),c_0_31]) ).
cnf(c_0_62,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_56,c_0_57]),c_0_48]) ).
cnf(c_0_63,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_58,c_0_59]),c_0_30])]),c_0_51]) ).
cnf(c_0_64,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_60,c_0_61]) ).
cnf(c_0_65,negated_conjecture,
( ~ ssList(X1)
| neq(X1,esk3_0)
| X1 = esk3_0 ),
inference(spm,[status(thm)],[c_0_35,c_0_37]) ).
cnf(c_0_66,negated_conjecture,
( ~ segmentP(esk4_0,tl(esk3_0))
| esk3_0 = nil
| tl(esk3_0) = nil ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,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_64,c_0_59]),c_0_30])]) ).
cnf(c_0_68,negated_conjecture,
( neq(nil,esk3_0)
| esk3_0 = nil ),
inference(spm,[status(thm)],[c_0_65,c_0_30]) ).
cnf(c_0_69,negated_conjecture,
( ~ neq(esk4_0,nil)
| neq(esk3_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_70,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_66,c_0_67]),c_0_51]),c_0_68]),c_0_48]) ).
cnf(c_0_71,negated_conjecture,
neq(esk3_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_55])]) ).
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,cons(hd(esk3_0),nil)) ),
inference(spm,[status(thm)],[c_0_38,c_0_61]) ).
cnf(c_0_73,negated_conjecture,
( esk3_0 = nil
| cons(hd(esk3_0),nil) = esk3_0 ),
inference(spm,[status(thm)],[c_0_50,c_0_70]) ).
cnf(c_0_74,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_56,c_0_71]),c_0_37])]) ).
cnf(c_0_75,negated_conjecture,
( segmentP(esk4_0,esk3_0)
| esk3_0 = nil ),
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_72,c_0_73]),c_0_37])]),c_0_51]),c_0_68]),c_0_48]) ).
fof(c_0_76,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_77,negated_conjecture,
( ~ segmentP(esk3_0,esk3_0)
| esk3_0 = nil ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_78,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_79,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| X1 != X2
| ~ neq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_80,negated_conjecture,
esk3_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_37])]) ).
cnf(c_0_81,plain,
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_79]) ).
cnf(c_0_82,negated_conjecture,
neq(nil,nil),
inference(rw,[status(thm)],[c_0_71,c_0_80]) ).
cnf(c_0_83,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC089+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n006.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 07:54:42 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 216.58/32.86 % Version: 3.5.1
% 216.58/32.86 % Preprocessing class: FSLSSMSSSSSNFFN.
% 216.58/32.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 216.58/32.86 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 216.58/32.86 % Starting new_bool_3 with 300s (1) cores
% 216.58/32.86 % Starting new_bool_1 with 300s (1) cores
% 216.58/32.86 % Starting sh5l with 300s (1) cores
% 216.58/32.86 % new_bool_3 with pid 2361232 completed with status 0
% 216.58/32.86 % Result found by new_bool_3
% 216.58/32.86 % Preprocessing class: FSLSSMSSSSSNFFN.
% 216.58/32.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 216.58/32.86 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 216.58/32.86 % Starting new_bool_3 with 300s (1) cores
% 216.58/32.86 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 216.58/32.86 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 216.58/32.86 % Search class: FGHSF-FFMM21-MFFFFFNN
% 216.58/32.86 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 216.58/32.86 % Starting SubtermCWHack with 31s (1) cores
% 216.58/32.86 % SubtermCWHack with pid 2361235 completed with status 8
% 216.58/32.86 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 216.58/32.86 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2361277 completed with status 0
% 216.58/32.86 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 216.58/32.86 % Preprocessing class: FSLSSMSSSSSNFFN.
% 216.58/32.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 216.58/32.86 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 216.58/32.86 % Starting new_bool_3 with 300s (1) cores
% 216.58/32.86 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 216.58/32.86 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 216.58/32.86 % Search class: FGHSF-FFMM21-MFFFFFNN
% 216.58/32.86 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 216.58/32.86 % Starting SubtermCWHack with 31s (1) cores
% 216.58/32.86 % SubtermCWHack with pid 2361235 completed with status 8
% 216.58/32.86 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 216.58/32.86 % Preprocessing time : 0.003 s
% 216.58/32.86 % Presaturation interreduction done
% 216.58/32.86
% 216.58/32.86 % Proof found!
% 216.58/32.86 % SZS status Theorem
% 216.58/32.86 % SZS output start CNFRefutation
% See solution above
% 216.58/32.86 % Parsed axioms : 96
% 216.58/32.86 % Removed by relevancy pruning/SinE : 60
% 216.58/32.86 % Initial clauses : 61
% 216.58/32.86 % Removed in clause preprocessing : 0
% 216.58/32.86 % Initial clauses in saturation : 61
% 216.58/32.86 % Processed clauses : 865
% 216.58/32.86 % ...of these trivial : 2
% 216.58/32.86 % ...subsumed : 314
% 216.58/32.86 % ...remaining for further processing : 549
% 216.58/32.86 % Other redundant clauses eliminated : 16
% 216.58/32.86 % Clauses deleted for lack of memory : 0
% 216.58/32.86 % Backward-subsumed : 68
% 216.58/32.86 % Backward-rewritten : 139
% 216.58/32.86 % Generated clauses : 5445
% 216.58/32.86 % ...of the previous two non-redundant : 5328
% 216.58/32.86 % ...aggressively subsumed : 0
% 216.58/32.86 % Contextual simplify-reflections : 176
% 216.58/32.86 % Paramodulations : 5428
% 216.58/32.86 % Factorizations : 0
% 216.58/32.86 % NegExts : 0
% 216.58/32.86 % Equation resolutions : 21
% 216.58/32.86 % Disequality decompositions : 0
% 216.58/32.86 % Total rewrite steps : 912
% 216.58/32.86 % ...of those cached : 902
% 216.58/32.86 % Propositional unsat checks : 0
% 216.58/32.86 % Propositional check models : 0
% 216.58/32.86 % Propositional check unsatisfiable : 0
% 216.58/32.86 % Propositional clauses : 0
% 216.58/32.86 % Propositional clauses after purity: 0
% 216.58/32.86 % Propositional unsat core size : 0
% 216.58/32.86 % Propositional preprocessing time : 0.000
% 216.58/32.86 % Propositional encoding time : 0.000
% 216.58/32.86 % Propositional solver time : 0.000
% 216.58/32.86 % Success case prop preproc time : 0.000
% 216.58/32.86 % Success case prop encoding time : 0.000
% 216.58/32.86 % Success case prop solver time : 0.000
% 216.58/32.86 % Current number of processed clauses : 277
% 216.58/32.86 % Positive orientable unit clauses : 13
% 216.58/32.86 % Positive unorientable unit clauses: 0
% 216.58/32.86 % Negative unit clauses : 1
% 216.58/32.86 % Non-unit-clauses : 263
% 216.58/32.86 % Current number of unprocessed clauses: 4566
% 216.58/32.86 % ...number of literals in the above : 20471
% 216.58/32.86 % Current number of archived formulas : 0
% 216.58/32.86 % Current number of archived clauses : 266
% 216.58/32.86 % Clause-clause subsumption calls (NU) : 41920
% 216.58/32.86 % Rec. Clause-clause subsumption calls : 10939
% 216.58/32.86 % Non-unit clause-clause subsumptions : 557
% 216.58/32.86 % Unit Clause-clause subsumption calls : 443
% 216.58/32.86 % Rewrite failures with RHS unbound : 0
% 216.58/32.86 % BW rewrite match attempts : 1
% 216.58/32.86 % BW rewrite match successes : 1
% 216.58/32.86 % Condensation attempts : 0
% 216.58/32.86 % Condensation successes : 0
% 216.58/32.86 % Termbank termtop insertions : 101618
% 216.58/32.86 % Search garbage collected termcells : 1839
% 216.58/32.86
% 216.58/32.86 % -------------------------------------------------
% 216.58/32.86 % User time : 30.246 s
% 216.58/32.86 % System time : 1.122 s
% 216.58/32.86 % Total time : 31.369 s
% 216.58/32.86 % Maximum resident set size: 3764 pages
% 216.58/32.86
% 216.58/32.86 % -------------------------------------------------
% 216.58/32.86 % User time : 30.251 s
% 216.58/32.86 % System time : 1.126 s
% 216.58/32.86 % Total time : 31.377 s
% 216.58/32.86 % Maximum resident set size: 4608 pages
% 216.58/32.86 % E exiting
%------------------------------------------------------------------------------