TSTP Solution File: SEU522^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU522^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n005.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 03:27:56 EDT 2024
% Result : Theorem 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 115
% Syntax : Number of formulae : 142 ( 15 unt; 73 typ; 0 def)
% Number of atoms : 517 ( 78 equ; 0 cnn)
% Maximal formula atoms : 140 ( 7 avg)
% Number of connectives : 1742 ( 123 ~; 129 |; 119 &;1084 @)
% ( 66 <=>; 221 =>; 0 <=; 0 <~>)
% Maximal formula depth : 158 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 111 ( 111 >; 0 *; 0 +; 0 <<)
% Number of symbols : 76 ( 73 usr; 46 con; 0-3 aty)
% Number of variables : 403 ( 31 ^ 322 !; 50 ?; 403 :)
% 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_40,type,
descr: ( $i > $o ) > $i ).
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_2: ( $i > $o ) > $i > $i ).
thf(decl_83,type,
esk12_1: ( $i > $o ) > $i ).
thf(decl_84,type,
esk13_2: ( $i > $o ) > $i > $i ).
thf(decl_85,type,
esk14_1: ( $i > $o ) > $i ).
thf(decl_86,type,
esk15_2: $i > $i > $i ).
thf(decl_87,type,
esk16_2: $i > $i > $i ).
thf(decl_88,type,
esk17_1: $i > $i ).
thf(decl_89,type,
esk18_1: $i > $i ).
thf(decl_90,type,
esk19_1: $i > $i ).
thf(decl_91,type,
esk20_2: $i > $i > $i ).
thf(decl_92,type,
esk21_0: $i ).
thf(decl_93,type,
esk22_0: $i ).
thf(decl_94,type,
esk23_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/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(exu,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(descrp,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
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/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
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/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI1,axiom,
( nonemptyI1
<=> ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( nonempty @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(setoftrueEq,axiom,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [X2: $i] : $true )
= X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
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/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(setextAx,axiom,
( setextAx
<=> ! [X4: $i,X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
<=> ( in @ X2 @ X5 ) )
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(setadjoinAx,axiom,
( setadjoinAx
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
<=> ( ( X3 = X2 )
| ( in @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(powersetAx,axiom,
( powersetAx
<=> ! [X4: $i,X5: $i] :
( ( in @ X5 @ ( powerset @ X4 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( in @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(setunionAx,axiom,
( setunionAx
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
<=> ? [X5: $i] :
( ( in @ X2 @ X5 )
& ( in @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
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/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
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/sandbox/benchmark/theBenchmark.p',foundationAx) ).
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/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X11: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X11 ) )
=> X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X12: $o] : X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',setext) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(emptyinunitempty,axiom,
( emptyinunitempty
<=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(setadjoinIR,axiom,
( setadjoinIR
<=> ! [X2: $i,X4: $i,X3: $i] :
( ( in @ X3 @ X4 )
=> ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(emptyinPowerset,axiom,
( emptyinPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyInPowerset,axiom,
( emptyInPowerset
<=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',powersetE) ).
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,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descrp]) ).
thf(c_0_44,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_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,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X123: $i] :
( ( X6 @ X2 @ X123 )
& ! [X124: $i] :
( ( X6 @ X2 @ X124 )
=> ( X123 = X124 ) ) ) )
=> ? [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_49,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X125: $i] :
( ( X1 @ X125 )
& ! [X126: $i] :
( ( X1 @ X126 )
=> ( X125 = X126 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_43,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] :
( ? [X127: $i] :
( ( X1 @ X127 )
& ! [X128: $i] :
( ( X1 @ X128 )
=> ( X127 = X128 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_44,c_0_42]) ).
thf(c_0_54,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X129: $i] :
( ( X1 @ X129 )
& ! [X130: $i] :
( ( X1 @ X130 )
=> ( X129 = X130 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_45,c_0_42]) ).
thf(c_0_55,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_56,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_46]) ).
thf(c_0_57,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_58,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_46]) ).
thf(c_0_59,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_60,plain,
( epred1_0
<=> ! [X160: $i] :
? [X161: $i] :
( ! [X162: $i] :
( ( in @ X162 @ X161 )
=> ! [X163: $i] :
( ( in @ X163 @ X162 )
=> ( in @ X163 @ X160 ) ) )
& ! [X164: $i,X165: $i] :
( ( ( in @ X164 @ X160 )
& ( in @ X165 @ X160 ) )
=> ( ! [X166: $i] :
( ( in @ X166 @ X161 )
=> ( ( in @ X164 @ X166 )
<=> ( in @ X165 @ X166 ) ) )
=> ( X164 = X165 ) ) )
& ! [X167: $i,X168: $i] :
( ( ( in @ X167 @ X161 )
& ( in @ X168 @ X161 ) )
=> ( ! [X169: $i] :
( ( in @ X169 @ X167 )
=> ( in @ X169 @ X168 ) )
| ! [X170: $i] :
( ( in @ X170 @ X168 )
=> ( in @ X170 @ X167 ) ) ) )
& ! [X171: $i] :
( ( ! [X172: $i] :
( ( in @ X172 @ X171 )
=> ( in @ X172 @ X160 ) )
& ? [X173: $i] : ( in @ X173 @ X171 ) )
=> ? [X174: $i,X175: $i] :
( ( in @ X174 @ X161 )
& ( in @ X175 @ X171 )
& ~ ? [X176: $i] :
( ( in @ X176 @ X174 )
& ( in @ X176 @ X171 ) )
& ! [X177: $i] :
( ( in @ X177 @ X161 )
=> ( ! [X178: $i] :
( ( in @ X178 @ X177 )
=> ( in @ X178 @ X174 ) )
| ( in @ X175 @ X177 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_61,negated_conjecture,
~ ( ! [X131: $i,X132: $i] :
( ! [X133: $i] :
( ( in @ X133 @ X131 )
<=> ( in @ X133 @ X132 ) )
=> ( X131 = X132 ) )
=> ( ! [X134: $i] :
~ ( in @ X134 @ emptyset )
=> ( ! [X135: $i,X136: $i,X137: $i] :
( ( in @ X137 @ ( setadjoin @ X135 @ X136 ) )
<=> ( ( X137 = X135 )
| ( in @ X137 @ X136 ) ) )
=> ( ! [X138: $i,X139: $i] :
( ( in @ X139 @ ( powerset @ X138 ) )
<=> ! [X140: $i] :
( ( in @ X140 @ X139 )
=> ( in @ X140 @ X138 ) ) )
=> ( ! [X141: $i,X142: $i] :
( ( in @ X142 @ ( setunion @ X141 ) )
<=> ? [X143: $i] :
( ( in @ X142 @ X143 )
& ( in @ X143 @ X141 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X144: $i] :
( ( in @ X144 @ omega )
=> ( in @ ( setadjoin @ X144 @ X144 ) @ omega ) )
=> ( ! [X145: $i] :
( ( ( in @ emptyset @ X145 )
& ! [X146: $i] :
( ( ( in @ X146 @ omega )
& ( in @ X146 @ X145 ) )
=> ( in @ ( setadjoin @ X146 @ X146 ) @ X145 ) ) )
=> ! [X147: $i] :
( ( in @ X147 @ omega )
=> ( in @ X147 @ X145 ) ) )
=> ( ! [X148: $i > $i > $o,X149: $i] :
( ! [X150: $i] :
( ( in @ X150 @ X149 )
=> ? [X151: $i] :
( ( X148 @ X150 @ X151 )
& ! [X152: $i] :
( ( X148 @ X150 @ X152 )
=> ( X151 = X152 ) ) ) )
=> ? [X153: $i] :
! [X154: $i] :
( ( in @ X154 @ X153 )
<=> ? [X155: $i] :
( ( in @ X155 @ X149 )
& ( X148 @ X155 @ X154 ) ) ) )
=> ( ! [X156: $i] :
( ? [X157: $i] : ( in @ X157 @ X156 )
=> ? [X158: $i] :
( ( in @ X158 @ X156 )
& ~ ? [X159: $i] :
( ( in @ X159 @ X158 )
& ( in @ X159 @ X156 ) ) ) )
=> ( epred1_0
=> ( ! [X179: $i > $o] :
( ? [X180: $i] :
( ( X179 @ X180 )
& ! [X181: $i] :
( ( X179 @ X181 )
=> ( X180 = X181 ) ) )
=> ( X179
@ ( descr
@ ^ [Z0: $i] : ( X179 @ Z0 ) ) ) )
=> ( ! [X182: $i,X183: $i > $o,X184: $i] :
( ( in @ X184 @ X182 )
=> ( ( X183 @ X184 )
=> ( in @ X184 @ ( dsetconstr @ X182 @ X183 ) ) ) )
=> ( ! [X185: $i,X186: $i > $o,X187: $i] :
( ( in @ X187 @ ( dsetconstr @ X185 @ X186 ) )
=> ( in @ X187 @ X185 ) )
=> ( ! [X188: $i,X189: $i > $o,X190: $i] :
( ( in @ X190 @ ( dsetconstr @ X188 @ X189 ) )
=> ( X189 @ X190 ) )
=> ( ! [X191: $i > $o] :
( ? [X192: $i] :
( ( X191 @ X192 )
& ! [X193: $i] :
( ( X191 @ X193 )
=> ( X192 = X193 ) ) )
=> ? [X194: $i] :
( ( X191 @ X194 )
& ! [X195: $i] :
( ( X191 @ X195 )
=> ( X194 = X195 ) ) ) )
=> ( ! [X196: $o,X197: $i] :
( ( in @ X197 @ ( prop2set @ X196 ) )
=> X196 )
=> ( ! [X198: $i] :
( ( in @ X198 @ emptyset )
=> ! [X199: $o] : X199 )
=> ( ! [X200: $i] :
( ( in @ X200 @ emptyset )
=> ~ $true )
=> ( ! [X201: $i] :
~ ( in @ X201 @ emptyset )
=> ( ! [X202: $i > $o] :
( ? [X203: $i] :
( ( X202 @ X203 )
& ! [X204: $i] :
( ( X202 @ X204 )
=> ( X203 = X204 ) ) )
=> ? [X205: $i] : ( X202 @ X205 ) )
=> ( ! [X206: $i,X207: $i] :
( ! [X208: $i] :
( ( in @ X208 @ X206 )
=> ( in @ X208 @ X207 ) )
=> ( ! [X209: $i] :
( ( in @ X209 @ X207 )
=> ( in @ X209 @ X206 ) )
=> ( X206 = X207 ) ) )
=> ( ! [X210: $i] :
( ! [X211: $i] :
~ ( in @ X211 @ X210 )
=> ( X210 = emptyset ) )
=> ( ! [X212: $i] :
( ! [X213: $i] :
~ ( in @ X213 @ X212 )
=> ( X212 = emptyset ) )
=> ( ! [X214: $i,X215: $i > $o,X216: $i] :
( ( in @ X216 @ X214 )
=> ( ( in @ X216 @ ( dsetconstr @ X214 @ X215 ) )
<=> ( X215 @ X216 ) ) )
=> ( ! [X217: $i] :
( ( X217 != emptyset )
=> ? [X218: $i] : ( in @ X218 @ X217 ) )
=> ( ! [X219: $i,X220: $i > $o,X221: $i] :
( ( in @ X221 @ X219 )
=> ( ( X220 @ X221 )
=> ( ( dsetconstr @ X219 @ X220 )
!= emptyset ) ) )
=> ( ! [X222: $i] :
( ? [X223: $i] : ( in @ X223 @ X222 )
=> ( X222 != emptyset ) )
=> ( ! [X224: $i,X225: $i] : ( in @ X224 @ ( setadjoin @ X224 @ X225 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X226: $i,X227: $i,X228: $i] :
( ( in @ X228 @ X227 )
=> ( in @ X228 @ ( setadjoin @ X226 @ X227 ) ) )
=> ( ! [X229: $i,X230: $i,X231: $i] :
( ( in @ X231 @ ( setadjoin @ X229 @ X230 ) )
=> ! [X232: $o] :
( ( ( X231 = X229 )
=> X232 )
=> ( ( ( in @ X231 @ X230 )
=> X232 )
=> X232 ) ) )
=> ( ! [X233: $i,X234: $i,X235: $i] :
( ( in @ X235 @ ( setadjoin @ X233 @ X234 ) )
=> ( ( X235 = X233 )
| ( in @ X235 @ X234 ) ) )
=> ( ! [X236: $i] :
( ( dsetconstr @ X236
@ ^ [Z0: $i] : $true )
= X236 )
=> ( ! [X237: $i,X238: $i] :
( ! [X239: $i] :
( ( in @ X239 @ X238 )
=> ( in @ X239 @ X237 ) )
=> ( in @ X238 @ ( powerset @ X237 ) ) )
=> ( ! [X240: $i] : ( in @ emptyset @ ( powerset @ X240 ) )
=> ( ! [X241: $i] : ( in @ emptyset @ ( powerset @ X241 ) )
=> ( ! [X242: $i,X243: $i,X244: $i] :
( ( in @ X243 @ ( powerset @ X242 ) )
=> ( ( in @ X244 @ X243 )
=> ( in @ X244 @ X242 ) ) )
=> ! [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(fool_unroll,[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(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[setunionI]),setextAx]),emptysetAx]),setadjoinAx]),powersetAx]),setunionAx]),omega0Ax]),omegaSAx]),omegaIndAx]),c_0_48]),foundationAx]),wellorderingAx]),c_0_49]),c_0_50]),c_0_51]),c_0_52]),c_0_53]),prop2setE]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_54]),setext]),emptyI]),noeltsimpempty]),c_0_55]),c_0_56]),c_0_57]),c_0_58]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_59]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE])])]),c_0_60]) ).
thf(c_0_62,negated_conjecture,
! [X247: $i,X248: $i,X250: $i,X251: $i,X252: $i,X253: $i,X254: $i,X255: $i,X256: $i,X257: $i,X258: $i,X260: $i,X261: $i,X263: $i,X264: $i,X265: $i,X266: $i,X267: $i,X269: $i,X270: $i > $i > $o,X271: $i,X273: $i,X276: $i,X278: $i,X279: $i,X280: $i,X281: $i,X283: $i,X284: $i > $o,X285: $i,X287: $i,X288: $i > $o,X289: $i,X290: $i,X291: $i > $o,X292: $i,X293: $i,X294: $i > $o,X295: $i,X296: $i > $o,X297: $i,X300: $i,X301: $o,X302: $i,X303: $i,X304: $o,X305: $i,X306: $i,X307: $i > $o,X308: $i,X311: $i,X312: $i,X315: $i,X317: $i,X319: $i,X320: $i > $o,X321: $i,X322: $i,X324: $i,X325: $i > $o,X326: $i,X327: $i,X328: $i,X329: $i,X330: $i,X331: $i,X332: $i,X333: $i,X334: $i,X335: $i,X336: $i,X337: $o,X338: $i,X339: $i,X340: $i,X341: $i,X342: $i,X343: $i,X345: $i,X346: $i,X347: $i,X348: $i,X349: $i] :
( ( ~ ( in @ ( esk1_2 @ X247 @ X248 ) @ X247 )
| ~ ( in @ ( esk1_2 @ X247 @ X248 ) @ X248 )
| ( X247 = X248 ) )
& ( ( in @ ( esk1_2 @ X247 @ X248 ) @ X247 )
| ( in @ ( esk1_2 @ X247 @ X248 ) @ X248 )
| ( X247 = X248 ) )
& ~ ( in @ X250 @ emptyset )
& ( ~ ( in @ X253 @ ( setadjoin @ X251 @ X252 ) )
| ( X253 = X251 )
| ( in @ X253 @ X252 ) )
& ( ( X253 != X251 )
| ( in @ X253 @ ( setadjoin @ X251 @ X252 ) ) )
& ( ~ ( in @ X253 @ X252 )
| ( in @ X253 @ ( setadjoin @ X251 @ X252 ) ) )
& ( ~ ( in @ X255 @ ( powerset @ X254 ) )
| ~ ( in @ X256 @ X255 )
| ( in @ X256 @ X254 ) )
& ( ( in @ ( esk2_2 @ X257 @ X258 ) @ X258 )
| ( in @ X258 @ ( powerset @ X257 ) ) )
& ( ~ ( in @ ( esk2_2 @ X257 @ X258 ) @ X257 )
| ( in @ X258 @ ( powerset @ X257 ) ) )
& ( ( in @ X261 @ ( esk3_2 @ X260 @ X261 ) )
| ~ ( in @ X261 @ ( setunion @ X260 ) ) )
& ( ( in @ ( esk3_2 @ X260 @ X261 ) @ X260 )
| ~ ( in @ X261 @ ( setunion @ X260 ) ) )
& ( ~ ( in @ X264 @ X265 )
| ~ ( in @ X265 @ X263 )
| ( in @ X264 @ ( setunion @ X263 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X266 @ omega )
| ( in @ ( setadjoin @ X266 @ X266 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X267 ) @ omega )
| ~ ( in @ emptyset @ X267 )
| ~ ( in @ X269 @ omega )
| ( in @ X269 @ X267 ) )
& ( ( in @ ( esk4_1 @ X267 ) @ X267 )
| ~ ( in @ emptyset @ X267 )
| ~ ( in @ X269 @ omega )
| ( in @ X269 @ X267 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X267 ) @ ( esk4_1 @ X267 ) ) @ X267 )
| ~ ( in @ emptyset @ X267 )
| ~ ( in @ X269 @ omega )
| ( in @ X269 @ X267 ) )
& ( ( in @ ( esk8_3 @ X270 @ X271 @ X276 ) @ X271 )
| ~ ( in @ X276 @ ( esk7_2 @ X270 @ X271 ) )
| ( in @ ( esk5_2 @ X270 @ X271 ) @ X271 ) )
& ( ( X270 @ ( esk8_3 @ X270 @ X271 @ X276 ) @ X276 )
| ~ ( in @ X276 @ ( esk7_2 @ X270 @ X271 ) )
| ( in @ ( esk5_2 @ X270 @ X271 ) @ X271 ) )
& ( ~ ( in @ X279 @ X271 )
| ~ ( X270 @ X279 @ X278 )
| ( in @ X278 @ ( esk7_2 @ X270 @ X271 ) )
| ( in @ ( esk5_2 @ X270 @ X271 ) @ X271 ) )
& ( ( in @ ( esk8_3 @ X270 @ X271 @ X276 ) @ X271 )
| ~ ( in @ X276 @ ( esk7_2 @ X270 @ X271 ) )
| ( X270 @ ( esk5_2 @ X270 @ X271 ) @ ( esk6_3 @ X270 @ X271 @ X273 ) )
| ~ ( X270 @ ( esk5_2 @ X270 @ X271 ) @ X273 ) )
& ( ( X270 @ ( esk8_3 @ X270 @ X271 @ X276 ) @ X276 )
| ~ ( in @ X276 @ ( esk7_2 @ X270 @ X271 ) )
| ( X270 @ ( esk5_2 @ X270 @ X271 ) @ ( esk6_3 @ X270 @ X271 @ X273 ) )
| ~ ( X270 @ ( esk5_2 @ X270 @ X271 ) @ X273 ) )
& ( ~ ( in @ X279 @ X271 )
| ~ ( X270 @ X279 @ X278 )
| ( in @ X278 @ ( esk7_2 @ X270 @ X271 ) )
| ( X270 @ ( esk5_2 @ X270 @ X271 ) @ ( esk6_3 @ X270 @ X271 @ X273 ) )
| ~ ( X270 @ ( esk5_2 @ X270 @ X271 ) @ X273 ) )
& ( ( in @ ( esk8_3 @ X270 @ X271 @ X276 ) @ X271 )
| ~ ( in @ X276 @ ( esk7_2 @ X270 @ X271 ) )
| ( X273
!= ( esk6_3 @ X270 @ X271 @ X273 ) )
| ~ ( X270 @ ( esk5_2 @ X270 @ X271 ) @ X273 ) )
& ( ( X270 @ ( esk8_3 @ X270 @ X271 @ X276 ) @ X276 )
| ~ ( in @ X276 @ ( esk7_2 @ X270 @ X271 ) )
| ( X273
!= ( esk6_3 @ X270 @ X271 @ X273 ) )
| ~ ( X270 @ ( esk5_2 @ X270 @ X271 ) @ X273 ) )
& ( ~ ( in @ X279 @ X271 )
| ~ ( X270 @ X279 @ X278 )
| ( in @ X278 @ ( esk7_2 @ X270 @ X271 ) )
| ( X273
!= ( esk6_3 @ X270 @ X271 @ X273 ) )
| ~ ( X270 @ ( esk5_2 @ X270 @ X271 ) @ X273 ) )
& ( ( in @ ( esk9_1 @ X280 ) @ X280 )
| ~ ( in @ X281 @ X280 ) )
& ( ~ ( in @ X283 @ ( esk9_1 @ X280 ) )
| ~ ( in @ X283 @ X280 )
| ~ ( in @ X281 @ X280 ) )
& epred1_0
& ( ( X284 @ ( esk10_2 @ X284 @ X285 ) )
| ~ ( X284 @ X285 )
| ( X284 @ ( descr @ X284 ) ) )
& ( ( X285
!= ( esk10_2 @ X284 @ X285 ) )
| ~ ( X284 @ X285 )
| ( X284 @ ( descr @ X284 ) ) )
& ( ~ ( in @ X289 @ X287 )
| ~ ( X288 @ X289 )
| ( in @ X289 @ ( dsetconstr @ X287 @ X288 ) ) )
& ( ~ ( in @ X292 @ ( dsetconstr @ X290 @ X291 ) )
| ( in @ X292 @ X290 ) )
& ( ~ ( in @ X295 @ ( dsetconstr @ X293 @ X294 ) )
| ( X294 @ X295 ) )
& ( ( X296 @ ( esk12_1 @ X296 ) )
| ( X296 @ ( esk11_2 @ X296 @ X297 ) )
| ~ ( X296 @ X297 ) )
& ( ~ ( X296 @ X300 )
| ( ( esk12_1 @ X296 )
= X300 )
| ( X296 @ ( esk11_2 @ X296 @ X297 ) )
| ~ ( X296 @ X297 ) )
& ( ( X296 @ ( esk12_1 @ X296 ) )
| ( X297
!= ( esk11_2 @ X296 @ X297 ) )
| ~ ( X296 @ X297 ) )
& ( ~ ( X296 @ X300 )
| ( ( esk12_1 @ X296 )
= X300 )
| ( X297
!= ( esk11_2 @ X296 @ X297 ) )
| ~ ( X296 @ X297 ) )
& ( ~ ( in @ X302 @ ( prop2set @ X301 ) )
| X301 )
& ( ~ ( in @ X303 @ emptyset )
| X304 )
& ( ~ ( in @ X305 @ emptyset )
| ~ $true )
& ~ ( in @ X306 @ emptyset )
& ( ( X307 @ ( esk13_2 @ X307 @ X308 ) )
| ~ ( X307 @ X308 )
| ( X307 @ ( esk14_1 @ X307 ) ) )
& ( ( X308
!= ( esk13_2 @ X307 @ X308 ) )
| ~ ( X307 @ X308 )
| ( X307 @ ( esk14_1 @ X307 ) ) )
& ( ( in @ ( esk16_2 @ X311 @ X312 ) @ X312 )
| ( X311 = X312 )
| ( in @ ( esk15_2 @ X311 @ X312 ) @ X311 ) )
& ( ~ ( in @ ( esk16_2 @ X311 @ X312 ) @ X311 )
| ( X311 = X312 )
| ( in @ ( esk15_2 @ X311 @ X312 ) @ X311 ) )
& ( ( in @ ( esk16_2 @ X311 @ X312 ) @ X312 )
| ( X311 = X312 )
| ~ ( in @ ( esk15_2 @ X311 @ X312 ) @ X312 ) )
& ( ~ ( in @ ( esk16_2 @ X311 @ X312 ) @ X311 )
| ( X311 = X312 )
| ~ ( in @ ( esk15_2 @ X311 @ X312 ) @ X312 ) )
& ( ( in @ ( esk17_1 @ X315 ) @ X315 )
| ( X315 = emptyset ) )
& ( ( in @ ( esk18_1 @ X317 ) @ X317 )
| ( X317 = emptyset ) )
& ( ~ ( in @ X321 @ ( dsetconstr @ X319 @ X320 ) )
| ( X320 @ X321 )
| ~ ( in @ X321 @ X319 ) )
& ( ~ ( X320 @ X321 )
| ( in @ X321 @ ( dsetconstr @ X319 @ X320 ) )
| ~ ( in @ X321 @ X319 ) )
& ( ( X322 = emptyset )
| ( in @ ( esk19_1 @ X322 ) @ X322 ) )
& ( ~ ( in @ X326 @ X324 )
| ~ ( X325 @ X326 )
| ( ( dsetconstr @ X324 @ X325 )
!= emptyset ) )
& ( ~ ( in @ X328 @ X327 )
| ( X327 != emptyset ) )
& ( in @ X329 @ ( setadjoin @ X329 @ X330 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X333 @ X332 )
| ( in @ X333 @ ( setadjoin @ X331 @ X332 ) ) )
& ( ( in @ X336 @ X335 )
| X337
| ( X336 = X334 )
| ~ ( in @ X336 @ ( setadjoin @ X334 @ X335 ) ) )
& ( ~ X337
| X337
| ( X336 = X334 )
| ~ ( in @ X336 @ ( setadjoin @ X334 @ X335 ) ) )
& ( ( in @ X336 @ X335 )
| X337
| ~ X337
| ~ ( in @ X336 @ ( setadjoin @ X334 @ X335 ) ) )
& ( ~ X337
| X337
| ~ X337
| ~ ( in @ X336 @ ( setadjoin @ X334 @ X335 ) ) )
& ( ~ ( in @ X340 @ ( setadjoin @ X338 @ X339 ) )
| ( X340 = X338 )
| ( in @ X340 @ X339 ) )
& ( ( dsetconstr @ X341
@ ^ [Z0: $i] : $true )
= X341 )
& ( ( in @ ( esk20_2 @ X342 @ X343 ) @ X343 )
| ( in @ X343 @ ( powerset @ X342 ) ) )
& ( ~ ( in @ ( esk20_2 @ X342 @ X343 ) @ X342 )
| ( in @ X343 @ ( powerset @ X342 ) ) )
& ( in @ emptyset @ ( powerset @ X345 ) )
& ( in @ emptyset @ ( powerset @ X346 ) )
& ( ~ ( in @ X348 @ ( powerset @ X347 ) )
| ~ ( in @ X349 @ X348 )
| ( in @ X349 @ X347 ) )
& ( in @ esk22_0 @ esk23_0 )
& ( in @ esk23_0 @ esk21_0 )
& ~ ( in @ esk22_0 @ ( setunion @ esk21_0 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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 @ esk23_0 @ esk21_0,
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_65,negated_conjecture,
! [X2: $i] :
( ( in @ X2 @ ( setunion @ esk21_0 ) )
| ~ ( in @ X2 @ esk23_0 ) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
thf(c_0_66,negated_conjecture,
in @ esk22_0 @ esk23_0,
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_67,negated_conjecture,
~ ( in @ esk22_0 @ ( setunion @ esk21_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_68,negated_conjecture,
$false,
inference(sr,[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.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 15:20:52 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running higher-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.19/0.52 # Version: 3.1.0-ho
% 0.19/0.52 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.19/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.52 # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.52 # Starting sh5l with 300s (1) cores
% 0.19/0.52 # Starting new_bool_1 with 300s (1) cores
% 0.19/0.52 # Starting new_bool_2 with 300s (1) cores
% 0.19/0.52 # new_ho_10 with pid 6906 completed with status 0
% 0.19/0.52 # Result found by new_ho_10
% 0.19/0.52 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.19/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.52 # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.52 # No SInE strategy applied
% 0.19/0.52 # Search class: HGHSM-FFMS31-SHFSMSBN
% 0.19/0.52 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.52 # Starting new_ho_10 with 901s (1) cores
% 0.19/0.52 # Starting sh5l with 151s (1) cores
% 0.19/0.52 # Starting new_bool_1 with 151s (1) cores
% 0.19/0.52 # Starting new_bool_2 with 151s (1) cores
% 0.19/0.52 # Starting new_bool_9 with 146s (1) cores
% 0.19/0.52 # new_bool_2 with pid 6916 completed with status 0
% 0.19/0.52 # Result found by new_bool_2
% 0.19/0.52 # Preprocessing class: HSMSSLSSMLLCHFA.
% 0.19/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.52 # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.52 # No SInE strategy applied
% 0.19/0.52 # Search class: HGHSM-FFMS31-SHFSMSBN
% 0.19/0.52 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.52 # Starting new_ho_10 with 901s (1) cores
% 0.19/0.52 # Starting sh5l with 151s (1) cores
% 0.19/0.52 # Starting new_bool_1 with 151s (1) cores
% 0.19/0.52 # Starting new_bool_2 with 151s (1) cores
% 0.19/0.52 # Preprocessing time : 0.004 s
% 0.19/0.52 # Presaturation interreduction done
% 0.19/0.52
% 0.19/0.52 # Proof found!
% 0.19/0.52 # SZS status Theorem
% 0.19/0.52 # SZS output start CNFRefutation
% See solution above
% 0.19/0.52 # Parsed axioms : 91
% 0.19/0.52 # Removed by relevancy pruning/SinE : 0
% 0.19/0.52 # Initial clauses : 137
% 0.19/0.52 # Removed in clause preprocessing : 52
% 0.19/0.52 # Initial clauses in saturation : 85
% 0.19/0.52 # Processed clauses : 293
% 0.19/0.52 # ...of these trivial : 7
% 0.19/0.52 # ...subsumed : 77
% 0.19/0.52 # ...remaining for further processing : 209
% 0.19/0.52 # Other redundant clauses eliminated : 23
% 0.19/0.52 # Clauses deleted for lack of memory : 0
% 0.19/0.52 # Backward-subsumed : 9
% 0.19/0.52 # Backward-rewritten : 3
% 0.19/0.52 # Generated clauses : 449
% 0.19/0.52 # ...of the previous two non-redundant : 382
% 0.19/0.52 # ...aggressively subsumed : 0
% 0.19/0.52 # Contextual simplify-reflections : 0
% 0.19/0.52 # Paramodulations : 371
% 0.19/0.52 # Factorizations : 0
% 0.19/0.52 # NegExts : 2
% 0.19/0.52 # Equation resolutions : 23
% 0.19/0.52 # Disequality decompositions : 0
% 0.19/0.52 # Total rewrite steps : 53
% 0.19/0.52 # ...of those cached : 34
% 0.19/0.52 # Propositional unsat checks : 0
% 0.19/0.52 # Propositional check models : 0
% 0.19/0.52 # Propositional check unsatisfiable : 0
% 0.19/0.52 # Propositional clauses : 0
% 0.19/0.52 # Propositional clauses after purity: 0
% 0.19/0.52 # Propositional unsat core size : 0
% 0.19/0.52 # Propositional preprocessing time : 0.000
% 0.19/0.52 # Propositional encoding time : 0.000
% 0.19/0.52 # Propositional solver time : 0.000
% 0.19/0.52 # Success case prop preproc time : 0.000
% 0.19/0.52 # Success case prop encoding time : 0.000
% 0.19/0.52 # Success case prop solver time : 0.000
% 0.19/0.52 # Current number of processed clauses : 121
% 0.19/0.52 # Positive orientable unit clauses : 29
% 0.19/0.52 # Positive unorientable unit clauses: 0
% 0.19/0.52 # Negative unit clauses : 25
% 0.19/0.52 # Non-unit-clauses : 67
% 0.19/0.52 # Current number of unprocessed clauses: 244
% 0.19/0.52 # ...number of literals in the above : 613
% 0.19/0.52 # Current number of archived formulas : 0
% 0.19/0.52 # Current number of archived clauses : 86
% 0.19/0.52 # Clause-clause subsumption calls (NU) : 2330
% 0.19/0.52 # Rec. Clause-clause subsumption calls : 1129
% 0.19/0.52 # Non-unit clause-clause subsumptions : 50
% 0.19/0.52 # Unit Clause-clause subsumption calls : 271
% 0.19/0.52 # Rewrite failures with RHS unbound : 0
% 0.19/0.52 # BW rewrite match attempts : 14
% 0.19/0.52 # BW rewrite match successes : 3
% 0.19/0.52 # Condensation attempts : 0
% 0.19/0.52 # Condensation successes : 0
% 0.19/0.52 # Termbank termtop insertions : 24709
% 0.19/0.52 # Search garbage collected termcells : 4126
% 0.19/0.52
% 0.19/0.52 # -------------------------------------------------
% 0.19/0.52 # User time : 0.029 s
% 0.19/0.52 # System time : 0.007 s
% 0.19/0.52 # Total time : 0.037 s
% 0.19/0.52 # Maximum resident set size: 2792 pages
% 0.19/0.52
% 0.19/0.52 # -------------------------------------------------
% 0.19/0.52 # User time : 0.123 s
% 0.19/0.52 # System time : 0.027 s
% 0.19/0.52 # Total time : 0.150 s
% 0.19/0.52 # Maximum resident set size: 1816 pages
% 0.19/0.52 % E---3.1 exiting
% 0.19/0.52 % E exiting
%------------------------------------------------------------------------------