TSTP Solution File: SWC088+1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SWC088+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n016.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 04:23:12 EDT 2024
% Result : Theorem 2.47s 0.85s
% Output : CNFRefutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 113 ( 23 unt; 0 def)
% Number of atoms : 408 ( 130 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 502 ( 207 ~; 211 |; 37 &)
% ( 4 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 172 ( 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/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)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) != X3
& app(cons(X6,nil),X7) = X4 ) )
| ( nil != X3
& nil = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
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(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(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(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax54) ).
fof(ax55,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
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(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(c_0_17,plain,
! [X26,X27,X28] :
( ~ ssList(X26)
| ~ ssList(X27)
| ~ ssList(X28)
| app(X28,X27) != app(X26,X27)
| X28 = X26 ),
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,
! [X34,X35,X36] :
( ~ ssList(X34)
| ~ ssList(X35)
| ~ ssList(X36)
| app(app(X34,X35),X36) = app(X34,app(X35,X36)) ),
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,
! [X20,X21] :
( ~ ssList(X20)
| ~ ssList(X21)
| ssList(app(X20,X21)) ),
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,
! [X25] :
( ~ ssList(X25)
| app(nil,X25) = X25 ),
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)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) != X3
& app(cons(X6,nil),X7) = X4 ) )
| ( nil != X3
& nil = X4 ) ) ) ) ) ),
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,X13,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) )
& ( ~ ssItem(X13)
| ~ ssList(X14)
| app(X14,cons(X13,nil)) = esk3_0
| app(cons(X13,nil),X14) != esk4_0 )
& ( nil = esk3_0
| nil != esk4_0 ) ),
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,
! [X37,X38] :
( ( nil = X38
| nil != app(X37,X38)
| ~ ssList(X38)
| ~ ssList(X37) )
& ( nil = X37
| nil != app(X37,X38)
| ~ ssList(X38)
| ~ ssList(X37) )
& ( nil != X38
| nil != X37
| nil = app(X37,X38)
| ~ ssList(X38)
| ~ ssList(X37) ) ),
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_29,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_30,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_31,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_33,plain,
! [X50,X51,X54,X55] :
( ( ssList(esk9_2(X50,X51))
| ~ segmentP(X50,X51)
| ~ ssList(X51)
| ~ ssList(X50) )
& ( ssList(esk10_2(X50,X51))
| ~ segmentP(X50,X51)
| ~ ssList(X51)
| ~ ssList(X50) )
& ( app(app(esk9_2(X50,X51),X51),esk10_2(X50,X51)) = X50
| ~ segmentP(X50,X51)
| ~ ssList(X51)
| ~ ssList(X50) )
& ( ~ ssList(X54)
| ~ ssList(X55)
| app(app(X54,X51),X55) != X50
| segmentP(X50,X51)
| ~ ssList(X51)
| ~ ssList(X50) ) ),
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_34,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_35,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,negated_conjecture,
neq(esk2_0,nil),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_37,plain,
! [X29,X30,X31] :
( ~ ssList(X29)
| ~ ssList(X30)
| ~ ssList(X31)
| app(X30,X31) != app(X30,X29)
| X31 = X29 ),
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_28]) ).
fof(c_0_39,plain,
! [X39] :
( ~ ssList(X39)
| app(X39,nil) = X39 ),
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_29,c_0_30]),c_0_26])]) ).
cnf(c_0_41,negated_conjecture,
ssList(esk4_0),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_42,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_33]) ).
fof(c_0_43,plain,
! [X22,X23,X24] :
( ~ ssList(X22)
| ~ ssList(X23)
| ~ ssItem(X24)
| cons(X24,app(X23,X22)) = app(cons(X24,X23),X22) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).
fof(c_0_44,plain,
! [X15] :
( ( ssList(esk5_1(X15))
| nil = X15
| ~ ssList(X15) )
& ( ssItem(esk6_1(X15))
| nil = X15
| ~ ssList(X15) )
& ( cons(esk6_1(X15),esk5_1(X15)) = X15
| nil = X15
| ~ ssList(X15) ) ),
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_45,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_34,c_0_35]),c_0_32]) ).
cnf(c_0_46,negated_conjecture,
neq(esk4_0,nil),
inference(rw,[status(thm)],[c_0_36,c_0_32]) ).
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_37]) ).
cnf(c_0_48,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_49,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_50,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_51,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]) ).
fof(c_0_52,plain,
! [X59,X60] :
( ~ ssList(X59)
| ~ ssList(X60)
| ~ segmentP(X59,X60)
| ~ segmentP(X60,X59)
| X59 = X60 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax54])])])]) ).
cnf(c_0_53,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_42]) ).
cnf(c_0_54,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_55,plain,
( cons(esk6_1(X1),esk5_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_56,plain,
( ssItem(esk6_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_57,plain,
( ssList(esk5_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_58,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_45,c_0_46]),c_0_41])]) ).
cnf(c_0_59,negated_conjecture,
( nil = esk3_0
| nil != esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_60,plain,
! [X61] :
( ~ ssList(X61)
| segmentP(X61,X61) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax55])])]) ).
fof(c_0_61,plain,
! [X40,X41] :
( ~ ssList(X40)
| ~ ssItem(X41)
| ssList(cons(X41,X40)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_62,plain,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
inference(fof_simplification,[status(thm)],[ax15]) ).
fof(c_0_63,plain,
! [X32,X33] :
( ~ ssList(X32)
| ~ ssItem(X33)
| cons(X33,X32) = app(cons(X33,nil),X32) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_64,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_48]),c_0_26])]) ).
cnf(c_0_65,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_49,c_0_23]),c_0_26])]),c_0_24]) ).
cnf(c_0_66,plain,
( ssList(app(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_48]),c_0_26])]) ).
cnf(c_0_67,negated_conjecture,
( app(nil,X1) = esk4_0
| app(esk4_0,esk4_0) != app(X1,esk4_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_41]) ).
cnf(c_0_68,plain,
( X1 = X2
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_69,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_53,c_0_49]),c_0_26])]),c_0_24]) ).
cnf(c_0_70,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_54,c_0_49]),c_0_26])]) ).
cnf(c_0_71,negated_conjecture,
( cons(esk6_1(esk4_0),esk5_1(esk4_0)) = esk4_0
| esk4_0 = nil ),
inference(spm,[status(thm)],[c_0_55,c_0_41]) ).
cnf(c_0_72,negated_conjecture,
( esk4_0 = nil
| ssItem(esk6_1(esk4_0)) ),
inference(spm,[status(thm)],[c_0_56,c_0_41]) ).
cnf(c_0_73,negated_conjecture,
( esk4_0 = nil
| ssList(esk5_1(esk4_0)) ),
inference(spm,[status(thm)],[c_0_57,c_0_41]) ).
cnf(c_0_74,negated_conjecture,
( esk4_0 != nil
| ~ segmentP(nil,esk4_0)
| ~ segmentP(esk4_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_75,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_76,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
fof(c_0_77,plain,
! [X70,X71] :
( ( ~ neq(X70,X71)
| X70 != X71
| ~ ssList(X71)
| ~ ssList(X70) )
& ( X70 = X71
| neq(X70,X71)
| ~ ssList(X71)
| ~ ssList(X70) ) ),
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_62])])])])]) ).
cnf(c_0_78,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_27]) ).
cnf(c_0_79,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_80,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_64,c_0_65]),c_0_26])]),c_0_66]) ).
cnf(c_0_81,negated_conjecture,
app(nil,esk4_0) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_67]),c_0_41])]) ).
cnf(c_0_82,plain,
( app(X1,X2) = X2
| ~ segmentP(X2,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_24]) ).
cnf(c_0_83,negated_conjecture,
( app(esk4_0,nil) = esk4_0
| esk4_0 = nil ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]),c_0_73]) ).
cnf(c_0_84,negated_conjecture,
( esk4_0 != nil
| ~ segmentP(nil,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_41])]) ).
cnf(c_0_85,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_54]),c_0_24]) ).
cnf(c_0_86,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_54,c_0_48]),c_0_26])]) ).
cnf(c_0_87,plain,
( X1 = X2
| neq(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_88,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_53,c_0_25]),c_0_26])]),c_0_24]) ).
cnf(c_0_89,negated_conjecture,
( app(X1,cons(X2,nil)) = esk3_0
| cons(X2,X1) != esk4_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_90,negated_conjecture,
( app(esk4_0,nil) = nil
| esk4_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_41])]) ).
cnf(c_0_91,negated_conjecture,
~ segmentP(nil,esk4_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_26]),c_0_41])]),c_0_84]) ).
cnf(c_0_92,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_26])]) ).
cnf(c_0_93,plain,
( X1 = nil
| neq(X1,nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_26]) ).
cnf(c_0_94,negated_conjecture,
( segmentP(esk3_0,X1)
| cons(X2,X1) != esk4_0
| ~ ssList(cons(X2,nil))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_95,negated_conjecture,
esk4_0 != nil,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_90]),c_0_41]),c_0_26])]),c_0_91]) ).
cnf(c_0_96,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_53,c_0_79]),c_0_92]),c_0_85]) ).
cnf(c_0_97,negated_conjecture,
( esk5_1(esk4_0) = nil
| esk4_0 = nil
| neq(esk5_1(esk4_0),nil) ),
inference(spm,[status(thm)],[c_0_93,c_0_73]) ).
cnf(c_0_98,negated_conjecture,
( segmentP(esk3_0,X1)
| cons(X2,X1) != esk4_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_76]),c_0_26])]) ).
cnf(c_0_99,negated_conjecture,
cons(esk6_1(esk4_0),esk5_1(esk4_0)) = esk4_0,
inference(sr,[status(thm)],[c_0_71,c_0_95]) ).
cnf(c_0_100,negated_conjecture,
ssList(esk5_1(esk4_0)),
inference(sr,[status(thm)],[c_0_73,c_0_95]) ).
cnf(c_0_101,negated_conjecture,
ssItem(esk6_1(esk4_0)),
inference(sr,[status(thm)],[c_0_72,c_0_95]) ).
cnf(c_0_102,plain,
( segmentP(cons(X1,X2),X2)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_70]),c_0_26])]) ).
cnf(c_0_103,negated_conjecture,
( esk5_1(esk4_0) = nil
| neq(esk5_1(esk4_0),nil) ),
inference(sr,[status(thm)],[c_0_97,c_0_95]) ).
cnf(c_0_104,negated_conjecture,
segmentP(esk3_0,esk5_1(esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]),c_0_101])]) ).
cnf(c_0_105,negated_conjecture,
segmentP(esk4_0,esk5_1(esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_99]),c_0_100]),c_0_101])]) ).
cnf(c_0_106,negated_conjecture,
esk5_1(esk4_0) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_103]),c_0_104]),c_0_105]),c_0_100])]) ).
cnf(c_0_107,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_69,c_0_81]),c_0_41]),c_0_26])]) ).
cnf(c_0_108,negated_conjecture,
( app(nil,cons(X1,nil)) = esk3_0
| cons(X1,nil) != esk4_0
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_86]),c_0_26])]) ).
cnf(c_0_109,negated_conjecture,
cons(esk6_1(esk4_0),nil) = esk4_0,
inference(rw,[status(thm)],[c_0_99,c_0_106]) ).
cnf(c_0_110,negated_conjecture,
~ segmentP(esk3_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_107])]) ).
cnf(c_0_111,negated_conjecture,
esk3_0 = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_81]),c_0_101])]) ).
cnf(c_0_112,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_111]),c_0_107])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWC088+1 : TPTP v8.2.0. Released v2.4.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun May 19 02:43:52 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.46 Running first-order theorem proving
% 0.18/0.46 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
% 2.47/0.85 # Version: 3.1.0
% 2.47/0.85 # Preprocessing class: FSLSSMSSSSSNFFN.
% 2.47/0.85 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.47/0.85 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.47/0.85 # Starting new_bool_3 with 300s (1) cores
% 2.47/0.85 # Starting new_bool_1 with 300s (1) cores
% 2.47/0.85 # Starting sh5l with 300s (1) cores
% 2.47/0.85 # new_bool_3 with pid 30516 completed with status 0
% 2.47/0.85 # Result found by new_bool_3
% 2.47/0.85 # Preprocessing class: FSLSSMSSSSSNFFN.
% 2.47/0.85 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.47/0.85 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.47/0.85 # Starting new_bool_3 with 300s (1) cores
% 2.47/0.85 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.47/0.85 # Search class: FGHSF-FFMM21-MFFFFFNN
% 2.47/0.85 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 2.47/0.85 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 2.47/0.85 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 30520 completed with status 0
% 2.47/0.85 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.47/0.85 # Preprocessing class: FSLSSMSSSSSNFFN.
% 2.47/0.85 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.47/0.85 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.47/0.85 # Starting new_bool_3 with 300s (1) cores
% 2.47/0.85 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.47/0.85 # Search class: FGHSF-FFMM21-MFFFFFNN
% 2.47/0.85 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 2.47/0.85 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 2.47/0.85 # Preprocessing time : 0.002 s
% 2.47/0.85 # Presaturation interreduction done
% 2.47/0.85
% 2.47/0.85 # Proof found!
% 2.47/0.85 # SZS status Theorem
% 2.47/0.85 # SZS output start CNFRefutation
% See solution above
% 2.47/0.85 # Parsed axioms : 96
% 2.47/0.85 # Removed by relevancy pruning/SinE : 70
% 2.47/0.85 # Initial clauses : 48
% 2.47/0.85 # Removed in clause preprocessing : 0
% 2.47/0.85 # Initial clauses in saturation : 48
% 2.47/0.85 # Processed clauses : 1503
% 2.47/0.85 # ...of these trivial : 34
% 2.47/0.85 # ...subsumed : 640
% 2.47/0.85 # ...remaining for further processing : 829
% 2.47/0.85 # Other redundant clauses eliminated : 35
% 2.47/0.85 # Clauses deleted for lack of memory : 0
% 2.47/0.85 # Backward-subsumed : 70
% 2.47/0.85 # Backward-rewritten : 326
% 2.47/0.85 # Generated clauses : 17833
% 2.47/0.85 # ...of the previous two non-redundant : 17320
% 2.47/0.85 # ...aggressively subsumed : 0
% 2.47/0.85 # Contextual simplify-reflections : 143
% 2.47/0.85 # Paramodulations : 17701
% 2.47/0.85 # Factorizations : 0
% 2.47/0.85 # NegExts : 0
% 2.47/0.85 # Equation resolutions : 49
% 2.47/0.85 # Disequality decompositions : 0
% 2.47/0.85 # Total rewrite steps : 4197
% 2.47/0.85 # ...of those cached : 4159
% 2.47/0.85 # Propositional unsat checks : 0
% 2.47/0.85 # Propositional check models : 0
% 2.47/0.85 # Propositional check unsatisfiable : 0
% 2.47/0.85 # Propositional clauses : 0
% 2.47/0.85 # Propositional clauses after purity: 0
% 2.47/0.85 # Propositional unsat core size : 0
% 2.47/0.85 # Propositional preprocessing time : 0.000
% 2.47/0.85 # Propositional encoding time : 0.000
% 2.47/0.85 # Propositional solver time : 0.000
% 2.47/0.85 # Success case prop preproc time : 0.000
% 2.47/0.85 # Success case prop encoding time : 0.000
% 2.47/0.85 # Success case prop solver time : 0.000
% 2.47/0.85 # Current number of processed clauses : 298
% 2.47/0.85 # Positive orientable unit clauses : 42
% 2.47/0.85 # Positive unorientable unit clauses: 0
% 2.47/0.85 # Negative unit clauses : 3
% 2.47/0.85 # Non-unit-clauses : 253
% 2.47/0.85 # Current number of unprocessed clauses: 15880
% 2.47/0.85 # ...number of literals in the above : 60206
% 2.47/0.85 # Current number of archived formulas : 0
% 2.47/0.85 # Current number of archived clauses : 526
% 2.47/0.85 # Clause-clause subsumption calls (NU) : 21267
% 2.47/0.85 # Rec. Clause-clause subsumption calls : 10901
% 2.47/0.85 # Non-unit clause-clause subsumptions : 800
% 2.47/0.85 # Unit Clause-clause subsumption calls : 1752
% 2.47/0.85 # Rewrite failures with RHS unbound : 0
% 2.47/0.85 # BW rewrite match attempts : 55
% 2.47/0.85 # BW rewrite match successes : 14
% 2.47/0.85 # Condensation attempts : 0
% 2.47/0.85 # Condensation successes : 0
% 2.47/0.85 # Termbank termtop insertions : 365265
% 2.47/0.85 # Search garbage collected termcells : 1579
% 2.47/0.85
% 2.47/0.85 # -------------------------------------------------
% 2.47/0.85 # User time : 0.330 s
% 2.47/0.85 # System time : 0.011 s
% 2.47/0.85 # Total time : 0.341 s
% 2.47/0.85 # Maximum resident set size: 2024 pages
% 2.47/0.85
% 2.47/0.85 # -------------------------------------------------
% 2.47/0.85 # User time : 0.333 s
% 2.47/0.85 # System time : 0.015 s
% 2.47/0.85 # Total time : 0.348 s
% 2.47/0.85 # Maximum resident set size: 1820 pages
% 2.47/0.85 % E---3.1 exiting
% 3.20/0.85 % E exiting
%------------------------------------------------------------------------------