TSTP Solution File: SEU522^1 by E---3.2.0
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%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : SEU522^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n018.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 : Mon Jun 24 15:08:39 EDT 2024
% Result : Theorem 0.20s 0.53s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 42
% Syntax : Number of formulae : 69 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 513 ( 77 equ; 0 cnn)
% Maximal formula atoms : 139 ( 7 avg)
% Number of connectives : 1717 ( 119 ~; 124 |; 116 &;1079 @)
% ( 64 <=>; 215 =>; 0 <=; 0 <~>)
% Maximal formula depth : 155 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 74 ( 71 usr; 46 con; 0-3 aty)
% Number of variables : 407 ( 43 ^ 316 !; 48 ?; 407 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
setextAx: $o ).
thf(decl_25,type,
emptyset: $i ).
thf(decl_26,type,
emptysetAx: $o ).
thf(decl_27,type,
setadjoin: $i > $i > $i ).
thf(decl_28,type,
setadjoinAx: $o ).
thf(decl_29,type,
powerset: $i > $i ).
thf(decl_30,type,
powersetAx: $o ).
thf(decl_31,type,
setunion: $i > $i ).
thf(decl_32,type,
setunionAx: $o ).
thf(decl_33,type,
omega: $i ).
thf(decl_34,type,
omega0Ax: $o ).
thf(decl_35,type,
omegaSAx: $o ).
thf(decl_36,type,
omegaIndAx: $o ).
thf(decl_37,type,
replAx: $o ).
thf(decl_38,type,
foundationAx: $o ).
thf(decl_39,type,
wellorderingAx: $o ).
thf(decl_41,type,
descrp: $o ).
thf(decl_42,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_43,type,
dsetconstrI: $o ).
thf(decl_44,type,
dsetconstrEL: $o ).
thf(decl_45,type,
dsetconstrER: $o ).
thf(decl_46,type,
exuE1: $o ).
thf(decl_47,type,
prop2set: $o > $i ).
thf(decl_48,type,
prop2setE: $o ).
thf(decl_49,type,
emptysetE: $o ).
thf(decl_50,type,
emptysetimpfalse: $o ).
thf(decl_51,type,
notinemptyset: $o ).
thf(decl_52,type,
exuE3e: $o ).
thf(decl_53,type,
setext: $o ).
thf(decl_54,type,
emptyI: $o ).
thf(decl_55,type,
noeltsimpempty: $o ).
thf(decl_56,type,
setbeta: $o ).
thf(decl_57,type,
nonempty: $i > $o ).
thf(decl_58,type,
nonemptyE1: $o ).
thf(decl_59,type,
nonemptyI: $o ).
thf(decl_60,type,
nonemptyI1: $o ).
thf(decl_61,type,
setadjoinIL: $o ).
thf(decl_62,type,
emptyinunitempty: $o ).
thf(decl_63,type,
setadjoinIR: $o ).
thf(decl_64,type,
setadjoinE: $o ).
thf(decl_65,type,
setadjoinOr: $o ).
thf(decl_66,type,
setoftrueEq: $o ).
thf(decl_67,type,
powersetI: $o ).
thf(decl_68,type,
emptyinPowerset: $o ).
thf(decl_69,type,
emptyInPowerset: $o ).
thf(decl_70,type,
powersetE: $o ).
thf(decl_71,type,
epred1_0: $o ).
thf(decl_72,type,
esk1_2: $i > $i > $i ).
thf(decl_73,type,
esk2_2: $i > $i > $i ).
thf(decl_74,type,
esk3_2: $i > $i > $i ).
thf(decl_75,type,
esk4_1: $i > $i ).
thf(decl_76,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_77,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_78,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_79,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_80,type,
esk9_1: $i > $i ).
thf(decl_81,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_82,type,
esk11_1: ( $i > $o ) > $i ).
thf(decl_83,type,
esk12_2: ( $i > $o ) > $i > $i ).
thf(decl_84,type,
esk13_1: ( $i > $o ) > $i ).
thf(decl_85,type,
esk14_2: $i > $i > $i ).
thf(decl_86,type,
esk15_2: $i > $i > $i ).
thf(decl_87,type,
esk16_1: $i > $i ).
thf(decl_88,type,
esk17_1: $i > $i ).
thf(decl_89,type,
esk18_1: $i > $i ).
thf(decl_90,type,
esk19_2: $i > $i > $i ).
thf(decl_91,type,
esk20_0: $i ).
thf(decl_92,type,
esk21_0: $i ).
thf(decl_93,type,
esk22_0: $i ).
thf(replAx,axiom,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',replAx) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',exu) ).
thf(exuE1,axiom,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',exuE1) ).
thf(prop2set,axiom,
( prop2set
= ( ^ [X10: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X2: $i] : X10 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',prop2set) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',exuE3e) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',nonempty) ).
thf(nonemptyI,axiom,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',nonemptyI) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',setoftrueEq) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',dsetconstrI) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',dsetconstrEL) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',dsetconstrER) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X11: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X11 ) )
=> X11 ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',prop2setE) ).
thf(setbeta,axiom,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',nonemptyI1) ).
thf(setunionI,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',setunionI) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',setunionAx) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',setadjoinIL) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',powersetAx) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',emptyinunitempty) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',setadjoinIR) ).
thf(omegaIndAx,axiom,
( omegaIndAx
<=> ! [X4: $i] :
( ( ( in @ emptyset @ X4 )
& ! [X2: $i] :
( ( ( in @ X2 @ omega )
& ( in @ X2 @ X4 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',omegaIndAx) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ! [X13: $o] :
( ( ( X3 = X2 )
=> X13 )
=> ( ( ( in @ X3 @ X4 )
=> X13 )
=> X13 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',setadjoinE) ).
thf(setadjoinOr,axiom,
( setadjoinOr
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',setadjoinOr) ).
thf(powersetI,axiom,
( powersetI
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( in @ X5 @ ( powerset @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',powersetI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',emptyinPowerset) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ? [X5: $i] :
( ( in @ X5 @ X4 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X5 )
& ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',foundationAx) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',emptyInPowerset) ).
thf(powersetE,axiom,
( powersetE
<=> ! [X4: $i,X5: $i,X2: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
=> ( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',powersetE) ).
thf(wellorderingAx,axiom,
( wellorderingAx
<=> ! [X4: $i] :
? [X5: $i] :
( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X4 )
& ( in @ X3 @ X4 ) )
=> ( ! [X7: $i] :
( ( in @ X7 @ X5 )
=> ( ( in @ X2 @ X7 )
<=> ( in @ X3 @ X7 ) ) )
=> ( X2 = X3 ) ) )
& ! [X7: $i,X8: $i] :
( ( ( in @ X7 @ X5 )
& ( in @ X8 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X8 ) )
| ! [X2: $i] :
( ( in @ X2 @ X8 )
=> ( in @ X2 @ X7 ) ) ) )
& ! [X7: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X7 )
=> ( in @ X2 @ X4 ) )
& ? [X2: $i] : ( in @ X2 @ X7 ) )
=> ? [X8: $i,X2: $i] :
( ( in @ X8 @ X5 )
& ( in @ X2 @ X7 )
& ~ ? [X3: $i] :
( ( in @ X3 @ X8 )
& ( in @ X3 @ X7 ) )
& ! [X9: $i] :
( ( in @ X9 @ X5 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X9 )
=> ( in @ X3 @ X8 ) )
| ( in @ X2 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',wellorderingAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',omega0Ax) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X12: $o] : X12 ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',emptysetE) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',emptysetimpfalse) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',notinemptyset) ).
thf(setext,axiom,
( setext
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X5 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) )
=> ( X4 = X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',setext) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',emptyI) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',noeltsimpempty) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',omegaSAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',setadjoinAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',emptysetAx) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p',setextAx) ).
thf(c_0_41,plain,
( replAx
<=> ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( exu
@ ^ [Z0: $i] : ( X6 @ X2 @ Z0 ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[replAx]) ).
thf(c_0_42,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_43,plain,
( exuE1
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuE1]) ).
thf(c_0_44,plain,
( prop2set
= ( ^ [Z0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z1: $i] : Z0 ) ) ),
inference(fof_simplification,[status(thm)],[prop2set]) ).
thf(c_0_45,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_46,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_47,plain,
( nonemptyI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[nonemptyI]) ).
thf(c_0_48,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_49,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X122: $i] :
( ( X6 @ X2 @ X122 )
& ! [X123: $i] :
( ( X6 @ X2 @ X123 )
=> ( X122 = X123 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_41,c_0_42]) ).
thf(c_0_50,plain,
( dsetconstrI
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrI]) ).
thf(c_0_51,plain,
( dsetconstrEL
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ( in @ X2 @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).
thf(c_0_52,plain,
( dsetconstrER
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
=> ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrER]) ).
thf(c_0_53,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X124: $i] :
( ( X1 @ X124 )
& ! [X125: $i] :
( ( X1 @ X125 )
=> ( X124 = X125 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_43,c_0_42]) ).
thf(c_0_54,axiom,
( prop2setE
= ( ! [X11: $o,X2: $i] :
( ( in @ X2
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X11 ) )
=> X11 ) ) ),
inference(apply_def,[status(thm)],[prop2setE,c_0_44]) ).
thf(c_0_55,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X126: $i] :
( ( X1 @ X126 )
& ! [X127: $i] :
( ( X1 @ X127 )
=> ( X126 = X127 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_45,c_0_42]) ).
thf(c_0_56,plain,
( setbeta
<=> ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ X2
@ ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
<=> ( X1 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[setbeta]) ).
thf(c_0_57,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_46]) ).
thf(c_0_58,plain,
( nonemptyI
= ( ! [X4: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X1 @ X2 )
=> ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
!= emptyset ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_47,c_0_46]) ).
thf(c_0_59,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_46]) ).
thf(c_0_60,plain,
( epred1_0
<=> ! [X157: $i] :
? [X158: $i] :
( ! [X159: $i] :
( ( in @ X159 @ X158 )
=> ! [X160: $i] :
( ( in @ X160 @ X159 )
=> ( in @ X160 @ X157 ) ) )
& ! [X161: $i,X162: $i] :
( ( ( in @ X161 @ X157 )
& ( in @ X162 @ X157 ) )
=> ( ! [X163: $i] :
( ( in @ X163 @ X158 )
=> ( ( in @ X161 @ X163 )
<=> ( in @ X162 @ X163 ) ) )
=> ( X161 = X162 ) ) )
& ! [X164: $i,X165: $i] :
( ( ( in @ X164 @ X158 )
& ( in @ X165 @ X158 ) )
=> ( ! [X166: $i] :
( ( in @ X166 @ X164 )
=> ( in @ X166 @ X165 ) )
| ! [X167: $i] :
( ( in @ X167 @ X165 )
=> ( in @ X167 @ X164 ) ) ) )
& ! [X168: $i] :
( ( ! [X169: $i] :
( ( in @ X169 @ X168 )
=> ( in @ X169 @ X157 ) )
& ? [X170: $i] : ( in @ X170 @ X168 ) )
=> ? [X171: $i,X172: $i] :
( ( in @ X171 @ X158 )
& ( in @ X172 @ X168 )
& ~ ? [X173: $i] :
( ( in @ X173 @ X171 )
& ( in @ X173 @ X168 ) )
& ! [X174: $i] :
( ( in @ X174 @ X158 )
=> ( ! [X175: $i] :
( ( in @ X175 @ X174 )
=> ( in @ X175 @ X171 ) )
| ( in @ X172 @ X174 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_61,negated_conjecture,
~ ( ! [X128: $i,X129: $i] :
( ! [X130: $i] :
( ( in @ X130 @ X128 )
<=> ( in @ X130 @ X129 ) )
=> ( X128 = X129 ) )
=> ( ! [X131: $i] :
~ ( in @ X131 @ emptyset )
=> ( ! [X132: $i,X133: $i,X134: $i] :
( ( in @ X134 @ ( setadjoin @ X132 @ X133 ) )
<=> ( ( X134 = X132 )
| ( in @ X134 @ X133 ) ) )
=> ( ! [X135: $i,X136: $i] :
( ( in @ X136 @ ( powerset @ X135 ) )
<=> ! [X137: $i] :
( ( in @ X137 @ X136 )
=> ( in @ X137 @ X135 ) ) )
=> ( ! [X138: $i,X139: $i] :
( ( in @ X139 @ ( setunion @ X138 ) )
<=> ? [X140: $i] :
( ( in @ X139 @ X140 )
& ( in @ X140 @ X138 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X141: $i] :
( ( in @ X141 @ omega )
=> ( in @ ( setadjoin @ X141 @ X141 ) @ omega ) )
=> ( ! [X142: $i] :
( ( ( in @ emptyset @ X142 )
& ! [X143: $i] :
( ( ( in @ X143 @ omega )
& ( in @ X143 @ X142 ) )
=> ( in @ ( setadjoin @ X143 @ X143 ) @ X142 ) ) )
=> ! [X144: $i] :
( ( in @ X144 @ omega )
=> ( in @ X144 @ X142 ) ) )
=> ( ! [X145: $i > $i > $o,X146: $i] :
( ! [X147: $i] :
( ( in @ X147 @ X146 )
=> ? [X148: $i] :
( ( X145 @ X147 @ X148 )
& ! [X149: $i] :
( ( X145 @ X147 @ X149 )
=> ( X148 = X149 ) ) ) )
=> ? [X150: $i] :
! [X151: $i] :
( ( in @ X151 @ X150 )
<=> ? [X152: $i] :
( ( in @ X152 @ X146 )
& ( X145 @ X152 @ X151 ) ) ) )
=> ( ! [X153: $i] :
( ? [X154: $i] : ( in @ X154 @ X153 )
=> ? [X155: $i] :
( ( in @ X155 @ X153 )
& ~ ? [X156: $i] :
( ( in @ X156 @ X155 )
& ( in @ X156 @ X153 ) ) ) )
=> ( epred1_0
=> ( descrp
=> ( ! [X176: $i,X177: $i > $o,X178: $i] :
( ( in @ X178 @ X176 )
=> ( ( X177 @ X178 )
=> ( in @ X178
@ ( dsetconstr @ X176
@ ^ [Z0: $i] : ( X177 @ Z0 ) ) ) ) )
=> ( ! [X179: $i,X180: $i > $o,X181: $i] :
( ( in @ X181
@ ( dsetconstr @ X179
@ ^ [Z0: $i] : ( X180 @ Z0 ) ) )
=> ( in @ X181 @ X179 ) )
=> ( ! [X182: $i,X183: $i > $o,X184: $i] :
( ( in @ X184
@ ( dsetconstr @ X182
@ ^ [Z0: $i] : ( X183 @ Z0 ) ) )
=> ( X183 @ X184 ) )
=> ( ! [X185: $i > $o] :
( ? [X186: $i] :
( ( X185 @ X186 )
& ! [X187: $i] :
( ( X185 @ X187 )
=> ( X186 = X187 ) ) )
=> ? [X188: $i] :
( ( X185 @ X188 )
& ! [X189: $i] :
( ( X185 @ X189 )
=> ( X188 = X189 ) ) ) )
=> ( ! [X190: $o,X191: $i] :
( ( in @ X191
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X190 ) )
=> X190 )
=> ( ! [X192: $i] :
( ( in @ X192 @ emptyset )
=> ! [X193: $o] : X193 )
=> ( ! [X194: $i] :
~ ( in @ X194 @ emptyset )
=> ( ! [X195: $i] :
~ ( in @ X195 @ emptyset )
=> ( ! [X196: $i > $o] :
( ? [X197: $i] :
( ( X196 @ X197 )
& ! [X198: $i] :
( ( X196 @ X198 )
=> ( X197 = X198 ) ) )
=> ? [X199: $i] : ( X196 @ X199 ) )
=> ( ! [X200: $i,X201: $i] :
( ! [X202: $i] :
( ( in @ X202 @ X200 )
=> ( in @ X202 @ X201 ) )
=> ( ! [X203: $i] :
( ( in @ X203 @ X201 )
=> ( in @ X203 @ X200 ) )
=> ( X200 = X201 ) ) )
=> ( ! [X204: $i] :
( ! [X205: $i] :
~ ( in @ X205 @ X204 )
=> ( X204 = emptyset ) )
=> ( ! [X206: $i] :
( ! [X207: $i] :
~ ( in @ X207 @ X206 )
=> ( X206 = emptyset ) )
=> ( ! [X208: $i,X209: $i > $o,X210: $i] :
( ( in @ X210 @ X208 )
=> ( ( in @ X210
@ ( dsetconstr @ X208
@ ^ [Z0: $i] : ( X209 @ Z0 ) ) )
<=> ( X209 @ X210 ) ) )
=> ( ! [X211: $i] :
( ( X211 != emptyset )
=> ? [X212: $i] : ( in @ X212 @ X211 ) )
=> ( ! [X213: $i,X214: $i > $o,X215: $i] :
( ( in @ X215 @ X213 )
=> ( ( X214 @ X215 )
=> ( ( dsetconstr @ X213
@ ^ [Z0: $i] : ( X214 @ Z0 ) )
!= emptyset ) ) )
=> ( ! [X216: $i] :
( ? [X217: $i] : ( in @ X217 @ X216 )
=> ( X216 != emptyset ) )
=> ( ! [X218: $i,X219: $i] : ( in @ X218 @ ( setadjoin @ X218 @ X219 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X220: $i,X221: $i,X222: $i] :
( ( in @ X222 @ X221 )
=> ( in @ X222 @ ( setadjoin @ X220 @ X221 ) ) )
=> ( ! [X223: $i,X224: $i,X225: $i] :
( ( in @ X225 @ ( setadjoin @ X223 @ X224 ) )
=> ! [X226: $o] :
( ( ( X225 = X223 )
=> X226 )
=> ( ( ( in @ X225 @ X224 )
=> X226 )
=> X226 ) ) )
=> ( ! [X227: $i,X228: $i,X229: $i] :
( ( in @ X229 @ ( setadjoin @ X227 @ X228 ) )
=> ( ( X229 = X227 )
| ( in @ X229 @ X228 ) ) )
=> ( ! [X230: $i] :
( ( dsetconstr @ X230
@ ^ [Z0: $i] : $true )
= X230 )
=> ( ! [X231: $i,X232: $i] :
( ! [X233: $i] :
( ( in @ X233 @ X232 )
=> ( in @ X233 @ X231 ) )
=> ( in @ X232 @ ( powerset @ X231 ) ) )
=> ( ! [X234: $i] : ( in @ emptyset @ ( powerset @ X234 ) )
=> ( ! [X235: $i] : ( in @ emptyset @ ( powerset @ X235 ) )
=> ( ! [X236: $i,X237: $i,X238: $i] :
( ( in @ X237 @ ( powerset @ X236 ) )
=> ( ( in @ X238 @ X237 )
=> ( in @ X238 @ X236 ) ) )
=> ! [X4: $i,X2: $i,X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> ( in @ X2 @ ( setunion @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[setunionI]),setunionAx]),setadjoinIL]),powersetAx]),emptyinunitempty]),setadjoinIR]),omegaIndAx]),setadjoinE]),setadjoinOr]),c_0_48]),c_0_49]),powersetI]),emptyinPowerset]),foundationAx]),emptyInPowerset]),powersetE]),wellorderingAx]),c_0_50]),omega0Ax]),c_0_51]),c_0_52]),c_0_53]),c_0_54]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_55]),setext]),emptyI]),noeltsimpempty]),c_0_56]),c_0_57]),omegaSAx]),c_0_58]),c_0_59]),setadjoinAx]),emptysetAx]),setextAx])]),c_0_60]) ).
thf(c_0_62,negated_conjecture,
! [X239: $i,X240: $i,X242: $i,X243: $i,X244: $i,X245: $i,X246: $i,X247: $i,X248: $i,X249: $i,X250: $i,X252: $i,X253: $i,X255: $i,X256: $i,X257: $i,X258: $i,X259: $i,X261: $i,X262: $i > $i > $o,X263: $i,X265: $i,X268: $i,X270: $i,X271: $i,X272: $i,X273: $i,X275: $i,X276: $i,X277: $i > $o,X278: $i,X279: $i,X280: $i > $o,X281: $i,X282: $i,X283: $i > $o,X284: $i,X285: $i > $o,X286: $i,X289: $i,X290: $o,X291: $i,X292: $i,X293: $o,X294: $i,X295: $i,X296: $i > $o,X297: $i,X300: $i,X301: $i,X304: $i,X306: $i,X308: $i,X309: $i > $o,X310: $i,X311: $i,X313: $i,X314: $i > $o,X315: $i,X316: $i,X317: $i,X318: $i,X319: $i,X320: $i,X321: $i,X322: $i,X323: $i,X324: $i,X325: $i,X326: $o,X327: $i,X328: $i,X329: $i,X330: $i,X331: $i,X332: $i,X334: $i,X335: $i,X336: $i,X337: $i,X338: $i] :
( ( ~ ( in @ ( esk1_2 @ X239 @ X240 ) @ X239 )
| ~ ( in @ ( esk1_2 @ X239 @ X240 ) @ X240 )
| ( X239 = X240 ) )
& ( ( in @ ( esk1_2 @ X239 @ X240 ) @ X239 )
| ( in @ ( esk1_2 @ X239 @ X240 ) @ X240 )
| ( X239 = X240 ) )
& ~ ( in @ X242 @ emptyset )
& ( ~ ( in @ X245 @ ( setadjoin @ X243 @ X244 ) )
| ( X245 = X243 )
| ( in @ X245 @ X244 ) )
& ( ( X245 != X243 )
| ( in @ X245 @ ( setadjoin @ X243 @ X244 ) ) )
& ( ~ ( in @ X245 @ X244 )
| ( in @ X245 @ ( setadjoin @ X243 @ X244 ) ) )
& ( ~ ( in @ X247 @ ( powerset @ X246 ) )
| ~ ( in @ X248 @ X247 )
| ( in @ X248 @ X246 ) )
& ( ( in @ ( esk2_2 @ X249 @ X250 ) @ X250 )
| ( in @ X250 @ ( powerset @ X249 ) ) )
& ( ~ ( in @ ( esk2_2 @ X249 @ X250 ) @ X249 )
| ( in @ X250 @ ( powerset @ X249 ) ) )
& ( ( in @ X253 @ ( esk3_2 @ X252 @ X253 ) )
| ~ ( in @ X253 @ ( setunion @ X252 ) ) )
& ( ( in @ ( esk3_2 @ X252 @ X253 ) @ X252 )
| ~ ( in @ X253 @ ( setunion @ X252 ) ) )
& ( ~ ( in @ X256 @ X257 )
| ~ ( in @ X257 @ X255 )
| ( in @ X256 @ ( setunion @ X255 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X258 @ omega )
| ( in @ ( setadjoin @ X258 @ X258 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X259 ) @ omega )
| ~ ( in @ emptyset @ X259 )
| ~ ( in @ X261 @ omega )
| ( in @ X261 @ X259 ) )
& ( ( in @ ( esk4_1 @ X259 ) @ X259 )
| ~ ( in @ emptyset @ X259 )
| ~ ( in @ X261 @ omega )
| ( in @ X261 @ X259 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X259 ) @ ( esk4_1 @ X259 ) ) @ X259 )
| ~ ( in @ emptyset @ X259 )
| ~ ( in @ X261 @ omega )
| ( in @ X261 @ X259 ) )
& ( ( in @ ( esk8_3 @ X262 @ X263 @ X268 ) @ X263 )
| ~ ( in @ X268 @ ( esk7_2 @ X262 @ X263 ) )
| ( in @ ( esk5_2 @ X262 @ X263 ) @ X263 ) )
& ( ( X262 @ ( esk8_3 @ X262 @ X263 @ X268 ) @ X268 )
| ~ ( in @ X268 @ ( esk7_2 @ X262 @ X263 ) )
| ( in @ ( esk5_2 @ X262 @ X263 ) @ X263 ) )
& ( ~ ( in @ X271 @ X263 )
| ~ ( X262 @ X271 @ X270 )
| ( in @ X270 @ ( esk7_2 @ X262 @ X263 ) )
| ( in @ ( esk5_2 @ X262 @ X263 ) @ X263 ) )
& ( ( in @ ( esk8_3 @ X262 @ X263 @ X268 ) @ X263 )
| ~ ( in @ X268 @ ( esk7_2 @ X262 @ X263 ) )
| ( X262 @ ( esk5_2 @ X262 @ X263 ) @ ( esk6_3 @ X262 @ X263 @ X265 ) )
| ~ ( X262 @ ( esk5_2 @ X262 @ X263 ) @ X265 ) )
& ( ( X262 @ ( esk8_3 @ X262 @ X263 @ X268 ) @ X268 )
| ~ ( in @ X268 @ ( esk7_2 @ X262 @ X263 ) )
| ( X262 @ ( esk5_2 @ X262 @ X263 ) @ ( esk6_3 @ X262 @ X263 @ X265 ) )
| ~ ( X262 @ ( esk5_2 @ X262 @ X263 ) @ X265 ) )
& ( ~ ( in @ X271 @ X263 )
| ~ ( X262 @ X271 @ X270 )
| ( in @ X270 @ ( esk7_2 @ X262 @ X263 ) )
| ( X262 @ ( esk5_2 @ X262 @ X263 ) @ ( esk6_3 @ X262 @ X263 @ X265 ) )
| ~ ( X262 @ ( esk5_2 @ X262 @ X263 ) @ X265 ) )
& ( ( in @ ( esk8_3 @ X262 @ X263 @ X268 ) @ X263 )
| ~ ( in @ X268 @ ( esk7_2 @ X262 @ X263 ) )
| ( X265
!= ( esk6_3 @ X262 @ X263 @ X265 ) )
| ~ ( X262 @ ( esk5_2 @ X262 @ X263 ) @ X265 ) )
& ( ( X262 @ ( esk8_3 @ X262 @ X263 @ X268 ) @ X268 )
| ~ ( in @ X268 @ ( esk7_2 @ X262 @ X263 ) )
| ( X265
!= ( esk6_3 @ X262 @ X263 @ X265 ) )
| ~ ( X262 @ ( esk5_2 @ X262 @ X263 ) @ X265 ) )
& ( ~ ( in @ X271 @ X263 )
| ~ ( X262 @ X271 @ X270 )
| ( in @ X270 @ ( esk7_2 @ X262 @ X263 ) )
| ( X265
!= ( esk6_3 @ X262 @ X263 @ X265 ) )
| ~ ( X262 @ ( esk5_2 @ X262 @ X263 ) @ X265 ) )
& ( ( in @ ( esk9_1 @ X272 ) @ X272 )
| ~ ( in @ X273 @ X272 ) )
& ( ~ ( in @ X275 @ ( esk9_1 @ X272 ) )
| ~ ( in @ X275 @ X272 )
| ~ ( in @ X273 @ X272 ) )
& epred1_0
& descrp
& ( ~ ( in @ X278 @ X276 )
| ~ ( X277 @ X278 )
| ( in @ X278
@ ( dsetconstr @ X276
@ ^ [Z0: $i] : ( X277 @ Z0 ) ) ) )
& ( ~ ( in @ X281
@ ( dsetconstr @ X279
@ ^ [Z0: $i] : ( X280 @ Z0 ) ) )
| ( in @ X281 @ X279 ) )
& ( ~ ( in @ X284
@ ( dsetconstr @ X282
@ ^ [Z0: $i] : ( X283 @ Z0 ) ) )
| ( X283 @ X284 ) )
& ( ( X285 @ ( esk11_1 @ X285 ) )
| ( X285 @ ( esk10_2 @ X285 @ X286 ) )
| ~ ( X285 @ X286 ) )
& ( ~ ( X285 @ X289 )
| ( ( esk11_1 @ X285 )
= X289 )
| ( X285 @ ( esk10_2 @ X285 @ X286 ) )
| ~ ( X285 @ X286 ) )
& ( ( X285 @ ( esk11_1 @ X285 ) )
| ( X286
!= ( esk10_2 @ X285 @ X286 ) )
| ~ ( X285 @ X286 ) )
& ( ~ ( X285 @ X289 )
| ( ( esk11_1 @ X285 )
= X289 )
| ( X286
!= ( esk10_2 @ X285 @ X286 ) )
| ~ ( X285 @ X286 ) )
& ( ~ ( in @ X291
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Z0: $i] : X290 ) )
| X290 )
& ( ~ ( in @ X292 @ emptyset )
| X293 )
& ~ ( in @ X294 @ emptyset )
& ~ ( in @ X295 @ emptyset )
& ( ( X296 @ ( esk12_2 @ X296 @ X297 ) )
| ~ ( X296 @ X297 )
| ( X296 @ ( esk13_1 @ X296 ) ) )
& ( ( X297
!= ( esk12_2 @ X296 @ X297 ) )
| ~ ( X296 @ X297 )
| ( X296 @ ( esk13_1 @ X296 ) ) )
& ( ( in @ ( esk15_2 @ X300 @ X301 ) @ X301 )
| ( X300 = X301 )
| ( in @ ( esk14_2 @ X300 @ X301 ) @ X300 ) )
& ( ~ ( in @ ( esk15_2 @ X300 @ X301 ) @ X300 )
| ( X300 = X301 )
| ( in @ ( esk14_2 @ X300 @ X301 ) @ X300 ) )
& ( ( in @ ( esk15_2 @ X300 @ X301 ) @ X301 )
| ( X300 = X301 )
| ~ ( in @ ( esk14_2 @ X300 @ X301 ) @ X301 ) )
& ( ~ ( in @ ( esk15_2 @ X300 @ X301 ) @ X300 )
| ( X300 = X301 )
| ~ ( in @ ( esk14_2 @ X300 @ X301 ) @ X301 ) )
& ( ( in @ ( esk16_1 @ X304 ) @ X304 )
| ( X304 = emptyset ) )
& ( ( in @ ( esk17_1 @ X306 ) @ X306 )
| ( X306 = emptyset ) )
& ( ~ ( in @ X310
@ ( dsetconstr @ X308
@ ^ [Z0: $i] : ( X309 @ Z0 ) ) )
| ( X309 @ X310 )
| ~ ( in @ X310 @ X308 ) )
& ( ~ ( X309 @ X310 )
| ( in @ X310
@ ( dsetconstr @ X308
@ ^ [Z0: $i] : ( X309 @ Z0 ) ) )
| ~ ( in @ X310 @ X308 ) )
& ( ( X311 = emptyset )
| ( in @ ( esk18_1 @ X311 ) @ X311 ) )
& ( ~ ( in @ X315 @ X313 )
| ~ ( X314 @ X315 )
| ( ( dsetconstr @ X313
@ ^ [Z0: $i] : ( X314 @ Z0 ) )
!= emptyset ) )
& ( ~ ( in @ X317 @ X316 )
| ( X316 != emptyset ) )
& ( in @ X318 @ ( setadjoin @ X318 @ X319 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X322 @ X321 )
| ( in @ X322 @ ( setadjoin @ X320 @ X321 ) ) )
& ( ( in @ X325 @ X324 )
| X326
| ( X325 = X323 )
| ~ ( in @ X325 @ ( setadjoin @ X323 @ X324 ) ) )
& ( ~ X326
| X326
| ( X325 = X323 )
| ~ ( in @ X325 @ ( setadjoin @ X323 @ X324 ) ) )
& ( ( in @ X325 @ X324 )
| X326
| ~ X326
| ~ ( in @ X325 @ ( setadjoin @ X323 @ X324 ) ) )
& ( ~ X326
| X326
| ~ X326
| ~ ( in @ X325 @ ( setadjoin @ X323 @ X324 ) ) )
& ( ~ ( in @ X329 @ ( setadjoin @ X327 @ X328 ) )
| ( X329 = X327 )
| ( in @ X329 @ X328 ) )
& ( ( dsetconstr @ X330
@ ^ [Z0: $i] : $true )
= X330 )
& ( ( in @ ( esk19_2 @ X331 @ X332 ) @ X332 )
| ( in @ X332 @ ( powerset @ X331 ) ) )
& ( ~ ( in @ ( esk19_2 @ X331 @ X332 ) @ X331 )
| ( in @ X332 @ ( powerset @ X331 ) ) )
& ( in @ emptyset @ ( powerset @ X334 ) )
& ( in @ emptyset @ ( powerset @ X335 ) )
& ( ~ ( in @ X337 @ ( powerset @ X336 ) )
| ~ ( in @ X338 @ X337 )
| ( in @ X338 @ X336 ) )
& ( in @ esk21_0 @ esk22_0 )
& ( in @ esk22_0 @ esk20_0 )
& ~ ( in @ esk21_0 @ ( setunion @ esk20_0 ) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])])])])]) ).
thf(c_0_63,negated_conjecture,
! [X2: $i,X3: $i,X4: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_64,negated_conjecture,
in @ esk22_0 @ esk20_0,
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_65,negated_conjecture,
~ ( in @ esk21_0 @ ( setunion @ esk20_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_66,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ ( setunion @ esk20_0 ) )
| ~ ( in @ X2 @ esk22_0 ) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
thf(c_0_67,negated_conjecture,
in @ esk21_0 @ esk22_0,
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_68,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU522^1 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n018.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 21 10:46:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.20/0.48 Running higher-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.CRxEXLS63V/E---3.1_4853.p
% 0.20/0.53 # Version: 3.2.0-ho
% 0.20/0.53 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.20/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.53 # Starting sh5l with 300s (1) cores
% 0.20/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.53 # Starting new_bool_2 with 300s (1) cores
% 0.20/0.53 # new_bool_2 with pid 4934 completed with status 0
% 0.20/0.53 # Result found by new_bool_2
% 0.20/0.53 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.20/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.53 # Starting sh5l with 300s (1) cores
% 0.20/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.53 # Starting new_bool_2 with 300s (1) cores
% 0.20/0.53 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.53 # Search class: HGHSM-FFMM31-SHFSMSBN
% 0.20/0.53 # partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.20/0.53 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.53 # Starting new_ho_10 with 181s (1) cores
% 0.20/0.53 # new_ho_10 with pid 4935 completed with status 0
% 0.20/0.53 # Result found by new_ho_10
% 0.20/0.53 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.20/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 # Starting new_ho_10 with 1500s (5) cores
% 0.20/0.53 # Starting sh5l with 300s (1) cores
% 0.20/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.53 # Starting new_bool_2 with 300s (1) cores
% 0.20/0.53 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.53 # Search class: HGHSM-FFMM31-SHFSMSBN
% 0.20/0.53 # partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.20/0.53 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.53 # Starting new_ho_10 with 181s (1) cores
% 0.20/0.53 # Preprocessing time : 0.003 s
% 0.20/0.53 # Presaturation interreduction done
% 0.20/0.53
% 0.20/0.53 # Proof found!
% 0.20/0.53 # SZS status Theorem
% 0.20/0.53 # SZS output start CNFRefutation
% See solution above
% 0.20/0.53 # Parsed axioms : 91
% 0.20/0.53 # Removed by relevancy pruning/SinE : 50
% 0.20/0.53 # Initial clauses : 84
% 0.20/0.53 # Removed in clause preprocessing : 3
% 0.20/0.53 # Initial clauses in saturation : 81
% 0.20/0.53 # Processed clauses : 195
% 0.20/0.53 # ...of these trivial : 9
% 0.20/0.53 # ...subsumed : 25
% 0.20/0.53 # ...remaining for further processing : 161
% 0.20/0.53 # Other redundant clauses eliminated : 3
% 0.20/0.53 # Clauses deleted for lack of memory : 0
% 0.20/0.53 # Backward-subsumed : 0
% 0.20/0.53 # Backward-rewritten : 4
% 0.20/0.53 # Generated clauses : 615
% 0.20/0.53 # ...of the previous two non-redundant : 572
% 0.20/0.53 # ...aggressively subsumed : 0
% 0.20/0.53 # Contextual simplify-reflections : 0
% 0.20/0.53 # Paramodulations : 610
% 0.20/0.53 # Factorizations : 2
% 0.20/0.53 # NegExts : 0
% 0.20/0.53 # Equation resolutions : 3
% 0.20/0.53 # Disequality decompositions : 0
% 0.20/0.53 # Total rewrite steps : 76
% 0.20/0.53 # ...of those cached : 62
% 0.20/0.53 # Propositional unsat checks : 0
% 0.20/0.53 # Propositional check models : 0
% 0.20/0.53 # Propositional check unsatisfiable : 0
% 0.20/0.53 # Propositional clauses : 0
% 0.20/0.53 # Propositional clauses after purity: 0
% 0.20/0.53 # Propositional unsat core size : 0
% 0.20/0.53 # Propositional preprocessing time : 0.000
% 0.20/0.53 # Propositional encoding time : 0.000
% 0.20/0.53 # Propositional solver time : 0.000
% 0.20/0.53 # Success case prop preproc time : 0.000
% 0.20/0.53 # Success case prop encoding time : 0.000
% 0.20/0.53 # Success case prop solver time : 0.000
% 0.20/0.53 # Current number of processed clauses : 87
% 0.20/0.53 # Positive orientable unit clauses : 16
% 0.20/0.53 # Positive unorientable unit clauses: 0
% 0.20/0.53 # Negative unit clauses : 3
% 0.20/0.53 # Non-unit-clauses : 68
% 0.20/0.53 # Current number of unprocessed clauses: 515
% 0.20/0.53 # ...number of literals in the above : 1957
% 0.20/0.53 # Current number of archived formulas : 0
% 0.20/0.53 # Current number of archived clauses : 72
% 0.20/0.53 # Clause-clause subsumption calls (NU) : 3396
% 0.20/0.53 # Rec. Clause-clause subsumption calls : 1267
% 0.20/0.53 # Non-unit clause-clause subsumptions : 12
% 0.20/0.53 # Unit Clause-clause subsumption calls : 26
% 0.20/0.53 # Rewrite failures with RHS unbound : 0
% 0.20/0.53 # BW rewrite match attempts : 10
% 0.20/0.53 # BW rewrite match successes : 4
% 0.20/0.53 # Condensation attempts : 195
% 0.20/0.53 # Condensation successes : 3
% 0.20/0.53 # Termbank termtop insertions : 21184
% 0.20/0.53 # Search garbage collected termcells : 3306
% 0.20/0.53
% 0.20/0.53 # -------------------------------------------------
% 0.20/0.53 # User time : 0.033 s
% 0.20/0.53 # System time : 0.007 s
% 0.20/0.53 # Total time : 0.039 s
% 0.20/0.53 # Maximum resident set size: 2820 pages
% 0.20/0.53
% 0.20/0.53 # -------------------------------------------------
% 0.20/0.53 # User time : 0.035 s
% 0.20/0.53 # System time : 0.010 s
% 0.20/0.53 # Total time : 0.045 s
% 0.20/0.53 # Maximum resident set size: 1816 pages
% 0.20/0.53 % E---3.1 exiting
% 0.20/0.53 % E exiting
%------------------------------------------------------------------------------