TSTP Solution File: SWC329+1 by E---3.1
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%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SWC329+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n011.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:40:27 EDT 2023
% Result : Theorem 51.78s 7.07s
% Output : CNFRefutation 51.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 17
% Syntax : Number of formulae : 121 ( 23 unt; 0 def)
% Number of atoms : 466 ( 130 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 600 ( 255 ~; 258 |; 39 &)
% ( 4 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 175 ( 0 sgn; 76 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax79,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X3,X2) = app(X1,X2)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.n6jUhQd0RS/E---3.1_30437.p',ax79) ).
fof(ax82,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.n6jUhQd0RS/E---3.1_30437.p',ax82) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.n6jUhQd0RS/E---3.1_30437.p',ax26) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/tmp/tmp.n6jUhQd0RS/E---3.1_30437.p',ax28) ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X3
| ~ memberP(X4,X5)
| ? [X6] :
( ssItem(X6)
& X5 != X6
& memberP(X4,X6)
& leq(X5,X6) ) ) )
& ( nil != X4
| nil != X3 ) )
| ( segmentP(X2,X1)
& equalelemsP(X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.n6jUhQd0RS/E---3.1_30437.p',co1) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/tmp/tmp.n6jUhQd0RS/E---3.1_30437.p',ax17) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.n6jUhQd0RS/E---3.1_30437.p',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/sandbox/tmp/tmp.n6jUhQd0RS/E---3.1_30437.p',ax7) ).
fof(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.n6jUhQd0RS/E---3.1_30437.p',ax80) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/tmp/tmp.n6jUhQd0RS/E---3.1_30437.p',ax84) ).
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/tmp/tmp.n6jUhQd0RS/E---3.1_30437.p',ax56) ).
fof(ax36,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(app(X2,X3),X1)
<=> ( memberP(X2,X1)
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.n6jUhQd0RS/E---3.1_30437.p',ax36) ).
fof(ax38,axiom,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
file('/export/starexec/sandbox/tmp/tmp.n6jUhQd0RS/E---3.1_30437.p',ax38) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.n6jUhQd0RS/E---3.1_30437.p',ax81) ).
fof(ax3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.n6jUhQd0RS/E---3.1_30437.p',ax3) ).
fof(ax73,axiom,
! [X1] :
( ssItem(X1)
=> equalelemsP(cons(X1,nil)) ),
file('/export/starexec/sandbox/tmp/tmp.n6jUhQd0RS/E---3.1_30437.p',ax73) ).
fof(ax74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox/tmp/tmp.n6jUhQd0RS/E---3.1_30437.p',ax74) ).
fof(c_0_17,plain,
! [X90,X91,X92] :
( ~ ssList(X90)
| ~ ssList(X91)
| ~ ssList(X92)
| app(X92,X91) != app(X90,X91)
| X92 = X90 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])]) ).
fof(c_0_18,plain,
! [X96,X97,X98] :
( ~ ssList(X96)
| ~ ssList(X97)
| ~ ssList(X98)
| app(app(X96,X97),X98) = app(X96,app(X97,X98)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])]) ).
fof(c_0_19,plain,
! [X87,X88] :
( ~ ssList(X87)
| ~ ssList(X88)
| ssList(app(X87,X88)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_20,plain,
! [X89] :
( ~ ssList(X89)
| app(nil,X89) = X89 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
fof(c_0_21,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X3
| ~ memberP(X4,X5)
| ? [X6] :
( ssItem(X6)
& X5 != X6
& memberP(X4,X6)
& leq(X5,X6) ) ) )
& ( nil != X4
| nil != X3 ) )
| ( segmentP(X2,X1)
& equalelemsP(X1) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
cnf(c_0_22,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_23,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_24,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_27,negated_conjecture,
! [X12] :
( ssList(esk1_0)
& ssList(esk2_0)
& ssList(esk3_0)
& ssList(esk4_0)
& esk2_0 = esk4_0
& esk1_0 = esk3_0
& ( nil = esk4_0
| ssItem(esk5_0) )
& ( nil = esk3_0
| ssItem(esk5_0) )
& ( nil = esk4_0
| cons(esk5_0,nil) = esk3_0 )
& ( nil = esk3_0
| cons(esk5_0,nil) = esk3_0 )
& ( nil = esk4_0
| memberP(esk4_0,esk5_0) )
& ( nil = esk3_0
| memberP(esk4_0,esk5_0) )
& ( nil = esk4_0
| ~ ssItem(X12)
| esk5_0 = X12
| ~ memberP(esk4_0,X12)
| ~ leq(esk5_0,X12) )
& ( nil = esk3_0
| ~ ssItem(X12)
| esk5_0 = X12
| ~ memberP(esk4_0,X12)
| ~ leq(esk5_0,X12) )
& ( ~ segmentP(esk2_0,esk1_0)
| ~ equalelemsP(esk1_0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])]) ).
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_22,c_0_23]),c_0_24]) ).
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_23,c_0_25]),c_0_26])]) ).
cnf(c_0_30,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,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_26])]) ).
cnf(c_0_33,negated_conjecture,
ssList(esk4_0),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
( X1 = app(nil,X2)
| app(X1,esk4_0) != app(X2,esk4_0)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_35,plain,
! [X99,X100] :
( ( nil = X100
| nil != app(X99,X100)
| ~ ssList(X100)
| ~ ssList(X99) )
& ( nil = X99
| nil != app(X99,X100)
| ~ ssList(X100)
| ~ ssList(X99) )
& ( nil != X100
| nil != X99
| nil = app(X99,X100)
| ~ ssList(X100)
| ~ ssList(X99) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax83])])])]) ).
fof(c_0_36,plain,
! [X23,X24,X27,X28] :
( ( ssList(esk10_2(X23,X24))
| ~ segmentP(X23,X24)
| ~ ssList(X24)
| ~ ssList(X23) )
& ( ssList(esk11_2(X23,X24))
| ~ segmentP(X23,X24)
| ~ ssList(X24)
| ~ ssList(X23) )
& ( app(app(esk10_2(X23,X24),X24),esk11_2(X23,X24)) = X23
| ~ segmentP(X23,X24)
| ~ ssList(X24)
| ~ ssList(X23) )
& ( ~ ssList(X27)
| ~ ssList(X28)
| app(app(X27,X24),X28) != X23
| segmentP(X23,X24)
| ~ ssList(X24)
| ~ ssList(X23) ) ),
inference(distribute,[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_37,negated_conjecture,
( app(nil,X1) = esk4_0
| app(esk4_0,esk4_0) != app(X1,esk4_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_38,plain,
( nil = X1
| nil != app(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_39,plain,
( app(app(esk10_2(X1,X2),X2),esk11_2(X1,X2)) = X1
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_40,plain,
( ssList(app(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_24]) ).
cnf(c_0_41,negated_conjecture,
app(nil,esk4_0) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_37]),c_0_33])]) ).
fof(c_0_42,plain,
! [X93,X94,X95] :
( ~ ssList(X93)
| ~ ssList(X94)
| ~ ssList(X95)
| app(X94,X95) != app(X94,X93)
| X95 = X93 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])]) ).
fof(c_0_43,plain,
! [X101] :
( ~ ssList(X101)
| app(X101,nil) = X101 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])]) ).
cnf(c_0_44,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,plain,
( esk11_2(nil,X1) = nil
| ~ segmentP(nil,X1)
| ~ ssList(app(esk10_2(nil,X1),X1))
| ~ ssList(esk11_2(nil,X1))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39])]),c_0_26])]) ).
cnf(c_0_46,negated_conjecture,
( ssList(app(X1,esk4_0))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_33]),c_0_26])]) ).
cnf(c_0_47,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,X3) != app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_49,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_44])]),c_0_26])]) ).
cnf(c_0_50,negated_conjecture,
( esk11_2(nil,esk4_0) = nil
| ~ segmentP(nil,esk4_0)
| ~ ssList(esk11_2(nil,esk4_0))
| ~ ssList(esk10_2(nil,esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_33])]) ).
cnf(c_0_51,plain,
( ssList(esk11_2(X1,X2))
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_52,negated_conjecture,
( X1 = esk4_0
| app(nil,X1) != esk4_0
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_41]),c_0_33]),c_0_26])]) ).
cnf(c_0_53,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_48,c_0_23]),c_0_26])]),c_0_24]) ).
cnf(c_0_54,plain,
( ssList(app(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_49]),c_0_26])]) ).
cnf(c_0_55,plain,
( ssList(esk10_2(X1,X2))
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_56,negated_conjecture,
( esk11_2(nil,esk4_0) = nil
| ~ segmentP(nil,esk4_0)
| ~ ssList(esk10_2(nil,esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_33]),c_0_26])]) ).
cnf(c_0_57,negated_conjecture,
( app(X1,nil) = esk4_0
| app(nil,X1) != esk4_0
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_26])]),c_0_54]) ).
cnf(c_0_58,plain,
( app(esk10_2(X1,X2),app(X2,esk11_2(X1,X2))) = X1
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_39]),c_0_55]),c_0_51]) ).
cnf(c_0_59,negated_conjecture,
( esk11_2(nil,esk4_0) = nil
| ~ segmentP(nil,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_55]),c_0_33]),c_0_26])]) ).
cnf(c_0_60,negated_conjecture,
app(esk4_0,nil) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_41]),c_0_33])]) ).
fof(c_0_61,plain,
! [X35,X36,X37,X38] :
( ~ ssList(X35)
| ~ ssList(X36)
| ~ ssList(X37)
| ~ ssList(X38)
| ~ segmentP(X35,X36)
| segmentP(app(app(X37,X35),X38),X36) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])]) ).
cnf(c_0_62,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_36]) ).
cnf(c_0_63,plain,
( X1 = nil
| app(nil,X1) != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_49]),c_0_26])]) ).
fof(c_0_64,plain,
! [X65,X66,X67] :
( ( ~ memberP(app(X66,X67),X65)
| memberP(X66,X65)
| memberP(X67,X65)
| ~ ssList(X67)
| ~ ssList(X66)
| ~ ssItem(X65) )
& ( ~ memberP(X66,X65)
| memberP(app(X66,X67),X65)
| ~ ssList(X67)
| ~ ssList(X66)
| ~ ssItem(X65) )
& ( ~ memberP(X67,X65)
| memberP(app(X66,X67),X65)
| ~ ssList(X67)
| ~ ssList(X66)
| ~ ssItem(X65) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])]) ).
cnf(c_0_65,plain,
( nil = X1
| nil != app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_66,negated_conjecture,
( app(esk10_2(nil,esk4_0),esk4_0) = nil
| ~ segmentP(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_58,c_0_59]),c_0_60]),c_0_33]),c_0_26])]) ).
fof(c_0_67,plain,
! [X1] :
( ssItem(X1)
=> ~ memberP(nil,X1) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
cnf(c_0_68,plain,
( segmentP(app(app(X3,X1),X4),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| ~ segmentP(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_69,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_62]) ).
cnf(c_0_70,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_63,c_0_53]),c_0_26])]),c_0_54]) ).
cnf(c_0_71,plain,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_72,negated_conjecture,
( esk10_2(nil,esk4_0) = nil
| ~ segmentP(nil,esk4_0)
| ~ ssList(esk10_2(nil,esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_33])]) ).
fof(c_0_73,plain,
! [X71] :
( ~ ssItem(X71)
| ~ memberP(nil,X71) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])]) ).
cnf(c_0_74,plain,
( segmentP(app(nil,X1),X2)
| ~ segmentP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_49]),c_0_26])]) ).
cnf(c_0_75,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_69,c_0_25]),c_0_26])]),c_0_24]) ).
cnf(c_0_76,negated_conjecture,
( app(esk4_0,nil) = nil
| esk4_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_41]),c_0_33])]) ).
fof(c_0_77,plain,
! [X85,X86] :
( ~ ssList(X85)
| ~ ssItem(X86)
| cons(X86,X85) = app(cons(X86,nil),X85) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_78,plain,
( memberP(X1,X2)
| ~ segmentP(X1,X3)
| ~ memberP(app(esk10_2(X1,X3),X3),X2)
| ~ ssList(app(esk10_2(X1,X3),X3))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_39]),c_0_51]) ).
cnf(c_0_79,negated_conjecture,
( esk10_2(nil,esk4_0) = nil
| ~ segmentP(nil,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_55]),c_0_33]),c_0_26])]) ).
cnf(c_0_80,plain,
( ~ ssItem(X1)
| ~ memberP(nil,X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_81,plain,
( segmentP(X1,X2)
| ~ segmentP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_74,c_0_25]) ).
cnf(c_0_82,negated_conjecture,
( segmentP(nil,esk4_0)
| esk4_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_33]),c_0_26])]) ).
cnf(c_0_83,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_84,negated_conjecture,
( nil = esk4_0
| cons(esk5_0,nil) = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_85,negated_conjecture,
( nil = esk4_0
| ssItem(esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_86,plain,
! [X59,X60,X63,X64] :
( ( ssList(esk14_2(X59,X60))
| ~ memberP(X59,X60)
| ~ ssItem(X60)
| ~ ssList(X59) )
& ( ssList(esk15_2(X59,X60))
| ~ memberP(X59,X60)
| ~ ssItem(X60)
| ~ ssList(X59) )
& ( app(esk14_2(X59,X60),cons(X60,esk15_2(X59,X60))) = X59
| ~ memberP(X59,X60)
| ~ ssItem(X60)
| ~ ssList(X59) )
& ( ~ ssList(X63)
| ~ ssList(X64)
| app(X63,cons(X60,X64)) != X59
| memberP(X59,X60)
| ~ ssItem(X60)
| ~ ssList(X59) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])]) ).
cnf(c_0_87,negated_conjecture,
( ~ segmentP(nil,esk4_0)
| ~ memberP(esk4_0,X1)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_41]),c_0_41]),c_0_33]),c_0_33]),c_0_26])]),c_0_80]) ).
cnf(c_0_88,negated_conjecture,
( segmentP(X1,esk4_0)
| esk4_0 != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_33])]) ).
cnf(c_0_89,negated_conjecture,
( cons(esk5_0,X1) = app(esk3_0,X1)
| esk4_0 = nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).
cnf(c_0_90,plain,
( ssList(esk15_2(X1,X2))
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_91,negated_conjecture,
( ~ segmentP(esk2_0,esk1_0)
| ~ equalelemsP(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_92,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_93,negated_conjecture,
( esk4_0 != nil
| ~ memberP(esk4_0,X1)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_26])]) ).
cnf(c_0_94,negated_conjecture,
( nil = esk3_0
| memberP(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_95,negated_conjecture,
( nil = esk3_0
| ssItem(esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_96,plain,
! [X22] :
( ~ ssItem(X22)
| equalelemsP(cons(X22,nil)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax73])]) ).
cnf(c_0_97,negated_conjecture,
( cons(esk5_0,esk15_2(X1,X2)) = app(esk3_0,esk15_2(X1,X2))
| esk4_0 = nil
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_98,negated_conjecture,
( nil = esk4_0
| memberP(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_99,negated_conjecture,
( ~ equalelemsP(esk3_0)
| ~ segmentP(esk4_0,esk3_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92]),c_0_31]),c_0_92]) ).
cnf(c_0_100,negated_conjecture,
( esk3_0 = nil
| esk4_0 != nil ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]) ).
cnf(c_0_101,plain,
equalelemsP(nil),
inference(split_conjunct,[status(thm)],[ax74]) ).
cnf(c_0_102,negated_conjecture,
segmentP(esk4_0,nil),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_41]),c_0_26]),c_0_33])]) ).
cnf(c_0_103,plain,
( equalelemsP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_104,negated_conjecture,
( cons(esk5_0,esk15_2(esk4_0,esk5_0)) = app(esk3_0,esk15_2(esk4_0,esk5_0))
| esk4_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_33])]),c_0_85]) ).
cnf(c_0_105,negated_conjecture,
esk4_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]),c_0_102])]) ).
cnf(c_0_106,negated_conjecture,
( esk4_0 = nil
| equalelemsP(esk3_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_84]),c_0_85]) ).
cnf(c_0_107,plain,
( app(esk14_2(X1,X2),cons(X2,esk15_2(X1,X2))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_108,negated_conjecture,
cons(esk5_0,esk15_2(esk4_0,esk5_0)) = app(esk3_0,esk15_2(esk4_0,esk5_0)),
inference(sr,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_109,negated_conjecture,
memberP(esk4_0,esk5_0),
inference(sr,[status(thm)],[c_0_98,c_0_105]) ).
cnf(c_0_110,negated_conjecture,
ssItem(esk5_0),
inference(sr,[status(thm)],[c_0_85,c_0_105]) ).
cnf(c_0_111,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_112,negated_conjecture,
equalelemsP(esk3_0),
inference(sr,[status(thm)],[c_0_106,c_0_105]) ).
cnf(c_0_113,plain,
( segmentP(app(X1,app(X2,X3)),X2)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_23]),c_0_40]) ).
cnf(c_0_114,negated_conjecture,
app(esk14_2(esk4_0,esk5_0),app(esk3_0,esk15_2(esk4_0,esk5_0))) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]),c_0_33]),c_0_110])]) ).
cnf(c_0_115,negated_conjecture,
ssList(esk3_0),
inference(rw,[status(thm)],[c_0_111,c_0_92]) ).
cnf(c_0_116,negated_conjecture,
~ segmentP(esk4_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_112])]) ).
cnf(c_0_117,negated_conjecture,
( ~ ssList(esk15_2(esk4_0,esk5_0))
| ~ ssList(esk14_2(esk4_0,esk5_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_115])]),c_0_116]) ).
cnf(c_0_118,negated_conjecture,
~ ssList(esk14_2(esk4_0,esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_90]),c_0_109]),c_0_33]),c_0_110])]) ).
cnf(c_0_119,plain,
( ssList(esk14_2(X1,X2))
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_120,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_109]),c_0_33]),c_0_110])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SWC329+1 : TPTP v8.1.2. Released v2.4.0.
% 0.16/0.15 % Command : run_E %s %d THM
% 0.16/0.36 % Computer : n011.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 2400
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Tue Oct 3 02:02:08 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.23/0.51 Running first-order theorem proving
% 0.23/0.51 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.n6jUhQd0RS/E---3.1_30437.p
% 51.78/7.07 # Version: 3.1pre001
% 51.78/7.07 # Preprocessing class: FSLSSMSSSSSNFFN.
% 51.78/7.07 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 51.78/7.07 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 51.78/7.07 # Starting new_bool_3 with 300s (1) cores
% 51.78/7.07 # Starting new_bool_1 with 300s (1) cores
% 51.78/7.07 # Starting sh5l with 300s (1) cores
% 51.78/7.07 # new_bool_3 with pid 30516 completed with status 0
% 51.78/7.07 # Result found by new_bool_3
% 51.78/7.07 # Preprocessing class: FSLSSMSSSSSNFFN.
% 51.78/7.07 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 51.78/7.07 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 51.78/7.07 # Starting new_bool_3 with 300s (1) cores
% 51.78/7.07 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 51.78/7.07 # Search class: FGHSF-FFMM21-MFFFFFNN
% 51.78/7.07 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 51.78/7.07 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 51.78/7.07 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 30520 completed with status 0
% 51.78/7.07 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 51.78/7.07 # Preprocessing class: FSLSSMSSSSSNFFN.
% 51.78/7.07 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 51.78/7.07 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 51.78/7.07 # Starting new_bool_3 with 300s (1) cores
% 51.78/7.07 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 51.78/7.07 # Search class: FGHSF-FFMM21-MFFFFFNN
% 51.78/7.07 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 51.78/7.07 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 51.78/7.07 # Preprocessing time : 0.002 s
% 51.78/7.07 # Presaturation interreduction done
% 51.78/7.07
% 51.78/7.07 # Proof found!
% 51.78/7.07 # SZS status Theorem
% 51.78/7.07 # SZS output start CNFRefutation
% See solution above
% 51.78/7.07 # Parsed axioms : 96
% 51.78/7.07 # Removed by relevancy pruning/SinE : 56
% 51.78/7.07 # Initial clauses : 80
% 51.78/7.07 # Removed in clause preprocessing : 0
% 51.78/7.07 # Initial clauses in saturation : 80
% 51.78/7.07 # Processed clauses : 24159
% 51.78/7.07 # ...of these trivial : 1365
% 51.78/7.07 # ...subsumed : 17203
% 51.78/7.07 # ...remaining for further processing : 5591
% 51.78/7.07 # Other redundant clauses eliminated : 122
% 51.78/7.07 # Clauses deleted for lack of memory : 0
% 51.78/7.07 # Backward-subsumed : 916
% 51.78/7.07 # Backward-rewritten : 796
% 51.78/7.07 # Generated clauses : 481512
% 51.78/7.07 # ...of the previous two non-redundant : 475686
% 51.78/7.07 # ...aggressively subsumed : 0
% 51.78/7.07 # Contextual simplify-reflections : 1478
% 51.78/7.07 # Paramodulations : 480428
% 51.78/7.07 # Factorizations : 2
% 51.78/7.07 # NegExts : 0
% 51.78/7.07 # Equation resolutions : 162
% 51.78/7.07 # Total rewrite steps : 171306
% 51.78/7.07 # Propositional unsat checks : 1
% 51.78/7.07 # Propositional check models : 0
% 51.78/7.07 # Propositional check unsatisfiable : 0
% 51.78/7.07 # Propositional clauses : 0
% 51.78/7.07 # Propositional clauses after purity: 0
% 51.78/7.07 # Propositional unsat core size : 0
% 51.78/7.07 # Propositional preprocessing time : 0.000
% 51.78/7.07 # Propositional encoding time : 0.416
% 51.78/7.07 # Propositional solver time : 0.264
% 51.78/7.07 # Success case prop preproc time : 0.000
% 51.78/7.07 # Success case prop encoding time : 0.000
% 51.78/7.07 # Success case prop solver time : 0.000
% 51.78/7.07 # Current number of processed clauses : 2875
% 51.78/7.07 # Positive orientable unit clauses : 350
% 51.78/7.07 # Positive unorientable unit clauses: 0
% 51.78/7.07 # Negative unit clauses : 296
% 51.78/7.07 # Non-unit-clauses : 2229
% 51.78/7.07 # Current number of unprocessed clauses: 441559
% 51.78/7.07 # ...number of literals in the above : 1907968
% 51.78/7.07 # Current number of archived formulas : 0
% 51.78/7.07 # Current number of archived clauses : 2709
% 51.78/7.07 # Clause-clause subsumption calls (NU) : 1175080
% 51.78/7.07 # Rec. Clause-clause subsumption calls : 496305
% 51.78/7.07 # Non-unit clause-clause subsumptions : 15983
% 51.78/7.07 # Unit Clause-clause subsumption calls : 62957
% 51.78/7.07 # Rewrite failures with RHS unbound : 0
% 51.78/7.07 # BW rewrite match attempts : 3959
% 51.78/7.07 # BW rewrite match successes : 40
% 51.78/7.07 # Condensation attempts : 0
% 51.78/7.07 # Condensation successes : 0
% 51.78/7.07 # Termbank termtop insertions : 15131973
% 51.78/7.07
% 51.78/7.07 # -------------------------------------------------
% 51.78/7.07 # User time : 6.044 s
% 51.78/7.07 # System time : 0.268 s
% 51.78/7.07 # Total time : 6.312 s
% 51.78/7.07 # Maximum resident set size: 2040 pages
% 51.78/7.07
% 51.78/7.07 # -------------------------------------------------
% 51.78/7.07 # User time : 6.046 s
% 51.78/7.07 # System time : 0.272 s
% 51.78/7.07 # Total time : 6.317 s
% 51.78/7.07 # Maximum resident set size: 1796 pages
% 51.78/7.07 % E---3.1 exiting
% 51.78/7.07 % E---3.1 exiting
%------------------------------------------------------------------------------