%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC084+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 : n012.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 02:42:55 PM UTC 2026
% Result : Theorem 200.18s 34.26s
% Output : CNFRefutation 200.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 121 ( 25 unt; 0 def)
% Number of atoms : 474 ( 147 equ)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 593 ( 240 ~; 241 |; 50 &)
% ( 5 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 186 ( 0 sgn 93 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X6] :
( ssItem(X6)
=> ( ? [X7] :
( leq(X6,X7)
& memberP(X4,X7)
& X6 != X7
& ssItem(X7) )
| ~ memberP(X4,X6)
| cons(X6,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(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax79) ).
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/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(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(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
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(ax56,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax56) ).
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(ax3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ? [X4] :
( app(X3,cons(X2,X4)) = X1
& ssList(X4) )
& ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(c_0_17,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X6] :
( ssItem(X6)
=> ( ? [X7] :
( leq(X6,X7)
& memberP(X4,X7)
& X6 != X7
& ssItem(X7) )
| ~ memberP(X4,X6)
| cons(X6,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_18,plain,
! [X92,X93,X94] :
( X94 = X92
| app(X94,X93) != app(X92,X93)
| ~ ssList(X94)
| ~ ssList(X93)
| ~ ssList(X92) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])])]) ).
fof(c_0_19,plain,
! [X98,X99,X100] :
( app(app(X98,X99),X100) = app(X98,app(X99,X100))
| ~ ssList(X100)
| ~ ssList(X99)
| ~ ssList(X98) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
fof(c_0_20,plain,
! [X89,X90] :
( ssList(app(X89,X90))
| ~ ssList(X90)
| ~ ssList(X89) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_21,plain,
! [X91] :
( app(nil,X91) = X91
| ~ ssList(X91) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
fof(c_0_22,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( nil != X3
| nil != X4 )
& ! [X6] :
( ssItem(X6)
=> ( ? [X7] :
( leq(X6,X7)
& memberP(X4,X7)
& X6 != X7
& ssItem(X7) )
| ~ memberP(X4,X6)
| cons(X6,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_17]) ).
cnf(c_0_23,plain,
( app(X3,X2) != app(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_28,negated_conjecture,
! [X12,X14] :
( ( ~ leq(esk5_0,X14)
| ~ memberP(esk4_0,X14)
| esk5_0 = X14
| ~ ssItem(X14)
| nil = esk3_0 )
& ( ~ leq(esk5_0,X14)
| ~ memberP(esk4_0,X14)
| esk5_0 = X14
| ~ ssItem(X14)
| nil = esk4_0 )
& ( memberP(esk4_0,esk5_0)
| nil = esk3_0 )
& ( memberP(esk4_0,esk5_0)
| nil = esk4_0 )
& ( cons(esk5_0,nil) = esk3_0
| nil = esk3_0 )
& ( cons(esk5_0,nil) = esk3_0
| nil = esk4_0 )
& ( ssItem(esk5_0)
| nil = esk3_0 )
& ( ssItem(esk5_0)
| nil = esk4_0 )
& ( ~ segmentP(esk1_0,X12)
| ~ segmentP(esk2_0,X12)
| ~ neq(X12,nil)
| ~ ssList(X12) )
& 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_22])])])])])]) ).
fof(c_0_29,plain,
! [X59,X60] :
( cons(X60,X59) = app(cons(X60,nil),X59)
| ~ ssItem(X60)
| ~ ssList(X59) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
fof(c_0_30,plain,
! [X101,X102] :
( ( ~ ssList(X101)
| ~ ssList(X102)
| nil = app(X101,X102)
| nil != X101
| nil != X102 )
& ( ~ ssList(X101)
| ~ ssList(X102)
| nil != app(X101,X102)
| nil = X101 )
& ( ~ ssList(X101)
| ~ ssList(X102)
| nil != app(X101,X102)
| nil = X102 ) ),
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_31,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X4)
| app(X1,X4) != app(X2,app(X3,X4))
| X1 = app(X2,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_32,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(nil,app(X1,X2)) = app(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_26]),c_0_27])]) ).
cnf(c_0_33,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,negated_conjecture,
( cons(esk5_0,nil) = esk3_0
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,negated_conjecture,
( ssItem(esk5_0)
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_38,plain,
! [X95,X96,X97] :
( X97 = X95
| app(X96,X97) != app(X96,X95)
| ~ ssList(X97)
| ~ ssList(X96)
| ~ ssList(X95) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])])]) ).
cnf(c_0_39,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| nil != X1
| nil = app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_40,plain,
! [X103] :
( app(X103,nil) = X103
| ~ ssList(X103) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_41,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(X1,X3) != app(X2,X3)
| X1 = app(nil,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_27])]) ).
cnf(c_0_42,negated_conjecture,
ssList(esk4_0),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
fof(c_0_43,plain,
! [X61,X62,X65,X66] :
( ( ~ ssList(X61)
| ~ ssList(X62)
| segmentP(X61,X62)
| app(app(X65,X62),X66) != X61
| ~ ssList(X66)
| ~ ssList(X65) )
& ( ~ ssList(X61)
| ~ ssList(X62)
| ~ segmentP(X61,X62)
| app(app(esk12_2(X61,X62),X62),esk13_2(X61,X62)) = X61 )
& ( ~ ssList(X61)
| ~ ssList(X62)
| ~ segmentP(X61,X62)
| ssList(esk13_2(X61,X62)) )
& ( ~ ssList(X61)
| ~ ssList(X62)
| ~ segmentP(X61,X62)
| ssList(esk12_2(X61,X62)) ) ),
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])])])])])]) ).
cnf(c_0_44,negated_conjecture,
( ~ ssList(X1)
| esk3_0 = nil
| cons(esk5_0,X1) = app(esk3_0,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_45,plain,
( app(X2,X3) != app(X2,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_39])]),c_0_27])]) ).
cnf(c_0_47,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_48,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ssList(app(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_24]),c_0_25]) ).
cnf(c_0_49,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| app(X1,esk4_0) != app(X2,esk4_0)
| X1 = app(nil,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_50,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_43]) ).
fof(c_0_51,plain,
! [X73,X74,X75,X76] :
( segmentP(app(app(X75,X73),X76),X74)
| ~ segmentP(X73,X74)
| ~ ssList(X76)
| ~ ssList(X75)
| ~ ssList(X74)
| ~ ssList(X73) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])])]) ).
cnf(c_0_52,negated_conjecture,
( esk3_0 = nil
| cons(esk5_0,nil) = app(esk3_0,nil) ),
inference(spm,[status(thm)],[c_0_44,c_0_27]) ).
cnf(c_0_53,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_54,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_55,plain,
( ~ ssList(X1)
| app(nil,X1) != nil
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_27])]) ).
cnf(c_0_56,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,app(X2,nil)) = app(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_24]),c_0_27])]),c_0_25]) ).
cnf(c_0_57,plain,
( ~ ssList(X1)
| ssList(app(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_46]),c_0_27])]) ).
cnf(c_0_58,negated_conjecture,
( ~ ssList(X1)
| app(esk4_0,esk4_0) != app(X1,esk4_0)
| app(nil,X1) = esk4_0 ),
inference(spm,[status(thm)],[c_0_49,c_0_42]) ).
cnf(c_0_59,negated_conjecture,
( ~ segmentP(esk1_0,X1)
| ~ segmentP(esk2_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_60,negated_conjecture,
neq(esk2_0,nil),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_61,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_50]) ).
cnf(c_0_62,plain,
( ~ segmentP(X1,X2)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| segmentP(app(app(X3,X1),X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_63,negated_conjecture,
( esk3_0 = nil
| app(esk3_0,nil) = esk3_0 ),
inference(spm,[status(thm)],[c_0_36,c_0_52]) ).
cnf(c_0_64,negated_conjecture,
ssList(esk3_0),
inference(rw,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_65,plain,
( ~ ssList(X1)
| app(nil,X1) != nil
| app(X1,nil) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_27])]),c_0_57]) ).
cnf(c_0_66,negated_conjecture,
app(nil,esk4_0) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_58]),c_0_42])]) ).
cnf(c_0_67,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_59,c_0_54]),c_0_34]) ).
cnf(c_0_68,negated_conjecture,
neq(esk4_0,nil),
inference(rw,[status(thm)],[c_0_60,c_0_34]) ).
cnf(c_0_69,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_61,c_0_47]),c_0_27])]),c_0_25]) ).
cnf(c_0_70,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(nil,X2)
| segmentP(app(nil,X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_46]),c_0_27])]) ).
cnf(c_0_71,negated_conjecture,
( esk3_0 = nil
| app(nil,esk3_0) = esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_63]),c_0_27]),c_0_64])]) ).
cnf(c_0_72,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_61,c_0_26]),c_0_27])]),c_0_25]) ).
cnf(c_0_73,negated_conjecture,
( esk4_0 != nil
| app(esk4_0,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_42])]) ).
cnf(c_0_74,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_67,c_0_68]),c_0_42])]) ).
cnf(c_0_75,negated_conjecture,
segmentP(esk4_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_66]),c_0_42]),c_0_27])]) ).
cnf(c_0_76,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(nil,X1)
| segmentP(esk3_0,X1)
| esk3_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_64])]) ).
cnf(c_0_77,negated_conjecture,
( esk4_0 != nil
| segmentP(nil,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_42]),c_0_27])]) ).
cnf(c_0_78,negated_conjecture,
~ segmentP(esk3_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
fof(c_0_79,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_80,negated_conjecture,
( cons(esk5_0,nil) = esk3_0
| nil = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_81,negated_conjecture,
( ssItem(esk5_0)
| nil = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_82,plain,
! [X33,X34,X37,X38] :
( ( ~ ssList(X33)
| ~ ssItem(X34)
| memberP(X33,X34)
| app(X37,cons(X34,X38)) != X33
| ~ ssList(X38)
| ~ ssList(X37) )
& ( ~ ssList(X33)
| ~ ssItem(X34)
| ~ memberP(X33,X34)
| app(esk8_2(X33,X34),cons(X34,esk9_2(X33,X34))) = X33 )
& ( ~ ssList(X33)
| ~ ssItem(X34)
| ~ memberP(X33,X34)
| ssList(esk9_2(X33,X34)) )
& ( ~ ssList(X33)
| ~ ssItem(X34)
| ~ memberP(X33,X34)
| ssList(esk8_2(X33,X34)) ) ),
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)],[ax3])])])])])]) ).
fof(c_0_83,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
inference(fof_simplification,[status(thm)],[ax18]) ).
cnf(c_0_84,negated_conjecture,
( esk4_0 != nil
| esk3_0 = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_42])]),c_0_78]) ).
fof(c_0_85,plain,
! [X81,X82] :
( ( ~ ssList(X81)
| ~ ssList(X82)
| neq(X81,X82)
| X81 = X82 )
& ( ~ ssList(X81)
| ~ ssList(X82)
| X81 != X82
| ~ neq(X81,X82) ) ),
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_79])])])])]) ).
fof(c_0_86,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_87,negated_conjecture,
( ~ ssList(X1)
| esk4_0 = nil
| cons(esk5_0,X1) = app(esk3_0,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_80]),c_0_81]) ).
cnf(c_0_88,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| ssList(esk9_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
fof(c_0_89,plain,
! [X50,X51] :
( cons(X51,X50) != X50
| ~ ssItem(X51)
| ~ ssList(X50) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_83])])])]) ).
cnf(c_0_90,negated_conjecture,
esk4_0 != nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_84]),c_0_77]) ).
cnf(c_0_91,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
fof(c_0_92,plain,
! [X48,X49] :
( ssList(cons(X49,X48))
| ~ ssItem(X49)
| ~ ssList(X48) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_93,plain,
! [X18,X19] :
( nil != cons(X19,X18)
| ~ ssItem(X19)
| ~ ssList(X18) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_86])])])]) ).
cnf(c_0_94,negated_conjecture,
( esk4_0 = nil
| cons(esk5_0,nil) = app(esk3_0,nil) ),
inference(spm,[status(thm)],[c_0_87,c_0_27]) ).
cnf(c_0_95,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| ~ memberP(X1,X2)
| esk3_0 = nil
| cons(esk5_0,esk9_2(X1,X2)) = app(esk3_0,esk9_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_44,c_0_88]) ).
cnf(c_0_96,negated_conjecture,
( memberP(esk4_0,esk5_0)
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_97,plain,
( cons(X2,X1) != X1
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_98,negated_conjecture,
cons(esk5_0,nil) = esk3_0,
inference(sr,[status(thm)],[c_0_80,c_0_90]) ).
cnf(c_0_99,negated_conjecture,
ssItem(esk5_0),
inference(sr,[status(thm)],[c_0_81,c_0_90]) ).
cnf(c_0_100,plain,
( ~ ssList(X1)
| neq(X1,nil)
| X1 = nil ),
inference(spm,[status(thm)],[c_0_91,c_0_27]) ).
cnf(c_0_101,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_102,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_103,negated_conjecture,
( esk4_0 = nil
| app(esk3_0,nil) = esk3_0 ),
inference(spm,[status(thm)],[c_0_80,c_0_94]) ).
cnf(c_0_104,negated_conjecture,
( esk3_0 = nil
| cons(esk5_0,esk9_2(esk4_0,esk5_0)) = app(esk3_0,esk9_2(esk4_0,esk5_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_42])]),c_0_37]) ).
cnf(c_0_105,negated_conjecture,
esk3_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_27]),c_0_99])]) ).
cnf(c_0_106,negated_conjecture,
( memberP(esk4_0,esk5_0)
| nil = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_107,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| neq(cons(X1,X2),nil) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]) ).
cnf(c_0_108,negated_conjecture,
( segmentP(esk3_0,esk3_0)
| esk4_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_103]),c_0_64]),c_0_27])]) ).
cnf(c_0_109,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| app(esk8_2(X1,X2),cons(X2,esk9_2(X1,X2))) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_110,negated_conjecture,
cons(esk5_0,esk9_2(esk4_0,esk5_0)) = app(esk3_0,esk9_2(esk4_0,esk5_0)),
inference(sr,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_111,negated_conjecture,
memberP(esk4_0,esk5_0),
inference(sr,[status(thm)],[c_0_106,c_0_90]) ).
cnf(c_0_112,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ segmentP(esk4_0,cons(X1,X2))
| ~ segmentP(esk3_0,cons(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_107]),c_0_101]) ).
cnf(c_0_113,negated_conjecture,
segmentP(esk3_0,esk3_0),
inference(sr,[status(thm)],[c_0_108,c_0_90]) ).
cnf(c_0_114,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(app(X1,app(X2,X3)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_24]),c_0_48]) ).
cnf(c_0_115,negated_conjecture,
app(esk8_2(esk4_0,esk5_0),app(esk3_0,esk9_2(esk4_0,esk5_0))) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_111]),c_0_42]),c_0_99])]) ).
cnf(c_0_116,negated_conjecture,
~ segmentP(esk4_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_98]),c_0_27]),c_0_99])]),c_0_113])]) ).
cnf(c_0_117,negated_conjecture,
( ~ ssList(esk8_2(esk4_0,esk5_0))
| ~ ssList(esk9_2(esk4_0,esk5_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_64])]),c_0_116]) ).
cnf(c_0_118,negated_conjecture,
~ ssList(esk8_2(esk4_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_117,c_0_88]),c_0_111]),c_0_42]),c_0_99])]) ).
cnf(c_0_119,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| ~ memberP(X1,X2)
| ssList(esk8_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_120,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_111]),c_0_42]),c_0_99])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC084+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 21 07:53:52 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 200.18/34.26 % Version: 3.5.1
% 200.18/34.26 % Preprocessing class: FSLSSMSSSSSNFFN.
% 200.18/34.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 200.18/34.26 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 200.18/34.26 % Starting new_bool_3 with 300s (1) cores
% 200.18/34.26 % Starting new_bool_1 with 300s (1) cores
% 200.18/34.26 % Starting sh5l with 300s (1) cores
% 200.18/34.26 % new_bool_3 with pid 1929808 completed with status 0
% 200.18/34.26 % Result found by new_bool_3
% 200.18/34.26 % Preprocessing class: FSLSSMSSSSSNFFN.
% 200.18/34.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 200.18/34.26 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 200.18/34.26 % Starting new_bool_3 with 300s (1) cores
% 200.18/34.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 200.18/34.26 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 200.18/34.26 % Search class: FGHSF-FFMM21-MFFFFFNN
% 200.18/34.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 200.18/34.26 % Starting SubtermCWHack with 31s (1) cores
% 200.18/34.26 % SubtermCWHack with pid 1929811 completed with status 8
% 200.18/34.26 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 200.18/34.26 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1930274 completed with status 0
% 200.18/34.26 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 200.18/34.26 % Preprocessing class: FSLSSMSSSSSNFFN.
% 200.18/34.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 200.18/34.26 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 200.18/34.26 % Starting new_bool_3 with 300s (1) cores
% 200.18/34.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 200.18/34.26 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 200.18/34.26 % Search class: FGHSF-FFMM21-MFFFFFNN
% 200.18/34.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 200.18/34.26 % Starting SubtermCWHack with 31s (1) cores
% 200.18/34.26 % SubtermCWHack with pid 1929811 completed with status 8
% 200.18/34.26 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 200.18/34.26 % Preprocessing time : 0.002 s
% 200.18/34.26 % Presaturation interreduction done
% 200.18/34.26
% 200.18/34.26 % Proof found!
% 200.18/34.26 % SZS status Theorem
% 200.18/34.26 % SZS output start CNFRefutation
% See solution above
% 200.18/34.26 % Parsed axioms : 96
% 200.18/34.26 % Removed by relevancy pruning/SinE : 57
% 200.18/34.26 % Initial clauses : 76
% 200.18/34.26 % Removed in clause preprocessing : 0
% 200.18/34.26 % Initial clauses in saturation : 76
% 200.18/34.26 % Processed clauses : 11256
% 200.18/34.26 % ...of these trivial : 510
% 200.18/34.26 % ...subsumed : 7293
% 200.18/34.26 % ...remaining for further processing : 3453
% 200.18/34.26 % Other redundant clauses eliminated : 70
% 200.18/34.26 % Clauses deleted for lack of memory : 0
% 200.18/34.26 % Backward-subsumed : 274
% 200.18/34.26 % Backward-rewritten : 291
% 200.18/34.26 % Generated clauses : 112985
% 200.18/34.26 % ...of the previous two non-redundant : 109727
% 200.18/34.26 % ...aggressively subsumed : 0
% 200.18/34.26 % Contextual simplify-reflections : 888
% 200.18/34.26 % Paramodulations : 112484
% 200.18/34.26 % Factorizations : 2
% 200.18/34.26 % NegExts : 0
% 200.18/34.26 % Equation resolutions : 104
% 200.18/34.26 % Disequality decompositions : 0
% 200.18/34.26 % Total rewrite steps : 70074
% 200.18/34.26 % ...of those cached : 69797
% 200.18/34.26 % Propositional unsat checks : 0
% 200.18/34.26 % Propositional check models : 0
% 200.18/34.26 % Propositional check unsatisfiable : 0
% 200.18/34.26 % Propositional clauses : 0
% 200.18/34.26 % Propositional clauses after purity: 0
% 200.18/34.26 % Propositional unsat core size : 0
% 200.18/34.26 % Propositional preprocessing time : 0.000
% 200.18/34.26 % Propositional encoding time : 0.000
% 200.18/34.26 % Propositional solver time : 0.000
% 200.18/34.26 % Success case prop preproc time : 0.000
% 200.18/34.26 % Success case prop encoding time : 0.000
% 200.18/34.26 % Success case prop solver time : 0.000
% 200.18/34.26 % Current number of processed clauses : 2412
% 200.18/34.26 % Positive orientable unit clauses : 316
% 200.18/34.26 % Positive unorientable unit clauses: 0
% 200.18/34.26 % Negative unit clauses : 263
% 200.18/34.26 % Non-unit-clauses : 1833
% 200.18/34.26 % Current number of unprocessed clauses: 93047
% 200.18/34.26 % ...number of literals in the above : 406568
% 200.18/34.26 % Current number of archived formulas : 0
% 200.18/34.26 % Current number of archived clauses : 1033
% 200.18/34.26 % Clause-clause subsumption calls (NU) : 341994
% 200.18/34.26 % Rec. Clause-clause subsumption calls : 118267
% 200.18/34.26 % Non-unit clause-clause subsumptions : 5811
% 200.18/34.26 % Unit Clause-clause subsumption calls : 21841
% 200.18/34.26 % Rewrite failures with RHS unbound : 0
% 200.18/34.26 % BW rewrite match attempts : 1097
% 200.18/34.26 % BW rewrite match successes : 32
% 200.18/34.26 % Condensation attempts : 0
% 200.18/34.26 % Condensation successes : 0
% 200.18/34.26 % Termbank termtop insertions : 2673498
% 200.18/34.26 % Search garbage collected termcells : 2063
% 200.18/34.26
% 200.18/34.26 % -------------------------------------------------
% 200.18/34.26 % User time : 32.092 s
% 200.18/34.26 % System time : 1.262 s
% 200.18/34.26 % Total time : 33.354 s
% 200.18/34.26 % Maximum resident set size: 3760 pages
% 200.18/34.26
% 200.18/34.26 % -------------------------------------------------
% 200.18/34.26 % User time : 32.096 s
% 200.18/34.26 % System time : 1.264 s
% 200.18/34.26 % Total time : 33.361 s
% 200.18/34.26 % Maximum resident set size: 4864 pages
% 200.18/34.26 % E exiting
%------------------------------------------------------------------------------