TSTP Solution File: SEU542^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU542^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:28:04 EDT 2024
% Result : Theorem 0.38s 0.55s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 159
% Syntax : Number of formulae : 186 ( 15 unt; 99 typ; 0 def)
% Number of atoms : 690 ( 111 equ; 0 cnn)
% Maximal formula atoms : 192 ( 7 avg)
% Number of connectives : 2340 ( 190 ~; 176 |; 164 &;1407 @)
% ( 89 <=>; 314 =>; 0 <=; 0 <~>)
% Maximal formula depth : 232 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 149 ( 149 >; 0 *; 0 +; 0 <<)
% Number of symbols : 102 ( 99 usr; 65 con; 0-3 aty)
% Number of variables : 554 ( 29 ^ 455 !; 70 ?; 554 :)
% 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,
setunionI: $o ).
thf(decl_72,type,
setunionE: $o ).
thf(decl_73,type,
subPowSU: $o ).
thf(decl_74,type,
exuE2: $o ).
thf(decl_75,type,
nonemptyImpWitness: $o ).
thf(decl_76,type,
uniqinunit: $o ).
thf(decl_77,type,
notinsingleton: $o ).
thf(decl_78,type,
eqinunit: $o ).
thf(decl_79,type,
singletonsswitch: $o ).
thf(decl_80,type,
upairsetE: $o ).
thf(decl_81,type,
upairsetIL: $o ).
thf(decl_82,type,
upairsetIR: $o ).
thf(decl_83,type,
emptyE1: $o ).
thf(decl_84,type,
vacuousDall: $o ).
thf(decl_85,type,
quantDeMorgan1: $o ).
thf(decl_86,type,
quantDeMorgan2: $o ).
thf(decl_87,type,
quantDeMorgan3: $o ).
thf(decl_88,type,
quantDeMorgan4: $o ).
thf(decl_89,type,
prop2setI: $o ).
thf(decl_91,type,
prop2set2propI: $o ).
thf(decl_92,type,
epred1_0: $o ).
thf(decl_93,type,
esk1_2: $i > $i > $i ).
thf(decl_94,type,
esk2_2: $i > $i > $i ).
thf(decl_95,type,
esk3_2: $i > $i > $i ).
thf(decl_96,type,
esk4_1: $i > $i ).
thf(decl_97,type,
esk5_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_98,type,
esk6_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_99,type,
esk7_2: ( $i > $i > $o ) > $i > $i ).
thf(decl_100,type,
esk8_3: ( $i > $i > $o ) > $i > $i > $i ).
thf(decl_101,type,
esk9_1: $i > $i ).
thf(decl_102,type,
esk10_2: ( $i > $o ) > $i > $i ).
thf(decl_103,type,
esk11_1: ( $i > $o ) > $i ).
thf(decl_104,type,
esk12_2: ( $i > $o ) > $i > $i ).
thf(decl_105,type,
esk13_1: ( $i > $o ) > $i ).
thf(decl_106,type,
esk14_2: $i > $i > $i ).
thf(decl_107,type,
esk15_2: $i > $i > $i ).
thf(decl_108,type,
esk16_1: $i > $i ).
thf(decl_109,type,
esk17_1: $i > $i ).
thf(decl_110,type,
esk18_1: $i > $i ).
thf(decl_111,type,
esk19_2: $i > $i > $i ).
thf(decl_112,type,
esk20_3: $i > $i > $o > $i ).
thf(decl_113,type,
esk21_2: ( $i > $o ) > $i > $i ).
thf(decl_114,type,
esk22_1: ( $i > $o ) > $i ).
thf(decl_115,type,
esk23_1: $i > $i ).
thf(decl_116,type,
esk24_2: $i > ( $i > $o ) > $i ).
thf(decl_117,type,
esk25_2: $i > ( $i > $o ) > $i ).
thf(decl_118,type,
esk26_2: $i > ( $i > $o ) > $i ).
thf(decl_119,type,
esk27_2: $i > ( $i > $o ) > $i ).
thf(decl_120,type,
esk28_0: $i ).
thf(decl_121,type,
epred2_0: $i > $o ).
thf(decl_122,type,
esk29_0: $i ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
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(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(exuE3e,axiom,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE2,axiom,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
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(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(nonemptyImpWitness,axiom,
( nonemptyImpWitness
<=> ! [X4: $i] :
( ( nonempty @ X4 )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
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(emptyE1,axiom,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
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(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(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(notdexE,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
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(noeltsimpempty,axiom,
( noeltsimpempty
<=> ! [X4: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X4 )
=> ( X4 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(prop2setI,axiom,
( prop2setI
<=> ! [X15: $o] :
( X15
=> ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(notinsingleton,axiom,
( notinsingleton
<=> ! [X2: $i,X3: $i] :
( ( X2 != X3 )
=> ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(eqinunit,axiom,
( eqinunit
<=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(singletonsswitch,axiom,
( singletonsswitch
<=> ! [X2: $i,X3: $i] :
( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
=> ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(upairsetE,axiom,
( upairsetE
<=> ! [X2: $i,X3: $i,X14: $i] :
( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X14 = X2 )
| ( X14 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,axiom,
( upairsetIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(prop2setE,axiom,
( prop2setE
<=> ! [X10: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X10 ) )
=> X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(upairsetIR,axiom,
( upairsetIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(emptysetE,axiom,
( emptysetE
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X11: $o] : X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(vacuousDall,axiom,
( vacuousDall
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ emptyset )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(quantDeMorgan1,axiom,
( quantDeMorgan1
<=> ! [X4: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(quantDeMorgan2,axiom,
( quantDeMorgan2
<=> ! [X4: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) )
=> ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,axiom,
( quantDeMorgan3
<=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(notinemptyset,axiom,
( notinemptyset
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(quantDeMorgan4,axiom,
( quantDeMorgan4
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ~ ( X1 @ X2 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
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(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 ) )
=> ! [X12: $o] :
( ( ( X3 = X2 )
=> X12 )
=> ( ( ( in @ X3 @ X4 )
=> X12 )
=> X12 ) ) ) ),
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(setunionI,axiom,
( setunionI
<=> ! [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(setunionE,axiom,
( setunionE
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X4 ) )
=> ! [X13: $o] :
( ! [X5: $i] :
( ( in @ X2 @ X5 )
=> ( ( in @ X5 @ X4 )
=> X13 ) )
=> X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(subPowSU,axiom,
( subPowSU
<=> ! [X4: $i,X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
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(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(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(omegaSAx,axiom,
( omegaSAx
<=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega0Ax,axiom,
( omega0Ax
<=> ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
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(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(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(emptysetAx,axiom,
( emptysetAx
<=> ! [X2: $i] :
~ ( in @ X2 @ emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
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(c_0_59,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_60,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_61,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu]) ).
thf(c_0_62,plain,
( exuE3e
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[exuE3e]) ).
thf(c_0_63,plain,
( exuE2
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[exuE2]) ).
thf(c_0_64,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_65,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_66,axiom,
( nonemptyImpWitness
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] :
( ( in @ X2 @ X4 )
& $true ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_59]) ).
thf(c_0_67,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_68,plain,
( exuE1
= ( ! [X1: $i > $o] :
( ? [X179: $i] :
( ( X1 @ X179 )
& ! [X180: $i] :
( ( X1 @ X180 )
=> ( X179 = X180 ) ) )
=> ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_60,c_0_61]) ).
thf(c_0_69,plain,
( emptyE1
<=> ! [X4: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X4
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
= emptyset )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[emptyE1]) ).
thf(c_0_70,plain,
( exuE3e
= ( ! [X1: $i > $o] :
( ? [X181: $i] :
( ( X1 @ X181 )
& ! [X182: $i] :
( ( X1 @ X182 )
=> ( X181 = X182 ) ) )
=> ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_62,c_0_61]) ).
thf(c_0_71,plain,
( exuE2
= ( ! [X1: $i > $o] :
( ? [X183: $i] :
( ( X1 @ X183 )
& ! [X184: $i] :
( ( X1 @ X184 )
=> ( X183 = X184 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
<=> ( X3 = X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_63,c_0_61]) ).
thf(c_0_72,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_73,axiom,
( nonemptyE1
= ( ! [X4: $i] :
( ( X4 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_59]) ).
thf(c_0_74,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_64,c_0_59]) ).
thf(c_0_75,axiom,
( nonemptyI1
= ( ! [X4: $i] :
( ? [X2: $i] : ( in @ X2 @ X4 )
=> ( X4 != emptyset ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyI1,c_0_59]) ).
thf(c_0_76,plain,
( setoftrueEq
<=> ! [X4: $i] :
( ( dsetconstr @ X4
@ ^ [Z0: $i] : $true )
= X4 ) ),
inference(fof_simplification,[status(thm)],[setoftrueEq]) ).
thf(c_0_77,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_78,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_79,plain,
( replAx
= ( ! [X6: $i > $i > $o,X4: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ? [X177: $i] :
( ( X6 @ X2 @ X177 )
& ! [X178: $i] :
( ( X6 @ X2 @ X178 )
=> ( X177 = X178 ) ) ) )
=> ? [X5: $i] :
! [X2: $i] :
( ( in @ X2 @ X5 )
<=> ? [X3: $i] :
( ( in @ X3 @ X4 )
& ( X6 @ X3 @ X2 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_65,c_0_61]) ).
thf(c_0_80,plain,
( epred1_0
<=> ! [X214: $i] :
? [X215: $i] :
( ! [X216: $i] :
( ( in @ X216 @ X215 )
=> ! [X217: $i] :
( ( in @ X217 @ X216 )
=> ( in @ X217 @ X214 ) ) )
& ! [X218: $i,X219: $i] :
( ( ( in @ X218 @ X214 )
& ( in @ X219 @ X214 ) )
=> ( ! [X220: $i] :
( ( in @ X220 @ X215 )
=> ( ( in @ X218 @ X220 )
<=> ( in @ X219 @ X220 ) ) )
=> ( X218 = X219 ) ) )
& ! [X221: $i,X222: $i] :
( ( ( in @ X221 @ X215 )
& ( in @ X222 @ X215 ) )
=> ( ! [X223: $i] :
( ( in @ X223 @ X221 )
=> ( in @ X223 @ X222 ) )
| ! [X224: $i] :
( ( in @ X224 @ X222 )
=> ( in @ X224 @ X221 ) ) ) )
& ! [X225: $i] :
( ( ! [X226: $i] :
( ( in @ X226 @ X225 )
=> ( in @ X226 @ X214 ) )
& ? [X227: $i] : ( in @ X227 @ X225 ) )
=> ? [X228: $i,X229: $i] :
( ( in @ X228 @ X215 )
& ( in @ X229 @ X225 )
& ~ ? [X230: $i] :
( ( in @ X230 @ X228 )
& ( in @ X230 @ X225 ) )
& ! [X231: $i] :
( ( in @ X231 @ X215 )
=> ( ! [X232: $i] :
( ( in @ X232 @ X231 )
=> ( in @ X232 @ X228 ) )
| ( in @ X229 @ X231 ) ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_81,negated_conjecture,
~ ( ! [X185: $i,X186: $i] :
( ! [X187: $i] :
( ( in @ X187 @ X185 )
<=> ( in @ X187 @ X186 ) )
=> ( X185 = X186 ) )
=> ( ! [X188: $i] :
~ ( in @ X188 @ emptyset )
=> ( ! [X189: $i,X190: $i,X191: $i] :
( ( in @ X191 @ ( setadjoin @ X189 @ X190 ) )
<=> ( ( X191 = X189 )
| ( in @ X191 @ X190 ) ) )
=> ( ! [X192: $i,X193: $i] :
( ( in @ X193 @ ( powerset @ X192 ) )
<=> ! [X194: $i] :
( ( in @ X194 @ X193 )
=> ( in @ X194 @ X192 ) ) )
=> ( ! [X195: $i,X196: $i] :
( ( in @ X196 @ ( setunion @ X195 ) )
<=> ? [X197: $i] :
( ( in @ X196 @ X197 )
& ( in @ X197 @ X195 ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [X198: $i] :
( ( in @ X198 @ omega )
=> ( in @ ( setadjoin @ X198 @ X198 ) @ omega ) )
=> ( ! [X199: $i] :
( ( ( in @ emptyset @ X199 )
& ! [X200: $i] :
( ( ( in @ X200 @ omega )
& ( in @ X200 @ X199 ) )
=> ( in @ ( setadjoin @ X200 @ X200 ) @ X199 ) ) )
=> ! [X201: $i] :
( ( in @ X201 @ omega )
=> ( in @ X201 @ X199 ) ) )
=> ( ! [X202: $i > $i > $o,X203: $i] :
( ! [X204: $i] :
( ( in @ X204 @ X203 )
=> ? [X205: $i] :
( ( X202 @ X204 @ X205 )
& ! [X206: $i] :
( ( X202 @ X204 @ X206 )
=> ( X205 = X206 ) ) ) )
=> ? [X207: $i] :
! [X208: $i] :
( ( in @ X208 @ X207 )
<=> ? [X209: $i] :
( ( in @ X209 @ X203 )
& ( X202 @ X209 @ X208 ) ) ) )
=> ( ! [X210: $i] :
( ? [X211: $i] : ( in @ X211 @ X210 )
=> ? [X212: $i] :
( ( in @ X212 @ X210 )
& ~ ? [X213: $i] :
( ( in @ X213 @ X212 )
& ( in @ X213 @ X210 ) ) ) )
=> ( epred1_0
=> ( descrp
=> ( ! [X233: $i,X234: $i > $o,X235: $i] :
( ( in @ X235 @ X233 )
=> ( ( X234 @ X235 )
=> ( in @ X235 @ ( dsetconstr @ X233 @ X234 ) ) ) )
=> ( ! [X236: $i,X237: $i > $o,X238: $i] :
( ( in @ X238 @ ( dsetconstr @ X236 @ X237 ) )
=> ( in @ X238 @ X236 ) )
=> ( ! [X239: $i,X240: $i > $o,X241: $i] :
( ( in @ X241 @ ( dsetconstr @ X239 @ X240 ) )
=> ( X240 @ X241 ) )
=> ( ! [X242: $i > $o] :
( ? [X243: $i] :
( ( X242 @ X243 )
& ! [X244: $i] :
( ( X242 @ X244 )
=> ( X243 = X244 ) ) )
=> ? [X245: $i] :
( ( X242 @ X245 )
& ! [X246: $i] :
( ( X242 @ X246 )
=> ( X245 = X246 ) ) ) )
=> ( ! [X247: $o,X248: $i] :
( ( in @ X248 @ ( prop2set @ X247 ) )
=> X247 )
=> ( ! [X249: $i] :
( ( in @ X249 @ emptyset )
=> ! [X250: $o] : X250 )
=> ( ! [X251: $i] :
( ( in @ X251 @ emptyset )
=> ~ $true )
=> ( ! [X252: $i] :
~ ( in @ X252 @ emptyset )
=> ( ! [X253: $i > $o] :
( ? [X254: $i] :
( ( X253 @ X254 )
& ! [X255: $i] :
( ( X253 @ X255 )
=> ( X254 = X255 ) ) )
=> ? [X256: $i] : ( X253 @ X256 ) )
=> ( ! [X257: $i,X258: $i] :
( ! [X259: $i] :
( ( in @ X259 @ X257 )
=> ( in @ X259 @ X258 ) )
=> ( ! [X260: $i] :
( ( in @ X260 @ X258 )
=> ( in @ X260 @ X257 ) )
=> ( X257 = X258 ) ) )
=> ( ! [X261: $i] :
( ! [X262: $i] :
~ ( in @ X262 @ X261 )
=> ( X261 = emptyset ) )
=> ( ! [X263: $i] :
( ! [X264: $i] :
~ ( in @ X264 @ X263 )
=> ( X263 = emptyset ) )
=> ( ! [X265: $i,X266: $i > $o,X267: $i] :
( ( in @ X267 @ X265 )
=> ( ( in @ X267 @ ( dsetconstr @ X265 @ X266 ) )
<=> ( X266 @ X267 ) ) )
=> ( ! [X268: $i] :
( ( X268 != emptyset )
=> ? [X269: $i] : ( in @ X269 @ X268 ) )
=> ( ! [X270: $i,X271: $i > $o,X272: $i] :
( ( in @ X272 @ X270 )
=> ( ( X271 @ X272 )
=> ( ( dsetconstr @ X270 @ X271 )
!= emptyset ) ) )
=> ( ! [X273: $i] :
( ? [X274: $i] : ( in @ X274 @ X273 )
=> ( X273 != emptyset ) )
=> ( ! [X275: $i,X276: $i] : ( in @ X275 @ ( setadjoin @ X275 @ X276 ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [X277: $i,X278: $i,X279: $i] :
( ( in @ X279 @ X278 )
=> ( in @ X279 @ ( setadjoin @ X277 @ X278 ) ) )
=> ( ! [X280: $i,X281: $i,X282: $i] :
( ( in @ X282 @ ( setadjoin @ X280 @ X281 ) )
=> ! [X283: $o] :
( ( ( X282 = X280 )
=> X283 )
=> ( ( ( in @ X282 @ X281 )
=> X283 )
=> X283 ) ) )
=> ( ! [X284: $i,X285: $i,X286: $i] :
( ( in @ X286 @ ( setadjoin @ X284 @ X285 ) )
=> ( ( X286 = X284 )
| ( in @ X286 @ X285 ) ) )
=> ( ! [X287: $i] :
( ( dsetconstr @ X287
@ ^ [Z0: $i] : $true )
= X287 )
=> ( ! [X288: $i,X289: $i] :
( ! [X290: $i] :
( ( in @ X290 @ X289 )
=> ( in @ X290 @ X288 ) )
=> ( in @ X289 @ ( powerset @ X288 ) ) )
=> ( ! [X291: $i] : ( in @ emptyset @ ( powerset @ X291 ) )
=> ( ! [X292: $i] : ( in @ emptyset @ ( powerset @ X292 ) )
=> ( ! [X293: $i,X294: $i,X295: $i] :
( ( in @ X294 @ ( powerset @ X293 ) )
=> ( ( in @ X295 @ X294 )
=> ( in @ X295 @ X293 ) ) )
=> ( ! [X296: $i,X297: $i,X298: $i] :
( ( in @ X297 @ X298 )
=> ( ( in @ X298 @ X296 )
=> ( in @ X297 @ ( setunion @ X296 ) ) ) )
=> ( ! [X299: $i,X300: $i] :
( ( in @ X300 @ ( setunion @ X299 ) )
=> ! [X301: $o] :
( ! [X302: $i] :
( ( in @ X300 @ X302 )
=> ( ( in @ X302 @ X299 )
=> X301 ) )
=> X301 ) )
=> ( ! [X303: $i,X304: $i] :
( ( in @ X304 @ X303 )
=> ( in @ X304 @ ( powerset @ ( setunion @ X303 ) ) ) )
=> ( ! [X305: $i > $o] :
( ? [X306: $i] :
( ( X305 @ X306 )
& ! [X307: $i] :
( ( X305 @ X307 )
=> ( X306 = X307 ) ) )
=> ? [X308: $i] :
! [X309: $i] :
( ( X305 @ X309 )
<=> ( X309 = X308 ) ) )
=> ( ! [X310: $i] :
( ( X310 != emptyset )
=> ? [X311: $i] :
( ( in @ X311 @ X310 )
& $true ) )
=> ( ! [X312: $i,X313: $i] :
( ( in @ X312 @ ( setadjoin @ X313 @ emptyset ) )
=> ( X312 = X313 ) )
=> ( ! [X314: $i,X315: $i] :
( ( X314 != X315 )
=> ~ ( in @ X315 @ ( setadjoin @ X314 @ emptyset ) ) )
=> ( ! [X316: $i,X317: $i] :
( ( X316 = X317 )
=> ( in @ X316 @ ( setadjoin @ X317 @ emptyset ) ) )
=> ( ! [X318: $i,X319: $i] :
( ( in @ X318 @ ( setadjoin @ X319 @ emptyset ) )
=> ( in @ X319 @ ( setadjoin @ X318 @ emptyset ) ) )
=> ( ! [X320: $i,X321: $i,X322: $i] :
( ( in @ X322 @ ( setadjoin @ X320 @ ( setadjoin @ X321 @ emptyset ) ) )
=> ( ( X322 = X320 )
| ( X322 = X321 ) ) )
=> ( ! [X323: $i,X324: $i] : ( in @ X323 @ ( setadjoin @ X323 @ ( setadjoin @ X324 @ emptyset ) ) )
=> ( ! [X325: $i,X326: $i] : ( in @ X326 @ ( setadjoin @ X325 @ ( setadjoin @ X326 @ emptyset ) ) )
=> ( ! [X327: $i,X328: $i > $o] :
( ? [X329: $i] :
( ( in @ X329 @ X327 )
& ( X328 @ X329 ) )
=> ( ( ( dsetconstr @ X327 @ X328 )
= emptyset )
=> ~ $true ) )
=> ( ! [X330: $i > $o,X331: $i] :
( ( in @ X331 @ emptyset )
=> ( X330 @ X331 ) )
=> ( ! [X332: $i,X333: $i > $o] :
( ~ ! [X334: $i] :
( ( in @ X334 @ X332 )
=> ( X333 @ X334 ) )
=> ? [X335: $i] :
( ( in @ X335 @ X332 )
& ~ ( X333 @ X335 ) ) )
=> ( ! [X336: $i,X337: $i > $o] :
( ! [X338: $i] :
( ( in @ X338 @ X336 )
=> ~ ( X337 @ X338 ) )
=> ~ ? [X339: $i] :
( ( in @ X339 @ X336 )
& ( X337 @ X339 ) ) )
=> ( ! [X340: $i,X341: $i > $o] :
( ~ ? [X342: $i] :
( ( in @ X342 @ X340 )
& ( X341 @ X342 ) )
=> ! [X343: $i] :
( ( in @ X343 @ X340 )
=> ~ ( X341 @ X343 ) ) )
=> ( ! [X344: $i,X345: $i > $o] :
( ? [X346: $i] :
( ( in @ X346 @ X344 )
& ~ ( X345 @ X346 ) )
=> ~ ! [X347: $i] :
( ( in @ X347 @ X344 )
=> ( X345 @ X347 ) ) )
=> ( ! [X348: $o] :
( X348
=> ( in @ emptyset @ ( prop2set @ X348 ) ) )
=> ( prop2set2propI
=> ! [X4: $i,X1: $i > $o] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ~ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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(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)],[notdexE]),noeltsimpempty]),prop2setI]),c_0_66]),uniqinunit]),notinsingleton]),c_0_67]),eqinunit]),singletonsswitch]),c_0_68]),upairsetE]),upairsetIL]),prop2setE]),upairsetIR]),c_0_69]),emptysetE]),vacuousDall]),quantDeMorgan1]),emptysetimpfalse]),quantDeMorgan2]),quantDeMorgan3]),notinemptyset]),quantDeMorgan4]),c_0_70]),setext]),emptyI]),c_0_71]),c_0_72]),c_0_73]),c_0_74]),c_0_75]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_76]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_77]),c_0_78]),wellorderingAx]),foundationAx]),c_0_79]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_80]) ).
thf(c_0_82,negated_conjecture,
! [X349: $i,X350: $i,X352: $i,X353: $i,X354: $i,X355: $i,X356: $i,X357: $i,X358: $i,X359: $i,X360: $i,X362: $i,X363: $i,X365: $i,X366: $i,X367: $i,X368: $i,X369: $i,X371: $i,X372: $i > $i > $o,X373: $i,X375: $i,X378: $i,X380: $i,X381: $i,X382: $i,X383: $i,X385: $i,X386: $i,X387: $i > $o,X388: $i,X389: $i,X390: $i > $o,X391: $i,X392: $i,X393: $i > $o,X394: $i,X395: $i > $o,X396: $i,X399: $i,X400: $o,X401: $i,X402: $i,X403: $o,X404: $i,X405: $i,X406: $i > $o,X407: $i,X410: $i,X411: $i,X414: $i,X416: $i,X418: $i,X419: $i > $o,X420: $i,X421: $i,X423: $i,X424: $i > $o,X425: $i,X426: $i,X427: $i,X428: $i,X429: $i,X430: $i,X431: $i,X432: $i,X433: $i,X434: $i,X435: $i,X436: $o,X437: $i,X438: $i,X439: $i,X440: $i,X441: $i,X442: $i,X444: $i,X445: $i,X446: $i,X447: $i,X448: $i,X449: $i,X450: $i,X451: $i,X452: $i,X453: $i,X454: $o,X456: $i,X457: $i,X458: $i > $o,X459: $i,X462: $i,X463: $i,X464: $i,X466: $i,X467: $i,X468: $i,X469: $i,X470: $i,X471: $i,X472: $i,X473: $i,X474: $i,X475: $i,X476: $i,X477: $i,X478: $i,X479: $i,X480: $i,X481: $i,X482: $i > $o,X483: $i,X484: $i > $o,X485: $i,X486: $i,X487: $i > $o,X488: $i,X490: $i,X491: $i > $o,X493: $i,X494: $i,X495: $i > $o,X497: $i,X498: $i,X499: $i > $o,X500: $i,X502: $o,X505: $i] :
( ( ~ ( in @ ( esk1_2 @ X349 @ X350 ) @ X349 )
| ~ ( in @ ( esk1_2 @ X349 @ X350 ) @ X350 )
| ( X349 = X350 ) )
& ( ( in @ ( esk1_2 @ X349 @ X350 ) @ X349 )
| ( in @ ( esk1_2 @ X349 @ X350 ) @ X350 )
| ( X349 = X350 ) )
& ~ ( in @ X352 @ emptyset )
& ( ~ ( in @ X355 @ ( setadjoin @ X353 @ X354 ) )
| ( X355 = X353 )
| ( in @ X355 @ X354 ) )
& ( ( X355 != X353 )
| ( in @ X355 @ ( setadjoin @ X353 @ X354 ) ) )
& ( ~ ( in @ X355 @ X354 )
| ( in @ X355 @ ( setadjoin @ X353 @ X354 ) ) )
& ( ~ ( in @ X357 @ ( powerset @ X356 ) )
| ~ ( in @ X358 @ X357 )
| ( in @ X358 @ X356 ) )
& ( ( in @ ( esk2_2 @ X359 @ X360 ) @ X360 )
| ( in @ X360 @ ( powerset @ X359 ) ) )
& ( ~ ( in @ ( esk2_2 @ X359 @ X360 ) @ X359 )
| ( in @ X360 @ ( powerset @ X359 ) ) )
& ( ( in @ X363 @ ( esk3_2 @ X362 @ X363 ) )
| ~ ( in @ X363 @ ( setunion @ X362 ) ) )
& ( ( in @ ( esk3_2 @ X362 @ X363 ) @ X362 )
| ~ ( in @ X363 @ ( setunion @ X362 ) ) )
& ( ~ ( in @ X366 @ X367 )
| ~ ( in @ X367 @ X365 )
| ( in @ X366 @ ( setunion @ X365 ) ) )
& ( in @ emptyset @ omega )
& ( ~ ( in @ X368 @ omega )
| ( in @ ( setadjoin @ X368 @ X368 ) @ omega ) )
& ( ( in @ ( esk4_1 @ X369 ) @ omega )
| ~ ( in @ emptyset @ X369 )
| ~ ( in @ X371 @ omega )
| ( in @ X371 @ X369 ) )
& ( ( in @ ( esk4_1 @ X369 ) @ X369 )
| ~ ( in @ emptyset @ X369 )
| ~ ( in @ X371 @ omega )
| ( in @ X371 @ X369 ) )
& ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X369 ) @ ( esk4_1 @ X369 ) ) @ X369 )
| ~ ( in @ emptyset @ X369 )
| ~ ( in @ X371 @ omega )
| ( in @ X371 @ X369 ) )
& ( ( in @ ( esk8_3 @ X372 @ X373 @ X378 ) @ X373 )
| ~ ( in @ X378 @ ( esk7_2 @ X372 @ X373 ) )
| ( in @ ( esk5_2 @ X372 @ X373 ) @ X373 ) )
& ( ( X372 @ ( esk8_3 @ X372 @ X373 @ X378 ) @ X378 )
| ~ ( in @ X378 @ ( esk7_2 @ X372 @ X373 ) )
| ( in @ ( esk5_2 @ X372 @ X373 ) @ X373 ) )
& ( ~ ( in @ X381 @ X373 )
| ~ ( X372 @ X381 @ X380 )
| ( in @ X380 @ ( esk7_2 @ X372 @ X373 ) )
| ( in @ ( esk5_2 @ X372 @ X373 ) @ X373 ) )
& ( ( in @ ( esk8_3 @ X372 @ X373 @ X378 ) @ X373 )
| ~ ( in @ X378 @ ( esk7_2 @ X372 @ X373 ) )
| ( X372 @ ( esk5_2 @ X372 @ X373 ) @ ( esk6_3 @ X372 @ X373 @ X375 ) )
| ~ ( X372 @ ( esk5_2 @ X372 @ X373 ) @ X375 ) )
& ( ( X372 @ ( esk8_3 @ X372 @ X373 @ X378 ) @ X378 )
| ~ ( in @ X378 @ ( esk7_2 @ X372 @ X373 ) )
| ( X372 @ ( esk5_2 @ X372 @ X373 ) @ ( esk6_3 @ X372 @ X373 @ X375 ) )
| ~ ( X372 @ ( esk5_2 @ X372 @ X373 ) @ X375 ) )
& ( ~ ( in @ X381 @ X373 )
| ~ ( X372 @ X381 @ X380 )
| ( in @ X380 @ ( esk7_2 @ X372 @ X373 ) )
| ( X372 @ ( esk5_2 @ X372 @ X373 ) @ ( esk6_3 @ X372 @ X373 @ X375 ) )
| ~ ( X372 @ ( esk5_2 @ X372 @ X373 ) @ X375 ) )
& ( ( in @ ( esk8_3 @ X372 @ X373 @ X378 ) @ X373 )
| ~ ( in @ X378 @ ( esk7_2 @ X372 @ X373 ) )
| ( X375
!= ( esk6_3 @ X372 @ X373 @ X375 ) )
| ~ ( X372 @ ( esk5_2 @ X372 @ X373 ) @ X375 ) )
& ( ( X372 @ ( esk8_3 @ X372 @ X373 @ X378 ) @ X378 )
| ~ ( in @ X378 @ ( esk7_2 @ X372 @ X373 ) )
| ( X375
!= ( esk6_3 @ X372 @ X373 @ X375 ) )
| ~ ( X372 @ ( esk5_2 @ X372 @ X373 ) @ X375 ) )
& ( ~ ( in @ X381 @ X373 )
| ~ ( X372 @ X381 @ X380 )
| ( in @ X380 @ ( esk7_2 @ X372 @ X373 ) )
| ( X375
!= ( esk6_3 @ X372 @ X373 @ X375 ) )
| ~ ( X372 @ ( esk5_2 @ X372 @ X373 ) @ X375 ) )
& ( ( in @ ( esk9_1 @ X382 ) @ X382 )
| ~ ( in @ X383 @ X382 ) )
& ( ~ ( in @ X385 @ ( esk9_1 @ X382 ) )
| ~ ( in @ X385 @ X382 )
| ~ ( in @ X383 @ X382 ) )
& epred1_0
& descrp
& ( ~ ( in @ X388 @ X386 )
| ~ ( X387 @ X388 )
| ( in @ X388 @ ( dsetconstr @ X386 @ X387 ) ) )
& ( ~ ( in @ X391 @ ( dsetconstr @ X389 @ X390 ) )
| ( in @ X391 @ X389 ) )
& ( ~ ( in @ X394 @ ( dsetconstr @ X392 @ X393 ) )
| ( X393 @ X394 ) )
& ( ( X395 @ ( esk11_1 @ X395 ) )
| ( X395 @ ( esk10_2 @ X395 @ X396 ) )
| ~ ( X395 @ X396 ) )
& ( ~ ( X395 @ X399 )
| ( ( esk11_1 @ X395 )
= X399 )
| ( X395 @ ( esk10_2 @ X395 @ X396 ) )
| ~ ( X395 @ X396 ) )
& ( ( X395 @ ( esk11_1 @ X395 ) )
| ( X396
!= ( esk10_2 @ X395 @ X396 ) )
| ~ ( X395 @ X396 ) )
& ( ~ ( X395 @ X399 )
| ( ( esk11_1 @ X395 )
= X399 )
| ( X396
!= ( esk10_2 @ X395 @ X396 ) )
| ~ ( X395 @ X396 ) )
& ( ~ ( in @ X401 @ ( prop2set @ X400 ) )
| X400 )
& ( ~ ( in @ X402 @ emptyset )
| X403 )
& ( ~ ( in @ X404 @ emptyset )
| ~ $true )
& ~ ( in @ X405 @ emptyset )
& ( ( X406 @ ( esk12_2 @ X406 @ X407 ) )
| ~ ( X406 @ X407 )
| ( X406 @ ( esk13_1 @ X406 ) ) )
& ( ( X407
!= ( esk12_2 @ X406 @ X407 ) )
| ~ ( X406 @ X407 )
| ( X406 @ ( esk13_1 @ X406 ) ) )
& ( ( in @ ( esk15_2 @ X410 @ X411 ) @ X411 )
| ( X410 = X411 )
| ( in @ ( esk14_2 @ X410 @ X411 ) @ X410 ) )
& ( ~ ( in @ ( esk15_2 @ X410 @ X411 ) @ X410 )
| ( X410 = X411 )
| ( in @ ( esk14_2 @ X410 @ X411 ) @ X410 ) )
& ( ( in @ ( esk15_2 @ X410 @ X411 ) @ X411 )
| ( X410 = X411 )
| ~ ( in @ ( esk14_2 @ X410 @ X411 ) @ X411 ) )
& ( ~ ( in @ ( esk15_2 @ X410 @ X411 ) @ X410 )
| ( X410 = X411 )
| ~ ( in @ ( esk14_2 @ X410 @ X411 ) @ X411 ) )
& ( ( in @ ( esk16_1 @ X414 ) @ X414 )
| ( X414 = emptyset ) )
& ( ( in @ ( esk17_1 @ X416 ) @ X416 )
| ( X416 = emptyset ) )
& ( ~ ( in @ X420 @ ( dsetconstr @ X418 @ X419 ) )
| ( X419 @ X420 )
| ~ ( in @ X420 @ X418 ) )
& ( ~ ( X419 @ X420 )
| ( in @ X420 @ ( dsetconstr @ X418 @ X419 ) )
| ~ ( in @ X420 @ X418 ) )
& ( ( X421 = emptyset )
| ( in @ ( esk18_1 @ X421 ) @ X421 ) )
& ( ~ ( in @ X425 @ X423 )
| ~ ( X424 @ X425 )
| ( ( dsetconstr @ X423 @ X424 )
!= emptyset ) )
& ( ~ ( in @ X427 @ X426 )
| ( X426 != emptyset ) )
& ( in @ X428 @ ( setadjoin @ X428 @ X429 ) )
& ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
& ( ~ ( in @ X432 @ X431 )
| ( in @ X432 @ ( setadjoin @ X430 @ X431 ) ) )
& ( ( in @ X435 @ X434 )
| X436
| ( X435 = X433 )
| ~ ( in @ X435 @ ( setadjoin @ X433 @ X434 ) ) )
& ( ~ X436
| X436
| ( X435 = X433 )
| ~ ( in @ X435 @ ( setadjoin @ X433 @ X434 ) ) )
& ( ( in @ X435 @ X434 )
| X436
| ~ X436
| ~ ( in @ X435 @ ( setadjoin @ X433 @ X434 ) ) )
& ( ~ X436
| X436
| ~ X436
| ~ ( in @ X435 @ ( setadjoin @ X433 @ X434 ) ) )
& ( ~ ( in @ X439 @ ( setadjoin @ X437 @ X438 ) )
| ( X439 = X437 )
| ( in @ X439 @ X438 ) )
& ( ( dsetconstr @ X440
@ ^ [Z0: $i] : $true )
= X440 )
& ( ( in @ ( esk19_2 @ X441 @ X442 ) @ X442 )
| ( in @ X442 @ ( powerset @ X441 ) ) )
& ( ~ ( in @ ( esk19_2 @ X441 @ X442 ) @ X441 )
| ( in @ X442 @ ( powerset @ X441 ) ) )
& ( in @ emptyset @ ( powerset @ X444 ) )
& ( in @ emptyset @ ( powerset @ X445 ) )
& ( ~ ( in @ X447 @ ( powerset @ X446 ) )
| ~ ( in @ X448 @ X447 )
| ( in @ X448 @ X446 ) )
& ( ~ ( in @ X450 @ X451 )
| ~ ( in @ X451 @ X449 )
| ( in @ X450 @ ( setunion @ X449 ) ) )
& ( ( in @ X453 @ ( esk20_3 @ X452 @ X453 @ X454 ) )
| X454
| ~ ( in @ X453 @ ( setunion @ X452 ) ) )
& ( ( in @ ( esk20_3 @ X452 @ X453 @ X454 ) @ X452 )
| X454
| ~ ( in @ X453 @ ( setunion @ X452 ) ) )
& ( ~ X454
| X454
| ~ ( in @ X453 @ ( setunion @ X452 ) ) )
& ( ~ ( in @ X457 @ X456 )
| ( in @ X457 @ ( powerset @ ( setunion @ X456 ) ) ) )
& ( ~ ( X458 @ X462 )
| ( X462
= ( esk22_1 @ X458 ) )
| ( X458 @ ( esk21_2 @ X458 @ X459 ) )
| ~ ( X458 @ X459 ) )
& ( ( X463
!= ( esk22_1 @ X458 ) )
| ( X458 @ X463 )
| ( X458 @ ( esk21_2 @ X458 @ X459 ) )
| ~ ( X458 @ X459 ) )
& ( ~ ( X458 @ X462 )
| ( X462
= ( esk22_1 @ X458 ) )
| ( X459
!= ( esk21_2 @ X458 @ X459 ) )
| ~ ( X458 @ X459 ) )
& ( ( X463
!= ( esk22_1 @ X458 ) )
| ( X458 @ X463 )
| ( X459
!= ( esk21_2 @ X458 @ X459 ) )
| ~ ( X458 @ X459 ) )
& ( ( in @ ( esk23_1 @ X464 ) @ X464 )
| ( X464 = emptyset ) )
& ( $true
| ( X464 = emptyset ) )
& ( ~ ( in @ X466 @ ( setadjoin @ X467 @ emptyset ) )
| ( X466 = X467 ) )
& ( ( X468 = X469 )
| ~ ( in @ X469 @ ( setadjoin @ X468 @ emptyset ) ) )
& ( ( X470 != X471 )
| ( in @ X470 @ ( setadjoin @ X471 @ emptyset ) ) )
& ( ~ ( in @ X472 @ ( setadjoin @ X473 @ emptyset ) )
| ( in @ X473 @ ( setadjoin @ X472 @ emptyset ) ) )
& ( ~ ( in @ X476 @ ( setadjoin @ X474 @ ( setadjoin @ X475 @ emptyset ) ) )
| ( X476 = X474 )
| ( X476 = X475 ) )
& ( in @ X477 @ ( setadjoin @ X477 @ ( setadjoin @ X478 @ emptyset ) ) )
& ( in @ X480 @ ( setadjoin @ X479 @ ( setadjoin @ X480 @ emptyset ) ) )
& ( ~ ( in @ X483 @ X481 )
| ~ ( X482 @ X483 )
| ( ( dsetconstr @ X481 @ X482 )
!= emptyset )
| ~ $true )
& ( ~ ( in @ X485 @ emptyset )
| ( X484 @ X485 ) )
& ( ( in @ ( esk24_2 @ X486 @ X487 ) @ X486 )
| ~ ( in @ X488 @ X486 )
| ( X487 @ X488 ) )
& ( ~ ( X487 @ ( esk24_2 @ X486 @ X487 ) )
| ~ ( in @ X488 @ X486 )
| ( X487 @ X488 ) )
& ( ( in @ ( esk25_2 @ X490 @ X491 ) @ X490 )
| ~ ( in @ X493 @ X490 )
| ~ ( X491 @ X493 ) )
& ( ( X491 @ ( esk25_2 @ X490 @ X491 ) )
| ~ ( in @ X493 @ X490 )
| ~ ( X491 @ X493 ) )
& ( ( in @ ( esk26_2 @ X494 @ X495 ) @ X494 )
| ~ ( in @ X497 @ X494 )
| ~ ( X495 @ X497 ) )
& ( ( X495 @ ( esk26_2 @ X494 @ X495 ) )
| ~ ( in @ X497 @ X494 )
| ~ ( X495 @ X497 ) )
& ( ( in @ ( esk27_2 @ X498 @ X499 ) @ X498 )
| ~ ( in @ X500 @ X498 )
| ( X499 @ X500 ) )
& ( ~ ( X499 @ ( esk27_2 @ X498 @ X499 ) )
| ~ ( in @ X500 @ X498 )
| ( X499 @ X500 ) )
& ( ~ X502
| ( in @ emptyset @ ( prop2set @ X502 ) ) )
& prop2set2propI
& ( ~ ( in @ X505 @ esk28_0 )
| ~ ( epred2_0 @ X505 ) )
& ( in @ esk29_0 @ esk28_0 )
& ( epred2_0 @ esk29_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_81])])])])])])]) ).
thf(c_0_83,negated_conjecture,
! [X2: $i] :
( ~ ( in @ X2 @ esk28_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
thf(c_0_84,negated_conjecture,
in @ esk29_0 @ esk28_0,
inference(split_conjunct,[status(thm)],[c_0_82]) ).
thf(c_0_85,negated_conjecture,
epred2_0 @ esk29_0,
inference(split_conjunct,[status(thm)],[c_0_82]) ).
thf(c_0_86,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU542^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun May 19 17:30:08 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running higher-order theorem proving
% 0.20/0.48 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
% 0.38/0.55 # Version: 3.1.0-ho
% 0.38/0.55 # Preprocessing class: HSMSSLSSMLLCHSA.
% 0.38/0.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.38/0.55 # Starting new_ho_10 with 1500s (5) cores
% 0.38/0.55 # Starting sh5l with 300s (1) cores
% 0.38/0.55 # Starting new_bool_1 with 300s (1) cores
% 0.38/0.55 # Starting new_bool_2 with 300s (1) cores
% 0.38/0.55 # new_bool_1 with pid 16822 completed with status 0
% 0.38/0.55 # Result found by new_bool_1
% 0.38/0.55 # Preprocessing class: HSMSSLSSMLLCHSA.
% 0.38/0.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.38/0.55 # Starting new_ho_10 with 1500s (5) cores
% 0.38/0.55 # Starting sh5l with 300s (1) cores
% 0.38/0.55 # Starting new_bool_1 with 300s (1) cores
% 0.38/0.55 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.38/0.55 # Search class: HGHSM-FFMM31-SHSSMSBN
% 0.38/0.55 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.38/0.55 # Starting new_ho_10 with 181s (1) cores
% 0.38/0.55 # new_ho_10 with pid 16832 completed with status 0
% 0.38/0.55 # Result found by new_ho_10
% 0.38/0.55 # Preprocessing class: HSMSSLSSMLLCHSA.
% 0.38/0.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.38/0.55 # Starting new_ho_10 with 1500s (5) cores
% 0.38/0.55 # Starting sh5l with 300s (1) cores
% 0.38/0.55 # Starting new_bool_1 with 300s (1) cores
% 0.38/0.55 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.38/0.55 # Search class: HGHSM-FFMM31-SHSSMSBN
% 0.38/0.55 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.38/0.55 # Starting new_ho_10 with 181s (1) cores
% 0.38/0.55 # Preprocessing time : 0.006 s
% 0.38/0.55 # Presaturation interreduction done
% 0.38/0.55
% 0.38/0.55 # Proof found!
% 0.38/0.55 # SZS status Theorem
% 0.38/0.55 # SZS output start CNFRefutation
% See solution above
% 0.38/0.55 # Parsed axioms : 131
% 0.38/0.55 # Removed by relevancy pruning/SinE : 72
% 0.38/0.55 # Initial clauses : 114
% 0.38/0.55 # Removed in clause preprocessing : 5
% 0.38/0.55 # Initial clauses in saturation : 109
% 0.38/0.55 # Processed clauses : 123
% 0.38/0.55 # ...of these trivial : 3
% 0.38/0.55 # ...subsumed : 14
% 0.38/0.55 # ...remaining for further processing : 106
% 0.38/0.55 # Other redundant clauses eliminated : 5
% 0.38/0.55 # Clauses deleted for lack of memory : 0
% 0.38/0.55 # Backward-subsumed : 0
% 0.38/0.55 # Backward-rewritten : 1
% 0.38/0.55 # Generated clauses : 6
% 0.38/0.55 # ...of the previous two non-redundant : 4
% 0.38/0.55 # ...aggressively subsumed : 0
% 0.38/0.55 # Contextual simplify-reflections : 0
% 0.38/0.55 # Paramodulations : 1
% 0.38/0.55 # Factorizations : 0
% 0.38/0.55 # NegExts : 0
% 0.38/0.55 # Equation resolutions : 5
% 0.38/0.55 # Disequality decompositions : 0
% 0.38/0.55 # Total rewrite steps : 19
% 0.38/0.55 # ...of those cached : 12
% 0.38/0.55 # Propositional unsat checks : 0
% 0.38/0.55 # Propositional check models : 0
% 0.38/0.55 # Propositional check unsatisfiable : 0
% 0.38/0.55 # Propositional clauses : 0
% 0.38/0.55 # Propositional clauses after purity: 0
% 0.38/0.55 # Propositional unsat core size : 0
% 0.38/0.55 # Propositional preprocessing time : 0.000
% 0.38/0.55 # Propositional encoding time : 0.000
% 0.38/0.55 # Propositional solver time : 0.000
% 0.38/0.55 # Success case prop preproc time : 0.000
% 0.38/0.55 # Success case prop encoding time : 0.000
% 0.38/0.55 # Success case prop solver time : 0.000
% 0.38/0.55 # Current number of processed clauses : 10
% 0.38/0.55 # Positive orientable unit clauses : 7
% 0.38/0.55 # Positive unorientable unit clauses: 0
% 0.38/0.55 # Negative unit clauses : 2
% 0.38/0.55 # Non-unit-clauses : 1
% 0.38/0.55 # Current number of unprocessed clauses: 80
% 0.38/0.55 # ...number of literals in the above : 241
% 0.38/0.55 # Current number of archived formulas : 0
% 0.38/0.55 # Current number of archived clauses : 91
% 0.38/0.55 # Clause-clause subsumption calls (NU) : 1716
% 0.38/0.55 # Rec. Clause-clause subsumption calls : 678
% 0.38/0.55 # Non-unit clause-clause subsumptions : 12
% 0.38/0.55 # Unit Clause-clause subsumption calls : 3
% 0.38/0.55 # Rewrite failures with RHS unbound : 0
% 0.38/0.55 # BW rewrite match attempts : 2
% 0.38/0.55 # BW rewrite match successes : 1
% 0.38/0.55 # Condensation attempts : 123
% 0.38/0.55 # Condensation successes : 3
% 0.38/0.55 # Termbank termtop insertions : 16405
% 0.38/0.55 # Search garbage collected termcells : 5805
% 0.38/0.55
% 0.38/0.55 # -------------------------------------------------
% 0.38/0.55 # User time : 0.033 s
% 0.38/0.55 # System time : 0.015 s
% 0.38/0.55 # Total time : 0.048 s
% 0.38/0.55 # Maximum resident set size: 3320 pages
% 0.38/0.55
% 0.38/0.55 # -------------------------------------------------
% 0.38/0.55 # User time : 0.038 s
% 0.38/0.55 # System time : 0.019 s
% 0.38/0.55 # Total time : 0.058 s
% 0.38/0.55 # Maximum resident set size: 1864 pages
% 0.38/0.55 % E---3.1 exiting
% 0.63/0.55 % E exiting
%------------------------------------------------------------------------------