%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWC063+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 : n014.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 02:42:50 PM UTC 2026
% Result : Theorem 0.18s 5.64s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 114 ( 27 unt; 0 def)
% Number of atoms : 408 ( 120 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 505 ( 211 ~; 204 |; 40 &)
% ( 3 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 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; 7 con; 0-2 aty)
% Number of variables : 153 ( 0 sgn 83 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( ( ? [X7] :
( segmentP(X1,X7)
& segmentP(X2,X7)
& neq(X7,nil)
& ssList(X7) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ( neq(X4,nil)
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( app(X6,cons(X5,nil)) != X4
| app(cons(X5,nil),X6) != X3
| ~ ssList(X6) ) ) )
| ( nil = X4
& nil != X3 )
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax21) ).
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(ax82,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax19,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ( cons(X3,X1) = cons(X4,X2)
=> ( X2 = X1
& X3 = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax19) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( ( ? [X7] :
( segmentP(X1,X7)
& segmentP(X2,X7)
& neq(X7,nil)
& ssList(X7) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ( neq(X4,nil)
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( app(X6,cons(X5,nil)) != X4
| app(cons(X5,nil),X6) != X3
| ~ ssList(X6) ) ) )
| ( nil = X4
& nil != X3 )
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ( ( ? [X7] :
( segmentP(X1,X7)
& segmentP(X2,X7)
& neq(X7,nil)
& ssList(X7) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ( neq(X4,nil)
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( app(X6,cons(X5,nil)) != X4
| app(cons(X5,nil),X6) != X3
| ~ ssList(X6) ) ) )
| ( nil = X4
& nil != X3 )
| X1 != X3
| X2 != X4
| ~ ssList(X4) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_17,negated_conjecture,
! [X14] :
( ( nil != esk1_0
| ~ segmentP(esk1_0,X14)
| ~ segmentP(esk2_0,X14)
| ~ neq(X14,nil)
| ~ ssList(X14) )
& ( nil != esk1_0
| neq(esk2_0,nil) )
& ( nil = esk2_0
| ~ segmentP(esk1_0,X14)
| ~ segmentP(esk2_0,X14)
| ~ neq(X14,nil)
| ~ ssList(X14) )
& ( nil = esk2_0
| neq(esk2_0,nil) )
& ( ~ neq(esk4_0,nil)
| app(esk6_0,cons(esk5_0,nil)) = esk4_0 )
& ( ~ neq(esk4_0,nil)
| app(cons(esk5_0,nil),esk6_0) = esk3_0 )
& ( ~ neq(esk4_0,nil)
| ssList(esk6_0) )
& ( ~ neq(esk4_0,nil)
| ssItem(esk5_0) )
& ( nil != esk4_0
| nil = 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_16])])])])])]) ).
cnf(c_0_18,negated_conjecture,
( ~ neq(esk4_0,nil)
| app(cons(esk5_0,nil),esk6_0) = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_19,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,plain,
! [X54,X55] :
( cons(X55,X54) = app(cons(X55,nil),X54)
| ~ ssItem(X55)
| ~ ssList(X54) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
fof(c_0_21,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_22,negated_conjecture,
( ~ neq(esk4_0,nil)
| app(cons(esk5_0,nil),esk6_0) = esk1_0 ),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( ~ neq(esk4_0,nil)
| ssItem(esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
( ~ neq(esk4_0,nil)
| ssList(esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,negated_conjecture,
( nil != esk1_0
| neq(esk2_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_28,plain,
! [X40,X41] :
( nil != cons(X41,X40)
| ~ ssItem(X41)
| ~ ssList(X40) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
cnf(c_0_29,negated_conjecture,
( ~ neq(esk4_0,nil)
| cons(esk5_0,esk6_0) = esk1_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25]) ).
cnf(c_0_30,negated_conjecture,
( esk1_0 != nil
| neq(esk4_0,nil) ),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( esk1_0 != nil
| cons(esk5_0,esk6_0) = esk1_0 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( esk1_0 != nil
| ssItem(esk5_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( esk1_0 != nil
| ssList(esk6_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( nil != esk4_0
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_36,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_37,negated_conjecture,
( nil = esk2_0
| neq(esk2_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_38,negated_conjecture,
esk1_0 != nil,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( esk4_0 != nil
| esk1_0 = nil ),
inference(rw,[status(thm)],[c_0_35,c_0_19]) ).
fof(c_0_40,plain,
! [X35,X36] :
( ( ~ ssList(X35)
| ~ ssList(X36)
| neq(X35,X36)
| X35 = X36 )
& ( ~ ssList(X35)
| ~ ssList(X36)
| X35 != X36
| ~ neq(X35,X36) ) ),
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_36])])])])]) ).
fof(c_0_41,plain,
! [X56,X57,X58] :
( app(app(X56,X57),X58) = app(X56,app(X57,X58))
| ~ ssList(X58)
| ~ ssList(X57)
| ~ ssList(X56) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
fof(c_0_42,plain,
! [X47] :
( app(nil,X47) = X47
| ~ ssList(X47) ),
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)
| esk4_0 = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_27]),c_0_27]) ).
cnf(c_0_44,negated_conjecture,
esk4_0 != nil,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_47,negated_conjecture,
ssList(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_48,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,negated_conjecture,
( ~ neq(esk4_0,nil)
| app(esk6_0,cons(esk5_0,nil)) = esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_51,negated_conjecture,
neq(esk4_0,nil),
inference(sr,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,negated_conjecture,
( ssList(esk6_0)
| esk4_0 = nil ),
inference(spm,[status(thm)],[c_0_25,c_0_43]) ).
fof(c_0_53,plain,
! [X66,X67,X68,X69] :
( ( ~ ssList(X66)
| ~ ssList(X67)
| ~ ssItem(X68)
| ~ ssItem(X69)
| cons(X68,X66) != cons(X69,X67)
| X67 = X66 )
& ( ~ ssList(X66)
| ~ ssList(X67)
| ~ ssItem(X68)
| ~ ssItem(X69)
| cons(X68,X66) != cons(X69,X67)
| X68 = X69 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax19])])])])]) ).
cnf(c_0_54,negated_conjecture,
( esk4_0 = nil
| cons(esk5_0,esk6_0) = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_55,negated_conjecture,
( ssItem(esk5_0)
| esk4_0 = nil ),
inference(spm,[status(thm)],[c_0_24,c_0_43]) ).
cnf(c_0_56,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_48,c_0_49]),c_0_46])]) ).
cnf(c_0_57,negated_conjecture,
app(esk6_0,cons(esk5_0,nil)) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]) ).
cnf(c_0_58,negated_conjecture,
ssList(esk6_0),
inference(sr,[status(thm)],[c_0_52,c_0_44]) ).
fof(c_0_59,plain,
! [X62,X63] :
( ssList(cons(X63,X62))
| ~ ssItem(X63)
| ~ ssList(X62) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
cnf(c_0_60,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X3)
| ~ ssItem(X4)
| cons(X3,X2) != cons(X4,X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_61,negated_conjecture,
cons(esk5_0,esk6_0) = esk1_0,
inference(sr,[status(thm)],[c_0_54,c_0_44]) ).
cnf(c_0_62,negated_conjecture,
ssItem(esk5_0),
inference(sr,[status(thm)],[c_0_55,c_0_44]) ).
fof(c_0_63,plain,
! [X44,X45,X46] :
( cons(X46,app(X45,X44)) = app(cons(X46,X45),X44)
| ~ ssItem(X46)
| ~ ssList(X45)
| ~ ssList(X44) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).
fof(c_0_64,plain,
! [X42,X43] :
( ssList(app(X42,X43))
| ~ ssList(X43)
| ~ ssList(X42) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_65,plain,
! [X27,X28,X29,X30] :
( segmentP(app(app(X29,X27),X30),X28)
| ~ segmentP(X27,X28)
| ~ ssList(X30)
| ~ ssList(X29)
| ~ ssList(X28)
| ~ ssList(X27) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])])]) ).
cnf(c_0_66,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| app(nil,esk4_0) = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58])]) ).
cnf(c_0_67,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_68,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) != esk1_0
| esk6_0 = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_58]),c_0_62])]) ).
cnf(c_0_69,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_70,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_71,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_65]) ).
cnf(c_0_72,negated_conjecture,
app(cons(esk5_0,nil),esk6_0) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_51])]) ).
fof(c_0_73,plain,
! [X61] :
( app(X61,nil) = X61
| ~ ssList(X61) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
fof(c_0_74,plain,
! [X15,X16,X19,X20] :
( ( ~ ssList(X15)
| ~ ssList(X16)
| segmentP(X15,X16)
| app(app(X19,X16),X20) != X15
| ~ ssList(X20)
| ~ ssList(X19) )
& ( ~ ssList(X15)
| ~ ssList(X16)
| ~ segmentP(X15,X16)
| app(app(esk7_2(X15,X16),X16),esk8_2(X15,X16)) = X15 )
& ( ~ ssList(X15)
| ~ ssList(X16)
| ~ segmentP(X15,X16)
| ssList(esk8_2(X15,X16)) )
& ( ~ ssList(X15)
| ~ ssList(X16)
| ~ segmentP(X15,X16)
| ssList(esk7_2(X15,X16)) ) ),
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_75,negated_conjecture,
app(nil,esk4_0) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_46]),c_0_62])]) ).
cnf(c_0_76,negated_conjecture,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(cons(X3,X1),X2) != esk1_0
| app(X1,X2) = esk6_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).
cnf(c_0_77,negated_conjecture,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(cons(esk5_0,nil))
| ~ segmentP(esk6_0,X2)
| segmentP(app(esk1_0,X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_58])]) ).
cnf(c_0_78,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_79,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_80,plain,
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X1,X3)
| segmentP(app(X1,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_49]),c_0_46])]) ).
cnf(c_0_81,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_74]) ).
cnf(c_0_82,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ssList(app(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_48]),c_0_70]) ).
cnf(c_0_83,negated_conjecture,
( ~ ssList(X1)
| app(nil,app(esk4_0,X1)) = app(esk4_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_75]),c_0_47]),c_0_46])]) ).
cnf(c_0_84,negated_conjecture,
app(nil,esk6_0) = esk6_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_72]),c_0_46]),c_0_58]),c_0_62])]) ).
cnf(c_0_85,negated_conjecture,
( ~ segmentP(esk1_0,X1)
| ~ segmentP(esk2_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1)
| nil = esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_86,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(cons(esk5_0,nil))
| ~ segmentP(esk6_0,X1)
| segmentP(esk1_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_46]),c_0_79])]) ).
fof(c_0_87,plain,
! [X26] :
( segmentP(X26,X26)
| ~ ssList(X26) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
cnf(c_0_88,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(cons(esk5_0,nil))
| ~ segmentP(esk6_0,X1)
| segmentP(esk4_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_57]),c_0_58])]) ).
cnf(c_0_89,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_81]) ).
cnf(c_0_90,negated_conjecture,
( ~ ssList(X1)
| ssList(app(esk4_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_47]),c_0_46])]) ).
cnf(c_0_91,negated_conjecture,
( ~ ssList(X1)
| ~ ssList(cons(esk5_0,nil))
| app(esk6_0,app(cons(esk5_0,nil),X1)) = app(esk4_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_57]),c_0_58])]) ).
cnf(c_0_92,negated_conjecture,
( ~ ssItem(X1)
| app(cons(X1,nil),esk6_0) = cons(X1,esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_84]),c_0_46]),c_0_58])]) ).
cnf(c_0_93,negated_conjecture,
( ~ neq(X1,nil)
| ~ ssList(X1)
| ~ segmentP(esk4_0,X1)
| ~ segmentP(esk1_0,X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_27]),c_0_27]),c_0_44]) ).
cnf(c_0_94,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk6_0,X1)
| segmentP(esk1_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_67]),c_0_46]),c_0_62])]) ).
cnf(c_0_95,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_96,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk6_0,X1)
| segmentP(esk4_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_67]),c_0_46]),c_0_62])]) ).
cnf(c_0_97,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,X2),nil) = cons(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_78]),c_0_46])]) ).
cnf(c_0_98,negated_conjecture,
( ~ ssList(X1)
| segmentP(app(esk4_0,X1),esk4_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_75]),c_0_47]),c_0_46])]),c_0_90]) ).
cnf(c_0_99,negated_conjecture,
( ~ ssList(cons(esk5_0,nil))
| app(esk6_0,esk1_0) = app(esk4_0,esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_61]),c_0_58]),c_0_62])]) ).
cnf(c_0_100,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk4_0,X1)
| ~ segmentP(esk1_0,X1)
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_45]),c_0_46])]) ).
cnf(c_0_101,negated_conjecture,
segmentP(esk1_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_58])]) ).
cnf(c_0_102,negated_conjecture,
segmentP(esk4_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_95]),c_0_58])]) ).
cnf(c_0_103,negated_conjecture,
app(esk1_0,nil) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_61]),c_0_58]),c_0_62])]) ).
cnf(c_0_104,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_78,c_0_48]),c_0_46])]),c_0_70]) ).
cnf(c_0_105,negated_conjecture,
( ~ segmentP(esk4_0,esk4_0)
| ~ segmentP(esk1_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_51]),c_0_47])]) ).
cnf(c_0_106,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_98,c_0_78]),c_0_46]),c_0_47])]) ).
cnf(c_0_107,negated_conjecture,
app(esk6_0,esk1_0) = app(esk4_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_67]),c_0_46]),c_0_62])]) ).
cnf(c_0_108,negated_conjecture,
esk6_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]),c_0_58])]) ).
cnf(c_0_109,negated_conjecture,
app(nil,esk1_0) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_103]),c_0_46]),c_0_79])]) ).
cnf(c_0_110,negated_conjecture,
app(esk4_0,nil) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_104]),c_0_75]),c_0_46]),c_0_47])]) ).
cnf(c_0_111,negated_conjecture,
~ segmentP(esk1_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106])]) ).
cnf(c_0_112,negated_conjecture,
esk1_0 = esk4_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_108]),c_0_109]),c_0_108]),c_0_110]) ).
cnf(c_0_113,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_112]),c_0_106])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC063+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.41 % Computer : n014.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Mon Sep 21 07:52:40 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.47 Running first-order theorem proving
% 0.13/5.47 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.64 % Version: 3.5.1
% 0.18/5.64 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.18/5.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/5.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.18/5.64 % Starting new_bool_3 with 300s (1) cores
% 0.18/5.64 % Starting new_bool_1 with 300s (1) cores
% 0.18/5.64 % Starting sh5l with 300s (1) cores
% 0.18/5.64 % new_bool_1 with pid 3575765 completed with status 0
% 0.18/5.64 % Result found by new_bool_1
% 0.18/5.64 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.18/5.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/5.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.18/5.64 % Starting new_bool_3 with 300s (1) cores
% 0.18/5.64 % Starting new_bool_1 with 300s (1) cores
% 0.18/5.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.18/5.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.18/5.64 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.18/5.64 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.18/5.64 % Starting SubtermCWHack with 31s (1) cores
% 0.18/5.64 % SubtermCWHack with pid 3575767 completed with status 0
% 0.18/5.64 % Result found by SubtermCWHack
% 0.18/5.64 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.18/5.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/5.64 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.18/5.64 % Starting new_bool_3 with 300s (1) cores
% 0.18/5.64 % Starting new_bool_1 with 300s (1) cores
% 0.18/5.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.18/5.64 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.18/5.64 % Search class: FGHSF-FFMM21-MFFFFFNN
% 0.18/5.64 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.18/5.64 % Starting SubtermCWHack with 31s (1) cores
% 0.18/5.64 % Preprocessing time : 0.002 s
% 0.18/5.64
% 0.18/5.64 % Proof found!
% 0.18/5.64 % SZS status Theorem
% 0.18/5.64 % SZS output start CNFRefutation
% See solution above
% 0.18/5.64 % Parsed axioms : 96
% 0.18/5.64 % Removed by relevancy pruning/SinE : 70
% 0.18/5.64 % Initial clauses : 53
% 0.18/5.64 % Removed in clause preprocessing : 0
% 0.18/5.64 % Initial clauses in saturation : 53
% 0.18/5.64 % Processed clauses : 1465
% 0.18/5.64 % ...of these trivial : 19
% 0.18/5.64 % ...subsumed : 952
% 0.18/5.64 % ...remaining for further processing : 494
% 0.18/5.64 % Other redundant clauses eliminated : 34
% 0.18/5.64 % Clauses deleted for lack of memory : 0
% 0.18/5.64 % Backward-subsumed : 43
% 0.18/5.64 % Backward-rewritten : 222
% 0.18/5.64 % Generated clauses : 6158
% 0.18/5.64 % ...of the previous two non-redundant : 5203
% 0.18/5.64 % ...aggressively subsumed : 0
% 0.18/5.64 % Contextual simplify-reflections : 82
% 0.18/5.64 % Paramodulations : 6109
% 0.18/5.64 % Factorizations : 0
% 0.18/5.64 % NegExts : 0
% 0.18/5.64 % Equation resolutions : 46
% 0.18/5.64 % Disequality decompositions : 0
% 0.18/5.64 % Total rewrite steps : 6673
% 0.18/5.64 % ...of those cached : 6630
% 0.18/5.64 % Propositional unsat checks : 0
% 0.18/5.64 % Propositional check models : 0
% 0.18/5.64 % Propositional check unsatisfiable : 0
% 0.18/5.64 % Propositional clauses : 0
% 0.18/5.64 % Propositional clauses after purity: 0
% 0.18/5.64 % Propositional unsat core size : 0
% 0.18/5.64 % Propositional preprocessing time : 0.000
% 0.18/5.64 % Propositional encoding time : 0.000
% 0.18/5.64 % Propositional solver time : 0.000
% 0.18/5.64 % Success case prop preproc time : 0.000
% 0.18/5.64 % Success case prop encoding time : 0.000
% 0.18/5.64 % Success case prop solver time : 0.000
% 0.18/5.64 % Current number of processed clauses : 220
% 0.18/5.64 % Positive orientable unit clauses : 24
% 0.18/5.64 % Positive unorientable unit clauses: 0
% 0.18/5.64 % Negative unit clauses : 11
% 0.18/5.64 % Non-unit-clauses : 185
% 0.18/5.64 % Current number of unprocessed clauses: 3729
% 0.18/5.64 % ...number of literals in the above : 19673
% 0.18/5.64 % Current number of archived formulas : 0
% 0.18/5.64 % Current number of archived clauses : 269
% 0.18/5.64 % Clause-clause subsumption calls (NU) : 14997
% 0.18/5.64 % Rec. Clause-clause subsumption calls : 7025
% 0.18/5.64 % Non-unit clause-clause subsumptions : 772
% 0.18/5.64 % Unit Clause-clause subsumption calls : 301
% 0.18/5.64 % Rewrite failures with RHS unbound : 0
% 0.18/5.64 % BW rewrite match attempts : 25
% 0.18/5.64 % BW rewrite match successes : 19
% 0.18/5.64 % Condensation attempts : 0
% 0.18/5.64 % Condensation successes : 0
% 0.18/5.64 % Termbank termtop insertions : 108075
% 0.18/5.64 % Search garbage collected termcells : 1610
% 0.18/5.64
% 0.18/5.64 % -------------------------------------------------
% 0.18/5.64 % User time : 0.108 s
% 0.18/5.64 % System time : 0.009 s
% 0.18/5.64 % Total time : 0.117 s
% 0.18/5.64 % Maximum resident set size: 3760 pages
% 0.18/5.64
% 0.18/5.64 % -------------------------------------------------
% 0.18/5.64 % User time : 0.111 s
% 0.18/5.64 % System time : 0.013 s
% 0.18/5.64 % Total time : 0.124 s
% 0.18/5.64 % Maximum resident set size: 4608 pages
% 0.18/5.64 % E exiting
%------------------------------------------------------------------------------