%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWC062+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 : n002.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 02:44:45 PM UTC 2026
% Result : Theorem 67.54s 10.39s
% Output : CNFRefutation 67.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 19
% Syntax : Number of formulae : 164 ( 18 unt; 0 def)
% Number of atoms : 604 ( 200 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 776 ( 336 ~; 331 |; 49 &)
% ( 4 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 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 : 251 ( 0 sgn 93 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ? [X7] :
( segmentP(X1,X7)
& segmentP(X2,X7)
& neq(X7,nil)
& ssList(X7) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ( nil = X4
& nil != X3 )
| ? [X5] :
( ? [X6] :
( app(cons(X5,nil),X6) = X4
& app(X6,cons(X5,nil)) != X3
& ssList(X6) )
& ssItem(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
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(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(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
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(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(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(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(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(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(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax54,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X2,X1)
& segmentP(X1,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax54) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
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(c_0_19,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ? [X7] :
( segmentP(X1,X7)
& segmentP(X2,X7)
& neq(X7,nil)
& ssList(X7) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ( nil = X4
& nil != X3 )
| ? [X5] :
( ? [X6] :
( app(cons(X5,nil),X6) = X4
& app(X6,cons(X5,nil)) != X3
& ssList(X6) )
& ssItem(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ( ? [X7] :
( segmentP(X1,X7)
& segmentP(X2,X7)
& neq(X7,nil)
& ssList(X7) )
| ~ neq(X2,nil) )
& ( nil = X1
| nil != X2 ) )
| ( nil = X4
& nil != X3 )
| ? [X5] :
( ? [X6] :
( app(cons(X5,nil),X6) = X4
& app(X6,cons(X5,nil)) != X3
& ssList(X6) )
& ssItem(X5) )
| X1 != X3
| X2 != X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_21,plain,
! [X59,X60] :
( ( ~ ssList(X59)
| ~ ssList(X60)
| nil = app(X59,X60)
| nil != X59
| nil != X60 )
& ( ~ ssList(X59)
| ~ ssList(X60)
| nil != app(X59,X60)
| nil = X59 )
& ( ~ ssList(X59)
| ~ ssList(X60)
| nil != app(X59,X60)
| nil = X60 ) ),
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])])])])]) ).
fof(c_0_22,negated_conjecture,
! [X12,X13,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) )
& ( nil != esk4_0
| nil = esk3_0 )
& ( app(cons(X12,nil),X13) != esk4_0
| app(X13,cons(X12,nil)) = esk3_0
| ~ ssList(X13)
| ~ ssItem(X12) )
& 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_20])])])])])]) ).
fof(c_0_23,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])])])]) ).
fof(c_0_24,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_25,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])])])]) ).
cnf(c_0_26,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| nil != X2
| nil != X1
| nil = app(X2,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,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_29,plain,
! [X47] :
( app(nil,X47) = X47
| ~ ssList(X47) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
fof(c_0_30,plain,
! [X61] :
( app(X61,nil) = X61
| ~ ssList(X61) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_31,negated_conjecture,
( app(cons(X1,nil),X2) != esk4_0
| ~ ssList(X2)
| ~ ssItem(X1)
| app(X2,cons(X1,nil)) = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_34,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])])])]) ).
cnf(c_0_35,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| ssList(cons(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_36,plain,
( ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_37,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ssList(app(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_26])]),c_0_27])]) ).
fof(c_0_39,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(esk5_2(X15,X16),X16),esk6_2(X15,X16)) = X15 )
& ( ~ ssList(X15)
| ~ ssList(X16)
| ~ segmentP(X15,X16)
| ssList(esk6_2(X15,X16)) )
& ( ~ ssList(X15)
| ~ ssList(X16)
| ~ segmentP(X15,X16)
| ssList(esk5_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_40,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),X3) = app(X1,app(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_41,plain,
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_42,plain,
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_43,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| app(cons(X2,nil),X1) != esk2_0
| app(X1,cons(X2,nil)) = esk1_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_44,plain,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) = app(cons(X2,nil),X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_45,plain,
( ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ssList(app(cons(X1,X2),X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_46,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_36,c_0_38]),c_0_27])]) ).
cnf(c_0_47,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_39]) ).
cnf(c_0_48,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_40,c_0_41]),c_0_27])]) ).
cnf(c_0_49,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_42,c_0_40]),c_0_27])]),c_0_37]) ).
cnf(c_0_50,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) != esk2_0
| app(X1,cons(X2,nil)) = esk1_0 ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,plain,
( ~ ssItem(X1)
| ssList(cons(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_27])]) ).
fof(c_0_52,plain,
! [X37] :
( ( ~ ssList(X37)
| nil = X37
| cons(esk8_1(X37),esk7_1(X37)) = X37 )
& ( ~ ssList(X37)
| nil = X37
| ssItem(esk8_1(X37)) )
& ( ~ ssList(X37)
| nil = X37
| ssList(esk7_1(X37)) ) ),
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_53,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_47]) ).
cnf(c_0_54,plain,
( ~ ssList(X1)
| app(nil,X1) = app(X1,nil) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_27])]) ).
cnf(c_0_55,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ssList(app(X1,app(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_40]),c_0_37]) ).
cnf(c_0_56,plain,
( ~ ssList(X1)
| app(nil,app(nil,X1)) = app(nil,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_38]),c_0_27])]) ).
fof(c_0_57,plain,
! [X51,X52,X53] :
( X53 = X51
| app(X52,X53) != app(X52,X51)
| ~ ssList(X53)
| ~ ssList(X52)
| ~ ssList(X51) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])])]) ).
cnf(c_0_58,negated_conjecture,
( ~ ssItem(X1)
| ~ ssList(X2)
| cons(X1,X2) != esk2_0
| app(nil,esk1_0) = esk1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_50]),c_0_51]) ).
cnf(c_0_59,plain,
( ~ ssList(X1)
| nil = X1
| cons(esk8_1(X1),esk7_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_60,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_61,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_53,c_0_41]),c_0_27])]),c_0_37]) ).
cnf(c_0_62,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(app(nil,X1),X2) = app(X1,app(nil,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_54]),c_0_27])]) ).
cnf(c_0_63,plain,
( ~ ssList(X1)
| ssList(app(nil,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_27])]) ).
cnf(c_0_64,plain,
( app(X2,X3) != app(X2,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_65,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,app(nil,X2)) = app(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_42]),c_0_27])]) ).
fof(c_0_66,plain,
! [X48,X49,X50] :
( X50 = X48
| app(X50,X49) != app(X48,X49)
| ~ ssList(X50)
| ~ ssList(X49)
| ~ ssList(X48) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])])]) ).
fof(c_0_67,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_68,negated_conjecture,
( ~ ssItem(esk8_1(esk2_0))
| ~ ssList(esk7_1(esk2_0))
| esk2_0 = nil
| app(nil,esk1_0) = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59])]),c_0_60])]) ).
cnf(c_0_69,plain,
( ~ ssList(X1)
| nil = X1
| ssItem(esk8_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_70,negated_conjecture,
( nil != esk1_0
| ~ segmentP(esk1_0,X1)
| ~ segmentP(esk2_0,X1)
| ~ neq(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_71,negated_conjecture,
( nil != esk1_0
| neq(esk2_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_72,negated_conjecture,
( nil != esk4_0
| nil = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_73,plain,
( ~ ssList(X1)
| segmentP(app(nil,X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_54]),c_0_27])]) ).
cnf(c_0_74,plain,
( ~ ssList(X1)
| app(nil,app(nil,X1)) = app(X1,nil) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_62]),c_0_38]),c_0_27])]),c_0_63]) ).
cnf(c_0_75,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(X3,X1) != app(X3,X2)
| X1 = app(nil,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_63]) ).
cnf(c_0_76,plain,
( app(X3,X2) != app(X1,X2)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| X3 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_77,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_67]) ).
cnf(c_0_78,negated_conjecture,
( ~ ssList(esk7_1(esk2_0))
| esk2_0 = nil
| app(nil,esk1_0) = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_60])]) ).
cnf(c_0_79,plain,
( ~ ssList(X1)
| nil = X1
| ssList(esk7_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_80,negated_conjecture,
( ~ segmentP(esk2_0,esk2_0)
| ~ segmentP(esk1_0,esk2_0)
| esk1_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_60])]) ).
cnf(c_0_81,negated_conjecture,
( esk2_0 != nil
| esk1_0 = nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_32]),c_0_33]) ).
fof(c_0_82,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_83,plain,
( ~ ssList(X1)
| segmentP(app(X1,nil),app(nil,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_63]) ).
cnf(c_0_84,plain,
( ~ ssList(X1)
| app(nil,app(nil,X1)) = X1 ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_41]),c_0_27])])]),c_0_63]) ).
cnf(c_0_85,plain,
( ~ ssList(X1)
| app(X1,nil) != nil
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_38]),c_0_27])]) ).
cnf(c_0_86,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_22]) ).
cnf(c_0_87,negated_conjecture,
( nil = esk2_0
| neq(esk2_0,nil) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_88,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_77,c_0_41]),c_0_27])]) ).
cnf(c_0_89,negated_conjecture,
( esk2_0 = nil
| app(nil,esk1_0) = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_60])]) ).
cnf(c_0_90,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_91,negated_conjecture,
( ~ segmentP(esk2_0,esk2_0)
| ~ segmentP(nil,esk2_0)
| esk2_0 != nil ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_92,plain,
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_93,plain,
( ~ ssList(X1)
| segmentP(app(app(nil,X1),nil),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_63]) ).
cnf(c_0_94,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,app(X2,nil)) != nil
| app(X1,X2) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_40]),c_0_27])]),c_0_37]) ).
cnf(c_0_95,negated_conjecture,
( ~ segmentP(esk2_0,esk2_0)
| ~ segmentP(esk1_0,esk2_0)
| esk2_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_60])]) ).
cnf(c_0_96,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(nil,X1)
| segmentP(esk1_0,X1)
| esk2_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]),c_0_27])]) ).
cnf(c_0_97,negated_conjecture,
( ~ segmentP(nil,esk2_0)
| esk2_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_60])]) ).
cnf(c_0_98,plain,
( ~ ssList(X1)
| segmentP(app(nil,app(X1,nil)),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_40]),c_0_27])]) ).
cnf(c_0_99,plain,
( ~ ssList(X1)
| app(X1,nil) != nil
| app(nil,X1) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_48]),c_0_27])]) ).
fof(c_0_100,plain,
! [X24,X25] :
( X24 = X25
| ~ segmentP(X25,X24)
| ~ segmentP(X24,X25)
| ~ ssList(X25)
| ~ ssList(X24) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax54])])])]) ).
cnf(c_0_101,plain,
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X4)
| ssList(app(X1,app(X2,app(X3,X4)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_40]),c_0_37]) ).
cnf(c_0_102,plain,
( ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,app(X2,app(nil,X3))) = app(app(X1,X2),X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_65]),c_0_37]),c_0_63]) ).
cnf(c_0_103,plain,
( ~ ssList(X1)
| ssList(app(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_38]),c_0_27])]) ).
cnf(c_0_104,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X1,app(nil,X2)) = app(nil,app(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_62]),c_0_27])]) ).
cnf(c_0_105,negated_conjecture,
( ~ segmentP(nil,esk2_0)
| ~ segmentP(esk2_0,esk2_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_60])]),c_0_97]) ).
cnf(c_0_106,plain,
( ~ ssList(X1)
| segmentP(app(nil,app(nil,X1)),X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_54]) ).
cnf(c_0_107,plain,
( ~ ssList(X1)
| app(X1,nil) != nil
| app(nil,app(nil,X1)) = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_62]),c_0_38]),c_0_27])]),c_0_63]) ).
cnf(c_0_108,plain,
( ~ segmentP(X2,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_109,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ssList(app(app(X1,X2),X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_27])]) ).
cnf(c_0_110,plain,
( ~ ssList(X1)
| segmentP(app(nil,X1),app(X1,nil)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_49]),c_0_27])]),c_0_103]) ).
cnf(c_0_111,plain,
( ~ ssList(X1)
| app(nil,app(X1,nil)) != nil
| app(X1,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_104]),c_0_27])]) ).
cnf(c_0_112,plain,
( ~ ssList(X1)
| app(nil,app(nil,X1)) = app(nil,app(X1,nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_54]),c_0_27])]) ).
cnf(c_0_113,negated_conjecture,
~ segmentP(nil,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_92]),c_0_60])]) ).
cnf(c_0_114,plain,
( ~ ssList(X1)
| app(X1,nil) != nil
| segmentP(nil,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_115,plain,
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X4)
| ~ ssList(X1)
| ~ segmentP(X3,X1)
| ~ segmentP(X1,app(app(X2,X3),X4))
| X1 = app(app(X2,X3),X4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_77]),c_0_109]) ).
cnf(c_0_116,plain,
( ~ ssList(X1)
| segmentP(X1,app(app(nil,X1),nil)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_84]),c_0_63]) ).
cnf(c_0_117,plain,
( ~ ssList(X1)
| app(nil,app(nil,X1)) != nil
| app(X1,nil) = nil ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_118,negated_conjecture,
app(esk2_0,nil) != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_60])]) ).
cnf(c_0_119,plain,
( ~ ssList(X1)
| app(app(nil,X1),nil) = X1 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_27])]),c_0_92]) ).
cnf(c_0_120,negated_conjecture,
( app(nil,esk1_0) != nil
| esk2_0 = nil
| app(esk1_0,nil) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_89]),c_0_90])]) ).
cnf(c_0_121,negated_conjecture,
esk2_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_42]),c_0_60])]) ).
fof(c_0_122,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_123,plain,
( ~ ssList(X1)
| app(app(X1,nil),nil) = X1 ),
inference(spm,[status(thm)],[c_0_119,c_0_54]) ).
cnf(c_0_124,negated_conjecture,
( app(nil,esk1_0) != nil
| segmentP(nil,app(nil,esk1_0))
| esk2_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_120]),c_0_90])]) ).
cnf(c_0_125,negated_conjecture,
app(nil,esk1_0) = esk1_0,
inference(sr,[status(thm)],[c_0_89,c_0_121]) ).
cnf(c_0_126,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) != esk2_0
| segmentP(esk1_0,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_50]),c_0_51]) ).
fof(c_0_127,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_128,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_122])])])]) ).
cnf(c_0_129,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ segmentP(X1,X2)
| ~ segmentP(nil,X1)
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_123]),c_0_27])]) ).
cnf(c_0_130,negated_conjecture,
( esk1_0 != nil
| segmentP(nil,esk1_0) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_125]),c_0_125]),c_0_121]) ).
cnf(c_0_131,negated_conjecture,
( ~ ssItem(esk8_1(esk2_0))
| ~ ssList(esk7_1(esk2_0))
| segmentP(esk1_0,esk7_1(esk2_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_59])]),c_0_60])]),c_0_121]) ).
fof(c_0_132,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_127])])])])]) ).
cnf(c_0_133,plain,
( nil != cons(X2,X1)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_134,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk1_0,X1)
| esk1_0 != nil
| esk1_0 = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_90])]) ).
cnf(c_0_135,negated_conjecture,
( ~ ssList(esk7_1(esk2_0))
| segmentP(esk1_0,esk7_1(esk2_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_69]),c_0_60])]),c_0_121]) ).
cnf(c_0_136,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| neq(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_137,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_53,c_0_42]),c_0_27])]),c_0_37]) ).
cnf(c_0_138,plain,
( ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| app(cons(X1,X2),X3) != nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_36]),c_0_37]) ).
cnf(c_0_139,negated_conjecture,
( ~ ssList(esk7_1(esk2_0))
| esk1_0 != nil
| esk7_1(esk2_0) = esk1_0 ),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_140,negated_conjecture,
( ~ ssList(X1)
| ~ segmentP(esk2_0,X1)
| ~ segmentP(esk1_0,X1)
| X1 = nil
| esk2_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_136]),c_0_27])]) ).
cnf(c_0_141,plain,
( ~ ssItem(X1)
| ~ ssList(X2)
| segmentP(cons(X1,X2),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_44]),c_0_51]) ).
cnf(c_0_142,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| app(X1,app(app(nil,X2),X3)) = app(app(X1,X2),X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_65]),c_0_63]) ).
cnf(c_0_143,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X1) != app(nil,X2)
| X1 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_54]),c_0_27])]) ).
cnf(c_0_144,plain,
( ~ ssItem(X1)
| cons(X1,nil) != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_46]),c_0_27])]) ).
cnf(c_0_145,negated_conjecture,
( esk1_0 != nil
| esk7_1(esk2_0) = esk1_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_79]),c_0_60])]),c_0_121]) ).
cnf(c_0_146,negated_conjecture,
( ~ ssList(esk7_1(esk2_0))
| ~ segmentP(esk2_0,esk7_1(esk2_0))
| esk7_1(esk2_0) = nil ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_135]),c_0_121]) ).
cnf(c_0_147,plain,
( ~ ssList(X1)
| segmentP(X1,esk7_1(X1))
| nil = X1 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_59]),c_0_69]),c_0_79]) ).
cnf(c_0_148,plain,
( ~ ssList(X2)
| ~ ssList(X1)
| app(app(X1,X2),nil) = app(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_119]),c_0_27])]) ).
cnf(c_0_149,negated_conjecture,
( ~ ssItem(X2)
| ~ ssList(X1)
| cons(X2,X1) != esk2_0
| app(nil,X1) != esk1_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_50]),c_0_51]),c_0_144]) ).
cnf(c_0_150,negated_conjecture,
( esk1_0 != nil
| cons(esk8_1(esk2_0),esk1_0) = esk2_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_145]),c_0_60])]),c_0_121]) ).
cnf(c_0_151,plain,
( ~ ssList(X1)
| segmentP(X1,app(X1,nil)) ),
inference(spm,[status(thm)],[c_0_110,c_0_41]) ).
cnf(c_0_152,negated_conjecture,
( ~ ssList(esk7_1(esk2_0))
| esk7_1(esk2_0) = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_60])]),c_0_121]) ).
cnf(c_0_153,negated_conjecture,
( esk2_0 = nil
| app(esk1_0,nil) = esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_89]),c_0_27]),c_0_90])]) ).
cnf(c_0_154,negated_conjecture,
( ~ ssItem(esk8_1(esk2_0))
| esk1_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_125]),c_0_90])]) ).
cnf(c_0_155,plain,
( ~ ssList(X1)
| segmentP(X1,app(nil,X1)) ),
inference(spm,[status(thm)],[c_0_151,c_0_54]) ).
cnf(c_0_156,negated_conjecture,
esk7_1(esk2_0) = nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_79]),c_0_60])]),c_0_121]) ).
cnf(c_0_157,negated_conjecture,
app(esk1_0,nil) = esk1_0,
inference(sr,[status(thm)],[c_0_153,c_0_121]) ).
cnf(c_0_158,negated_conjecture,
esk1_0 != nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_69]),c_0_60])]),c_0_121]) ).
cnf(c_0_159,negated_conjecture,
( ~ ssItem(X1)
| cons(X1,nil) != esk2_0
| segmentP(cons(X1,nil),esk1_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_50]),c_0_27])]),c_0_51]) ).
cnf(c_0_160,negated_conjecture,
cons(esk8_1(esk2_0),nil) = esk2_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_156]),c_0_60])]),c_0_121]) ).
cnf(c_0_161,negated_conjecture,
~ segmentP(esk2_0,esk1_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_151]),c_0_90])]),c_0_157]),c_0_157]),c_0_157]),c_0_90])]),c_0_121]),c_0_158]) ).
cnf(c_0_162,negated_conjecture,
~ ssItem(esk8_1(esk2_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_161]) ).
cnf(c_0_163,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_69]),c_0_60])]),c_0_121]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC062+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n002.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 07:55:17 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.50 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
% 67.54/10.39 % Version: 3.5.1
% 67.54/10.39 % Preprocessing class: FSLSSMSSSSSNFFN.
% 67.54/10.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 67.54/10.39 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 67.54/10.39 % Starting new_bool_3 with 300s (1) cores
% 67.54/10.39 % Starting new_bool_1 with 300s (1) cores
% 67.54/10.39 % Starting sh5l with 300s (1) cores
% 67.54/10.39 % new_bool_1 with pid 2809421 completed with status 0
% 67.54/10.39 % Result found by new_bool_1
% 67.54/10.39 % Preprocessing class: FSLSSMSSSSSNFFN.
% 67.54/10.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 67.54/10.39 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 67.54/10.39 % Starting new_bool_3 with 300s (1) cores
% 67.54/10.39 % Starting new_bool_1 with 300s (1) cores
% 67.54/10.39 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 67.54/10.39 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 67.54/10.39 % Search class: FGHSF-FFMM21-MFFFFFNN
% 67.54/10.39 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 67.54/10.39 % Starting SubtermCWHack with 31s (1) cores
% 67.54/10.39 % SubtermCWHack with pid 2809424 completed with status 0
% 67.54/10.39 % Result found by SubtermCWHack
% 67.54/10.39 % Preprocessing class: FSLSSMSSSSSNFFN.
% 67.54/10.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 67.54/10.39 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 67.54/10.39 % Starting new_bool_3 with 300s (1) cores
% 67.54/10.39 % Starting new_bool_1 with 300s (1) cores
% 67.54/10.39 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 67.54/10.39 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 67.54/10.39 % Search class: FGHSF-FFMM21-MFFFFFNN
% 67.54/10.39 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 67.54/10.39 % Starting SubtermCWHack with 31s (1) cores
% 67.54/10.39 % Preprocessing time : 0.002 s
% 67.54/10.39
% 67.54/10.39 % Proof found!
% 67.54/10.39 % SZS status Theorem
% 67.54/10.39 % SZS output start CNFRefutation
% See solution above
% 67.54/10.39 % Parsed axioms : 96
% 67.54/10.39 % Removed by relevancy pruning/SinE : 70
% 67.54/10.39 % Initial clauses : 50
% 67.54/10.39 % Removed in clause preprocessing : 0
% 67.54/10.39 % Initial clauses in saturation : 50
% 67.54/10.39 % Processed clauses : 25017
% 67.54/10.39 % ...of these trivial : 216
% 67.54/10.39 % ...subsumed : 22295
% 67.54/10.39 % ...remaining for further processing : 2506
% 67.54/10.39 % Other redundant clauses eliminated : 1220
% 67.54/10.39 % Clauses deleted for lack of memory : 0
% 67.54/10.39 % Backward-subsumed : 151
% 67.54/10.39 % Backward-rewritten : 86
% 67.54/10.39 % Generated clauses : 603996
% 67.54/10.39 % ...of the previous two non-redundant : 573159
% 67.54/10.39 % ...aggressively subsumed : 0
% 67.54/10.39 % Contextual simplify-reflections : 1314
% 67.54/10.39 % Paramodulations : 602582
% 67.54/10.39 % Factorizations : 0
% 67.54/10.40 % NegExts : 0
% 67.54/10.40 % Equation resolutions : 1347
% 67.54/10.40 % Disequality decompositions : 0
% 67.54/10.40 % Total rewrite steps : 418058
% 67.54/10.40 % ...of those cached : 417943
% 67.54/10.40 % Propositional unsat checks : 0
% 67.54/10.40 % Propositional check models : 0
% 67.54/10.40 % Propositional check unsatisfiable : 0
% 67.54/10.40 % Propositional clauses : 0
% 67.54/10.40 % Propositional clauses after purity: 0
% 67.54/10.40 % Propositional unsat core size : 0
% 67.54/10.40 % Propositional preprocessing time : 0.000
% 67.54/10.40 % Propositional encoding time : 0.000
% 67.54/10.40 % Propositional solver time : 0.000
% 67.54/10.40 % Success case prop preproc time : 0.000
% 67.54/10.40 % Success case prop encoding time : 0.000
% 67.54/10.40 % Success case prop solver time : 0.000
% 67.54/10.40 % Current number of processed clauses : 2196
% 67.54/10.40 % Positive orientable unit clauses : 112
% 67.54/10.40 % Positive unorientable unit clauses: 0
% 67.54/10.40 % Negative unit clauses : 16
% 67.54/10.40 % Non-unit-clauses : 2068
% 67.54/10.40 % Current number of unprocessed clauses: 547866
% 67.54/10.40 % ...number of literals in the above : 3610247
% 67.54/10.40 % Current number of archived formulas : 0
% 67.54/10.40 % Current number of archived clauses : 305
% 67.54/10.40 % Clause-clause subsumption calls (NU) : 1146384
% 67.54/10.40 % Rec. Clause-clause subsumption calls : 611612
% 67.54/10.40 % Non-unit clause-clause subsumptions : 23587
% 67.54/10.40 % Unit Clause-clause subsumption calls : 4296
% 67.54/10.40 % Rewrite failures with RHS unbound : 0
% 67.54/10.40 % BW rewrite match attempts : 1513
% 67.54/10.40 % BW rewrite match successes : 18
% 67.54/10.40 % Condensation attempts : 0
% 67.54/10.40 % Condensation successes : 0
% 67.54/10.40 % Termbank termtop insertions : 14079982
% 67.54/10.40 % Search garbage collected termcells : 1593
% 67.54/10.40
% 67.54/10.40 % -------------------------------------------------
% 67.54/10.40 % User time : 9.295 s
% 67.54/10.40 % System time : 0.350 s
% 67.54/10.40 % Total time : 9.645 s
% 67.54/10.40 % Maximum resident set size: 3760 pages
% 67.54/10.40
% 67.54/10.40 % -------------------------------------------------
% 67.54/10.40 % User time : 9.302 s
% 67.54/10.40 % System time : 0.356 s
% 67.54/10.40 % Total time : 9.658 s
% 67.54/10.40 % Maximum resident set size: 4608 pages
% 67.54/10.40 % E exiting
%------------------------------------------------------------------------------