TSTP Solution File: SWC084+1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SWC084+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n027.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 04:23:09 EDT 2024
% Result : Theorem 17.07s 2.56s
% Output : CNFRefutation 17.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 120 ( 25 unt; 0 def)
% Number of atoms : 454 ( 141 equ)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 565 ( 231 ~; 234 |; 43 &)
% ( 5 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 179 ( 0 sgn 88 !; 8 ?)
% 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/benchmark/Axioms/SWC001+0.ax',ax79) ).
fof(ax82,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax82) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(co1,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ( ! [X6] :
( ssItem(X6)
=> ( cons(X6,nil) != X3
| ~ memberP(X4,X6)
| ? [X7] :
( ssItem(X7)
& X6 != X7
& memberP(X4,X7)
& leq(X6,X7) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(ax83,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(ax80,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( app(X2,X3) = app(X2,X1)
=> X3 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(ax7,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(ax56,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(ax15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(ax3,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ( memberP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(ax18,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(ax21,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(c_0_17,plain,
! [X92,X93,X94] :
( ~ ssList(X92)
| ~ ssList(X93)
| ~ ssList(X94)
| app(X94,X93) != app(X92,X93)
| X94 = X92 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])])]) ).
fof(c_0_18,plain,
! [X98,X99,X100] :
( ~ ssList(X98)
| ~ ssList(X99)
| ~ ssList(X100)
| app(app(X98,X99),X100) = app(X98,app(X99,X100)) ),
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,
! [X89,X90] :
( ~ ssList(X89)
| ~ ssList(X90)
| ssList(app(X89,X90)) ),
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,
! [X91] :
( ~ ssList(X91)
| app(nil,X91) = X91 ),
inference(fof_nnf,[status(thm)],[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
| ~ neq(X2,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X2,X5)
& segmentP(X1,X5) )
| ( ! [X6] :
( ssItem(X6)
=> ( cons(X6,nil) != X3
| ~ memberP(X4,X6)
| ? [X7] :
( ssItem(X7)
& X6 != X7
& memberP(X4,X7)
& leq(X6,X7) ) ) )
& ( nil != X4
| nil != X3 ) ) ) ) ) ) ),
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,X14] :
( ssList(esk1_0)
& ssList(esk2_0)
& ssList(esk3_0)
& ssList(esk4_0)
& esk2_0 = esk4_0
& esk1_0 = esk3_0
& neq(esk2_0,nil)
& ( ~ ssList(X12)
| ~ neq(X12,nil)
| ~ segmentP(esk2_0,X12)
| ~ segmentP(esk1_0,X12) )
& ( 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(X14)
| esk5_0 = X14
| ~ memberP(esk4_0,X14)
| ~ leq(esk5_0,X14) )
& ( nil = esk3_0
| ~ ssItem(X14)
| esk5_0 = X14
| ~ memberP(esk4_0,X14)
| ~ leq(esk5_0,X14) ) ),
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_21])])])])])]) ).
fof(c_0_28,plain,
! [X59,X60] :
( ~ ssList(X59)
| ~ ssItem(X60)
| cons(X60,X59) = app(cons(X60,nil),X59) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
fof(c_0_29,plain,
! [X101,X102] :
( ( nil = X102
| nil != app(X101,X102)
| ~ ssList(X102)
| ~ ssList(X101) )
& ( nil = X101
| nil != app(X101,X102)
| ~ ssList(X102)
| ~ ssList(X101) )
& ( nil != X102
| nil != X101
| nil = app(X101,X102)
| ~ ssList(X102)
| ~ ssList(X101) ) ),
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_30,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_31,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_32,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( nil = esk3_0
| cons(esk5_0,nil) = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,negated_conjecture,
( nil = esk3_0
| ssItem(esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_37,plain,
! [X95,X96,X97] :
( ~ ssList(X95)
| ~ ssList(X96)
| ~ ssList(X97)
| app(X96,X97) != app(X96,X95)
| X97 = X95 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])])]) ).
cnf(c_0_38,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_39,plain,
! [X103] :
( ~ ssList(X103)
| app(X103,nil) = X103 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_40,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_30,c_0_31]),c_0_26])]) ).
cnf(c_0_41,negated_conjecture,
ssList(esk4_0),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_42,plain,
! [X61,X62,X65,X66] :
( ( ssList(esk12_2(X61,X62))
| ~ segmentP(X61,X62)
| ~ ssList(X62)
| ~ ssList(X61) )
& ( ssList(esk13_2(X61,X62))
| ~ segmentP(X61,X62)
| ~ ssList(X62)
| ~ ssList(X61) )
& ( app(app(esk12_2(X61,X62),X62),esk13_2(X61,X62)) = X61
| ~ segmentP(X61,X62)
| ~ ssList(X62)
| ~ ssList(X61) )
& ( ~ ssList(X65)
| ~ ssList(X66)
| app(app(X65,X62),X66) != X61
| segmentP(X61,X62)
| ~ ssList(X62)
| ~ ssList(X61) ) ),
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_43,negated_conjecture,
( cons(esk5_0,X1) = app(esk3_0,X1)
| esk3_0 = nil
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_44,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,X3) != app(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_38])]),c_0_26])]) ).
cnf(c_0_46,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,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_48,negated_conjecture,
( X1 = app(nil,X2)
| app(X1,esk4_0) != app(X2,esk4_0)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,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_42]) ).
fof(c_0_50,plain,
! [X73,X74,X75,X76] :
( ~ ssList(X73)
| ~ ssList(X74)
| ~ ssList(X75)
| ~ ssList(X76)
| ~ segmentP(X73,X74)
| segmentP(app(app(X75,X73),X76),X74) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax56])])])]) ).
cnf(c_0_51,negated_conjecture,
( cons(esk5_0,nil) = app(esk3_0,nil)
| esk3_0 = nil ),
inference(spm,[status(thm)],[c_0_43,c_0_26]) ).
cnf(c_0_52,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_53,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_54,plain,
( X1 = nil
| app(nil,X1) != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_26])]) ).
cnf(c_0_55,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_46,c_0_23]),c_0_26])]),c_0_24]) ).
cnf(c_0_56,plain,
( ssList(app(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_45]),c_0_26])]) ).
cnf(c_0_57,negated_conjecture,
( app(nil,X1) = esk4_0
| app(esk4_0,esk4_0) != app(X1,esk4_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_41]) ).
cnf(c_0_58,negated_conjecture,
( ~ ssList(X1)
| ~ neq(X1,nil)
| ~ segmentP(esk2_0,X1)
| ~ segmentP(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_59,negated_conjecture,
neq(esk2_0,nil),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_60,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_49]) ).
cnf(c_0_61,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_50]) ).
cnf(c_0_62,negated_conjecture,
( app(esk3_0,nil) = esk3_0
| esk3_0 = nil ),
inference(spm,[status(thm)],[c_0_35,c_0_51]) ).
cnf(c_0_63,negated_conjecture,
ssList(esk3_0),
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_64,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_54,c_0_55]),c_0_26])]),c_0_56]) ).
cnf(c_0_65,negated_conjecture,
app(nil,esk4_0) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_57]),c_0_41])]) ).
cnf(c_0_66,negated_conjecture,
( ~ segmentP(esk3_0,X1)
| ~ segmentP(esk4_0,X1)
| ~ ssList(X1)
| ~ neq(X1,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_53]),c_0_33]) ).
cnf(c_0_67,negated_conjecture,
neq(esk4_0,nil),
inference(rw,[status(thm)],[c_0_59,c_0_33]) ).
cnf(c_0_68,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_60,c_0_46]),c_0_26])]),c_0_24]) ).
cnf(c_0_69,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_61,c_0_45]),c_0_26])]) ).
cnf(c_0_70,negated_conjecture,
( app(nil,esk3_0) = esk3_0
| esk3_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_62]),c_0_26]),c_0_63])]) ).
cnf(c_0_71,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_60,c_0_25]),c_0_26])]),c_0_24]) ).
cnf(c_0_72,negated_conjecture,
( app(esk4_0,nil) = nil
| esk4_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_41])]) ).
cnf(c_0_73,negated_conjecture,
( ~ segmentP(esk3_0,esk4_0)
| ~ segmentP(esk4_0,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_41])]) ).
cnf(c_0_74,negated_conjecture,
segmentP(esk4_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_65]),c_0_41]),c_0_26])]) ).
cnf(c_0_75,negated_conjecture,
( esk3_0 = nil
| segmentP(esk3_0,X1)
| ~ segmentP(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_63])]) ).
cnf(c_0_76,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_71,c_0_72]),c_0_41]),c_0_26])]) ).
cnf(c_0_77,negated_conjecture,
~ segmentP(esk3_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74])]) ).
fof(c_0_78,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
cnf(c_0_79,negated_conjecture,
( nil = esk4_0
| cons(esk5_0,nil) = esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_80,negated_conjecture,
( nil = esk4_0
| ssItem(esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_81,plain,
! [X33,X34,X37,X38] :
( ( ssList(esk8_2(X33,X34))
| ~ memberP(X33,X34)
| ~ ssItem(X34)
| ~ ssList(X33) )
& ( ssList(esk9_2(X33,X34))
| ~ memberP(X33,X34)
| ~ ssItem(X34)
| ~ ssList(X33) )
& ( app(esk8_2(X33,X34),cons(X34,esk9_2(X33,X34))) = X33
| ~ memberP(X33,X34)
| ~ ssItem(X34)
| ~ ssList(X33) )
& ( ~ ssList(X37)
| ~ ssList(X38)
| app(X37,cons(X34,X38)) != X33
| memberP(X33,X34)
| ~ ssItem(X34)
| ~ ssList(X33) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])])])]) ).
fof(c_0_82,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) != X1 ) ),
inference(fof_simplification,[status(thm)],[ax18]) ).
cnf(c_0_83,negated_conjecture,
( esk3_0 = nil
| esk4_0 != nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_41])]),c_0_77]) ).
fof(c_0_84,plain,
! [X81,X82] :
( ( ~ neq(X81,X82)
| X81 != X82
| ~ ssList(X82)
| ~ ssList(X81) )
& ( X81 = X82
| neq(X81,X82)
| ~ ssList(X82)
| ~ ssList(X81) ) ),
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_78])])])])]) ).
fof(c_0_85,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[ax21]) ).
cnf(c_0_86,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_34,c_0_79]),c_0_80]) ).
cnf(c_0_87,plain,
( ssList(esk9_2(X1,X2))
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
fof(c_0_88,plain,
! [X50,X51] :
( ~ ssList(X50)
| ~ ssItem(X51)
| cons(X51,X50) != X50 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_82])])])]) ).
cnf(c_0_89,negated_conjecture,
esk4_0 != nil,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_83]),c_0_76]) ).
cnf(c_0_90,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
fof(c_0_91,plain,
! [X48,X49] :
( ~ ssList(X48)
| ~ ssItem(X49)
| ssList(cons(X49,X48)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_92,plain,
! [X18,X19] :
( ~ ssList(X18)
| ~ ssItem(X19)
| nil != cons(X19,X18) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_85])])])]) ).
cnf(c_0_93,negated_conjecture,
( cons(esk5_0,nil) = app(esk3_0,nil)
| esk4_0 = nil ),
inference(spm,[status(thm)],[c_0_86,c_0_26]) ).
cnf(c_0_94,negated_conjecture,
( cons(esk5_0,esk9_2(X1,X2)) = app(esk3_0,esk9_2(X1,X2))
| esk3_0 = nil
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_87]) ).
cnf(c_0_95,negated_conjecture,
( nil = esk3_0
| memberP(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_96,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,X1) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_97,negated_conjecture,
cons(esk5_0,nil) = esk3_0,
inference(sr,[status(thm)],[c_0_79,c_0_89]) ).
cnf(c_0_98,negated_conjecture,
ssItem(esk5_0),
inference(sr,[status(thm)],[c_0_80,c_0_89]) ).
cnf(c_0_99,plain,
( X1 = nil
| neq(X1,nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_26]) ).
cnf(c_0_100,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_101,plain,
( ~ ssList(X1)
| ~ ssItem(X2)
| nil != cons(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_102,negated_conjecture,
( app(esk3_0,nil) = esk3_0
| esk4_0 = nil ),
inference(spm,[status(thm)],[c_0_79,c_0_93]) ).
cnf(c_0_103,negated_conjecture,
( cons(esk5_0,esk9_2(esk4_0,esk5_0)) = app(esk3_0,esk9_2(esk4_0,esk5_0))
| esk3_0 = nil ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_41])]),c_0_36]) ).
cnf(c_0_104,negated_conjecture,
esk3_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_26]),c_0_98])]) ).
cnf(c_0_105,negated_conjecture,
( nil = esk4_0
| memberP(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_106,plain,
( neq(cons(X1,X2),nil)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]) ).
cnf(c_0_107,negated_conjecture,
( esk4_0 = nil
| segmentP(esk3_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_102]),c_0_63]),c_0_26])]) ).
cnf(c_0_108,plain,
( app(esk8_2(X1,X2),cons(X2,esk9_2(X1,X2))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_109,negated_conjecture,
cons(esk5_0,esk9_2(esk4_0,esk5_0)) = app(esk3_0,esk9_2(esk4_0,esk5_0)),
inference(sr,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_110,negated_conjecture,
memberP(esk4_0,esk5_0),
inference(sr,[status(thm)],[c_0_105,c_0_89]) ).
cnf(c_0_111,negated_conjecture,
( ~ segmentP(esk3_0,cons(X1,X2))
| ~ segmentP(esk4_0,cons(X1,X2))
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_106]),c_0_100]) ).
cnf(c_0_112,negated_conjecture,
segmentP(esk3_0,esk3_0),
inference(sr,[status(thm)],[c_0_107,c_0_89]) ).
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_60,c_0_23]),c_0_47]) ).
cnf(c_0_114,negated_conjecture,
app(esk8_2(esk4_0,esk5_0),app(esk3_0,esk9_2(esk4_0,esk5_0))) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_110]),c_0_41]),c_0_98])]) ).
cnf(c_0_115,negated_conjecture,
~ segmentP(esk4_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_97]),c_0_26]),c_0_98])]),c_0_112])]) ).
cnf(c_0_116,negated_conjecture,
( ~ ssList(esk9_2(esk4_0,esk5_0))
| ~ ssList(esk8_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_63])]),c_0_115]) ).
cnf(c_0_117,negated_conjecture,
~ ssList(esk8_2(esk4_0,esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_87]),c_0_110]),c_0_41]),c_0_98])]) ).
cnf(c_0_118,plain,
( ssList(esk8_2(X1,X2))
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_119,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_117,c_0_118]),c_0_110]),c_0_41]),c_0_98])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : SWC084+1 : TPTP v8.2.0. Released v2.4.0.
% 0.08/0.11 % Command : run_E %s %d THM
% 0.10/0.30 % Computer : n027.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % 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 03:42:07 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 17.07/2.56 # Version: 3.1.0
% 17.07/2.56 # Preprocessing class: FSLSSMSSSSSNFFN.
% 17.07/2.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.07/2.56 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 17.07/2.56 # Starting new_bool_3 with 300s (1) cores
% 17.07/2.56 # Starting new_bool_1 with 300s (1) cores
% 17.07/2.56 # Starting sh5l with 300s (1) cores
% 17.07/2.56 # new_bool_3 with pid 13678 completed with status 0
% 17.07/2.56 # Result found by new_bool_3
% 17.07/2.56 # Preprocessing class: FSLSSMSSSSSNFFN.
% 17.07/2.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.07/2.56 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 17.07/2.56 # Starting new_bool_3 with 300s (1) cores
% 17.07/2.56 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 17.07/2.56 # Search class: FGHSF-FFMM21-MFFFFFNN
% 17.07/2.56 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 17.07/2.56 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 17.07/2.56 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 13682 completed with status 0
% 17.07/2.56 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 17.07/2.56 # Preprocessing class: FSLSSMSSSSSNFFN.
% 17.07/2.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.07/2.56 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 17.07/2.56 # Starting new_bool_3 with 300s (1) cores
% 17.07/2.56 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 17.07/2.56 # Search class: FGHSF-FFMM21-MFFFFFNN
% 17.07/2.56 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 17.07/2.56 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 17.07/2.56 # Preprocessing time : 0.002 s
% 17.07/2.56 # Presaturation interreduction done
% 17.07/2.56
% 17.07/2.56 # Proof found!
% 17.07/2.56 # SZS status Theorem
% 17.07/2.56 # SZS output start CNFRefutation
% See solution above
% 17.13/2.56 # Parsed axioms : 96
% 17.13/2.56 # Removed by relevancy pruning/SinE : 57
% 17.13/2.56 # Initial clauses : 76
% 17.13/2.56 # Removed in clause preprocessing : 0
% 17.13/2.56 # Initial clauses in saturation : 76
% 17.13/2.56 # Processed clauses : 11355
% 17.13/2.56 # ...of these trivial : 519
% 17.13/2.56 # ...subsumed : 7355
% 17.13/2.56 # ...remaining for further processing : 3481
% 17.13/2.56 # Other redundant clauses eliminated : 72
% 17.13/2.56 # Clauses deleted for lack of memory : 0
% 17.13/2.56 # Backward-subsumed : 283
% 17.13/2.56 # Backward-rewritten : 301
% 17.13/2.56 # Generated clauses : 114493
% 17.13/2.56 # ...of the previous two non-redundant : 111149
% 17.13/2.56 # ...aggressively subsumed : 0
% 17.13/2.56 # Contextual simplify-reflections : 900
% 17.13/2.56 # Paramodulations : 113980
% 17.13/2.56 # Factorizations : 2
% 17.13/2.56 # NegExts : 0
% 17.13/2.56 # Equation resolutions : 106
% 17.13/2.56 # Disequality decompositions : 0
% 17.13/2.56 # Total rewrite steps : 70522
% 17.13/2.56 # ...of those cached : 70244
% 17.13/2.56 # Propositional unsat checks : 0
% 17.13/2.56 # Propositional check models : 0
% 17.13/2.56 # Propositional check unsatisfiable : 0
% 17.13/2.56 # Propositional clauses : 0
% 17.13/2.56 # Propositional clauses after purity: 0
% 17.13/2.56 # Propositional unsat core size : 0
% 17.13/2.56 # Propositional preprocessing time : 0.000
% 17.13/2.56 # Propositional encoding time : 0.000
% 17.13/2.56 # Propositional solver time : 0.000
% 17.13/2.56 # Success case prop preproc time : 0.000
% 17.13/2.56 # Success case prop encoding time : 0.000
% 17.13/2.56 # Success case prop solver time : 0.000
% 17.13/2.56 # Current number of processed clauses : 2411
% 17.13/2.56 # Positive orientable unit clauses : 316
% 17.13/2.56 # Positive unorientable unit clauses: 0
% 17.13/2.56 # Negative unit clauses : 262
% 17.13/2.56 # Non-unit-clauses : 1833
% 17.13/2.56 # Current number of unprocessed clauses: 94282
% 17.13/2.56 # ...number of literals in the above : 412450
% 17.13/2.56 # Current number of archived formulas : 0
% 17.13/2.56 # Current number of archived clauses : 1062
% 17.13/2.56 # Clause-clause subsumption calls (NU) : 329101
% 17.13/2.56 # Rec. Clause-clause subsumption calls : 108840
% 17.13/2.56 # Non-unit clause-clause subsumptions : 5891
% 17.13/2.56 # Unit Clause-clause subsumption calls : 19040
% 17.13/2.56 # Rewrite failures with RHS unbound : 0
% 17.13/2.56 # BW rewrite match attempts : 1107
% 17.13/2.56 # BW rewrite match successes : 33
% 17.13/2.56 # Condensation attempts : 0
% 17.13/2.56 # Condensation successes : 0
% 17.13/2.56 # Termbank termtop insertions : 2705205
% 17.13/2.56 # Search garbage collected termcells : 2064
% 17.13/2.56
% 17.13/2.56 # -------------------------------------------------
% 17.13/2.56 # User time : 2.053 s
% 17.13/2.56 # System time : 0.057 s
% 17.13/2.56 # Total time : 2.110 s
% 17.13/2.56 # Maximum resident set size: 2060 pages
% 17.13/2.56
% 17.13/2.56 # -------------------------------------------------
% 17.13/2.56 # User time : 2.057 s
% 17.13/2.56 # System time : 0.058 s
% 17.13/2.56 # Total time : 2.115 s
% 17.13/2.56 # Maximum resident set size: 1824 pages
% 17.13/2.56 % E---3.1 exiting
% 17.13/2.56 % E exiting
%------------------------------------------------------------------------------