TSTP Solution File: SWC409+1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SWC409+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n032.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 04:26:32 EDT 2024
% Result : Theorem 16.73s 2.58s
% Output : CNFRefutation 16.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of formulae : 106 ( 24 unt; 0 def)
% Number of atoms : 405 ( 127 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 501 ( 202 ~; 218 |; 34 &)
% ( 4 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 167 ( 0 sgn 76 !; 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
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) != X3
& app(cons(X5,nil),X6) = X4 ) )
| ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X2,X7)
| memberP(X1,X7) ) )
| ( 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(ax84,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
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(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(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/benchmark/Axioms/SWC001+0.ax',ax36) ).
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(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(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(ax37,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(c_0_16,plain,
! [X41,X42,X43] :
( ~ ssList(X41)
| ~ ssList(X42)
| ~ ssList(X43)
| app(X43,X42) != app(X41,X42)
| X43 = X41 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax79])])])]) ).
fof(c_0_17,plain,
! [X49,X50,X51] :
( ~ ssList(X49)
| ~ ssList(X50)
| ~ ssList(X51)
| app(app(X49,X50),X51) = app(X49,app(X50,X51)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax82])])])]) ).
fof(c_0_18,plain,
! [X35,X36] :
( ~ ssList(X35)
| ~ ssList(X36)
| ssList(app(X35,X36)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])])]) ).
fof(c_0_19,plain,
! [X40] :
( ~ ssList(X40)
| app(nil,X40) = X40 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])])]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) != X3
& app(cons(X5,nil),X6) = X4 ) )
| ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X2,X7)
| memberP(X1,X7) ) )
| ( nil != X3
& nil = X4 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
cnf(c_0_21,plain,
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X3,X2) != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( app(app(X1,X2),X3) = app(X1,app(X2,X3))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
fof(c_0_26,negated_conjecture,
! [X12,X13] :
( ssList(esk1_0)
& ssList(esk2_0)
& ssList(esk3_0)
& ssList(esk4_0)
& esk2_0 = esk4_0
& esk1_0 = esk3_0
& ( ~ ssItem(X12)
| ~ ssList(X13)
| app(X13,cons(X12,nil)) = esk3_0
| app(cons(X12,nil),X13) != esk4_0 )
& ssItem(esk5_0)
& memberP(esk2_0,esk5_0)
& ~ memberP(esk1_0,esk5_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_20])])])])]) ).
cnf(c_0_27,plain,
( X1 = app(X2,X3)
| app(X1,X4) != app(X2,app(X3,X4))
| ~ ssList(X4)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_28,plain,
( app(nil,app(X1,X2)) = app(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_24]),c_0_25])]) ).
cnf(c_0_29,negated_conjecture,
ssList(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,negated_conjecture,
esk2_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,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_27,c_0_28]),c_0_25])]) ).
cnf(c_0_32,negated_conjecture,
ssList(esk4_0),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
ssList(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,negated_conjecture,
esk1_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,negated_conjecture,
( X1 = app(nil,X2)
| app(X1,esk4_0) != app(X2,esk4_0)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
ssList(esk3_0),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
fof(c_0_37,plain,
! [X54] :
( ~ ssList(X54)
| app(X54,nil) = X54 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax84])])]) ).
cnf(c_0_38,negated_conjecture,
( app(nil,X1) = esk3_0
| app(esk3_0,esk4_0) != app(X1,esk4_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_39,plain,
! [X52,X53] :
( ( nil = X53
| nil != app(X52,X53)
| ~ ssList(X53)
| ~ ssList(X52) )
& ( nil = X52
| nil != app(X52,X53)
| ~ ssList(X53)
| ~ ssList(X52) )
& ( nil != X53
| nil != X52
| nil = app(X52,X53)
| ~ ssList(X53)
| ~ ssList(X52) ) ),
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_40,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_41,negated_conjecture,
app(nil,esk3_0) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_38]),c_0_36])]) ).
fof(c_0_42,plain,
! [X44,X45,X46] :
( ~ ssList(X44)
| ~ ssList(X45)
| ~ ssList(X46)
| app(X45,X46) != app(X45,X44)
| X46 = X44 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax80])])])]) ).
cnf(c_0_43,plain,
( nil = app(X2,X1)
| nil != X1
| nil != X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,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_40,c_0_22]),c_0_25])]),c_0_23]) ).
cnf(c_0_45,negated_conjecture,
( app(nil,app(esk3_0,X1)) = app(esk3_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_41]),c_0_36]),c_0_25])]) ).
cnf(c_0_46,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_47,plain,
app(nil,nil) = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_43])]),c_0_25])]) ).
cnf(c_0_48,plain,
( ssList(app(X1,app(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_23]) ).
cnf(c_0_49,negated_conjecture,
app(esk3_0,nil) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_41]),c_0_36]),c_0_25])]) ).
cnf(c_0_50,plain,
( X1 = nil
| app(nil,X1) != nil
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_25])]) ).
cnf(c_0_51,plain,
( ssList(app(X1,nil))
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_47]),c_0_25])]) ).
cnf(c_0_52,negated_conjecture,
( app(nil,X1) = esk4_0
| app(esk4_0,esk4_0) != app(X1,esk4_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_53,negated_conjecture,
( app(esk3_0,app(nil,X1)) = app(esk3_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_49]),c_0_25]),c_0_36])]) ).
cnf(c_0_54,plain,
( app(X1,nil) = app(nil,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_28]),c_0_25])]) ).
cnf(c_0_55,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_50,c_0_44]),c_0_25])]),c_0_51]) ).
cnf(c_0_56,negated_conjecture,
app(nil,esk4_0) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_52]),c_0_32])]) ).
fof(c_0_57,plain,
! [X55,X56] :
( ~ ssList(X55)
| ~ ssItem(X56)
| ssList(cons(X56,X55)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])])]) ).
fof(c_0_58,plain,
! [X37,X38,X39] :
( ~ ssList(X37)
| ~ ssList(X38)
| ~ ssItem(X39)
| cons(X39,app(X38,X37)) = app(cons(X39,X38),X37) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])])]) ).
fof(c_0_59,plain,
! [X26,X27,X28] :
( ( ~ memberP(app(X27,X28),X26)
| memberP(X27,X26)
| memberP(X28,X26)
| ~ ssList(X28)
| ~ ssList(X27)
| ~ ssItem(X26) )
& ( ~ memberP(X27,X26)
| memberP(app(X27,X28),X26)
| ~ ssList(X28)
| ~ ssList(X27)
| ~ ssItem(X26) )
& ( ~ memberP(X28,X26)
| memberP(app(X27,X28),X26)
| ~ ssList(X28)
| ~ ssList(X27)
| ~ ssItem(X26) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])])]) ).
cnf(c_0_60,negated_conjecture,
( app(esk3_0,app(X1,nil)) = app(esk3_0,X1)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_61,negated_conjecture,
( app(esk4_0,nil) = nil
| esk4_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_32])]) ).
fof(c_0_62,plain,
! [X15] :
( ( ssList(esk6_1(X15))
| nil = X15
| ~ ssList(X15) )
& ( ssItem(esk7_1(X15))
| nil = X15
| ~ ssList(X15) )
& ( cons(esk7_1(X15),esk6_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])])])])]) ).
fof(c_0_63,plain,
! [X20,X21,X24,X25] :
( ( ssList(esk8_2(X20,X21))
| ~ memberP(X20,X21)
| ~ ssItem(X21)
| ~ ssList(X20) )
& ( ssList(esk9_2(X20,X21))
| ~ memberP(X20,X21)
| ~ ssItem(X21)
| ~ ssList(X20) )
& ( app(esk8_2(X20,X21),cons(X21,esk9_2(X20,X21))) = X20
| ~ memberP(X20,X21)
| ~ ssItem(X21)
| ~ ssList(X20) )
& ( ~ ssList(X24)
| ~ ssList(X25)
| app(X24,cons(X21,X25)) != X20
| memberP(X20,X21)
| ~ ssItem(X21)
| ~ ssList(X20) ) ),
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_64,plain,
! [X47,X48] :
( ~ ssList(X47)
| ~ ssItem(X48)
| cons(X48,X47) = app(cons(X48,nil),X47) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])])]) ).
cnf(c_0_65,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_66,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_67,negated_conjecture,
~ memberP(esk1_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_68,plain,
( memberP(app(X3,X1),X2)
| ~ memberP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_69,negated_conjecture,
( app(esk3_0,esk4_0) = esk3_0
| esk4_0 != nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_49]),c_0_32])]) ).
cnf(c_0_70,negated_conjecture,
memberP(esk2_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_71,plain,
! [X29,X30,X31] :
( ( ~ memberP(cons(X30,X31),X29)
| X29 = X30
| memberP(X31,X29)
| ~ ssList(X31)
| ~ ssItem(X30)
| ~ ssItem(X29) )
& ( X29 != X30
| memberP(cons(X30,X31),X29)
| ~ ssList(X31)
| ~ ssItem(X30)
| ~ ssItem(X29) )
& ( ~ memberP(X31,X29)
| memberP(cons(X30,X31),X29)
| ~ ssList(X31)
| ~ ssItem(X30)
| ~ ssItem(X29) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])])]) ).
cnf(c_0_72,plain,
( cons(esk7_1(X1),esk6_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_73,plain,
( ssItem(esk7_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_74,plain,
( ssList(esk6_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_75,plain,
( memberP(X4,X3)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,cons(X3,X2)) != X4
| ~ ssItem(X3)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_76,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_26]) ).
cnf(c_0_77,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_78,plain,
( ssList(app(cons(X1,X2),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_23]) ).
cnf(c_0_79,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_66,c_0_47]),c_0_25])]) ).
cnf(c_0_80,negated_conjecture,
~ memberP(esk3_0,esk5_0),
inference(rw,[status(thm)],[c_0_67,c_0_34]) ).
cnf(c_0_81,negated_conjecture,
( memberP(esk3_0,X1)
| esk4_0 != nil
| ~ memberP(esk4_0,X1)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_36]),c_0_32])]) ).
cnf(c_0_82,negated_conjecture,
memberP(esk4_0,esk5_0),
inference(rw,[status(thm)],[c_0_70,c_0_30]) ).
cnf(c_0_83,negated_conjecture,
ssItem(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_84,plain,
( X3 = X1
| memberP(X2,X3)
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_85,negated_conjecture,
( cons(esk7_1(esk4_0),esk6_1(esk4_0)) = esk4_0
| esk4_0 = nil ),
inference(spm,[status(thm)],[c_0_72,c_0_32]) ).
cnf(c_0_86,negated_conjecture,
( esk4_0 = nil
| ssItem(esk7_1(esk4_0)) ),
inference(spm,[status(thm)],[c_0_73,c_0_32]) ).
cnf(c_0_87,negated_conjecture,
( esk4_0 = nil
| ssList(esk6_1(esk4_0)) ),
inference(spm,[status(thm)],[c_0_74,c_0_32]) ).
cnf(c_0_88,plain,
( memberP(app(X1,cons(X2,X3)),X2)
| ~ ssList(app(X1,cons(X2,X3)))
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(er,[status(thm)],[c_0_75]) ).
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_76,c_0_77]) ).
cnf(c_0_90,plain,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_91,plain,
( ssList(cons(X1,nil))
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_25])]) ).
cnf(c_0_92,negated_conjecture,
esk4_0 != nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_83])]) ).
cnf(c_0_93,negated_conjecture,
( esk7_1(esk4_0) = X1
| esk4_0 = nil
| memberP(esk6_1(esk4_0),X1)
| ~ memberP(esk4_0,X1)
| ~ ssItem(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]),c_0_87]) ).
cnf(c_0_94,negated_conjecture,
( memberP(esk3_0,X1)
| cons(X1,X2) != esk4_0
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_36]),c_0_25])]) ).
cnf(c_0_95,negated_conjecture,
( memberP(esk3_0,X1)
| cons(X2,X3) != esk4_0
| ~ memberP(X3,X1)
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ ssItem(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_89]),c_0_91]) ).
cnf(c_0_96,negated_conjecture,
cons(esk7_1(esk4_0),esk6_1(esk4_0)) = esk4_0,
inference(sr,[status(thm)],[c_0_85,c_0_92]) ).
cnf(c_0_97,negated_conjecture,
ssList(esk6_1(esk4_0)),
inference(sr,[status(thm)],[c_0_87,c_0_92]) ).
cnf(c_0_98,negated_conjecture,
ssItem(esk7_1(esk4_0)),
inference(sr,[status(thm)],[c_0_86,c_0_92]) ).
cnf(c_0_99,negated_conjecture,
( esk7_1(esk4_0) = esk5_0
| esk4_0 = nil
| memberP(esk6_1(esk4_0),esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_82]),c_0_83])]) ).
cnf(c_0_100,negated_conjecture,
( esk4_0 = nil
| memberP(esk3_0,esk7_1(esk4_0)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_85]),c_0_86]),c_0_87]) ).
cnf(c_0_101,negated_conjecture,
( memberP(esk3_0,X1)
| ~ memberP(esk6_1(esk4_0),X1)
| ~ ssItem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]),c_0_98])]) ).
cnf(c_0_102,negated_conjecture,
( esk7_1(esk4_0) = esk5_0
| memberP(esk6_1(esk4_0),esk5_0) ),
inference(sr,[status(thm)],[c_0_99,c_0_92]) ).
cnf(c_0_103,negated_conjecture,
memberP(esk3_0,esk7_1(esk4_0)),
inference(sr,[status(thm)],[c_0_100,c_0_92]) ).
cnf(c_0_104,negated_conjecture,
esk7_1(esk4_0) = esk5_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_83])]),c_0_80]) ).
cnf(c_0_105,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104]),c_0_80]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SWC409+1 : TPTP v8.2.0. Released v2.4.0.
% 0.02/0.10 % Command : run_E %s %d THM
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Sun May 19 03:26:07 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 16.73/2.58 # Version: 3.1.0
% 16.73/2.58 # Preprocessing class: FSLSSMSSSSSNFFN.
% 16.73/2.58 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 16.73/2.58 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 16.73/2.58 # Starting new_bool_3 with 300s (1) cores
% 16.73/2.58 # Starting new_bool_1 with 300s (1) cores
% 16.73/2.58 # Starting sh5l with 300s (1) cores
% 16.73/2.58 # new_bool_1 with pid 4409 completed with status 0
% 16.73/2.58 # Result found by new_bool_1
% 16.73/2.58 # Preprocessing class: FSLSSMSSSSSNFFN.
% 16.73/2.58 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 16.73/2.58 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 16.73/2.58 # Starting new_bool_3 with 300s (1) cores
% 16.73/2.58 # Starting new_bool_1 with 300s (1) cores
% 16.73/2.58 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 16.73/2.58 # Search class: FGHSF-FFMM21-MFFFFFNN
% 16.73/2.58 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 16.73/2.58 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 16.73/2.58 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 4411 completed with status 0
% 16.73/2.58 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 16.73/2.58 # Preprocessing class: FSLSSMSSSSSNFFN.
% 16.73/2.58 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 16.73/2.58 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 16.73/2.58 # Starting new_bool_3 with 300s (1) cores
% 16.73/2.58 # Starting new_bool_1 with 300s (1) cores
% 16.73/2.58 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 16.73/2.58 # Search class: FGHSF-FFMM21-MFFFFFNN
% 16.73/2.58 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 16.73/2.58 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 16.73/2.58 # Preprocessing time : 0.002 s
% 16.73/2.58 # Presaturation interreduction done
% 16.73/2.58
% 16.73/2.58 # Proof found!
% 16.73/2.58 # SZS status Theorem
% 16.73/2.58 # SZS output start CNFRefutation
% See solution above
% 16.73/2.58 # Parsed axioms : 96
% 16.73/2.58 # Removed by relevancy pruning/SinE : 75
% 16.73/2.58 # Initial clauses : 45
% 16.73/2.58 # Removed in clause preprocessing : 0
% 16.73/2.58 # Initial clauses in saturation : 45
% 16.73/2.58 # Processed clauses : 6862
% 16.73/2.58 # ...of these trivial : 475
% 16.73/2.58 # ...subsumed : 4245
% 16.73/2.58 # ...remaining for further processing : 2142
% 16.73/2.58 # Other redundant clauses eliminated : 44
% 16.73/2.58 # Clauses deleted for lack of memory : 0
% 16.73/2.58 # Backward-subsumed : 196
% 16.73/2.58 # Backward-rewritten : 137
% 16.73/2.58 # Generated clauses : 113000
% 16.73/2.58 # ...of the previous two non-redundant : 110517
% 16.73/2.58 # ...aggressively subsumed : 0
% 16.73/2.58 # Contextual simplify-reflections : 659
% 16.73/2.58 # Paramodulations : 112747
% 16.73/2.58 # Factorizations : 0
% 16.73/2.58 # NegExts : 0
% 16.73/2.58 # Equation resolutions : 72
% 16.73/2.58 # Disequality decompositions : 0
% 16.73/2.58 # Total rewrite steps : 31167
% 16.73/2.58 # ...of those cached : 31024
% 16.73/2.58 # Propositional unsat checks : 0
% 16.73/2.58 # Propositional check models : 0
% 16.73/2.58 # Propositional check unsatisfiable : 0
% 16.73/2.58 # Propositional clauses : 0
% 16.73/2.58 # Propositional clauses after purity: 0
% 16.73/2.58 # Propositional unsat core size : 0
% 16.73/2.58 # Propositional preprocessing time : 0.000
% 16.73/2.58 # Propositional encoding time : 0.000
% 16.73/2.58 # Propositional solver time : 0.000
% 16.73/2.58 # Success case prop preproc time : 0.000
% 16.73/2.58 # Success case prop encoding time : 0.000
% 16.73/2.58 # Success case prop solver time : 0.000
% 16.73/2.58 # Current number of processed clauses : 1581
% 16.73/2.58 # Positive orientable unit clauses : 178
% 16.73/2.58 # Positive unorientable unit clauses: 0
% 16.73/2.58 # Negative unit clauses : 61
% 16.73/2.58 # Non-unit-clauses : 1342
% 16.73/2.58 # Current number of unprocessed clauses: 103335
% 16.73/2.58 # ...number of literals in the above : 425794
% 16.73/2.58 # Current number of archived formulas : 0
% 16.73/2.58 # Current number of archived clauses : 558
% 16.73/2.58 # Clause-clause subsumption calls (NU) : 314264
% 16.73/2.58 # Rec. Clause-clause subsumption calls : 159621
% 16.73/2.58 # Non-unit clause-clause subsumptions : 4557
% 16.73/2.58 # Unit Clause-clause subsumption calls : 21511
% 16.73/2.58 # Rewrite failures with RHS unbound : 0
% 16.73/2.58 # BW rewrite match attempts : 4848
% 16.73/2.58 # BW rewrite match successes : 17
% 16.73/2.58 # Condensation attempts : 0
% 16.73/2.58 # Condensation successes : 0
% 16.73/2.58 # Termbank termtop insertions : 3400197
% 16.73/2.58 # Search garbage collected termcells : 1499
% 16.73/2.58
% 16.73/2.58 # -------------------------------------------------
% 16.73/2.58 # User time : 2.030 s
% 16.73/2.58 # System time : 0.084 s
% 16.73/2.58 # Total time : 2.115 s
% 16.73/2.58 # Maximum resident set size: 1896 pages
% 16.73/2.58
% 16.73/2.58 # -------------------------------------------------
% 16.73/2.58 # User time : 2.032 s
% 16.73/2.58 # System time : 0.088 s
% 16.73/2.58 # Total time : 2.120 s
% 16.73/2.58 # Maximum resident set size: 1820 pages
% 16.73/2.58 % E---3.1 exiting
% 16.73/2.58 % E exiting
%------------------------------------------------------------------------------