TSTP Solution File: SWC062+1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SWC062+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 04:22:56 EDT 2024
% Result : Theorem 2.52s 0.72s
% Output : CNFRefutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of formulae : 114 ( 20 unt; 0 def)
% Number of atoms : 432 ( 147 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 541 ( 223 ~; 230 |; 41 &)
% ( 4 <=>; 43 =>; 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 : 173 ( 0 sgn 75 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
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(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) != X3
& app(cons(X5,nil),X6) = X4 ) )
| ( nil != X3
& nil = X4 )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X7] :
( ssList(X7)
& neq(X7,nil)
& segmentP(X2,X7)
& segmentP(X1,X7) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
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(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(ax54,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X2,X1) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax54) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
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(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(c_0_17,plain,
! [X48,X49,X50] :
( ~ ssList(X48)
| ~ ssList(X49)
| ~ ssList(X50)
| app(X50,X49) != app(X48,X49)
| X50 = 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_18,plain,
! [X56,X57,X58] :
( ~ ssList(X56)
| ~ ssList(X57)
| ~ ssList(X58)
| app(app(X56,X57),X58) = app(X56,app(X57,X58)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
fof(c_0_19,plain,
! [X42,X43] :
( ~ ssList(X42)
| ~ ssList(X43)
| ssList(app(X42,X43)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_20,plain,
! [X47] :
( ~ ssList(X47)
| app(nil,X47) = X47 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
cnf(c_0_21,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X3,X2) != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_26,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) != X3
& app(cons(X5,nil),X6) = X4 ) )
| ( nil != X3
& nil = X4 )
| ( ( nil != X2
| nil = X1 )
& ( ~ neq(X2,nil)
| ? [X7] :
( ssList(X7)
& neq(X7,nil)
& segmentP(X2,X7)
& segmentP(X1,X7) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
fof(c_0_27,plain,
! [X59,X60] :
( ( nil = X60
| nil != app(X59,X60)
| ~ ssList(X60)
| ~ ssList(X59) )
& ( nil = X59
| nil != app(X59,X60)
| ~ ssList(X60)
| ~ ssList(X59) )
& ( nil != X60
| nil != X59
| nil = app(X59,X60)
| ~ ssList(X60)
| ~ ssList(X59) ) ),
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_28,plain,
( X1 = app(X2,X3)
| app(X1,X4) != app(X2,app(X3,X4))
| ~ ssList(X4)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_29,plain,
( app(nil,app(X1,X2)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_24]),c_0_25])]) ).
fof(c_0_30,negated_conjecture,
! [X12,X13,X14] :
( ssList(esk1_0)
& ssList(esk2_0)
& ssList(esk3_0)
& ssList(esk4_0)
& esk2_0 = esk4_0
& esk1_0 = esk3_0
& ( ~ ssItem(X12)
| ~ ssList(X13)
| app(X13,cons(X12,nil)) = esk3_0
| app(cons(X12,nil),X13) != esk4_0 )
& ( nil = esk3_0
| nil != esk4_0 )
& ( neq(esk2_0,nil)
| nil = esk2_0 )
& ( ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(esk2_0,X14)
| ~ segmentP(esk1_0,X14)
| nil = esk2_0 )
& ( neq(esk2_0,nil)
| nil != esk1_0 )
& ( ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(esk2_0,X14)
| ~ segmentP(esk1_0,X14)
| nil != 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_26])])])])])]) ).
fof(c_0_31,plain,
! [X15,X16,X19,X20] :
( ( ssList(esk5_2(X15,X16))
| ~ segmentP(X15,X16)
| ~ ssList(X16)
| ~ ssList(X15) )
& ( ssList(esk6_2(X15,X16))
| ~ segmentP(X15,X16)
| ~ ssList(X16)
| ~ ssList(X15) )
& ( app(app(esk5_2(X15,X16),X16),esk6_2(X15,X16)) = X15
| ~ segmentP(X15,X16)
| ~ ssList(X16)
| ~ ssList(X15) )
& ( ~ ssList(X19)
| ~ ssList(X20)
| app(app(X19,X16),X20) != X15
| segmentP(X15,X16)
| ~ ssList(X16)
| ~ ssList(X15) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax7])])])])])]) ).
fof(c_0_32,plain,
! [X51,X52,X53] :
( ~ ssList(X51)
| ~ ssList(X52)
| ~ ssList(X53)
| app(X52,X53) != app(X52,X51)
| X53 = 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_33,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_34,plain,
! [X61] :
( ~ ssList(X61)
| app(X61,nil) = X61 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_35,plain,
( X1 = app(nil,X2)
| app(X1,X3) != app(X2,X3)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_25])]) ).
cnf(c_0_36,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
( segmentP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X1,X3),X2) != X4
| ~ ssList(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_38,plain,
! [X44,X45,X46] :
( ~ ssList(X44)
| ~ ssList(X45)
| ~ ssItem(X46)
| cons(X46,app(X45,X44)) = app(cons(X46,X45),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_39,plain,
! [X37] :
( ( ssList(esk7_1(X37))
| nil = X37
| ~ ssList(X37) )
& ( ssItem(esk8_1(X37))
| nil = X37
| ~ ssList(X37) )
& ( cons(esk8_1(X37),esk7_1(X37)) = X37
| nil = X37
| ~ ssList(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_40,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk2_0,X1)
| ~ segmentP(esk1_0,X1)
| nil != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_41,negated_conjecture,
( neq(esk2_0,nil)
| nil != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_42,negated_conjecture,
( nil = esk3_0
| nil != esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_43,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_44,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_45,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,X3) != app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
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_33])]),c_0_25])]) ).
cnf(c_0_47,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_48,plain,
( ssList(app(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_23]) ).
cnf(c_0_49,negated_conjecture,
( X1 = app(nil,X2)
| app(X1,esk2_0) != app(X2,esk2_0)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_50,plain,
! [X24,X25] :
( ~ ssList(X24)
| ~ ssList(X25)
| ~ segmentP(X24,X25)
| ~ segmentP(X25,X24)
| X24 = X25 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax54])])])]) ).
cnf(c_0_51,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(app(app(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_52,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_53,plain,
( cons(esk8_1(X1),esk7_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_54,plain,
( ssItem(esk8_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_55,plain,
( ssList(esk7_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_56,negated_conjecture,
( esk1_0 != nil
| ~ segmentP(esk1_0,esk2_0)
| ~ segmentP(esk2_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_36])]) ).
cnf(c_0_57,negated_conjecture,
( esk1_0 = nil
| esk2_0 != nil ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
fof(c_0_58,plain,
! [X26] :
( ~ ssList(X26)
| segmentP(X26,X26) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
fof(c_0_59,plain,
! [X62,X63] :
( ~ ssList(X62)
| ~ ssItem(X63)
| ssList(cons(X63,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_60,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_61,plain,
( X1 = nil
| app(nil,X1) != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_25])]) ).
cnf(c_0_62,plain,
( app(X1,app(X2,nil)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_22]),c_0_25])]),c_0_23]) ).
cnf(c_0_63,plain,
( ssList(app(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_46]),c_0_25])]) ).
cnf(c_0_64,negated_conjecture,
( app(nil,X1) = esk2_0
| app(esk2_0,esk2_0) != app(X1,esk2_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_36]) ).
cnf(c_0_65,plain,
( X1 = X2
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_66,plain,
( segmentP(app(X1,X2),X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_47]),c_0_25])]),c_0_23]) ).
cnf(c_0_67,plain,
( app(cons(X1,X2),nil) = cons(X1,X2)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_47]),c_0_25])]) ).
cnf(c_0_68,negated_conjecture,
( cons(esk8_1(esk2_0),esk7_1(esk2_0)) = esk2_0
| esk2_0 = nil ),
inference(spm,[status(thm)],[c_0_53,c_0_36]) ).
cnf(c_0_69,negated_conjecture,
( esk2_0 = nil
| ssItem(esk8_1(esk2_0)) ),
inference(spm,[status(thm)],[c_0_54,c_0_36]) ).
cnf(c_0_70,negated_conjecture,
( esk2_0 = nil
| ssList(esk7_1(esk2_0)) ),
inference(spm,[status(thm)],[c_0_55,c_0_36]) ).
cnf(c_0_71,negated_conjecture,
( esk2_0 != nil
| ~ segmentP(nil,esk2_0)
| ~ segmentP(esk2_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_72,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_73,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
fof(c_0_74,plain,
! [X35,X36] :
( ( ~ neq(X35,X36)
| X35 != X36
| ~ ssList(X36)
| ~ ssList(X35) )
& ( X35 = X36
| neq(X35,X36)
| ~ ssList(X36)
| ~ ssList(X35) ) ),
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_60])])])])]) ).
cnf(c_0_75,negated_conjecture,
( app(X2,cons(X1,nil)) = esk3_0
| ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,nil),X2) != esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_76,plain,
! [X54,X55] :
( ~ ssList(X54)
| ~ ssItem(X55)
| cons(X55,X54) = app(cons(X55,nil),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_77,plain,
( app(X1,nil) = nil
| app(nil,X1) != nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_25])]),c_0_63]) ).
cnf(c_0_78,negated_conjecture,
app(nil,esk2_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_64]),c_0_36])]) ).
cnf(c_0_79,plain,
( app(X1,X2) = X2
| ~ segmentP(X2,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_23]) ).
cnf(c_0_80,negated_conjecture,
( app(esk2_0,nil) = esk2_0
| esk2_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_70]) ).
cnf(c_0_81,negated_conjecture,
( esk2_0 != nil
| ~ segmentP(nil,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_36])]) ).
cnf(c_0_82,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_52]),c_0_23]) ).
cnf(c_0_83,plain,
( app(cons(X1,nil),nil) = cons(X1,nil)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_46]),c_0_25])]) ).
cnf(c_0_84,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_85,negated_conjecture,
( app(X1,cons(X2,nil)) = esk1_0
| app(cons(X2,nil),X1) != esk2_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_43]),c_0_44]) ).
cnf(c_0_86,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_87,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_24]),c_0_25])]),c_0_23]) ).
cnf(c_0_88,negated_conjecture,
( app(esk2_0,nil) = nil
| esk2_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_36])]) ).
cnf(c_0_89,negated_conjecture,
~ segmentP(nil,esk2_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_25]),c_0_36])]),c_0_81]) ).
cnf(c_0_90,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_25])]) ).
cnf(c_0_91,plain,
( X1 = nil
| neq(X1,nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_25]) ).
cnf(c_0_92,negated_conjecture,
( app(X1,cons(X2,nil)) = esk1_0
| cons(X2,X1) != esk2_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_93,negated_conjecture,
esk2_0 != nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_36]),c_0_25])]),c_0_89]) ).
cnf(c_0_94,plain,
( segmentP(app(cons(X1,X2),X3),X2)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_86]),c_0_90]),c_0_82]) ).
cnf(c_0_95,negated_conjecture,
( nil = esk2_0
| ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk2_0,X1)
| ~ segmentP(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_96,negated_conjecture,
( esk7_1(esk2_0) = nil
| esk2_0 = nil
| neq(esk7_1(esk2_0),nil) ),
inference(spm,[status(thm)],[c_0_91,c_0_70]) ).
cnf(c_0_97,negated_conjecture,
( segmentP(esk1_0,X1)
| cons(X2,X1) != esk2_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_92]),c_0_90]) ).
cnf(c_0_98,negated_conjecture,
cons(esk8_1(esk2_0),esk7_1(esk2_0)) = esk2_0,
inference(sr,[status(thm)],[c_0_68,c_0_93]) ).
cnf(c_0_99,negated_conjecture,
ssList(esk7_1(esk2_0)),
inference(sr,[status(thm)],[c_0_70,c_0_93]) ).
cnf(c_0_100,negated_conjecture,
ssItem(esk8_1(esk2_0)),
inference(sr,[status(thm)],[c_0_69,c_0_93]) ).
cnf(c_0_101,plain,
( segmentP(cons(X1,X2),X2)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_67]),c_0_25])]) ).
cnf(c_0_102,negated_conjecture,
( esk7_1(esk2_0) = nil
| esk2_0 = nil
| ~ segmentP(esk1_0,esk7_1(esk2_0))
| ~ segmentP(esk2_0,esk7_1(esk2_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_70]) ).
cnf(c_0_103,negated_conjecture,
segmentP(esk1_0,esk7_1(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]),c_0_100])]) ).
cnf(c_0_104,negated_conjecture,
segmentP(esk2_0,esk7_1(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_98]),c_0_99]),c_0_100])]) ).
cnf(c_0_105,negated_conjecture,
( neq(esk2_0,nil)
| nil = esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_106,negated_conjecture,
( app(nil,cons(X1,nil)) = esk1_0
| cons(X1,nil) != esk2_0
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_83]),c_0_25])]) ).
cnf(c_0_107,negated_conjecture,
esk7_1(esk2_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_103])]),c_0_93]),c_0_104])]) ).
cnf(c_0_108,negated_conjecture,
neq(esk2_0,nil),
inference(sr,[status(thm)],[c_0_105,c_0_93]) ).
cnf(c_0_109,negated_conjecture,
segmentP(esk2_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_78]),c_0_36]),c_0_25])]) ).
cnf(c_0_110,negated_conjecture,
( segmentP(esk1_0,cons(X1,nil))
| cons(X1,nil) != esk2_0
| ~ ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_106]),c_0_25])]) ).
cnf(c_0_111,negated_conjecture,
cons(esk8_1(esk2_0),nil) = esk2_0,
inference(rw,[status(thm)],[c_0_98,c_0_107]) ).
cnf(c_0_112,negated_conjecture,
~ segmentP(esk1_0,esk2_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_108]),c_0_109]),c_0_36])]),c_0_93]) ).
cnf(c_0_113,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_36]),c_0_100])]),c_0_112]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SWC062+1 : TPTP v8.2.0. Released v2.4.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n029.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sun May 19 02:55:38 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 2.52/0.72 # Version: 3.1.0
% 2.52/0.72 # Preprocessing class: FSLSSMSSSSSNFFN.
% 2.52/0.72 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.52/0.72 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.52/0.72 # Starting new_bool_3 with 300s (1) cores
% 2.52/0.72 # Starting new_bool_1 with 300s (1) cores
% 2.52/0.72 # Starting sh5l with 300s (1) cores
% 2.52/0.72 # new_bool_1 with pid 6895 completed with status 0
% 2.52/0.72 # Result found by new_bool_1
% 2.52/0.72 # Preprocessing class: FSLSSMSSSSSNFFN.
% 2.52/0.72 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.52/0.72 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.52/0.72 # Starting new_bool_3 with 300s (1) cores
% 2.52/0.72 # Starting new_bool_1 with 300s (1) cores
% 2.52/0.72 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.52/0.72 # Search class: FGHSF-FFMM21-MFFFFFNN
% 2.52/0.72 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 2.52/0.72 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 2.52/0.72 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 6898 completed with status 0
% 2.52/0.72 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.52/0.72 # Preprocessing class: FSLSSMSSSSSNFFN.
% 2.52/0.72 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.52/0.72 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.52/0.72 # Starting new_bool_3 with 300s (1) cores
% 2.52/0.72 # Starting new_bool_1 with 300s (1) cores
% 2.52/0.72 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.52/0.72 # Search class: FGHSF-FFMM21-MFFFFFNN
% 2.52/0.72 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 2.52/0.72 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 2.52/0.72 # Preprocessing time : 0.001 s
% 2.52/0.72 # Presaturation interreduction done
% 2.52/0.72
% 2.52/0.72 # Proof found!
% 2.52/0.72 # SZS status Theorem
% 2.52/0.72 # SZS output start CNFRefutation
% See solution above
% 2.52/0.72 # Parsed axioms : 96
% 2.52/0.72 # Removed by relevancy pruning/SinE : 70
% 2.52/0.72 # Initial clauses : 50
% 2.52/0.72 # Removed in clause preprocessing : 0
% 2.52/0.72 # Initial clauses in saturation : 50
% 2.52/0.72 # Processed clauses : 1756
% 2.52/0.72 # ...of these trivial : 46
% 2.52/0.72 # ...subsumed : 791
% 2.52/0.72 # ...remaining for further processing : 919
% 2.52/0.72 # Other redundant clauses eliminated : 37
% 2.52/0.72 # Clauses deleted for lack of memory : 0
% 2.52/0.72 # Backward-subsumed : 101
% 2.52/0.72 # Backward-rewritten : 86
% 2.52/0.72 # Generated clauses : 18516
% 2.52/0.72 # ...of the previous two non-redundant : 17837
% 2.52/0.72 # ...aggressively subsumed : 0
% 2.52/0.72 # Contextual simplify-reflections : 173
% 2.52/0.72 # Paramodulations : 18362
% 2.52/0.72 # Factorizations : 0
% 2.52/0.72 # NegExts : 0
% 2.52/0.72 # Equation resolutions : 51
% 2.52/0.72 # Disequality decompositions : 0
% 2.52/0.72 # Total rewrite steps : 6806
% 2.52/0.72 # ...of those cached : 6748
% 2.52/0.72 # Propositional unsat checks : 0
% 2.52/0.72 # Propositional check models : 0
% 2.52/0.72 # Propositional check unsatisfiable : 0
% 2.52/0.72 # Propositional clauses : 0
% 2.52/0.72 # Propositional clauses after purity: 0
% 2.52/0.72 # Propositional unsat core size : 0
% 2.52/0.72 # Propositional preprocessing time : 0.000
% 2.52/0.72 # Propositional encoding time : 0.000
% 2.52/0.72 # Propositional solver time : 0.000
% 2.52/0.72 # Success case prop preproc time : 0.000
% 2.52/0.72 # Success case prop encoding time : 0.000
% 2.52/0.72 # Success case prop solver time : 0.000
% 2.52/0.72 # Current number of processed clauses : 575
% 2.52/0.72 # Positive orientable unit clauses : 83
% 2.52/0.72 # Positive unorientable unit clauses: 0
% 2.52/0.72 # Negative unit clauses : 24
% 2.52/0.72 # Non-unit-clauses : 468
% 2.52/0.72 # Current number of unprocessed clauses: 16090
% 2.52/0.72 # ...number of literals in the above : 62759
% 2.52/0.72 # Current number of archived formulas : 0
% 2.52/0.72 # Current number of archived clauses : 339
% 2.52/0.72 # Clause-clause subsumption calls (NU) : 27534
% 2.52/0.72 # Rec. Clause-clause subsumption calls : 15286
% 2.52/0.72 # Non-unit clause-clause subsumptions : 922
% 2.52/0.72 # Unit Clause-clause subsumption calls : 2958
% 2.52/0.72 # Rewrite failures with RHS unbound : 0
% 2.52/0.72 # BW rewrite match attempts : 147
% 2.52/0.72 # BW rewrite match successes : 21
% 2.52/0.72 # Condensation attempts : 0
% 2.52/0.72 # Condensation successes : 0
% 2.52/0.72 # Termbank termtop insertions : 384255
% 2.52/0.72 # Search garbage collected termcells : 1594
% 2.52/0.72
% 2.52/0.72 # -------------------------------------------------
% 2.52/0.72 # User time : 0.284 s
% 2.52/0.72 # System time : 0.009 s
% 2.52/0.72 # Total time : 0.293 s
% 2.52/0.72 # Maximum resident set size: 2020 pages
% 2.52/0.72
% 2.52/0.72 # -------------------------------------------------
% 2.52/0.72 # User time : 0.286 s
% 2.52/0.72 # System time : 0.012 s
% 2.52/0.72 # Total time : 0.298 s
% 2.52/0.72 # Maximum resident set size: 1820 pages
% 2.52/0.72 % E---3.1 exiting
% 2.52/0.73 % E exiting
%------------------------------------------------------------------------------