%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC111+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 : n011.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 02:43:03 PM UTC 2026
% Result : Theorem 211.83s 36.20s
% Output : CNFRefutation 211.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 92 ( 17 unt; 0 def)
% Number of atoms : 353 ( 91 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 431 ( 170 ~; 174 |; 44 &)
% ( 5 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 121 ( 0 sgn 63 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ( segmentP(X2,X1)
& neq(X1,nil) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ? [X5] :
( totalorderedP(X5)
& segmentP(X5,X3)
& segmentP(X4,X5)
& neq(X3,X5)
& ssList(X5) )
| ~ totalorderedP(X3)
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax58,axiom,
! [X1] :
( ssList(X1)
=> ( segmentP(nil,X1)
<=> nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X1
& nil = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
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(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax66) ).
fof(ax57,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( ? [X2] :
( ? [X3] :
( cons(X3,X2) = X1
& ssItem(X3) )
& ssList(X2) )
| nil = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(ax65,axiom,
! [X1] :
( ssItem(X1)
=> totalorderedP(cons(X1,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax65) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ( segmentP(X2,X1)
& neq(X1,nil) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ? [X5] :
( totalorderedP(X5)
& segmentP(X5,X3)
& segmentP(X4,X5)
& neq(X3,X5)
& ssList(X5) )
| ~ totalorderedP(X3)
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_17,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_18,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ( segmentP(X2,X1)
& neq(X1,nil) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ? [X5] :
( totalorderedP(X5)
& segmentP(X5,X3)
& segmentP(X4,X5)
& neq(X3,X5)
& ssList(X5) )
| ~ totalorderedP(X3)
| ~ segmentP(X4,X3)
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X32,X33] :
( ( ~ ssList(X32)
| ~ ssList(X33)
| neq(X32,X33)
| X32 = X33 )
& ( ~ ssList(X32)
| ~ ssList(X33)
| X32 != X33
| ~ neq(X32,X33) ) ),
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_17])])])])]) ).
fof(c_0_20,negated_conjecture,
! [X11] :
( ( nil != esk1_0
| ~ segmentP(esk2_0,esk1_0)
| ~ neq(esk1_0,nil) )
& ( nil != esk1_0
| neq(esk2_0,nil) )
& ( nil = esk2_0
| ~ segmentP(esk2_0,esk1_0)
| ~ neq(esk1_0,nil) )
& ( nil = esk2_0
| neq(esk2_0,nil) )
& ( ~ totalorderedP(X11)
| ~ segmentP(X11,esk3_0)
| ~ segmentP(esk4_0,X11)
| ~ neq(esk3_0,X11)
| ~ ssList(X11) )
& totalorderedP(esk3_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(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])])]) ).
cnf(c_0_21,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,negated_conjecture,
segmentP(esk4_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_27,negated_conjecture,
( ~ totalorderedP(X1)
| ~ segmentP(X1,esk3_0)
| ~ segmentP(esk4_0,X1)
| ~ neq(esk3_0,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( ~ ssList(X1)
| neq(X1,esk2_0)
| X1 = esk2_0 ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,negated_conjecture,
( ~ segmentP(esk2_0,esk1_0)
| ~ neq(esk1_0,nil)
| nil = esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,negated_conjecture,
segmentP(esk2_0,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_32,plain,
( ~ ssList(X1)
| neq(X1,nil)
| X1 = nil ),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
fof(c_0_33,plain,
! [X29] :
( ( ~ ssList(X29)
| segmentP(nil,X29)
| nil != X29 )
& ( ~ ssList(X29)
| nil = X29
| ~ segmentP(nil,X29) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax58])])])]) ).
fof(c_0_34,plain,
! [X70,X71] :
( ( ~ ssList(X70)
| ~ ssList(X71)
| nil = app(X70,X71)
| nil != X70
| nil != X71 )
& ( ~ ssList(X70)
| ~ ssList(X71)
| nil != app(X70,X71)
| nil = X70 )
& ( ~ ssList(X70)
| ~ ssList(X71)
| nil != app(X70,X71)
| nil = X71 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])])]) ).
cnf(c_0_35,negated_conjecture,
( ~ neq(esk1_0,X1)
| ~ ssList(X1)
| ~ segmentP(esk2_0,X1)
| ~ segmentP(X1,esk1_0)
| ~ totalorderedP(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_25]),c_0_25]),c_0_24]) ).
cnf(c_0_36,negated_conjecture,
( neq(esk1_0,esk2_0)
| esk2_0 = esk1_0 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,negated_conjecture,
( ~ neq(esk1_0,nil)
| esk2_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_38,negated_conjecture,
( neq(esk1_0,nil)
| esk1_0 = nil ),
inference(spm,[status(thm)],[c_0_32,c_0_29]) ).
cnf(c_0_39,plain,
( ~ ssList(X1)
| nil != X1
| segmentP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_40,plain,
! [X75,X76] :
( ssList(cons(X76,X75))
| ~ ssItem(X76)
| ~ ssList(X75) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_41,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
fof(c_0_42,plain,
! [X12,X13,X16,X17] :
( ( ~ ssList(X12)
| ~ ssList(X13)
| segmentP(X12,X13)
| app(app(X16,X13),X17) != X12
| ~ ssList(X17)
| ~ ssList(X16) )
& ( ~ ssList(X12)
| ~ ssList(X13)
| ~ segmentP(X12,X13)
| app(app(esk5_2(X12,X13),X13),esk6_2(X12,X13)) = X12 )
& ( ~ ssList(X12)
| ~ ssList(X13)
| ~ segmentP(X12,X13)
| ssList(esk6_2(X12,X13)) )
& ( ~ ssList(X12)
| ~ ssList(X13)
| ~ segmentP(X12,X13)
| ssList(esk5_2(X12,X13)) ) ),
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_43,plain,
! [X55,X56,X57] :
( cons(X57,app(X56,X55)) = app(cons(X57,X56),X55)
| ~ ssItem(X57)
| ~ ssList(X56)
| ~ ssList(X55) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).
fof(c_0_44,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])])])]) ).
cnf(c_0_45,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| nil != X1
| nil = app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_46,negated_conjecture,
( ~ segmentP(esk2_0,esk2_0)
| ~ totalorderedP(esk2_0)
| esk2_0 = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_31]),c_0_22])]) ).
cnf(c_0_47,negated_conjecture,
( esk2_0 = nil
| esk1_0 = nil ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_48,plain,
totalorderedP(nil),
inference(split_conjunct,[status(thm)],[ax66]) ).
cnf(c_0_49,plain,
segmentP(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_39]),c_0_26])]) ).
fof(c_0_50,plain,
! [X28] :
( segmentP(X28,nil)
| ~ ssList(X28) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax57])])]) ).
cnf(c_0_51,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_52,plain,
! [X37,X38] :
( nil != cons(X38,X37)
| ~ ssItem(X38)
| ~ ssList(X37) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])]) ).
cnf(c_0_53,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_42]) ).
fof(c_0_54,plain,
! [X58] :
( app(nil,X58) = X58
| ~ ssList(X58) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_55,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_56,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_57,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_45])]),c_0_26])]) ).
cnf(c_0_58,negated_conjecture,
esk1_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_49])]) ).
cnf(c_0_59,plain,
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_60,plain,
( ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| neq(X1,cons(X2,X3))
| X1 = cons(X2,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_51]) ).
cnf(c_0_61,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_62,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_53]) ).
cnf(c_0_63,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_64,plain,
! [X65,X66] :
( cons(X66,X65) = app(cons(X66,nil),X65)
| ~ ssItem(X66)
| ~ ssList(X65) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_65,plain,
( ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ssList(app(cons(X1,X2),X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_55]),c_0_56]) ).
cnf(c_0_66,plain,
( ~ ssItem(X1)
| app(cons(X1,nil),nil) = cons(X1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_57]),c_0_26])]) ).
fof(c_0_67,plain,
! [X34] :
( ( ~ ssList(X34)
| nil = X34
| cons(esk8_1(X34),esk7_1(X34)) = X34 )
& ( ~ ssList(X34)
| nil = X34
| ssItem(esk8_1(X34)) )
& ( ~ ssList(X34)
| nil = X34
| ssList(esk7_1(X34)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])])]) ).
cnf(c_0_68,negated_conjecture,
( ~ neq(nil,X1)
| ~ ssList(X1)
| ~ segmentP(esk2_0,X1)
| ~ totalorderedP(X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_58]),c_0_58]),c_0_59]) ).
cnf(c_0_69,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| neq(nil,cons(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_26]),c_0_61]) ).
fof(c_0_70,plain,
! [X50] :
( totalorderedP(cons(X50,nil))
| ~ ssItem(X50) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax65])])]) ).
cnf(c_0_71,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_62,c_0_63]),c_0_26])]),c_0_56]) ).
cnf(c_0_72,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_73,plain,
( ~ ssItem(X1)
| ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_26])]) ).
cnf(c_0_74,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk8_1(X1),esk7_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_75,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk8_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_76,plain,
( ~ ssList(X1)
| nil = X1
| ssList(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_77,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ segmentP(esk2_0,cons(X1,X2))
| ~ totalorderedP(cons(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_51]) ).
cnf(c_0_78,plain,
( ~ ssItem(X1)
| totalorderedP(cons(X1,nil)) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_79,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| segmentP(cons(X1,X2),cons(X1,nil)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_80,negated_conjecture,
( esk2_0 = nil
| cons(esk8_1(esk2_0),esk7_1(esk2_0)) = esk2_0 ),
inference(spm,[status(thm)],[c_0_74,c_0_22]) ).
cnf(c_0_81,negated_conjecture,
( ssItem(esk8_1(esk2_0))
| esk2_0 = nil ),
inference(spm,[status(thm)],[c_0_75,c_0_22]) ).
cnf(c_0_82,negated_conjecture,
( ssList(esk7_1(esk2_0))
| esk2_0 = nil ),
inference(spm,[status(thm)],[c_0_76,c_0_22]) ).
cnf(c_0_83,negated_conjecture,
( nil != esk1_0
| ~ segmentP(esk2_0,esk1_0)
| ~ neq(esk1_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_84,negated_conjecture,
( nil != esk1_0
| neq(esk2_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_85,negated_conjecture,
( ~ ssItem(X1)
| ~ segmentP(esk2_0,cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_26])]) ).
cnf(c_0_86,negated_conjecture,
( segmentP(esk2_0,cons(esk8_1(esk2_0),nil))
| esk2_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_82]) ).
cnf(c_0_87,negated_conjecture,
( ~ neq(esk1_0,nil)
| esk1_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_31])]) ).
cnf(c_0_88,negated_conjecture,
neq(esk2_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_58])]) ).
cnf(c_0_89,negated_conjecture,
esk2_0 = nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_81]) ).
cnf(c_0_90,negated_conjecture,
~ neq(nil,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_58]),c_0_58])]) ).
cnf(c_0_91,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_89]),c_0_90]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC111+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.46 % Computer : n011.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Mon Sep 21 07:56:28 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.51 Running first-order theorem proving
% 0.18/0.51 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 211.83/36.20 % Version: 3.5.1
% 211.83/36.20 % Preprocessing class: FSLSSMSSSSSNFFN.
% 211.83/36.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 211.83/36.20 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 211.83/36.20 % Starting new_bool_3 with 300s (1) cores
% 211.83/36.20 % Starting new_bool_1 with 300s (1) cores
% 211.83/36.20 % Starting sh5l with 300s (1) cores
% 211.83/36.20 % new_bool_3 with pid 1399725 completed with status 0
% 211.83/36.20 % Result found by new_bool_3
% 211.83/36.20 % Preprocessing class: FSLSSMSSSSSNFFN.
% 211.83/36.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 211.83/36.20 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 211.83/36.20 % Starting new_bool_3 with 300s (1) cores
% 211.83/36.20 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 211.83/36.20 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 211.83/36.20 % Search class: FGHSF-FFMM21-MFFFFFNN
% 211.83/36.20 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 211.83/36.20 % Starting SubtermCWHack with 31s (1) cores
% 211.83/36.20 % SubtermCWHack with pid 1399733 completed with status 8
% 211.83/36.20 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 211.83/36.20 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1399890 completed with status 0
% 211.83/36.20 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 211.83/36.20 % Preprocessing class: FSLSSMSSSSSNFFN.
% 211.83/36.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 211.83/36.20 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 211.83/36.20 % Starting new_bool_3 with 300s (1) cores
% 211.83/36.20 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 211.83/36.20 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 211.83/36.20 % Search class: FGHSF-FFMM21-MFFFFFNN
% 211.83/36.20 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 211.83/36.20 % Starting SubtermCWHack with 31s (1) cores
% 211.83/36.20 % SubtermCWHack with pid 1399733 completed with status 8
% 211.83/36.20 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 211.83/36.20 % Preprocessing time : 0.003 s
% 211.83/36.20 % Presaturation interreduction done
% 211.83/36.20
% 211.83/36.20 % Proof found!
% 211.83/36.20 % SZS status Theorem
% 211.83/36.20 % SZS output start CNFRefutation
% See solution above
% 211.83/36.20 % Parsed axioms : 96
% 211.83/36.20 % Removed by relevancy pruning/SinE : 47
% 211.83/36.20 % Initial clauses : 89
% 211.83/36.20 % Removed in clause preprocessing : 1
% 211.83/36.20 % Initial clauses in saturation : 88
% 211.83/36.20 % Processed clauses : 12668
% 211.83/36.20 % ...of these trivial : 244
% 211.83/36.20 % ...subsumed : 9168
% 211.83/36.20 % ...remaining for further processing : 3256
% 211.83/36.20 % Other redundant clauses eliminated : 247
% 211.83/36.20 % Clauses deleted for lack of memory : 0
% 211.83/36.20 % Backward-subsumed : 123
% 211.83/36.20 % Backward-rewritten : 2372
% 211.83/36.20 % Generated clauses : 199373
% 211.83/36.20 % ...of the previous two non-redundant : 194083
% 211.83/36.20 % ...aggressively subsumed : 0
% 211.83/36.20 % Contextual simplify-reflections : 441
% 211.83/36.20 % Paramodulations : 199053
% 211.83/36.20 % Factorizations : 0
% 211.83/36.20 % NegExts : 0
% 211.83/36.20 % Equation resolutions : 321
% 211.83/36.20 % Disequality decompositions : 0
% 211.83/36.20 % Total rewrite steps : 43883
% 211.83/36.20 % ...of those cached : 43855
% 211.83/36.20 % Propositional unsat checks : 0
% 211.83/36.20 % Propositional check models : 0
% 211.83/36.20 % Propositional check unsatisfiable : 0
% 211.83/36.20 % Propositional clauses : 0
% 211.83/36.20 % Propositional clauses after purity: 0
% 211.83/36.20 % Propositional unsat core size : 0
% 211.83/36.20 % Propositional preprocessing time : 0.000
% 211.83/36.20 % Propositional encoding time : 0.000
% 211.83/36.20 % Propositional solver time : 0.000
% 211.83/36.20 % Success case prop preproc time : 0.000
% 211.83/36.20 % Success case prop encoding time : 0.000
% 211.83/36.20 % Success case prop solver time : 0.000
% 211.83/36.20 % Current number of processed clauses : 670
% 211.83/36.20 % Positive orientable unit clauses : 19
% 211.83/36.20 % Positive unorientable unit clauses: 0
% 211.83/36.20 % Negative unit clauses : 2
% 211.83/36.20 % Non-unit-clauses : 649
% 211.83/36.20 % Current number of unprocessed clauses: 180891
% 211.83/36.20 % ...number of literals in the above : 957403
% 211.83/36.20 % Current number of archived formulas : 0
% 211.83/36.20 % Current number of archived clauses : 2578
% 211.83/36.20 % Clause-clause subsumption calls (NU) : 880791
% 211.83/36.20 % Rec. Clause-clause subsumption calls : 185211
% 211.83/36.20 % Non-unit clause-clause subsumptions : 9719
% 211.83/36.20 % Unit Clause-clause subsumption calls : 1409
% 211.83/36.20 % Rewrite failures with RHS unbound : 0
% 211.83/36.20 % BW rewrite match attempts : 15
% 211.83/36.20 % BW rewrite match successes : 14
% 211.83/36.20 % Condensation attempts : 0
% 211.83/36.20 % Condensation successes : 0
% 211.83/36.20 % Termbank termtop insertions : 4625365
% 211.83/36.20 % Search garbage collected termcells : 2210
% 211.83/36.20
% 211.83/36.20 % -------------------------------------------------
% 211.83/36.20 % User time : 33.787 s
% 211.83/36.20 % System time : 1.231 s
% 211.83/36.20 % Total time : 35.018 s
% 211.83/36.20 % Maximum resident set size: 3760 pages
% 211.83/36.20
% 211.83/36.20 % -------------------------------------------------
% 211.83/36.20 % User time : 33.791 s
% 211.83/36.20 % System time : 1.242 s
% 211.83/36.20 % Total time : 35.033 s
% 211.83/36.20 % Maximum resident set size: 4608 pages
% 211.83/36.20 % E exiting
%------------------------------------------------------------------------------