TSTP Solution File: SWC409+1 by E-SAT---3.1
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%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SWC409+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n004.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 19:43:02 EDT 2023
% Result : Theorem 1.32s 0.70s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 15
% Syntax : Number of formulae : 99 ( 24 unt; 0 def)
% Number of atoms : 365 ( 104 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 428 ( 162 ~; 190 |; 34 &)
% ( 4 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 130 ( 0 sgn; 67 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/tmp/tmp.RdWlYyLosF/E---3.1_1605.p',co1) ).
fof(ax5,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.RdWlYyLosF/E---3.1_1605.p',ax5) ).
fof(ax26,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.RdWlYyLosF/E---3.1_1605.p',ax26) ).
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/sandbox2/tmp/tmp.RdWlYyLosF/E---3.1_1605.p',ax3) ).
fof(ax16,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.RdWlYyLosF/E---3.1_1605.p',ax16) ).
fof(ax85,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil != X1
=> hd(app(X1,X2)) = hd(X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.RdWlYyLosF/E---3.1_1605.p',ax85) ).
fof(ax22,axiom,
! [X1] :
( ssList(X1)
=> ( nil != X1
=> ssItem(hd(X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.RdWlYyLosF/E---3.1_1605.p',ax22) ).
fof(ax28,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.RdWlYyLosF/E---3.1_1605.p',ax28) ).
fof(ax81,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.RdWlYyLosF/E---3.1_1605.p',ax81) ).
fof(ax20,axiom,
! [X1] :
( ssList(X1)
=> ( nil = X1
| ? [X2] :
( ssList(X2)
& ? [X3] :
( ssItem(X3)
& cons(X3,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.RdWlYyLosF/E---3.1_1605.p',ax20) ).
fof(ax23,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> hd(cons(X2,X1)) = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.RdWlYyLosF/E---3.1_1605.p',ax23) ).
fof(ax27,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssItem(X3)
=> cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.RdWlYyLosF/E---3.1_1605.p',ax27) ).
fof(ax17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/tmp/tmp.RdWlYyLosF/E---3.1_1605.p',ax17) ).
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/sandbox2/tmp/tmp.RdWlYyLosF/E---3.1_1605.p',ax36) ).
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/sandbox2/tmp/tmp.RdWlYyLosF/E---3.1_1605.p',ax37) ).
fof(c_0_15,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])]) ).
fof(c_0_16,negated_conjecture,
! [X256,X257] :
( ssList(esk48_0)
& ssList(esk49_0)
& ssList(esk50_0)
& ssList(esk51_0)
& esk49_0 = esk51_0
& esk48_0 = esk50_0
& ( ~ ssItem(X256)
| ~ ssList(X257)
| app(X257,cons(X256,nil)) = esk50_0
| app(cons(X256,nil),X257) != esk51_0 )
& ssItem(esk52_0)
& memberP(esk49_0,esk52_0)
& ~ memberP(esk48_0,esk52_0)
& ( nil = esk50_0
| nil != esk51_0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
fof(c_0_17,plain,
! [X21,X22,X24] :
( ( ssList(esk6_2(X21,X22))
| ~ frontsegP(X21,X22)
| ~ ssList(X22)
| ~ ssList(X21) )
& ( app(X22,esk6_2(X21,X22)) = X21
| ~ frontsegP(X21,X22)
| ~ ssList(X22)
| ~ ssList(X21) )
& ( ~ ssList(X24)
| app(X22,X24) != X21
| frontsegP(X21,X22)
| ~ ssList(X22)
| ~ ssList(X21) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax5])])])])]) ).
fof(c_0_18,plain,
! [X131,X132] :
( ~ ssList(X131)
| ~ ssList(X132)
| ssList(app(X131,X132)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax26])])]) ).
fof(c_0_19,plain,
! [X12,X13,X16,X17] :
( ( ssList(esk3_2(X12,X13))
| ~ memberP(X12,X13)
| ~ ssItem(X13)
| ~ ssList(X12) )
& ( ssList(esk4_2(X12,X13))
| ~ memberP(X12,X13)
| ~ ssItem(X13)
| ~ ssList(X12) )
& ( app(esk3_2(X12,X13),cons(X13,esk4_2(X12,X13))) = X12
| ~ memberP(X12,X13)
| ~ ssItem(X13)
| ~ ssList(X12) )
& ( ~ ssList(X16)
| ~ ssList(X17)
| app(X16,cons(X13,X17)) != X12
| memberP(X12,X13)
| ~ ssItem(X13)
| ~ ssList(X12) ) ),
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_20,negated_conjecture,
memberP(esk49_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
esk49_0 = esk51_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
ssList(esk49_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( frontsegP(X3,X2)
| ~ ssList(X1)
| app(X2,X1) != X3
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( app(esk3_2(X1,X2),cons(X2,esk4_2(X1,X2))) = X1
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
memberP(esk51_0,esk52_0),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
ssList(esk51_0),
inference(rw,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_28,negated_conjecture,
ssItem(esk52_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_29,plain,
( ssList(esk3_2(X1,X2))
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_30,plain,
( frontsegP(app(X1,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_23]),c_0_24]) ).
cnf(c_0_31,negated_conjecture,
app(esk3_2(esk51_0,esk52_0),cons(esk52_0,esk4_2(esk51_0,esk52_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_32,negated_conjecture,
ssList(esk3_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_26]),c_0_27]),c_0_28])]) ).
fof(c_0_33,plain,
! [X112,X113] :
( ~ ssList(X112)
| ~ ssItem(X113)
| ssList(cons(X113,X112)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax16])])]) ).
cnf(c_0_34,plain,
( ssList(esk4_2(X1,X2))
| ~ memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_35,negated_conjecture,
( frontsegP(esk51_0,esk3_2(esk51_0,esk52_0))
| ~ ssList(cons(esk52_0,esk4_2(esk51_0,esk52_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_36,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_37,negated_conjecture,
ssList(esk4_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_26]),c_0_27]),c_0_28])]) ).
fof(c_0_38,plain,
! [X229,X230] :
( ~ ssList(X229)
| ~ ssList(X230)
| nil = X229
| hd(app(X229,X230)) = hd(X229) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax85])])]) ).
cnf(c_0_39,plain,
( app(X1,esk6_2(X2,X1)) = X2
| ~ frontsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_40,negated_conjecture,
frontsegP(esk51_0,esk3_2(esk51_0,esk52_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_28])]) ).
cnf(c_0_41,plain,
( ssList(esk6_2(X1,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_42,plain,
! [X125] :
( ~ ssList(X125)
| nil = X125
| ssItem(hd(X125)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax22])]) ).
cnf(c_0_43,plain,
( nil = X1
| hd(app(X1,X2)) = hd(X1)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,negated_conjecture,
app(esk3_2(esk51_0,esk52_0),esk6_2(esk51_0,esk3_2(esk51_0,esk52_0))) = esk51_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_27]),c_0_32])]) ).
cnf(c_0_45,negated_conjecture,
ssList(esk6_2(esk51_0,esk3_2(esk51_0,esk52_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_40]),c_0_32]),c_0_27])]) ).
cnf(c_0_46,plain,
( nil = X1
| ssItem(hd(X1))
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_47,negated_conjecture,
( hd(esk3_2(esk51_0,esk52_0)) = hd(esk51_0)
| esk3_2(esk51_0,esk52_0) = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_32])]) ).
fof(c_0_48,plain,
! [X136] :
( ~ ssList(X136)
| app(nil,X136) = X136 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax28])]) ).
cnf(c_0_49,negated_conjecture,
( esk3_2(esk51_0,esk52_0) = nil
| ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_32])]) ).
fof(c_0_50,plain,
! [X221,X222] :
( ~ ssList(X221)
| ~ ssItem(X222)
| cons(X222,X221) = app(cons(X222,nil),X221) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])])]) ).
cnf(c_0_51,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( app(nil,cons(esk52_0,esk4_2(esk51_0,esk52_0))) = esk51_0
| ssItem(hd(esk51_0)) ),
inference(spm,[status(thm)],[c_0_31,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
( app(X2,cons(X1,nil)) = esk50_0
| ~ ssItem(X1)
| ~ ssList(X2)
| app(cons(X1,nil),X2) != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_54,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_55,plain,
! [X120] :
( ( ssList(esk44_1(X120))
| nil = X120
| ~ ssList(X120) )
& ( ssItem(esk45_1(X120))
| nil = X120
| ~ ssList(X120) )
& ( cons(esk45_1(X120),esk44_1(X120)) = X120
| nil = X120
| ~ ssList(X120) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax20])])])]) ).
cnf(c_0_56,negated_conjecture,
( cons(esk52_0,esk4_2(esk51_0,esk52_0)) = esk51_0
| ssItem(hd(esk51_0))
| ~ ssList(cons(esk52_0,esk4_2(esk51_0,esk52_0))) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,negated_conjecture,
( app(X1,cons(X2,nil)) = esk50_0
| cons(X2,X1) != esk51_0
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,plain,
( cons(esk45_1(X1),esk44_1(X1)) = X1
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_59,plain,
! [X126,X127] :
( ~ ssList(X126)
| ~ ssItem(X127)
| hd(cons(X127,X126)) = X127 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
cnf(c_0_60,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_19]) ).
cnf(c_0_61,negated_conjecture,
( cons(esk52_0,esk4_2(esk51_0,esk52_0)) = esk51_0
| ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_36]),c_0_37]),c_0_28])]) ).
cnf(c_0_62,negated_conjecture,
ssList(esk48_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_63,negated_conjecture,
esk48_0 = esk50_0,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_64,negated_conjecture,
~ memberP(esk48_0,esk52_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_65,plain,
! [X133,X134,X135] :
( ~ ssList(X133)
| ~ ssList(X134)
| ~ ssItem(X135)
| cons(X135,app(X134,X133)) = app(cons(X135,X134),X133) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])])]) ).
cnf(c_0_66,negated_conjecture,
( app(esk44_1(esk51_0),cons(esk45_1(esk51_0),nil)) = esk50_0
| esk51_0 = nil
| ~ ssList(esk44_1(esk51_0))
| ~ ssItem(esk45_1(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58])]),c_0_27])]) ).
cnf(c_0_67,plain,
( ssList(esk44_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_68,plain,
( hd(cons(X2,X1)) = X2
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_69,plain,
( ssItem(esk45_1(X1))
| nil = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_70,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_60]) ).
cnf(c_0_71,negated_conjecture,
( app(esk4_2(esk51_0,esk52_0),cons(esk52_0,nil)) = esk50_0
| ssItem(hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_61]),c_0_37]),c_0_28])]) ).
cnf(c_0_72,negated_conjecture,
ssList(esk50_0),
inference(rw,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_73,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[ax17]) ).
cnf(c_0_74,negated_conjecture,
~ memberP(esk50_0,esk52_0),
inference(rw,[status(thm)],[c_0_64,c_0_63]) ).
cnf(c_0_75,plain,
( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_76,negated_conjecture,
( app(esk44_1(esk51_0),cons(esk45_1(esk51_0),nil)) = esk50_0
| esk51_0 = nil
| ~ ssItem(esk45_1(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_27])]) ).
cnf(c_0_77,plain,
( esk45_1(X1) = hd(X1)
| nil = X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_58]),c_0_69]),c_0_67]) ).
cnf(c_0_78,negated_conjecture,
ssItem(hd(esk51_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]),c_0_73]),c_0_37]),c_0_28])]),c_0_74]) ).
cnf(c_0_79,plain,
( cons(esk45_1(X1),app(esk44_1(X1),X2)) = app(X1,X2)
| nil = X1
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_58]),c_0_69]),c_0_67]) ).
cnf(c_0_80,negated_conjecture,
( app(esk44_1(esk51_0),cons(hd(esk51_0),nil)) = esk50_0
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_27])]) ).
fof(c_0_81,plain,
! [X152,X153,X154] :
( ( ~ memberP(app(X153,X154),X152)
| memberP(X153,X152)
| memberP(X154,X152)
| ~ ssList(X154)
| ~ ssList(X153)
| ~ ssItem(X152) )
& ( ~ memberP(X153,X152)
| memberP(app(X153,X154),X152)
| ~ ssList(X154)
| ~ ssList(X153)
| ~ ssItem(X152) )
& ( ~ memberP(X154,X152)
| memberP(app(X153,X154),X152)
| ~ ssList(X154)
| ~ ssList(X153)
| ~ ssItem(X152) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax36])])])]) ).
cnf(c_0_82,negated_conjecture,
( cons(esk45_1(esk51_0),esk50_0) = app(esk51_0,cons(hd(esk51_0),nil))
| esk51_0 = nil
| ~ ssList(cons(hd(esk51_0),nil)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_27])]) ).
cnf(c_0_83,plain,
( memberP(app(X1,X3),X2)
| ~ memberP(X1,X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_84,negated_conjecture,
( cons(esk45_1(esk51_0),esk50_0) = app(esk51_0,cons(hd(esk51_0),nil))
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_36]),c_0_73]),c_0_78])]) ).
cnf(c_0_85,negated_conjecture,
( memberP(app(esk51_0,X1),esk52_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_86,negated_conjecture,
( app(esk51_0,cons(hd(esk51_0),nil)) = cons(hd(esk51_0),esk50_0)
| esk51_0 = nil ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_77]),c_0_27])]) ).
fof(c_0_87,plain,
! [X155,X156,X157] :
( ( ~ memberP(cons(X156,X157),X155)
| X155 = X156
| memberP(X157,X155)
| ~ ssList(X157)
| ~ ssItem(X156)
| ~ ssItem(X155) )
& ( X155 != X156
| memberP(cons(X156,X157),X155)
| ~ ssList(X157)
| ~ ssItem(X156)
| ~ ssItem(X155) )
& ( ~ memberP(X157,X155)
| memberP(cons(X156,X157),X155)
| ~ ssList(X157)
| ~ ssItem(X156)
| ~ ssItem(X155) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])])]) ).
cnf(c_0_88,negated_conjecture,
( esk51_0 = nil
| memberP(cons(hd(esk51_0),esk50_0),esk52_0)
| ~ ssList(cons(hd(esk51_0),nil)) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_89,negated_conjecture,
( esk51_0 = nil
| memberP(esk50_0,hd(esk51_0))
| ~ ssList(esk44_1(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_80]),c_0_72]),c_0_73]),c_0_78])]) ).
cnf(c_0_90,plain,
( X3 = X1
| memberP(X2,X3)
| ~ memberP(cons(X1,X2),X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X3) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_91,negated_conjecture,
( esk51_0 = nil
| memberP(cons(hd(esk51_0),esk50_0),esk52_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_36]),c_0_73]),c_0_78])]) ).
cnf(c_0_92,negated_conjecture,
( esk51_0 = nil
| memberP(esk50_0,hd(esk51_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_67]),c_0_27])]) ).
cnf(c_0_93,negated_conjecture,
( hd(esk51_0) = esk52_0
| esk51_0 = nil ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_72]),c_0_28]),c_0_78])]),c_0_74]) ).
cnf(c_0_94,negated_conjecture,
( nil = esk50_0
| nil != esk51_0 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_95,negated_conjecture,
esk51_0 = nil,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_74]) ).
cnf(c_0_96,negated_conjecture,
esk50_0 = nil,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95])]) ).
cnf(c_0_97,negated_conjecture,
~ memberP(nil,esk52_0),
inference(rw,[status(thm)],[c_0_74,c_0_96]) ).
cnf(c_0_98,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_95]),c_0_97]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC409+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.15/0.35 % Computer : n004.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 2400
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Oct 3 01:50:00 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 Running first-order model finding
% 0.21/0.49 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.RdWlYyLosF/E---3.1_1605.p
% 1.32/0.70 # Version: 3.1pre001
% 1.32/0.70 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.32/0.70 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.32/0.70 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.32/0.70 # Starting new_bool_3 with 300s (1) cores
% 1.32/0.70 # Starting new_bool_1 with 300s (1) cores
% 1.32/0.70 # Starting sh5l with 300s (1) cores
% 1.32/0.70 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1707 completed with status 0
% 1.32/0.70 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.32/0.70 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.32/0.70 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.32/0.70 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.32/0.70 # No SInE strategy applied
% 1.32/0.70 # Search class: FGHSF-FSLM21-MFFFFFNN
% 1.32/0.70 # Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 1.32/0.70 # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 1.32/0.70 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.32/0.70 # Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 136s (1) cores
% 1.32/0.70 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_TT_S0Y with 136s (1) cores
% 1.32/0.70 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S2o with 136s (1) cores
% 1.32/0.70 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1716 completed with status 0
% 1.32/0.70 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.32/0.70 # Preprocessing class: FSLSSMSSSSSNFFN.
% 1.32/0.70 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.32/0.70 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.32/0.70 # No SInE strategy applied
% 1.32/0.70 # Search class: FGHSF-FSLM21-MFFFFFNN
% 1.32/0.70 # Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 1.32/0.70 # Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 1.32/0.70 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.32/0.70 # Preprocessing time : 0.004 s
% 1.32/0.70 # Presaturation interreduction done
% 1.32/0.70
% 1.32/0.70 # Proof found!
% 1.32/0.70 # SZS status Theorem
% 1.32/0.70 # SZS output start CNFRefutation
% See solution above
% 1.32/0.70 # Parsed axioms : 96
% 1.32/0.70 # Removed by relevancy pruning/SinE : 0
% 1.32/0.70 # Initial clauses : 201
% 1.32/0.70 # Removed in clause preprocessing : 2
% 1.32/0.70 # Initial clauses in saturation : 199
% 1.32/0.70 # Processed clauses : 1673
% 1.32/0.70 # ...of these trivial : 3
% 1.32/0.70 # ...subsumed : 718
% 1.32/0.70 # ...remaining for further processing : 951
% 1.32/0.70 # Other redundant clauses eliminated : 147
% 1.32/0.70 # Clauses deleted for lack of memory : 0
% 1.32/0.70 # Backward-subsumed : 104
% 1.32/0.70 # Backward-rewritten : 208
% 1.32/0.70 # Generated clauses : 5432
% 1.32/0.70 # ...of the previous two non-redundant : 5030
% 1.32/0.70 # ...aggressively subsumed : 0
% 1.32/0.70 # Contextual simplify-reflections : 203
% 1.32/0.70 # Paramodulations : 5280
% 1.32/0.70 # Factorizations : 0
% 1.32/0.70 # NegExts : 0
% 1.32/0.70 # Equation resolutions : 154
% 1.32/0.70 # Total rewrite steps : 3754
% 1.32/0.70 # Propositional unsat checks : 0
% 1.32/0.70 # Propositional check models : 0
% 1.32/0.70 # Propositional check unsatisfiable : 0
% 1.32/0.70 # Propositional clauses : 0
% 1.32/0.70 # Propositional clauses after purity: 0
% 1.32/0.70 # Propositional unsat core size : 0
% 1.32/0.70 # Propositional preprocessing time : 0.000
% 1.32/0.70 # Propositional encoding time : 0.000
% 1.32/0.70 # Propositional solver time : 0.000
% 1.32/0.70 # Success case prop preproc time : 0.000
% 1.32/0.70 # Success case prop encoding time : 0.000
% 1.32/0.70 # Success case prop solver time : 0.000
% 1.32/0.70 # Current number of processed clauses : 423
% 1.32/0.70 # Positive orientable unit clauses : 29
% 1.32/0.70 # Positive unorientable unit clauses: 0
% 1.32/0.70 # Negative unit clauses : 4
% 1.32/0.70 # Non-unit-clauses : 390
% 1.32/0.70 # Current number of unprocessed clauses: 3609
% 1.32/0.70 # ...number of literals in the above : 21361
% 1.32/0.70 # Current number of archived formulas : 0
% 1.32/0.70 # Current number of archived clauses : 505
% 1.32/0.70 # Clause-clause subsumption calls (NU) : 62713
% 1.32/0.70 # Rec. Clause-clause subsumption calls : 15310
% 1.32/0.70 # Non-unit clause-clause subsumptions : 824
% 1.32/0.70 # Unit Clause-clause subsumption calls : 384
% 1.32/0.70 # Rewrite failures with RHS unbound : 0
% 1.32/0.70 # BW rewrite match attempts : 11
% 1.32/0.70 # BW rewrite match successes : 11
% 1.32/0.70 # Condensation attempts : 0
% 1.32/0.70 # Condensation successes : 0
% 1.32/0.70 # Termbank termtop insertions : 116681
% 1.32/0.70
% 1.32/0.70 # -------------------------------------------------
% 1.32/0.70 # User time : 0.183 s
% 1.32/0.70 # System time : 0.007 s
% 1.32/0.70 # Total time : 0.190 s
% 1.32/0.70 # Maximum resident set size: 2484 pages
% 1.32/0.70
% 1.32/0.70 # -------------------------------------------------
% 1.32/0.70 # User time : 0.807 s
% 1.32/0.70 # System time : 0.024 s
% 1.32/0.70 # Total time : 0.832 s
% 1.32/0.70 # Maximum resident set size: 1800 pages
% 1.32/0.70 % E---3.1 exiting
%------------------------------------------------------------------------------