%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU544^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:44:55 AM UTC 2026
% Result : Theorem 3.15s 0.79s
% Output : CNFRefutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 63
% Syntax : Number of formulae : 1197 ( 413 unt; 0 typ; 62 def)
% Number of atoms : 9460 (3231 equ; 0 cnn)
% Maximal formula atoms : 62 ( 7 avg)
% Number of connectives : 20421 (4923 ~;3448 |; 126 &;11340 @)
% ( 32 <=>; 552 =>; 0 <=; 0 <~>)
% Maximal formula depth : 68 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 594 ( 594 >; 0 *; 0 +; 0 <<)
% Number of symbols : 125 ( 122 usr; 65 con; 0-4 aty)
% Number of variables : 4337 ( 122 ^;4093 !; 122 ?;4337 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_descr,type,
descr: ( $i > $o ) > $i ).
thf(tp_descrp,type,
descrp: $o ).
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrEL,type,
dsetconstrEL: $o ).
thf(tp_dsetconstrER,type,
dsetconstrER: $o ).
thf(tp_dsetconstrI,type,
dsetconstrI: $o ).
thf(tp_emptyE1,type,
emptyE1: $o ).
thf(tp_emptyI,type,
emptyI: $o ).
thf(tp_emptyInPowerset,type,
emptyInPowerset: $o ).
thf(tp_emptyinPowerset,type,
emptyinPowerset: $o ).
thf(tp_emptyinunitempty,type,
emptyinunitempty: $o ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_emptysetAx,type,
emptysetAx: $o ).
thf(tp_emptysetE,type,
emptysetE: $o ).
thf(tp_emptysetimpfalse,type,
emptysetimpfalse: $o ).
thf(tp_eqinunit,type,
eqinunit: $o ).
thf(tp_exu,type,
exu: ( $i > $o ) > $o ).
thf(tp_exuE1,type,
exuE1: $o ).
thf(tp_exuE2,type,
exuE2: $o ).
thf(tp_exuE3e,type,
exuE3e: $o ).
thf(tp_foundationAx,type,
foundationAx: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_noeltsimpempty,type,
noeltsimpempty: $o ).
thf(tp_nonempty,type,
nonempty: $i > $o ).
thf(tp_nonemptyE1,type,
nonemptyE1: $o ).
thf(tp_nonemptyI,type,
nonemptyI: $o ).
thf(tp_nonemptyI1,type,
nonemptyI1: $o ).
thf(tp_nonemptyImpWitness,type,
nonemptyImpWitness: $o ).
thf(tp_notdallE,type,
notdallE: $o ).
thf(tp_notdexE,type,
notdexE: $o ).
thf(tp_notinemptyset,type,
notinemptyset: $o ).
thf(tp_notinsingleton,type,
notinsingleton: $o ).
thf(tp_omega,type,
omega: $i ).
thf(tp_omega0Ax,type,
omega0Ax: $o ).
thf(tp_omegaIndAx,type,
omegaIndAx: $o ).
thf(tp_omegaSAx,type,
omegaSAx: $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetAx,type,
powersetAx: $o ).
thf(tp_powersetE,type,
powersetE: $o ).
thf(tp_powersetI,type,
powersetI: $o ).
thf(tp_prop2set,type,
prop2set: $o > $i ).
thf(tp_prop2set2propI,type,
prop2set2propI: $o ).
thf(tp_prop2setE,type,
prop2setE: $o ).
thf(tp_prop2setI,type,
prop2setI: $o ).
thf(tp_quantDeMorgan1,type,
quantDeMorgan1: $o ).
thf(tp_quantDeMorgan2,type,
quantDeMorgan2: $o ).
thf(tp_quantDeMorgan3,type,
quantDeMorgan3: $o ).
thf(tp_quantDeMorgan4,type,
quantDeMorgan4: $o ).
thf(tp_replAx,type,
replAx: $o ).
thf(tp_sK10_SY521,type,
sK10_SY521: $i ).
thf(tp_sK11_SY398,type,
sK11_SY398: $i > $i ).
thf(tp_sK12_SY483,type,
sK12_SY483: $i > $i ).
thf(tp_sK13_SY537,type,
sK13_SY537: ( $i > $o ) > $i > $i ).
thf(tp_sK14_SY554,type,
sK14_SY554: ( $i > $o ) > $i > $i ).
thf(tp_sK15_SY597,type,
sK15_SY597: $o > $i > $i > $i ).
thf(tp_sK16_SX0,type,
sK16_SX0: $i > $i > $i ).
thf(tp_sK17_SX0,type,
sK17_SX0: $i > $i > $i ).
thf(tp_sK18_SY460,type,
sK18_SY460: $i > $i > $i ).
thf(tp_sK19_SY558,type,
sK19_SY558: $i > $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i > $o ).
thf(tp_sK20_SY496,type,
sK20_SY496: $i > $i ).
thf(tp_sK21_SY550,type,
sK21_SY550: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK22_SY567,type,
sK22_SY567: $i > $i > $i ).
thf(tp_sK23_SY572,type,
sK23_SY572: $i > $i > $i ).
thf(tp_sK24_SY527,type,
sK24_SY527: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK25_SY536,type,
sK25_SY536: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK26_SY572,type,
sK26_SY572: $i > $i > $i ).
thf(tp_sK27_SY598,type,
sK27_SY598: $i > $i ).
thf(tp_sK28_SY599,type,
sK28_SY599: $i > ( $i > $o ) > $i ).
thf(tp_sK29_SY600,type,
sK29_SY600: $i > ( $i > $o ) > $i ).
thf(tp_sK2_SY402,type,
sK2_SY402: $i > $i ).
thf(tp_sK30_SY601,type,
sK30_SY601: $i > ( $i > $o ) > $i ).
thf(tp_sK31_SY604,type,
sK31_SY604: $i > ( $i > $o ) > $i ).
thf(tp_sK32_SY606,type,
sK32_SY606: $i > $i > $i ).
thf(tp_sK33_SY452,type,
sK33_SY452: $i > ( $i > $o ) > $i ).
thf(tp_sK34_SY464,type,
sK34_SY464: $i > ( $i > $o ) > $i ).
thf(tp_sK35_SY614,type,
sK35_SY614: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK36_SY481,type,
sK36_SY481: $i > ( $i > $o ) > $i ).
thf(tp_sK37_SY562,type,
sK37_SY562: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK38_SY452,type,
sK38_SY452: $i > ( $i > $o ) > $i ).
thf(tp_sK39_SY464,type,
sK39_SY464: $i > ( $i > $o ) > $i ).
thf(tp_sK3_SY512,type,
sK3_SY512: $i > $i ).
thf(tp_sK40_SY481,type,
sK40_SY481: $i > ( $i > $o ) > $i ).
thf(tp_sK41_SY550,type,
sK41_SY550: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK42_SY621,type,
sK42_SY621: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK43_SY550,type,
sK43_SY550: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK44_SY608,type,
sK44_SY608: $i > $i > $i > $i ).
thf(tp_sK45_SY608,type,
sK45_SY608: $i > $i > $i > $i ).
thf(tp_sK46_SY630,type,
sK46_SY630: $i > $i > $i > $i ).
thf(tp_sK47_SY643,type,
sK47_SY643: $i > $i > $i > $i ).
thf(tp_sK48_SY647,type,
sK48_SY647: $i > $i > $i > $i ).
thf(tp_sK49_SY639,type,
sK49_SY639: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK4_SY513,type,
sK4_SY513: $i > $i ).
thf(tp_sK50_SY641,type,
sK50_SY641: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK5_SY532,type,
sK5_SY532: ( $i > $o ) > $i > $i ).
thf(tp_sK6_SY534,type,
sK6_SY534: $i > $i > $i ).
thf(tp_sK7_SY547,type,
sK7_SY547: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK8_SY556,type,
sK8_SY556: $i > $i > $i ).
thf(tp_sK9_SY571,type,
sK9_SY571: $i > $i > $i ).
thf(tp_set2prop,type,
set2prop: $i > $o ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinAx,type,
setadjoinAx: $o ).
thf(tp_setadjoinE,type,
setadjoinE: $o ).
thf(tp_setadjoinIL,type,
setadjoinIL: $o ).
thf(tp_setadjoinIR,type,
setadjoinIR: $o ).
thf(tp_setadjoinOr,type,
setadjoinOr: $o ).
thf(tp_setbeta,type,
setbeta: $o ).
thf(tp_setext,type,
setext: $o ).
thf(tp_setextAx,type,
setextAx: $o ).
thf(tp_setoftrueEq,type,
setoftrueEq: $o ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunionAx,type,
setunionAx: $o ).
thf(tp_setunionE,type,
setunionE: $o ).
thf(tp_setunionI,type,
setunionI: $o ).
thf(tp_singletonsswitch,type,
singletonsswitch: $o ).
thf(tp_subPowSU,type,
subPowSU: $o ).
thf(tp_uniqinunit,type,
uniqinunit: $o ).
thf(tp_upairsetE,type,
upairsetE: $o ).
thf(tp_upairsetIL,type,
upairsetIL: $o ).
thf(tp_upairsetIR,type,
upairsetIR: $o ).
thf(tp_vacuousDall,type,
vacuousDall: $o ).
thf(tp_wellorderingAx,type,
wellorderingAx: $o ).
thf(descrp,definition,
( descrp
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( Xphi
@ ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrI,definition,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(emptyE1,definition,
( emptyE1
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(emptyI,definition,
( emptyI
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(emptyInPowerset,definition,
( emptyInPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,definition,
( emptyinPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyinunitempty,definition,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(eqinunit,definition,
( eqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(exuE1,definition,
( exuE1
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(exuE2,definition,
( exuE2
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(exuE3e,definition,
( exuE3e
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] : ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(noeltsimpempty,definition,
( noeltsimpempty
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyE1,definition,
( nonemptyE1
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] : ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI,definition,
( nonemptyI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( nonempty
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(nonemptyI1,definition,
( nonemptyI1
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ( nonempty @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyImpWitness,definition,
( nonemptyImpWitness
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& $true ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(notdallE,definition,
( notdallE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,definition,
( notdexE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(notinemptyset,definition,
( notinemptyset
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(notinsingleton,definition,
( notinsingleton
= ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaIndAx,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(powersetE,definition,
( powersetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(powersetI,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(prop2set2propI,definition,
( prop2set2propI
= ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(prop2setI,definition,
( prop2setI
= ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan1,definition,
( quantDeMorgan1
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,definition,
( quantDeMorgan2
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,definition,
( quantDeMorgan3
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,definition,
( quantDeMorgan4
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(replAx,definition,
( replAx
= ( ! [Xphi: $i > $i > $o,A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( exu
@ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xphi @ Xy @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(setadjoinE,definition,
( setadjoinE
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(setadjoinIR,definition,
( setadjoinIR
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinOr,definition,
( setadjoinOr
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setbeta,definition,
( setbeta
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(setext,definition,
( setext
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(setextAx,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(setoftrueEq,definition,
( setoftrueEq
= ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(setunionAx,definition,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(setunionE,definition,
( setunionE
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(setunionI,definition,
( setunionI
= ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(singletonsswitch,definition,
( singletonsswitch
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(subPowSU,definition,
( subPowSU
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(upairsetE,definition,
( upairsetE
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,definition,
( upairsetIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,definition,
( upairsetIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(vacuousDall,definition,
( vacuousDall
= ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(wellorderingAx,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(1,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
=> ( notdexE
=> ( notdallE
=> ! [Xphi: $i > $o] :
( ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(2,negated_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
=> ( notdexE
=> ( notdallE
=> ! [Xphi: $i > $o] :
( ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) )
=> ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) )
=> ( ! [SY23: $i > $i > $o,SY24: $i] :
( ! [SY25: $i] :
( ( in @ SY25 @ SY24 )
=> ? [SY27: $i] :
( ( SY23 @ SY25 @ SY27 )
& ! [SY28: $i] :
( ( SY23 @ SY25 @ SY28 )
=> ( SY27 = SY28 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY24 )
& ( SY23 @ Xy @ Xx ) ) ) )
=> ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) )
=> ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) )
=> ( ! [SY55: $i > $o] :
( ? [SY57: $i] :
( ( SY55 @ SY57 )
& ! [SY58: $i] :
( ( SY55 @ SY58 )
=> ( SY57 = SY58 ) ) )
=> ( SY55
@ ( descr
@ ^ [Xx: $i] : ( SY55 @ Xx ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) )
=> ( ! [SY72: $i > $o] :
( ? [SY74: $i] :
( ( SY72 @ SY74 )
& ! [SY75: $i] :
( ( SY72 @ SY75 )
=> ( SY74 = SY75 ) ) )
=> ? [Xx: $i] :
( ( SY72 @ Xx )
& ! [Xy: $i] :
( ( SY72 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [SY84: $i > $o] :
( ? [SY86: $i] :
( ( SY84 @ SY86 )
& ! [SY87: $i] :
( ( SY84 @ SY87 )
=> ( SY86 = SY87 ) ) )
=> ? [Xx: $i] : ( SY84 @ Xx ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) )
=> ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) )
=> ( ! [SY101: $i] :
( ( SY101 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY101 ) )
=> ( ! [SY103: $i,SY104: $i > $o,SY105: $i] :
( ( in @ SY105 @ SY103 )
=> ( ( SY104 @ SY105 )
=> ( ( dsetconstr @ SY103
@ ^ [Xy: $i] : ( SY104 @ Xy ) )
!= emptyset ) ) )
=> ( ! [SY107: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY107 )
=> ( SY107 != emptyset ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
=> ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) )
=> ( ! [SY140: $i > $o] :
( ? [SY142: $i] :
( ( SY140 @ SY142 )
& ! [SY143: $i] :
( ( SY140 @ SY143 )
=> ( SY142 = SY143 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY140 @ Xy )
<=> ( Xy = Xx ) ) )
=> ( ! [SY146: $i] :
( ( SY146 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY146 )
& $true ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) )
=> ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) )
=> ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) )
=> ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) )
=> ! [SY0: $i > $o] :
( ? [Xx: $i] :
( ( SY0 @ Xx )
& ! [Xy: $i] :
( ( SY0 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY4: $i] :
( ( SY0 @ SY4 )
& ! [SY5: $i] :
( ( SY0 @ SY5 )
=> ( SY4 = SY5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [SY23: $i > $i > $o,SY24: $i] :
( ! [SY25: $i] :
( ( in @ SY25 @ SY24 )
=> ? [SY27: $i] :
( ( SY23 @ SY25 @ SY27 )
& ! [SY28: $i] :
( ( SY23 @ SY25 @ SY28 )
=> ( SY27 = SY28 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY24 )
& ( SY23 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [SY55: $i > $o] :
( ? [SY57: $i] :
( ( SY55 @ SY57 )
& ! [SY58: $i] :
( ( SY55 @ SY58 )
=> ( SY57 = SY58 ) ) )
=> ( SY55
@ ( descr
@ ^ [Xx: $i] : ( SY55 @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [SY72: $i > $o] :
( ? [SY74: $i] :
( ( SY72 @ SY74 )
& ! [SY75: $i] :
( ( SY72 @ SY75 )
=> ( SY74 = SY75 ) ) )
=> ? [Xx: $i] :
( ( SY72 @ Xx )
& ! [Xy: $i] :
( ( SY72 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(24,plain,
( ( ! [SY84: $i > $o] :
( ? [SY86: $i] :
( ( SY84 @ SY86 )
& ! [SY87: $i] :
( ( SY84 @ SY87 )
=> ( SY86 = SY87 ) ) )
=> ? [Xx: $i] : ( SY84 @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(27,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(29,plain,
( ( ! [SY101: $i] :
( ( SY101 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY101 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [SY103: $i,SY104: $i > $o,SY105: $i] :
( ( in @ SY105 @ SY103 )
=> ( ( SY104 @ SY105 )
=> ( ( dsetconstr @ SY103
@ ^ [Xy: $i] : ( SY104 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [SY107: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY107 )
=> ( SY107 != emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(32,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(33,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(34,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(35,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(36,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(39,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(40,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(41,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(42,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(43,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(44,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(45,plain,
( ( ! [SY140: $i > $o] :
( ? [SY142: $i] :
( ( SY140 @ SY142 )
& ! [SY143: $i] :
( ( SY140 @ SY143 )
=> ( SY142 = SY143 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY140 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(46,plain,
( ( ! [SY146: $i] :
( ( SY146 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY146 )
& $true ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(47,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(48,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(49,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(50,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(51,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(52,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(53,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(54,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(55,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(56,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(57,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(58,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(59,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(60,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(61,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(62,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(63,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(64,plain,
( ( ! [SY0: $i > $o] :
( ? [Xx: $i] :
( ( SY0 @ Xx )
& ! [Xy: $i] :
( ( SY0 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY4: $i] :
( ( SY0 @ SY4 )
& ! [SY5: $i] :
( ( SY0 @ SY5 )
=> ( SY4 = SY5 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(65,plain,
( ( ~ ! [SY0: $i > $o] :
( ? [Xx: $i] :
( ( SY0 @ Xx )
& ! [Xy: $i] :
( ( SY0 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY4: $i] :
( ( SY0 @ SY4 )
& ! [SY5: $i] :
( ( SY0 @ SY5 )
=> ( SY4 = SY5 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[64]) ).
thf(66,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(67,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(68,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(69,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(70,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(71,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(72,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(73,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(74,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(75,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(76,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(77,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(78,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(79,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(80,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(81,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(82,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(83,plain,
( ( ! [SY146: $i] :
( ( SY146 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY146 )
& $true ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(84,plain,
( ( ! [SY140: $i > $o] :
( ? [SY142: $i] :
( ( SY140 @ SY142 )
& ! [SY143: $i] :
( ( SY140 @ SY143 )
=> ( SY142 = SY143 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY140 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(85,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(86,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(87,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(88,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(89,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(90,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(92,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(93,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(94,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(95,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(96,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(97,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(98,plain,
( ( ! [SY107: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY107 )
=> ( SY107 != emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(99,plain,
( ( ! [SY103: $i,SY104: $i > $o,SY105: $i] :
( ( in @ SY105 @ SY103 )
=> ( ( SY104 @ SY105 )
=> ( ( dsetconstr @ SY103
@ ^ [Xy: $i] : ( SY104 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(100,plain,
( ( ! [SY101: $i] :
( ( SY101 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY101 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(101,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(102,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(103,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(104,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(105,plain,
( ( ! [SY84: $i > $o] :
( ? [SY86: $i] :
( ( SY84 @ SY86 )
& ! [SY87: $i] :
( ( SY84 @ SY87 )
=> ( SY86 = SY87 ) ) )
=> ? [Xx: $i] : ( SY84 @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(106,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(107,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(108,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(109,plain,
( ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(110,plain,
( ( ! [SY72: $i > $o] :
( ? [SY74: $i] :
( ( SY72 @ SY74 )
& ! [SY75: $i] :
( ( SY72 @ SY75 )
=> ( SY74 = SY75 ) ) )
=> ? [Xx: $i] :
( ( SY72 @ Xx )
& ! [Xy: $i] :
( ( SY72 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(111,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(112,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(113,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(114,plain,
( ( ! [SY55: $i > $o] :
( ? [SY57: $i] :
( ( SY55 @ SY57 )
& ! [SY58: $i] :
( ( SY55 @ SY58 )
=> ( SY57 = SY58 ) ) )
=> ( SY55
@ ( descr
@ ^ [Xx: $i] : ( SY55 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(115,plain,
( ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(116,plain,
( ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(117,plain,
( ( ! [SY23: $i > $i > $o,SY24: $i] :
( ! [SY25: $i] :
( ( in @ SY25 @ SY24 )
=> ? [SY27: $i] :
( ( SY23 @ SY25 @ SY27 )
& ! [SY28: $i] :
( ( SY23 @ SY25 @ SY28 )
=> ( SY27 = SY28 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY24 )
& ( SY23 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(118,plain,
( ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(119,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(120,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(121,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(122,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(123,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(124,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(125,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(126,plain,
( ( ~ ! [SY0: $i > $o] :
( ? [Xx: $i] :
( ( SY0 @ Xx )
& ! [Xy: $i] :
( ( SY0 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY4: $i] :
( ( SY0 @ SY4 )
& ! [SY5: $i] :
( ( SY0 @ SY5 )
=> ( SY4 = SY5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(127,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ! [SX2: $o] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX1 @ SX3 )
| ~ ( in @ SX3 @ SX0 )
| SX2 )
| SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(128,plain,
( ( ~ ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(129,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(130,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(131,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(132,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX3 @ SX0 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX1 )
| ~ ( ~ ( ~ ( in @ SX2 @ SX4 )
| ( in @ SX3 @ SX4 ) )
| ~ ( ~ ( in @ SX3 @ SX4 )
| ( in @ SX2 @ SX4 ) ) ) )
| ( SX2 = SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX3 @ SX1 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ( in @ SX4 @ SX2 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SX2 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(133,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(134,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(135,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(136,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ( SX0
@ ( descr
@ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(137,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(138,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(139,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(140,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(141,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(142,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(143,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ( ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[75,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(144,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(145,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ( in @ SX1 @ emptyset )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(146,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ( ~ ( ~ ( SX0 @ SX2 )
| ( SX2 = SX1 ) )
| ~ ( ( SX2 != SX1 )
| ( SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(147,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(148,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(149,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(150,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(151,plain,
( ( ! [SX0: $i > $i > $o,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( SX0 @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( SX0 @ SX2 @ SX4 )
| ( SX3 = SX4 ) ) ) )
| ~ ! [SX2: $i] :
~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ~ ( SX0 @ SX4 @ SX3 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ~ ( SX0 @ SX4 @ SX3 ) )
| ( in @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(152,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(153,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(154,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[107,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(155,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(156,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 != emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(157,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(158,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(159,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(160,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( set2prop @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(161,plain,
( ( ! [SX0: $o,SX1: $i] :
( ~ ( in @ SX1 @ ( prop2set @ SX0 ) )
| SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[109,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(162,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ! [SX3: $o] :
( ~ ( ( SX2 != SX0 )
| SX3 )
| ~ ( ~ ( in @ SX2 @ SX1 )
| SX3 )
| SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(163,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(164,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(165,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( in @ emptyset @ SX0 )
| ~ ! [SX1: $i] :
( ~ ~ ( ~ ( in @ SX1 @ omega )
| ~ ( in @ SX1 @ SX0 ) )
| ( in @ ( setadjoin @ SX1 @ SX1 ) @ SX0 ) ) )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ omega )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(166,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(167,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( in @ emptyset @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(168,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) )
| ~ ( ~ ( SX1 @ SX2 )
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(169,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(170,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(171,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(172,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(173,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(174,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(175,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(176,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| ! [SX1: $o] : SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[108,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(177,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,foundationAx,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,powersetAx,powersetE,powersetI,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(178,plain,
! [SV1: $i] :
( ( ! [SY389: $i] : ( in @ SY389 @ ( setadjoin @ SV1 @ ( setadjoin @ SY389 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(179,plain,
! [SV2: $i] :
( ( ! [SY390: $i] : ( in @ SV2 @ ( setadjoin @ SV2 @ ( setadjoin @ SY390 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(180,plain,
! [SV3: $i] :
( ( in @ emptyset @ ( powerset @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(181,plain,
! [SV4: $i] :
( ( in @ emptyset @ ( powerset @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(182,plain,
! [SV5: $i] :
( ( ( dsetconstr @ SV5
@ ^ [Xx: $i] : $true )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(183,plain,
! [SV6: $i] :
( ( ! [SY392: $i] : ( in @ SV6 @ ( setadjoin @ SV6 @ SY392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(184,plain,
! [SV7: $i] :
( ( ~ ( in @ SV7 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(185,plain,
! [SV8: $i] :
( ( ~ ( in @ SV8 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(186,plain,
! [SV9: $i] :
( ( ! [SY393: $i] :
( ~ ( in @ SY393 @ ( setunion @ SV9 ) )
| ! [SY394: $o] :
( ~ ! [SY395: $i] :
( ~ ( in @ SY393 @ SY395 )
| ~ ( in @ SY395 @ SV9 )
| SY394 )
| SY394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(187,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(188,plain,
! [SV10: $i] :
( ( ! [SY396: $i,SY397: $i] :
( ~ ( in @ SY396 @ ( powerset @ SV10 ) )
| ~ ( in @ SY397 @ SY396 )
| ( in @ SY397 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(189,plain,
! [SV11: $i] :
( ( ~ ( ( SV11 != emptyset ) )
| ~ ! [SY398: $i] :
~ ~ ( ~ ( in @ SY398 @ SV11 )
| ~ $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(190,plain,
! [SV12: $i] :
( ( ! [SY399: $i > $o] :
( ~ ~ ! [SY400: $i] :
( ~ ( in @ SY400 @ SV12 )
| ( SY399 @ SY400 ) )
| ~ ! [SY401: $i] :
~ ~ ( ~ ( in @ SY401 @ SV12 )
| ~ ~ ( SY399 @ SY401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(191,plain,
! [SV13: $i] :
( ( ~ ! [SY402: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY403: $i] :
( ~ ( in @ SY403 @ SY402 )
| ! [SY404: $i] :
( ~ ( in @ SY404 @ SY403 )
| ( in @ SY404 @ SV13 ) ) )
| ~ ! [SY405: $i,SY406: $i] :
( ~ ~ ( ~ ( in @ SY405 @ SV13 )
| ~ ( in @ SY406 @ SV13 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY402 )
| ~ ( ~ ( ~ ( in @ SY405 @ SX4 )
| ( in @ SY406 @ SX4 ) )
| ~ ( ~ ( in @ SY406 @ SX4 )
| ( in @ SY405 @ SX4 ) ) ) )
| ( SY405 = SY406 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY402 )
| ~ ( in @ SX3 @ SY402 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY412: $i] :
( ~ ~ ( ~ ! [SY413: $i] :
( ~ ( in @ SY413 @ SY412 )
| ( in @ SY413 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY412 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY402 )
| ~ ( in @ SX4 @ SY412 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY412 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY402 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(192,plain,
! [SV14: $i] :
( ( ! [SY420: $i,SY421: $i] :
( ~ ( in @ SY421 @ SY420 )
| ( in @ SY421 @ ( setadjoin @ SV14 @ SY420 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(193,plain,
! [SV15: $i] :
( ( ~ ( in @ SV15 @ omega )
| ( in @ ( setadjoin @ SV15 @ SV15 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(194,plain,
! [SV16: $i] :
( ( ! [SY422: $i,SY423: $i] :
( ~ ( in @ SY423 @ ( setadjoin @ SV16 @ SY422 ) )
| ( SY423 = SV16 )
| ( in @ SY423 @ SY422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(195,plain,
! [SV17: $i > $o] :
( ( ~ ~ ! [SY424: $i] :
~ ~ ( ~ ( SV17 @ SY424 )
| ~ ! [SY425: $i] :
( ~ ( SV17 @ SY425 )
| ( SY424 = SY425 ) ) )
| ( SV17
@ ( descr
@ ^ [SY426: $i] : ( SV17 @ SY426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(196,plain,
! [SV18: $i] :
( ( ! [SY427: $i > $o,SY428: $i] :
( ~ ( in @ SY428 @ SV18 )
| ~ ( SY427 @ SY428 )
| ( ( dsetconstr @ SV18
@ ^ [SX3: $i] : ( SY427 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(197,plain,
! [SV19: $i] :
( ( ! [SY430: $i > $o] :
( ~ ! [SY431: $i] :
( ~ ( in @ SY431 @ SV19 )
| ~ ( SY430 @ SY431 ) )
| ~ ~ ! [SY432: $i] :
~ ~ ( ~ ( in @ SY432 @ SV19 )
| ~ ( SY430 @ SY432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(198,plain,
! [SV20: $i] :
( ( ! [SY433: $i] :
( ~ ! [SY434: $i] :
( ~ ( in @ SY434 @ SY433 )
| ( in @ SY434 @ SV20 ) )
| ( in @ SY433 @ ( powerset @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(199,plain,
! [SV21: $i] :
( ( ! [SY435: $i > $o] :
( ~ ~ ! [SY436: $i] :
( ~ ( in @ SY436 @ SV21 )
| ( SY435 @ SY436 ) )
| ~ ! [SY437: $i] :
~ ~ ( ~ ( in @ SY437 @ SV21 )
| ~ ~ ( SY435 @ SY437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(200,plain,
! [SV22: $i] :
( ( ! [SY438: $i > $o] :
( ~ ~ ~ ! [SY439: $i] :
~ ~ ( ~ ( in @ SY439 @ SV22 )
| ~ ( SY438 @ SY439 ) )
| ! [SY440: $i] :
( ~ ( in @ SY440 @ SV22 )
| ~ ( SY438 @ SY440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(201,plain,
! [SV23: $i] :
( ( ! [SY441: $i,SY442: $i] :
~ ( ~ ( ~ ( in @ SY442 @ ( setadjoin @ SV23 @ SY441 ) )
| ( SY442 = SV23 )
| ( in @ SY442 @ SY441 ) )
| ~ ( ~ ( ( SY442 = SV23 )
| ( in @ SY442 @ SY441 ) )
| ( in @ SY442 @ ( setadjoin @ SV23 @ SY441 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(202,plain,
! [SV24: $i] :
( ( ! [SY443: $i > $o] :
( ~ ~ ! [SY444: $i] :
~ ~ ( ~ ( in @ SY444 @ SV24 )
| ~ ( SY443 @ SY444 ) )
| ( ( dsetconstr @ SV24
@ ^ [SX2: $i] : ( SY443 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(203,plain,
! [SV25: $i] :
( ( ! [SY446: $i > $o,SY447: $i] :
( ~ ( in @ SY447
@ ( dsetconstr @ SV25
@ ^ [SX3: $i] : ( SY446 @ SX3 ) ) )
| ( in @ SY447 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(204,plain,
! [SV26: $i > $o] :
( ( ! [SY449: $i] :
( ~ ( in @ SY449 @ emptyset )
| ( SV26 @ SY449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(205,plain,
! [SV27: $i > $o] :
( ( ~ ~ ! [SY450: $i] :
~ ~ ( ~ ( SV27 @ SY450 )
| ~ ! [SY451: $i] :
( ~ ( SV27 @ SY451 )
| ( SY450 = SY451 ) ) )
| ~ ! [SY452: $i] :
~ ! [SY453: $i] :
~ ( ~ ( ~ ( SV27 @ SY453 )
| ( SY453 = SY452 ) )
| ~ ( ( SY453 != SY452 )
| ( SV27 @ SY453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(206,plain,
! [SV28: $i] :
( ( ! [SY454: $i > $o,SY455: $i] :
( ~ ( in @ SY455 @ SV28 )
| ~ ( SY454 @ SY455 )
| ( in @ SY455
@ ( dsetconstr @ SV28
@ ^ [SX3: $i] : ( SY454 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(207,plain,
! [SV29: $i] :
( ( ! [SY457: $i,SY458: $i] :
( ~ ( in @ SY457 @ SY458 )
| ~ ( in @ SY458 @ SV29 )
| ( in @ SY457 @ ( setunion @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(208,plain,
! [SV30: $i] :
( ( ~ ~ ! [SY459: $i] :
~ ( in @ SY459 @ SV30 )
| ~ ! [SY460: $i] :
~ ~ ( ~ ( in @ SY460 @ SV30 )
| ~ ~ ~ ! [SY461: $i] :
~ ~ ( ~ ( in @ SY461 @ SY460 )
| ~ ( in @ SY461 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(209,plain,
! [SV31: $i > $o] :
( ( ~ ~ ! [SY462: $i] :
~ ~ ( ~ ( SV31 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV31 @ SY463 )
| ( SY462 = SY463 ) ) )
| ~ ! [SY464: $i] :
~ ~ ( ~ ( SV31 @ SY464 )
| ~ ! [SY465: $i] :
( ~ ( SV31 @ SY465 )
| ( SY464 = SY465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(210,plain,
! [SV32: $i > $i > $o] :
( ( ! [SY466: $i] :
( ~ ! [SY467: $i] :
( ~ ( in @ SY467 @ SY466 )
| ~ ! [SY468: $i] :
~ ~ ( ~ ( SV32 @ SY467 @ SY468 )
| ~ ! [SY469: $i] :
( ~ ( SV32 @ SY467 @ SY469 )
| ( SY468 = SY469 ) ) ) )
| ~ ! [SY470: $i] :
~ ! [SY471: $i] :
~ ( ~ ( ~ ( in @ SY471 @ SY470 )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( in @ SY472 @ SY466 )
| ~ ( SV32 @ SY472 @ SY471 ) ) )
| ~ ( ~ ~ ! [SY473: $i] :
~ ~ ( ~ ( in @ SY473 @ SY466 )
| ~ ( SV32 @ SY473 @ SY471 ) )
| ( in @ SY471 @ SY470 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(211,plain,
! [SV33: $i] :
( ( ! [SY474: $i > $o] :
( ~ ~ ~ ! [SY475: $i] :
~ ~ ( ~ ( in @ SY475 @ SV33 )
| ~ ( SY474 @ SY475 ) )
| ! [SY476: $i] :
( ~ ( in @ SY476 @ SV33 )
| ~ ( SY474 @ SY476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(212,plain,
! [SV34: $i] :
( ( ! [SY477: $i] :
( ~ ! [SY478: $i] :
~ ( ~ ( ~ ( in @ SY478 @ SV34 )
| ( in @ SY478 @ SY477 ) )
| ~ ( ~ ( in @ SY478 @ SY477 )
| ( in @ SY478 @ SV34 ) ) )
| ( SV34 = SY477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(213,plain,
! [SV35: $i] :
( ( ~ ( in @ SV35 @ emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(214,plain,
! [SV36: $i > $o] :
( ( ~ ~ ! [SY479: $i] :
~ ~ ( ~ ( SV36 @ SY479 )
| ~ ! [SY480: $i] :
( ~ ( SV36 @ SY480 )
| ( SY479 = SY480 ) ) )
| ~ ! [SY481: $i] :
~ ( SV36 @ SY481 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(215,plain,
! [SV37: $i] :
( ( ~ ~ ! [SY482: $i] :
~ ( in @ SY482 @ SV37 )
| ( SV37 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(216,plain,
! [SV38: $i] :
( ( ~ ( ( SV38 != emptyset ) )
| ~ ! [SY483: $i] :
~ ( in @ SY483 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(217,plain,
! [SV39: $i] :
( ( ! [SY484: $i] :
( ~ ( in @ SY484 @ SV39 )
| ( in @ SY484 @ ( powerset @ ( setunion @ SV39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(218,plain,
! [SV40: $i] :
( ( ! [SY485: $i] :
~ ( ~ ( ~ ( in @ SY485 @ ( powerset @ SV40 ) )
| ! [SY486: $i] :
( ~ ( in @ SY486 @ SY485 )
| ( in @ SY486 @ SV40 ) ) )
| ~ ( ~ ! [SY487: $i] :
( ~ ( in @ SY487 @ SY485 )
| ( in @ SY487 @ SV40 ) )
| ( in @ SY485 @ ( powerset @ SV40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(219,plain,
! [SV41: $o] :
( ( ~ SV41
| ( set2prop @ ( prop2set @ SV41 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[160]) ).
thf(220,plain,
( ( ~ $true
| ( set2prop @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[160]) ).
thf(221,plain,
( ( ~ $false
| ( set2prop @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[160]) ).
thf(222,plain,
! [SV42: $o] :
( ( ! [SY488: $i] :
( ~ ( in @ SY488 @ ( prop2set @ SV42 ) )
| SV42 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[161]) ).
thf(223,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $true ) )
| $true ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[161]) ).
thf(224,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $false ) )
| $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[161]) ).
thf(225,plain,
! [SV43: $i] :
( ( ! [SY489: $i,SY490: $i] :
( ~ ( in @ SY490 @ ( setadjoin @ SV43 @ SY489 ) )
| ! [SY491: $o] :
( ~ ( ( SY490 != SV43 )
| SY491 )
| ~ ( ~ ( in @ SY490 @ SY489 )
| SY491 )
| SY491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(226,plain,
! [SV44: $i] :
( ( ! [SY492: $i > $o] :
( ~ ~ ! [SY493: $i] :
~ ~ ( ~ ( in @ SY493 @ SV44 )
| ~ ~ ( SY492 @ SY493 ) )
| ~ ! [SY494: $i] :
( ~ ( in @ SY494 @ SV44 )
| ( SY492 @ SY494 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(227,plain,
! [SV45: $i] :
( ( ! [SY495: $i] :
( ~ ( ( SV45 != SY495 ) )
| ~ ( in @ SY495 @ ( setadjoin @ SV45 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(228,plain,
! [SV46: $i] :
( ( ~ ~ ( ~ ( in @ emptyset @ SV46 )
| ~ ! [SY496: $i] :
( ~ ~ ( ~ ( in @ SY496 @ omega )
| ~ ( in @ SY496 @ SV46 ) )
| ( in @ ( setadjoin @ SY496 @ SY496 ) @ SV46 ) ) )
| ! [SY497: $i] :
( ~ ( in @ SY497 @ omega )
| ( in @ SY497 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(229,plain,
! [SV47: $i] :
( ( ! [SY498: $i,SY499: $i] :
( ~ ( in @ SY499 @ ( setadjoin @ SV47 @ ( setadjoin @ SY498 @ emptyset ) ) )
| ( SY499 = SV47 )
| ( SY499 = SY498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(230,plain,
! [SV48: $o] :
( ( ~ SV48
| ( in @ emptyset @ ( prop2set @ SV48 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[167]) ).
thf(231,plain,
( ( ~ $true
| ( in @ emptyset @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[167]) ).
thf(232,plain,
( ( ~ $false
| ( in @ emptyset @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[167]) ).
thf(233,plain,
! [SV49: $i] :
( ( ! [SY500: $i > $o,SY501: $i] :
( ~ ( in @ SY501 @ SV49 )
| ~ ( ~ ( ~ ( in @ SY501
@ ( dsetconstr @ SV49
@ ^ [SX3: $i] : ( SY500 @ SX3 ) ) )
| ( SY500 @ SY501 ) )
| ~ ( ~ ( SY500 @ SY501 )
| ( in @ SY501
@ ( dsetconstr @ SV49
@ ^ [SX3: $i] : ( SY500 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(234,plain,
! [SV50: $i] :
( ( ! [SY504: $i] :
~ ( ~ ( ~ ( in @ SY504 @ ( setunion @ SV50 ) )
| ~ ! [SY505: $i] :
~ ~ ( ~ ( in @ SY504 @ SY505 )
| ~ ( in @ SY505 @ SV50 ) ) )
| ~ ( ~ ~ ! [SY506: $i] :
~ ~ ( ~ ( in @ SY504 @ SY506 )
| ~ ( in @ SY506 @ SV50 ) )
| ( in @ SY504 @ ( setunion @ SV50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(235,plain,
! [SV51: $i] :
( ( ! [SY507: $i] :
( ~ ( in @ SV51 @ ( setadjoin @ SY507 @ emptyset ) )
| ( in @ SY507 @ ( setadjoin @ SV51 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(236,plain,
! [SV52: $i] :
( ( ! [SY508: $i] :
( ~ ( in @ SV52 @ ( setadjoin @ SY508 @ emptyset ) )
| ( SV52 = SY508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(237,plain,
! [SV53: $i] :
( ( ! [SY509: $i > $o,SY510: $i] :
( ~ ( in @ SY510
@ ( dsetconstr @ SV53
@ ^ [SX3: $i] : ( SY509 @ SX3 ) ) )
| ( SY509 @ SY510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(238,plain,
! [SV54: $i] :
( ( ~ ! [SY512: $i] :
~ ( in @ SY512 @ SV54 )
| ( SV54 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(239,plain,
! [SV55: $i] :
( ( ~ ! [SY513: $i] :
~ ( in @ SY513 @ SV55 )
| ( SV55 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(240,plain,
! [SV56: $i] :
( ( ! [SY514: $i] :
( ~ ! [SY515: $i] :
( ~ ( in @ SY515 @ SV56 )
| ( in @ SY515 @ SY514 ) )
| ~ ! [SY516: $i] :
( ~ ( in @ SY516 @ SY514 )
| ( in @ SY516 @ SV56 ) )
| ( SV56 = SY514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(241,plain,
! [SV57: $i] :
( ( ~ ( in @ SV57 @ emptyset )
| ! [SX1: $o] : SX1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(242,plain,
! [SV58: $i] :
( ( ! [SY518: $i] :
( ( SV58 != SY518 )
| ( in @ SV58 @ ( setadjoin @ SY518 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(243,plain,
! [SV1: $i,SV59: $i] :
( ( in @ SV59 @ ( setadjoin @ SV1 @ ( setadjoin @ SV59 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(244,plain,
! [SV60: $i,SV2: $i] :
( ( in @ SV2 @ ( setadjoin @ SV2 @ ( setadjoin @ SV60 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(245,plain,
! [SV61: $i,SV6: $i] :
( ( in @ SV6 @ ( setadjoin @ SV6 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(246,plain,
! [SV7: $i] :
( ( in @ SV7 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(247,plain,
! [SV8: $i] :
( ( in @ SV8 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(248,plain,
! [SV9: $i,SV62: $i] :
( ( ~ ( in @ SV62 @ ( setunion @ SV9 ) )
| ! [SY519: $o] :
( ~ ! [SY520: $i] :
( ~ ( in @ SV62 @ SY520 )
| ~ ( in @ SY520 @ SV9 )
| SY519 )
| SY519 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(249,plain,
( ( ~ ~ ! [SY521: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY521 )
| ~ ! [SY522: $i] :
( ~ ( sK1_SX0 @ SY522 )
| ( SY521 = SY522 ) ) )
| ~ ! [SY523: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY523 )
| ~ ! [SY524: $i] :
( ~ ( sK1_SX0 @ SY524 )
| ( SY523 = SY524 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[187]) ).
thf(250,plain,
! [SV10: $i,SV63: $i] :
( ( ! [SY525: $i] :
( ~ ( in @ SV63 @ ( powerset @ SV10 ) )
| ~ ( in @ SY525 @ SV63 )
| ( in @ SY525 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(251,plain,
! [SV11: $i] :
( ( ( ~ ( ( SV11 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY398: $i] :
~ ~ ( ~ ( in @ SY398 @ SV11 )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(252,plain,
! [SV64: $i > $o,SV12: $i] :
( ( ~ ~ ! [SY526: $i] :
( ~ ( in @ SY526 @ SV12 )
| ( SV64 @ SY526 ) )
| ~ ! [SY527: $i] :
~ ~ ( ~ ( in @ SY527 @ SV12 )
| ~ ~ ( SV64 @ SY527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(253,plain,
! [SV13: $i] :
( ( ! [SY402: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY403: $i] :
( ~ ( in @ SY403 @ SY402 )
| ! [SY404: $i] :
( ~ ( in @ SY404 @ SY403 )
| ( in @ SY404 @ SV13 ) ) )
| ~ ! [SY405: $i,SY406: $i] :
( ~ ~ ( ~ ( in @ SY405 @ SV13 )
| ~ ( in @ SY406 @ SV13 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY402 )
| ~ ( ~ ( ~ ( in @ SY405 @ SX4 )
| ( in @ SY406 @ SX4 ) )
| ~ ( ~ ( in @ SY406 @ SX4 )
| ( in @ SY405 @ SX4 ) ) ) )
| ( SY405 = SY406 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY402 )
| ~ ( in @ SX3 @ SY402 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY412: $i] :
( ~ ~ ( ~ ! [SY413: $i] :
( ~ ( in @ SY413 @ SY412 )
| ( in @ SY413 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY412 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY402 )
| ~ ( in @ SX4 @ SY412 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY412 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY402 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(254,plain,
! [SV14: $i,SV65: $i] :
( ( ! [SY528: $i] :
( ~ ( in @ SY528 @ SV65 )
| ( in @ SY528 @ ( setadjoin @ SV14 @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(255,plain,
! [SV15: $i] :
( ( ( ~ ( in @ SV15 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV15 @ SV15 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(256,plain,
! [SV66: $i,SV16: $i] :
( ( ! [SY529: $i] :
( ~ ( in @ SY529 @ ( setadjoin @ SV16 @ SV66 ) )
| ( SY529 = SV16 )
| ( in @ SY529 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(257,plain,
! [SV17: $i > $o] :
( ( ( ~ ~ ! [SY424: $i] :
~ ~ ( ~ ( SV17 @ SY424 )
| ~ ! [SY425: $i] :
( ~ ( SV17 @ SY425 )
| ( SY424 = SY425 ) ) ) )
= $true )
| ( ( SV17
@ ( descr
@ ^ [SY426: $i] : ( SV17 @ SY426 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(258,plain,
! [SV67: $i > $o,SV18: $i] :
( ( ! [SY530: $i] :
( ~ ( in @ SY530 @ SV18 )
| ~ ( SV67 @ SY530 )
| ( ( dsetconstr @ SV18
@ ^ [SY531: $i] : ( SV67 @ SY531 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(259,plain,
! [SV68: $i > $o,SV19: $i] :
( ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SV19 )
| ~ ( SV68 @ SY532 ) )
| ~ ~ ! [SY533: $i] :
~ ~ ( ~ ( in @ SY533 @ SV19 )
| ~ ( SV68 @ SY533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(260,plain,
! [SV20: $i,SV69: $i] :
( ( ~ ! [SY534: $i] :
( ~ ( in @ SY534 @ SV69 )
| ( in @ SY534 @ SV20 ) )
| ( in @ SV69 @ ( powerset @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(261,plain,
! [SV70: $i > $o,SV21: $i] :
( ( ~ ~ ! [SY535: $i] :
( ~ ( in @ SY535 @ SV21 )
| ( SV70 @ SY535 ) )
| ~ ! [SY536: $i] :
~ ~ ( ~ ( in @ SY536 @ SV21 )
| ~ ~ ( SV70 @ SY536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(262,plain,
! [SV71: $i > $o,SV22: $i] :
( ( ~ ~ ~ ! [SY537: $i] :
~ ~ ( ~ ( in @ SY537 @ SV22 )
| ~ ( SV71 @ SY537 ) )
| ! [SY538: $i] :
( ~ ( in @ SY538 @ SV22 )
| ~ ( SV71 @ SY538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(263,plain,
! [SV72: $i,SV23: $i] :
( ( ! [SY539: $i] :
~ ( ~ ( ~ ( in @ SY539 @ ( setadjoin @ SV23 @ SV72 ) )
| ( SY539 = SV23 )
| ( in @ SY539 @ SV72 ) )
| ~ ( ~ ( ( SY539 = SV23 )
| ( in @ SY539 @ SV72 ) )
| ( in @ SY539 @ ( setadjoin @ SV23 @ SV72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(264,plain,
! [SV73: $i > $o,SV24: $i] :
( ( ~ ~ ! [SY540: $i] :
~ ~ ( ~ ( in @ SY540 @ SV24 )
| ~ ( SV73 @ SY540 ) )
| ( ( dsetconstr @ SV24
@ ^ [SY541: $i] : ( SV73 @ SY541 ) )
!= emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(265,plain,
! [SV74: $i > $o,SV25: $i] :
( ( ! [SY542: $i] :
( ~ ( in @ SY542
@ ( dsetconstr @ SV25
@ ^ [SY543: $i] : ( SV74 @ SY543 ) ) )
| ( in @ SY542 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(266,plain,
! [SV26: $i > $o,SV75: $i] :
( ( ~ ( in @ SV75 @ emptyset )
| ( SV26 @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(267,plain,
! [SV27: $i > $o] :
( ( ( ~ ~ ! [SY450: $i] :
~ ~ ( ~ ( SV27 @ SY450 )
| ~ ! [SY451: $i] :
( ~ ( SV27 @ SY451 )
| ( SY450 = SY451 ) ) ) )
= $true )
| ( ( ~ ! [SY452: $i] :
~ ! [SY453: $i] :
~ ( ~ ( ~ ( SV27 @ SY453 )
| ( SY453 = SY452 ) )
| ~ ( ( SY453 != SY452 )
| ( SV27 @ SY453 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(268,plain,
! [SV76: $i > $o,SV28: $i] :
( ( ! [SY544: $i] :
( ~ ( in @ SY544 @ SV28 )
| ~ ( SV76 @ SY544 )
| ( in @ SY544
@ ( dsetconstr @ SV28
@ ^ [SY545: $i] : ( SV76 @ SY545 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(269,plain,
! [SV29: $i,SV77: $i] :
( ( ! [SY546: $i] :
( ~ ( in @ SV77 @ SY546 )
| ~ ( in @ SY546 @ SV29 )
| ( in @ SV77 @ ( setunion @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(270,plain,
! [SV30: $i] :
( ( ( ~ ~ ! [SY459: $i] :
~ ( in @ SY459 @ SV30 ) )
= $true )
| ( ( ~ ! [SY460: $i] :
~ ~ ( ~ ( in @ SY460 @ SV30 )
| ~ ~ ~ ! [SY461: $i] :
~ ~ ( ~ ( in @ SY461 @ SY460 )
| ~ ( in @ SY461 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(271,plain,
! [SV31: $i > $o] :
( ( ( ~ ~ ! [SY462: $i] :
~ ~ ( ~ ( SV31 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV31 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true )
| ( ( ~ ! [SY464: $i] :
~ ~ ( ~ ( SV31 @ SY464 )
| ~ ! [SY465: $i] :
( ~ ( SV31 @ SY465 )
| ( SY464 = SY465 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(272,plain,
! [SV32: $i > $i > $o,SV78: $i] :
( ( ~ ! [SY547: $i] :
( ~ ( in @ SY547 @ SV78 )
| ~ ! [SY468: $i] :
~ ~ ( ~ ( SV32 @ SY547 @ SY468 )
| ~ ! [SY469: $i] :
( ~ ( SV32 @ SY547 @ SY469 )
| ( SY468 = SY469 ) ) ) )
| ~ ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(273,plain,
! [SV79: $i > $o,SV33: $i] :
( ( ~ ~ ~ ! [SY554: $i] :
~ ~ ( ~ ( in @ SY554 @ SV33 )
| ~ ( SV79 @ SY554 ) )
| ! [SY555: $i] :
( ~ ( in @ SY555 @ SV33 )
| ~ ( SV79 @ SY555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(274,plain,
! [SV80: $i,SV34: $i] :
( ( ~ ! [SY556: $i] :
~ ( ~ ( ~ ( in @ SY556 @ SV34 )
| ( in @ SY556 @ SV80 ) )
| ~ ( ~ ( in @ SY556 @ SV80 )
| ( in @ SY556 @ SV34 ) ) )
| ( SV34 = SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(275,plain,
! [SV35: $i] :
( ( ( ~ ( in @ SV35 @ emptyset ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(276,plain,
! [SV36: $i > $o] :
( ( ( ~ ~ ! [SY479: $i] :
~ ~ ( ~ ( SV36 @ SY479 )
| ~ ! [SY480: $i] :
( ~ ( SV36 @ SY480 )
| ( SY479 = SY480 ) ) ) )
= $true )
| ( ( ~ ! [SY481: $i] :
~ ( SV36 @ SY481 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(277,plain,
! [SV37: $i] :
( ( ( ~ ~ ! [SY482: $i] :
~ ( in @ SY482 @ SV37 ) )
= $true )
| ( ( SV37 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(278,plain,
! [SV38: $i] :
( ( ( ~ ( ( SV38 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY483: $i] :
~ ( in @ SY483 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(279,plain,
! [SV39: $i,SV81: $i] :
( ( ~ ( in @ SV81 @ SV39 )
| ( in @ SV81 @ ( powerset @ ( setunion @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(280,plain,
! [SV40: $i,SV82: $i] :
( ( ~ ( ~ ( ~ ( in @ SV82 @ ( powerset @ SV40 ) )
| ! [SY557: $i] :
( ~ ( in @ SY557 @ SV82 )
| ( in @ SY557 @ SV40 ) ) )
| ~ ( ~ ! [SY558: $i] :
( ~ ( in @ SY558 @ SV82 )
| ( in @ SY558 @ SV40 ) )
| ( in @ SV82 @ ( powerset @ SV40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(281,plain,
! [SV41: $o] :
( ( ( ~ SV41 ) = $true )
| ( ( set2prop @ ( prop2set @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(282,plain,
( ( ( ~ $true ) = $true )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(283,plain,
( ( ( ~ $false ) = $true )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(284,plain,
! [SV42: $o,SV83: $i] :
( ( ~ ( in @ SV83 @ ( prop2set @ SV42 ) )
| SV42 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(285,plain,
! [SV84: $i] :
( ( ~ ( in @ SV84 @ ( prop2set @ $true ) )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(286,plain,
! [SV85: $i] :
( ( ~ ( in @ SV85 @ ( prop2set @ $false ) )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(287,plain,
! [SV86: $i,SV43: $i] :
( ( ! [SY559: $i] :
( ~ ( in @ SY559 @ ( setadjoin @ SV43 @ SV86 ) )
| ! [SY560: $o] :
( ~ ( ( SY559 != SV43 )
| SY560 )
| ~ ( ~ ( in @ SY559 @ SV86 )
| SY560 )
| SY560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(288,plain,
! [SV87: $i > $o,SV44: $i] :
( ( ~ ~ ! [SY561: $i] :
~ ~ ( ~ ( in @ SY561 @ SV44 )
| ~ ~ ( SV87 @ SY561 ) )
| ~ ! [SY562: $i] :
( ~ ( in @ SY562 @ SV44 )
| ( SV87 @ SY562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(289,plain,
! [SV88: $i,SV45: $i] :
( ( ~ ( ( SV45 != SV88 ) )
| ~ ( in @ SV88 @ ( setadjoin @ SV45 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(290,plain,
! [SV46: $i] :
( ( ( ~ ~ ( ~ ( in @ emptyset @ SV46 )
| ~ ! [SY496: $i] :
( ~ ~ ( ~ ( in @ SY496 @ omega )
| ~ ( in @ SY496 @ SV46 ) )
| ( in @ ( setadjoin @ SY496 @ SY496 ) @ SV46 ) ) ) )
= $true )
| ( ( ! [SY497: $i] :
( ~ ( in @ SY497 @ omega )
| ( in @ SY497 @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(291,plain,
! [SV89: $i,SV47: $i] :
( ( ! [SY563: $i] :
( ~ ( in @ SY563 @ ( setadjoin @ SV47 @ ( setadjoin @ SV89 @ emptyset ) ) )
| ( SY563 = SV47 )
| ( SY563 = SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(292,plain,
! [SV48: $o] :
( ( ( ~ SV48 ) = $true )
| ( ( in @ emptyset @ ( prop2set @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(293,plain,
( ( ( ~ $true ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(294,plain,
( ( ( ~ $false ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(295,plain,
! [SV90: $i > $o,SV49: $i] :
( ( ! [SY564: $i] :
( ~ ( in @ SY564 @ SV49 )
| ~ ( ~ ( ~ ( in @ SY564
@ ( dsetconstr @ SV49
@ ^ [SY565: $i] : ( SV90 @ SY565 ) ) )
| ( SV90 @ SY564 ) )
| ~ ( ~ ( SV90 @ SY564 )
| ( in @ SY564
@ ( dsetconstr @ SV49
@ ^ [SY566: $i] : ( SV90 @ SY566 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(296,plain,
! [SV50: $i,SV91: $i] :
( ( ~ ( ~ ( ~ ( in @ SV91 @ ( setunion @ SV50 ) )
| ~ ! [SY567: $i] :
~ ~ ( ~ ( in @ SV91 @ SY567 )
| ~ ( in @ SY567 @ SV50 ) ) )
| ~ ( ~ ~ ! [SY568: $i] :
~ ~ ( ~ ( in @ SV91 @ SY568 )
| ~ ( in @ SY568 @ SV50 ) )
| ( in @ SV91 @ ( setunion @ SV50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(297,plain,
! [SV92: $i,SV51: $i] :
( ( ~ ( in @ SV51 @ ( setadjoin @ SV92 @ emptyset ) )
| ( in @ SV92 @ ( setadjoin @ SV51 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(298,plain,
! [SV93: $i,SV52: $i] :
( ( ~ ( in @ SV52 @ ( setadjoin @ SV93 @ emptyset ) )
| ( SV52 = SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(299,plain,
! [SV94: $i > $o,SV53: $i] :
( ( ! [SY569: $i] :
( ~ ( in @ SY569
@ ( dsetconstr @ SV53
@ ^ [SY570: $i] : ( SV94 @ SY570 ) ) )
| ( SV94 @ SY569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(300,plain,
! [SV54: $i] :
( ( ( ~ ! [SY512: $i] :
~ ( in @ SY512 @ SV54 ) )
= $true )
| ( ( SV54 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(301,plain,
! [SV55: $i] :
( ( ( ~ ! [SY513: $i] :
~ ( in @ SY513 @ SV55 ) )
= $true )
| ( ( SV55 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(302,plain,
! [SV95: $i,SV56: $i] :
( ( ~ ! [SY571: $i] :
( ~ ( in @ SY571 @ SV56 )
| ( in @ SY571 @ SV95 ) )
| ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV95 )
| ( in @ SY572 @ SV56 ) )
| ( SV56 = SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(303,plain,
! [SV57: $i] :
( ( ( ~ ( in @ SV57 @ emptyset ) )
= $true )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(304,plain,
! [SV96: $i,SV58: $i] :
( ( ( SV58 != SV96 )
| ( in @ SV58 @ ( setadjoin @ SV96 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(305,plain,
! [SV9: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ ( setunion @ SV9 ) ) )
= $true )
| ( ( ! [SY519: $o] :
( ~ ! [SY520: $i] :
( ~ ( in @ SV62 @ SY520 )
| ~ ( in @ SY520 @ SV9 )
| SY519 )
| SY519 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(306,plain,
( ( ~ ~ ! [SY521: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY521 )
| ~ ! [SY522: $i] :
( ~ ( sK1_SX0 @ SY522 )
| ( SY521 = SY522 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(307,plain,
( ( ~ ! [SY523: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY523 )
| ~ ! [SY524: $i] :
( ~ ( sK1_SX0 @ SY524 )
| ( SY523 = SY524 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(308,plain,
! [SV97: $i,SV10: $i,SV63: $i] :
( ( ~ ( in @ SV63 @ ( powerset @ SV10 ) )
| ~ ( in @ SV97 @ SV63 )
| ( in @ SV97 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(309,plain,
! [SV11: $i] :
( ( ( SV11 != emptyset )
= $false )
| ( ( ~ ! [SY398: $i] :
~ ~ ( ~ ( in @ SY398 @ SV11 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(310,plain,
! [SV64: $i > $o,SV12: $i] :
( ( ( ~ ~ ! [SY526: $i] :
( ~ ( in @ SY526 @ SV12 )
| ( SV64 @ SY526 ) ) )
= $true )
| ( ( ~ ! [SY527: $i] :
~ ~ ( ~ ( in @ SY527 @ SV12 )
| ~ ~ ( SV64 @ SY527 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(311,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ ( sK2_SY402 @ SV13 ) )
| ! [SY404: $i] :
( ~ ( in @ SY404 @ SY573 )
| ( in @ SY404 @ SV13 ) ) )
| ~ ! [SY575: $i,SY576: $i] :
( ~ ~ ( ~ ( in @ SY575 @ SV13 )
| ~ ( in @ SY576 @ SV13 ) )
| ~ ! [SY577: $i] :
( ~ ( in @ SY577 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY575 @ SY577 )
| ( in @ SY576 @ SY577 ) )
| ~ ( ~ ( in @ SY576 @ SY577 )
| ( in @ SY575 @ SY577 ) ) ) )
| ( SY575 = SY576 ) ) )
| ~ ! [SY578: $i,SY579: $i] :
( ~ ~ ( ~ ( in @ SY578 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY579 @ ( sK2_SY402 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY578 )
| ( in @ SX4 @ SY579 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY579 )
| ( in @ SX4 @ SY578 ) ) ) )
| ~ ! [SY582: $i] :
( ~ ~ ( ~ ! [SY413: $i] :
( ~ ( in @ SY413 @ SY582 )
| ( in @ SY413 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY582 ) )
| ~ ! [SY585: $i] :
~ ~ ! [SY586: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY585 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY586 @ SY582 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY585 )
| ~ ( in @ SX5 @ SY582 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY585 ) )
| ( in @ SY586 @ SY588 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[253]) ).
thf(312,plain,
! [SV14: $i,SV65: $i,SV98: $i] :
( ( ~ ( in @ SV98 @ SV65 )
| ( in @ SV98 @ ( setadjoin @ SV14 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(313,plain,
! [SV15: $i] :
( ( ( in @ SV15 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV15 @ SV15 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(314,plain,
! [SV66: $i,SV16: $i,SV99: $i] :
( ( ~ ( in @ SV99 @ ( setadjoin @ SV16 @ SV66 ) )
| ( SV99 = SV16 )
| ( in @ SV99 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(315,plain,
! [SV17: $i > $o] :
( ( ( ~ ! [SY424: $i] :
~ ~ ( ~ ( SV17 @ SY424 )
| ~ ! [SY425: $i] :
( ~ ( SV17 @ SY425 )
| ( SY424 = SY425 ) ) ) )
= $false )
| ( ( SV17
@ ( descr
@ ^ [SY426: $i] : ( SV17 @ SY426 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(316,plain,
! [SV67: $i > $o,SV18: $i,SV100: $i] :
( ( ~ ( in @ SV100 @ SV18 )
| ~ ( SV67 @ SV100 )
| ( ( dsetconstr @ SV18
@ ^ [SY531: $i] : ( SV67 @ SY531 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(317,plain,
! [SV68: $i > $o,SV19: $i] :
( ( ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SV19 )
| ~ ( SV68 @ SY532 ) ) )
= $true )
| ( ( ~ ~ ! [SY533: $i] :
~ ~ ( ~ ( in @ SY533 @ SV19 )
| ~ ( SV68 @ SY533 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(318,plain,
! [SV20: $i,SV69: $i] :
( ( ( ~ ! [SY534: $i] :
( ~ ( in @ SY534 @ SV69 )
| ( in @ SY534 @ SV20 ) ) )
= $true )
| ( ( in @ SV69 @ ( powerset @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(319,plain,
! [SV70: $i > $o,SV21: $i] :
( ( ( ~ ~ ! [SY535: $i] :
( ~ ( in @ SY535 @ SV21 )
| ( SV70 @ SY535 ) ) )
= $true )
| ( ( ~ ! [SY536: $i] :
~ ~ ( ~ ( in @ SY536 @ SV21 )
| ~ ~ ( SV70 @ SY536 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(320,plain,
! [SV71: $i > $o,SV22: $i] :
( ( ( ~ ~ ~ ! [SY537: $i] :
~ ~ ( ~ ( in @ SY537 @ SV22 )
| ~ ( SV71 @ SY537 ) ) )
= $true )
| ( ( ! [SY538: $i] :
( ~ ( in @ SY538 @ SV22 )
| ~ ( SV71 @ SY538 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(321,plain,
! [SV72: $i,SV23: $i,SV101: $i] :
( ( ~ ( ~ ( ~ ( in @ SV101 @ ( setadjoin @ SV23 @ SV72 ) )
| ( SV101 = SV23 )
| ( in @ SV101 @ SV72 ) )
| ~ ( ~ ( ( SV101 = SV23 )
| ( in @ SV101 @ SV72 ) )
| ( in @ SV101 @ ( setadjoin @ SV23 @ SV72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(322,plain,
! [SV73: $i > $o,SV24: $i] :
( ( ( ~ ~ ! [SY540: $i] :
~ ~ ( ~ ( in @ SY540 @ SV24 )
| ~ ( SV73 @ SY540 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV24
@ ^ [SY541: $i] : ( SV73 @ SY541 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(323,plain,
! [SV74: $i > $o,SV25: $i,SV102: $i] :
( ( ~ ( in @ SV102
@ ( dsetconstr @ SV25
@ ^ [SY543: $i] : ( SV74 @ SY543 ) ) )
| ( in @ SV102 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(324,plain,
! [SV26: $i > $o,SV75: $i] :
( ( ( ~ ( in @ SV75 @ emptyset ) )
= $true )
| ( ( SV26 @ SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(325,plain,
! [SV27: $i > $o] :
( ( ( ~ ! [SY450: $i] :
~ ~ ( ~ ( SV27 @ SY450 )
| ~ ! [SY451: $i] :
( ~ ( SV27 @ SY451 )
| ( SY450 = SY451 ) ) ) )
= $false )
| ( ( ~ ! [SY452: $i] :
~ ! [SY453: $i] :
~ ( ~ ( ~ ( SV27 @ SY453 )
| ( SY453 = SY452 ) )
| ~ ( ( SY453 != SY452 )
| ( SV27 @ SY453 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(326,plain,
! [SV76: $i > $o,SV28: $i,SV103: $i] :
( ( ~ ( in @ SV103 @ SV28 )
| ~ ( SV76 @ SV103 )
| ( in @ SV103
@ ( dsetconstr @ SV28
@ ^ [SY545: $i] : ( SV76 @ SY545 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(327,plain,
! [SV29: $i,SV104: $i,SV77: $i] :
( ( ~ ( in @ SV77 @ SV104 )
| ~ ( in @ SV104 @ SV29 )
| ( in @ SV77 @ ( setunion @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(328,plain,
! [SV30: $i] :
( ( ( ~ ! [SY459: $i] :
~ ( in @ SY459 @ SV30 ) )
= $false )
| ( ( ~ ! [SY460: $i] :
~ ~ ( ~ ( in @ SY460 @ SV30 )
| ~ ~ ~ ! [SY461: $i] :
~ ~ ( ~ ( in @ SY461 @ SY460 )
| ~ ( in @ SY461 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(329,plain,
! [SV31: $i > $o] :
( ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV31 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV31 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $false )
| ( ( ~ ! [SY464: $i] :
~ ~ ( ~ ( SV31 @ SY464 )
| ~ ! [SY465: $i] :
( ~ ( SV31 @ SY465 )
| ( SY464 = SY465 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(330,plain,
! [SV32: $i > $i > $o,SV78: $i] :
( ( ( ~ ! [SY547: $i] :
( ~ ( in @ SY547 @ SV78 )
| ~ ! [SY468: $i] :
~ ~ ( ~ ( SV32 @ SY547 @ SY468 )
| ~ ! [SY469: $i] :
( ~ ( SV32 @ SY547 @ SY469 )
| ( SY468 = SY469 ) ) ) ) )
= $true )
| ( ( ~ ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(331,plain,
! [SV79: $i > $o,SV33: $i] :
( ( ( ~ ~ ~ ! [SY554: $i] :
~ ~ ( ~ ( in @ SY554 @ SV33 )
| ~ ( SV79 @ SY554 ) ) )
= $true )
| ( ( ! [SY555: $i] :
( ~ ( in @ SY555 @ SV33 )
| ~ ( SV79 @ SY555 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(332,plain,
! [SV80: $i,SV34: $i] :
( ( ( ~ ! [SY556: $i] :
~ ( ~ ( ~ ( in @ SY556 @ SV34 )
| ( in @ SY556 @ SV80 ) )
| ~ ( ~ ( in @ SY556 @ SV80 )
| ( in @ SY556 @ SV34 ) ) ) )
= $true )
| ( ( SV34 = SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(333,plain,
! [SV35: $i] :
( ( ( in @ SV35 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(334,plain,
! [SV36: $i > $o] :
( ( ( ~ ! [SY479: $i] :
~ ~ ( ~ ( SV36 @ SY479 )
| ~ ! [SY480: $i] :
( ~ ( SV36 @ SY480 )
| ( SY479 = SY480 ) ) ) )
= $false )
| ( ( ~ ! [SY481: $i] :
~ ( SV36 @ SY481 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(335,plain,
! [SV37: $i] :
( ( ( ~ ! [SY482: $i] :
~ ( in @ SY482 @ SV37 ) )
= $false )
| ( ( SV37 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(336,plain,
! [SV38: $i] :
( ( ( SV38 != emptyset )
= $false )
| ( ( ~ ! [SY483: $i] :
~ ( in @ SY483 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(337,plain,
! [SV39: $i,SV81: $i] :
( ( ( ~ ( in @ SV81 @ SV39 ) )
= $true )
| ( ( in @ SV81 @ ( powerset @ ( setunion @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(338,plain,
! [SV40: $i,SV82: $i] :
( ( ~ ( ~ ( in @ SV82 @ ( powerset @ SV40 ) )
| ! [SY557: $i] :
( ~ ( in @ SY557 @ SV82 )
| ( in @ SY557 @ SV40 ) ) )
| ~ ( ~ ! [SY558: $i] :
( ~ ( in @ SY558 @ SV82 )
| ( in @ SY558 @ SV40 ) )
| ( in @ SV82 @ ( powerset @ SV40 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(339,plain,
! [SV41: $o] :
( ( SV41 = $false )
| ( ( set2prop @ ( prop2set @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(340,plain,
( ( $true = $false )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(341,plain,
( ( $false = $false )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(342,plain,
! [SV42: $o,SV83: $i] :
( ( ( ~ ( in @ SV83 @ ( prop2set @ SV42 ) ) )
= $true )
| ( SV42 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(343,plain,
! [SV84: $i] :
( ( ( ~ ( in @ SV84 @ ( prop2set @ $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(344,plain,
! [SV85: $i] :
( ( ( ~ ( in @ SV85 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(345,plain,
! [SV86: $i,SV43: $i,SV105: $i] :
( ( ~ ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
| ! [SY593: $o] :
( ~ ( ( SV105 != SV43 )
| SY593 )
| ~ ( ~ ( in @ SV105 @ SV86 )
| SY593 )
| SY593 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(346,plain,
! [SV87: $i > $o,SV44: $i] :
( ( ( ~ ~ ! [SY561: $i] :
~ ~ ( ~ ( in @ SY561 @ SV44 )
| ~ ~ ( SV87 @ SY561 ) ) )
= $true )
| ( ( ~ ! [SY562: $i] :
( ~ ( in @ SY562 @ SV44 )
| ( SV87 @ SY562 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(347,plain,
! [SV88: $i,SV45: $i] :
( ( ( ~ ( ( SV45 != SV88 ) ) )
= $true )
| ( ( ~ ( in @ SV88 @ ( setadjoin @ SV45 @ emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(348,plain,
! [SV46: $i] :
( ( ( ~ ( ~ ( in @ emptyset @ SV46 )
| ~ ! [SY496: $i] :
( ~ ~ ( ~ ( in @ SY496 @ omega )
| ~ ( in @ SY496 @ SV46 ) )
| ( in @ ( setadjoin @ SY496 @ SY496 ) @ SV46 ) ) ) )
= $false )
| ( ( ! [SY497: $i] :
( ~ ( in @ SY497 @ omega )
| ( in @ SY497 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(349,plain,
! [SV89: $i,SV47: $i,SV106: $i] :
( ( ~ ( in @ SV106 @ ( setadjoin @ SV47 @ ( setadjoin @ SV89 @ emptyset ) ) )
| ( SV106 = SV47 )
| ( SV106 = SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(350,plain,
! [SV48: $o] :
( ( SV48 = $false )
| ( ( in @ emptyset @ ( prop2set @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(351,plain,
( ( $true = $false )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(352,plain,
( ( $false = $false )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(353,plain,
! [SV90: $i > $o,SV49: $i,SV107: $i] :
( ( ~ ( in @ SV107 @ SV49 )
| ~ ( ~ ( ~ ( in @ SV107
@ ( dsetconstr @ SV49
@ ^ [SY565: $i] : ( SV90 @ SY565 ) ) )
| ( SV90 @ SV107 ) )
| ~ ( ~ ( SV90 @ SV107 )
| ( in @ SV107
@ ( dsetconstr @ SV49
@ ^ [SY566: $i] : ( SV90 @ SY566 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(354,plain,
! [SV50: $i,SV91: $i] :
( ( ~ ( ~ ( in @ SV91 @ ( setunion @ SV50 ) )
| ~ ! [SY567: $i] :
~ ~ ( ~ ( in @ SV91 @ SY567 )
| ~ ( in @ SY567 @ SV50 ) ) )
| ~ ( ~ ~ ! [SY568: $i] :
~ ~ ( ~ ( in @ SV91 @ SY568 )
| ~ ( in @ SY568 @ SV50 ) )
| ( in @ SV91 @ ( setunion @ SV50 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(355,plain,
! [SV92: $i,SV51: $i] :
( ( ( ~ ( in @ SV51 @ ( setadjoin @ SV92 @ emptyset ) ) )
= $true )
| ( ( in @ SV92 @ ( setadjoin @ SV51 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(356,plain,
! [SV93: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ ( setadjoin @ SV93 @ emptyset ) ) )
= $true )
| ( ( SV52 = SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(357,plain,
! [SV94: $i > $o,SV53: $i,SV108: $i] :
( ( ~ ( in @ SV108
@ ( dsetconstr @ SV53
@ ^ [SY570: $i] : ( SV94 @ SY570 ) ) )
| ( SV94 @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(358,plain,
! [SV54: $i] :
( ( ( ! [SY512: $i] :
~ ( in @ SY512 @ SV54 ) )
= $false )
| ( ( SV54 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(359,plain,
! [SV55: $i] :
( ( ( ! [SY513: $i] :
~ ( in @ SY513 @ SV55 ) )
= $false )
| ( ( SV55 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(360,plain,
! [SV95: $i,SV56: $i] :
( ( ( ~ ! [SY571: $i] :
( ~ ( in @ SY571 @ SV56 )
| ( in @ SY571 @ SV95 ) ) )
= $true )
| ( ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV95 )
| ( in @ SY572 @ SV56 ) )
| ( SV56 = SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(361,plain,
! [SV57: $i] :
( ( ( in @ SV57 @ emptyset )
= $false )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(362,plain,
! [SV96: $i,SV58: $i] :
( ( ( SV58 != SV96 )
= $true )
| ( ( in @ SV58 @ ( setadjoin @ SV96 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(363,plain,
! [SV9: $i,SV62: $i] :
( ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false )
| ( ( ! [SY519: $o] :
( ~ ! [SY520: $i] :
( ~ ( in @ SV62 @ SY520 )
| ~ ( in @ SY520 @ SV9 )
| SY519 )
| SY519 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(364,plain,
( ( ~ ! [SY521: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY521 )
| ~ ! [SY522: $i] :
( ~ ( sK1_SX0 @ SY522 )
| ( SY521 = SY522 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(365,plain,
( ( ! [SY523: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY523 )
| ~ ! [SY524: $i] :
( ~ ( sK1_SX0 @ SY524 )
| ( SY523 = SY524 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(366,plain,
! [SV97: $i,SV10: $i,SV63: $i] :
( ( ( ~ ( in @ SV63 @ ( powerset @ SV10 ) ) )
= $true )
| ( ( ~ ( in @ SV97 @ SV63 )
| ( in @ SV97 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(367,plain,
! [SV11: $i] :
( ( ( SV11 = emptyset )
= $true )
| ( ( ~ ! [SY398: $i] :
~ ~ ( ~ ( in @ SY398 @ SV11 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(368,plain,
! [SV64: $i > $o,SV12: $i] :
( ( ( ~ ! [SY526: $i] :
( ~ ( in @ SY526 @ SV12 )
| ( SV64 @ SY526 ) ) )
= $false )
| ( ( ~ ! [SY527: $i] :
~ ~ ( ~ ( in @ SY527 @ SV12 )
| ~ ~ ( SV64 @ SY527 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(369,plain,
! [SV13: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ ( sK2_SY402 @ SV13 ) )
| ! [SY404: $i] :
( ~ ( in @ SY404 @ SY573 )
| ( in @ SY404 @ SV13 ) ) )
| ~ ! [SY575: $i,SY576: $i] :
( ~ ~ ( ~ ( in @ SY575 @ SV13 )
| ~ ( in @ SY576 @ SV13 ) )
| ~ ! [SY577: $i] :
( ~ ( in @ SY577 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY575 @ SY577 )
| ( in @ SY576 @ SY577 ) )
| ~ ( ~ ( in @ SY576 @ SY577 )
| ( in @ SY575 @ SY577 ) ) ) )
| ( SY575 = SY576 ) ) )
| ~ ! [SY578: $i,SY579: $i] :
( ~ ~ ( ~ ( in @ SY578 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY579 @ ( sK2_SY402 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY578 )
| ( in @ SX4 @ SY579 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY579 )
| ( in @ SX4 @ SY578 ) ) ) )
| ~ ! [SY582: $i] :
( ~ ~ ( ~ ! [SY413: $i] :
( ~ ( in @ SY413 @ SY582 )
| ( in @ SY413 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY582 ) )
| ~ ! [SY585: $i] :
~ ~ ! [SY586: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY585 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY586 @ SY582 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY585 )
| ~ ( in @ SX5 @ SY582 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY585 ) )
| ( in @ SY586 @ SY588 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(370,plain,
! [SV14: $i,SV65: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ SV65 ) )
= $true )
| ( ( in @ SV98 @ ( setadjoin @ SV14 @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(371,plain,
! [SV66: $i,SV16: $i,SV99: $i] :
( ( ( ~ ( in @ SV99 @ ( setadjoin @ SV16 @ SV66 ) ) )
= $true )
| ( ( ( SV99 = SV16 )
| ( in @ SV99 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(372,plain,
! [SV17: $i > $o] :
( ( ( ! [SY424: $i] :
~ ~ ( ~ ( SV17 @ SY424 )
| ~ ! [SY425: $i] :
( ~ ( SV17 @ SY425 )
| ( SY424 = SY425 ) ) ) )
= $true )
| ( ( SV17
@ ( descr
@ ^ [SY426: $i] : ( SV17 @ SY426 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(373,plain,
! [SV67: $i > $o,SV18: $i,SV100: $i] :
( ( ( ~ ( in @ SV100 @ SV18 ) )
= $true )
| ( ( ~ ( SV67 @ SV100 )
| ( ( dsetconstr @ SV18
@ ^ [SY531: $i] : ( SV67 @ SY531 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(374,plain,
! [SV68: $i > $o,SV19: $i] :
( ( ( ! [SY532: $i] :
( ~ ( in @ SY532 @ SV19 )
| ~ ( SV68 @ SY532 ) ) )
= $false )
| ( ( ~ ~ ! [SY533: $i] :
~ ~ ( ~ ( in @ SY533 @ SV19 )
| ~ ( SV68 @ SY533 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(375,plain,
! [SV20: $i,SV69: $i] :
( ( ( ! [SY534: $i] :
( ~ ( in @ SY534 @ SV69 )
| ( in @ SY534 @ SV20 ) ) )
= $false )
| ( ( in @ SV69 @ ( powerset @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(376,plain,
! [SV70: $i > $o,SV21: $i] :
( ( ( ~ ! [SY535: $i] :
( ~ ( in @ SY535 @ SV21 )
| ( SV70 @ SY535 ) ) )
= $false )
| ( ( ~ ! [SY536: $i] :
~ ~ ( ~ ( in @ SY536 @ SV21 )
| ~ ~ ( SV70 @ SY536 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(377,plain,
! [SV71: $i > $o,SV22: $i] :
( ( ( ~ ~ ! [SY537: $i] :
~ ~ ( ~ ( in @ SY537 @ SV22 )
| ~ ( SV71 @ SY537 ) ) )
= $false )
| ( ( ! [SY538: $i] :
( ~ ( in @ SY538 @ SV22 )
| ~ ( SV71 @ SY538 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(378,plain,
! [SV72: $i,SV23: $i,SV101: $i] :
( ( ~ ( ~ ( in @ SV101 @ ( setadjoin @ SV23 @ SV72 ) )
| ( SV101 = SV23 )
| ( in @ SV101 @ SV72 ) )
| ~ ( ~ ( ( SV101 = SV23 )
| ( in @ SV101 @ SV72 ) )
| ( in @ SV101 @ ( setadjoin @ SV23 @ SV72 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(379,plain,
! [SV73: $i > $o,SV24: $i] :
( ( ( ~ ! [SY540: $i] :
~ ~ ( ~ ( in @ SY540 @ SV24 )
| ~ ( SV73 @ SY540 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV24
@ ^ [SY541: $i] : ( SV73 @ SY541 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(380,plain,
! [SV74: $i > $o,SV25: $i,SV102: $i] :
( ( ( ~ ( in @ SV102
@ ( dsetconstr @ SV25
@ ^ [SY543: $i] : ( SV74 @ SY543 ) ) ) )
= $true )
| ( ( in @ SV102 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(381,plain,
! [SV26: $i > $o,SV75: $i] :
( ( ( in @ SV75 @ emptyset )
= $false )
| ( ( SV26 @ SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(382,plain,
! [SV27: $i > $o] :
( ( ( ! [SY450: $i] :
~ ~ ( ~ ( SV27 @ SY450 )
| ~ ! [SY451: $i] :
( ~ ( SV27 @ SY451 )
| ( SY450 = SY451 ) ) ) )
= $true )
| ( ( ~ ! [SY452: $i] :
~ ! [SY453: $i] :
~ ( ~ ( ~ ( SV27 @ SY453 )
| ( SY453 = SY452 ) )
| ~ ( ( SY453 != SY452 )
| ( SV27 @ SY453 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(383,plain,
! [SV76: $i > $o,SV28: $i,SV103: $i] :
( ( ( ~ ( in @ SV103 @ SV28 ) )
= $true )
| ( ( ~ ( SV76 @ SV103 )
| ( in @ SV103
@ ( dsetconstr @ SV28
@ ^ [SY545: $i] : ( SV76 @ SY545 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(384,plain,
! [SV29: $i,SV104: $i,SV77: $i] :
( ( ( ~ ( in @ SV77 @ SV104 ) )
= $true )
| ( ( ~ ( in @ SV104 @ SV29 )
| ( in @ SV77 @ ( setunion @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(385,plain,
! [SV30: $i] :
( ( ( ! [SY459: $i] :
~ ( in @ SY459 @ SV30 ) )
= $true )
| ( ( ~ ! [SY460: $i] :
~ ~ ( ~ ( in @ SY460 @ SV30 )
| ~ ~ ~ ! [SY461: $i] :
~ ~ ( ~ ( in @ SY461 @ SY460 )
| ~ ( in @ SY461 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(386,plain,
! [SV31: $i > $o] :
( ( ( ! [SY462: $i] :
~ ~ ( ~ ( SV31 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV31 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true )
| ( ( ~ ! [SY464: $i] :
~ ~ ( ~ ( SV31 @ SY464 )
| ~ ! [SY465: $i] :
( ~ ( SV31 @ SY465 )
| ( SY464 = SY465 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(387,plain,
! [SV32: $i > $i > $o,SV78: $i] :
( ( ( ! [SY547: $i] :
( ~ ( in @ SY547 @ SV78 )
| ~ ! [SY468: $i] :
~ ~ ( ~ ( SV32 @ SY547 @ SY468 )
| ~ ! [SY469: $i] :
( ~ ( SV32 @ SY547 @ SY469 )
| ( SY468 = SY469 ) ) ) ) )
= $false )
| ( ( ~ ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(388,plain,
! [SV79: $i > $o,SV33: $i] :
( ( ( ~ ~ ! [SY554: $i] :
~ ~ ( ~ ( in @ SY554 @ SV33 )
| ~ ( SV79 @ SY554 ) ) )
= $false )
| ( ( ! [SY555: $i] :
( ~ ( in @ SY555 @ SV33 )
| ~ ( SV79 @ SY555 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(389,plain,
! [SV80: $i,SV34: $i] :
( ( ( ! [SY556: $i] :
~ ( ~ ( ~ ( in @ SY556 @ SV34 )
| ( in @ SY556 @ SV80 ) )
| ~ ( ~ ( in @ SY556 @ SV80 )
| ( in @ SY556 @ SV34 ) ) ) )
= $false )
| ( ( SV34 = SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(390,plain,
! [SV36: $i > $o] :
( ( ( ! [SY479: $i] :
~ ~ ( ~ ( SV36 @ SY479 )
| ~ ! [SY480: $i] :
( ~ ( SV36 @ SY480 )
| ( SY479 = SY480 ) ) ) )
= $true )
| ( ( ~ ! [SY481: $i] :
~ ( SV36 @ SY481 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(391,plain,
! [SV37: $i] :
( ( ( ! [SY482: $i] :
~ ( in @ SY482 @ SV37 ) )
= $true )
| ( ( SV37 != emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(392,plain,
! [SV38: $i] :
( ( ( SV38 = emptyset )
= $true )
| ( ( ~ ! [SY483: $i] :
~ ( in @ SY483 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(393,plain,
! [SV39: $i,SV81: $i] :
( ( ( in @ SV81 @ SV39 )
= $false )
| ( ( in @ SV81 @ ( powerset @ ( setunion @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(394,plain,
! [SV40: $i,SV82: $i] :
( ( ~ ( ~ ( in @ SV82 @ ( powerset @ SV40 ) )
| ! [SY557: $i] :
( ~ ( in @ SY557 @ SV82 )
| ( in @ SY557 @ SV40 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[338]) ).
thf(395,plain,
! [SV40: $i,SV82: $i] :
( ( ~ ( ~ ! [SY558: $i] :
( ~ ( in @ SY558 @ SV82 )
| ( in @ SY558 @ SV40 ) )
| ( in @ SV82 @ ( powerset @ SV40 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[338]) ).
thf(396,plain,
! [SV42: $o,SV83: $i] :
( ( ( in @ SV83 @ ( prop2set @ SV42 ) )
= $false )
| ( SV42 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(397,plain,
! [SV84: $i] :
( ( ( in @ SV84 @ ( prop2set @ $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(398,plain,
! [SV85: $i] :
( ( ( in @ SV85 @ ( prop2set @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(399,plain,
! [SV86: $i,SV43: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) ) )
= $true )
| ( ( ! [SY593: $o] :
( ~ ( ( SV105 != SV43 )
| SY593 )
| ~ ( ~ ( in @ SV105 @ SV86 )
| SY593 )
| SY593 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(400,plain,
! [SV87: $i > $o,SV44: $i] :
( ( ( ~ ! [SY561: $i] :
~ ~ ( ~ ( in @ SY561 @ SV44 )
| ~ ~ ( SV87 @ SY561 ) ) )
= $false )
| ( ( ~ ! [SY562: $i] :
( ~ ( in @ SY562 @ SV44 )
| ( SV87 @ SY562 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(401,plain,
! [SV88: $i,SV45: $i] :
( ( ( SV45 != SV88 )
= $false )
| ( ( ~ ( in @ SV88 @ ( setadjoin @ SV45 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(402,plain,
! [SV46: $i] :
( ( ( ~ ( in @ emptyset @ SV46 )
| ~ ! [SY496: $i] :
( ~ ~ ( ~ ( in @ SY496 @ omega )
| ~ ( in @ SY496 @ SV46 ) )
| ( in @ ( setadjoin @ SY496 @ SY496 ) @ SV46 ) ) )
= $true )
| ( ( ! [SY497: $i] :
( ~ ( in @ SY497 @ omega )
| ( in @ SY497 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[348]) ).
thf(403,plain,
! [SV89: $i,SV47: $i,SV106: $i] :
( ( ( ~ ( in @ SV106 @ ( setadjoin @ SV47 @ ( setadjoin @ SV89 @ emptyset ) ) ) )
= $true )
| ( ( ( SV106 = SV47 )
| ( SV106 = SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(404,plain,
! [SV90: $i > $o,SV49: $i,SV107: $i] :
( ( ( ~ ( in @ SV107 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV107
@ ( dsetconstr @ SV49
@ ^ [SY565: $i] : ( SV90 @ SY565 ) ) )
| ( SV90 @ SV107 ) )
| ~ ( ~ ( SV90 @ SV107 )
| ( in @ SV107
@ ( dsetconstr @ SV49
@ ^ [SY566: $i] : ( SV90 @ SY566 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(405,plain,
! [SV50: $i,SV91: $i] :
( ( ~ ( ~ ( in @ SV91 @ ( setunion @ SV50 ) )
| ~ ! [SY567: $i] :
~ ~ ( ~ ( in @ SV91 @ SY567 )
| ~ ( in @ SY567 @ SV50 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(406,plain,
! [SV50: $i,SV91: $i] :
( ( ~ ( ~ ~ ! [SY568: $i] :
~ ~ ( ~ ( in @ SV91 @ SY568 )
| ~ ( in @ SY568 @ SV50 ) )
| ( in @ SV91 @ ( setunion @ SV50 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(407,plain,
! [SV92: $i,SV51: $i] :
( ( ( in @ SV51 @ ( setadjoin @ SV92 @ emptyset ) )
= $false )
| ( ( in @ SV92 @ ( setadjoin @ SV51 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(408,plain,
! [SV93: $i,SV52: $i] :
( ( ( in @ SV52 @ ( setadjoin @ SV93 @ emptyset ) )
= $false )
| ( ( SV52 = SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(409,plain,
! [SV94: $i > $o,SV53: $i,SV108: $i] :
( ( ( ~ ( in @ SV108
@ ( dsetconstr @ SV53
@ ^ [SY570: $i] : ( SV94 @ SY570 ) ) ) )
= $true )
| ( ( SV94 @ SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(410,plain,
! [SV54: $i] :
( ( ( ~ ( in @ ( sK3_SY512 @ SV54 ) @ SV54 ) )
= $false )
| ( ( SV54 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[358]) ).
thf(411,plain,
! [SV55: $i] :
( ( ( ~ ( in @ ( sK4_SY513 @ SV55 ) @ SV55 ) )
= $false )
| ( ( SV55 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[359]) ).
thf(412,plain,
! [SV95: $i,SV56: $i] :
( ( ( ! [SY571: $i] :
( ~ ( in @ SY571 @ SV56 )
| ( in @ SY571 @ SV95 ) ) )
= $false )
| ( ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV95 )
| ( in @ SY572 @ SV56 ) )
| ( SV56 = SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(413,plain,
! [SV57: $i,SV109: $o] :
( ( SV109 = $true )
| ( ( in @ SV57 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[361]) ).
thf(414,plain,
! [SV57: $i] :
( ( $true = $true )
| ( ( in @ SV57 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[361]) ).
thf(415,plain,
! [SV57: $i] :
( ( $false = $true )
| ( ( in @ SV57 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[361]) ).
thf(416,plain,
! [SV96: $i,SV58: $i] :
( ( ( SV58 = SV96 )
= $false )
| ( ( in @ SV58 @ ( setadjoin @ SV96 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(417,plain,
! [SV110: $o,SV9: $i,SV62: $i] :
( ( ( ~ ! [SY597: $i] :
( ~ ( in @ SV62 @ SY597 )
| ~ ( in @ SY597 @ SV9 )
| SV110 )
| SV110 )
= $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[363]) ).
thf(418,plain,
! [SV9: $i,SV62: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV62 @ SX0 )
| ~ ( in @ SX0 @ SV9 )
| $true )
| $true )
= $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[363]) ).
thf(419,plain,
! [SV9: $i,SV62: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV62 @ SX0 )
| ~ ( in @ SX0 @ SV9 )
| $false )
| $false )
= $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[363]) ).
thf(420,plain,
( ( ! [SY521: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY521 )
| ~ ! [SY522: $i] :
( ~ ( sK1_SX0 @ SY522 )
| ( SY521 = SY522 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(421,plain,
! [SV111: $i] :
( ( ~ ~ ( ~ ( sK1_SX0 @ SV111 )
| ~ ! [SY598: $i] :
( ~ ( sK1_SX0 @ SY598 )
| ( SV111 = SY598 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(422,plain,
! [SV97: $i,SV10: $i,SV63: $i] :
( ( ( in @ SV63 @ ( powerset @ SV10 ) )
= $false )
| ( ( ~ ( in @ SV97 @ SV63 )
| ( in @ SV97 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(423,plain,
! [SV11: $i] :
( ( ( ! [SY398: $i] :
~ ~ ( ~ ( in @ SY398 @ SV11 )
| ~ $true ) )
= $false )
| ( ( SV11 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(424,plain,
! [SV64: $i > $o,SV12: $i] :
( ( ( ! [SY526: $i] :
( ~ ( in @ SY526 @ SV12 )
| ( SV64 @ SY526 ) ) )
= $true )
| ( ( ~ ! [SY527: $i] :
~ ~ ( ~ ( in @ SY527 @ SV12 )
| ~ ~ ( SV64 @ SY527 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(425,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ ( sK2_SY402 @ SV13 ) )
| ! [SY404: $i] :
( ~ ( in @ SY404 @ SY573 )
| ( in @ SY404 @ SV13 ) ) )
| ~ ! [SY575: $i,SY576: $i] :
( ~ ~ ( ~ ( in @ SY575 @ SV13 )
| ~ ( in @ SY576 @ SV13 ) )
| ~ ! [SY577: $i] :
( ~ ( in @ SY577 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY575 @ SY577 )
| ( in @ SY576 @ SY577 ) )
| ~ ( ~ ( in @ SY576 @ SY577 )
| ( in @ SY575 @ SY577 ) ) ) )
| ( SY575 = SY576 ) ) )
| ~ ! [SY578: $i,SY579: $i] :
( ~ ~ ( ~ ( in @ SY578 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY579 @ ( sK2_SY402 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY578 )
| ( in @ SX4 @ SY579 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY579 )
| ( in @ SX4 @ SY578 ) ) ) )
| ~ ! [SY582: $i] :
( ~ ~ ( ~ ! [SY413: $i] :
( ~ ( in @ SY413 @ SY582 )
| ( in @ SY413 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY582 ) )
| ~ ! [SY585: $i] :
~ ~ ! [SY586: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY585 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY586 @ SY582 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY585 )
| ~ ( in @ SX5 @ SY582 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY585 ) )
| ( in @ SY586 @ SY588 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(426,plain,
! [SV14: $i,SV65: $i,SV98: $i] :
( ( ( in @ SV98 @ SV65 )
= $false )
| ( ( in @ SV98 @ ( setadjoin @ SV14 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(427,plain,
! [SV66: $i,SV16: $i,SV99: $i] :
( ( ( in @ SV99 @ ( setadjoin @ SV16 @ SV66 ) )
= $false )
| ( ( ( SV99 = SV16 )
| ( in @ SV99 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(428,plain,
! [SV112: $i,SV17: $i > $o] :
( ( ( ~ ~ ( ~ ( SV17 @ SV112 )
| ~ ! [SY599: $i] :
( ~ ( SV17 @ SY599 )
| ( SV112 = SY599 ) ) ) )
= $true )
| ( ( SV17
@ ( descr
@ ^ [SY426: $i] : ( SV17 @ SY426 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(429,plain,
! [SV67: $i > $o,SV18: $i,SV100: $i] :
( ( ( in @ SV100 @ SV18 )
= $false )
| ( ( ~ ( SV67 @ SV100 )
| ( ( dsetconstr @ SV18
@ ^ [SY531: $i] : ( SV67 @ SY531 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(430,plain,
! [SV19: $i,SV68: $i > $o] :
( ( ( ~ ( in @ ( sK5_SY532 @ SV68 @ SV19 ) @ SV19 )
| ~ ( SV68 @ ( sK5_SY532 @ SV68 @ SV19 ) ) )
= $false )
| ( ( ~ ~ ! [SY533: $i] :
~ ~ ( ~ ( in @ SY533 @ SV19 )
| ~ ( SV68 @ SY533 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[374]) ).
thf(431,plain,
! [SV69: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK6_SY534 @ SV20 @ SV69 ) @ SV69 )
| ( in @ ( sK6_SY534 @ SV20 @ SV69 ) @ SV20 ) )
= $false )
| ( ( in @ SV69 @ ( powerset @ SV20 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[375]) ).
thf(432,plain,
! [SV70: $i > $o,SV21: $i] :
( ( ( ! [SY535: $i] :
( ~ ( in @ SY535 @ SV21 )
| ( SV70 @ SY535 ) ) )
= $true )
| ( ( ~ ! [SY536: $i] :
~ ~ ( ~ ( in @ SY536 @ SV21 )
| ~ ~ ( SV70 @ SY536 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(433,plain,
! [SV71: $i > $o,SV22: $i] :
( ( ( ~ ! [SY537: $i] :
~ ~ ( ~ ( in @ SY537 @ SV22 )
| ~ ( SV71 @ SY537 ) ) )
= $true )
| ( ( ! [SY538: $i] :
( ~ ( in @ SY538 @ SV22 )
| ~ ( SV71 @ SY538 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(434,plain,
! [SV72: $i,SV23: $i,SV101: $i] :
( ( ~ ( ~ ( in @ SV101 @ ( setadjoin @ SV23 @ SV72 ) )
| ( SV101 = SV23 )
| ( in @ SV101 @ SV72 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[378]) ).
thf(435,plain,
! [SV72: $i,SV23: $i,SV101: $i] :
( ( ~ ( ~ ( ( SV101 = SV23 )
| ( in @ SV101 @ SV72 ) )
| ( in @ SV101 @ ( setadjoin @ SV23 @ SV72 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[378]) ).
thf(436,plain,
! [SV73: $i > $o,SV24: $i] :
( ( ( ! [SY540: $i] :
~ ~ ( ~ ( in @ SY540 @ SV24 )
| ~ ( SV73 @ SY540 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV24
@ ^ [SY541: $i] : ( SV73 @ SY541 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[379]) ).
thf(437,plain,
! [SV74: $i > $o,SV25: $i,SV102: $i] :
( ( ( in @ SV102
@ ( dsetconstr @ SV25
@ ^ [SY543: $i] : ( SV74 @ SY543 ) ) )
= $false )
| ( ( in @ SV102 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(438,plain,
! [SV113: $i,SV27: $i > $o] :
( ( ( ~ ~ ( ~ ( SV27 @ SV113 )
| ~ ! [SY600: $i] :
( ~ ( SV27 @ SY600 )
| ( SV113 = SY600 ) ) ) )
= $true )
| ( ( ~ ! [SY452: $i] :
~ ! [SY453: $i] :
~ ( ~ ( ~ ( SV27 @ SY453 )
| ( SY453 = SY452 ) )
| ~ ( ( SY453 != SY452 )
| ( SV27 @ SY453 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(439,plain,
! [SV76: $i > $o,SV28: $i,SV103: $i] :
( ( ( in @ SV103 @ SV28 )
= $false )
| ( ( ~ ( SV76 @ SV103 )
| ( in @ SV103
@ ( dsetconstr @ SV28
@ ^ [SY545: $i] : ( SV76 @ SY545 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(440,plain,
! [SV29: $i,SV104: $i,SV77: $i] :
( ( ( in @ SV77 @ SV104 )
= $false )
| ( ( ~ ( in @ SV104 @ SV29 )
| ( in @ SV77 @ ( setunion @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(441,plain,
! [SV30: $i,SV114: $i] :
( ( ( ~ ( in @ SV114 @ SV30 ) )
= $true )
| ( ( ~ ! [SY460: $i] :
~ ~ ( ~ ( in @ SY460 @ SV30 )
| ~ ~ ~ ! [SY461: $i] :
~ ~ ( ~ ( in @ SY461 @ SY460 )
| ~ ( in @ SY461 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(442,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ~ ~ ( ~ ( SV31 @ SV115 )
| ~ ! [SY601: $i] :
( ~ ( SV31 @ SY601 )
| ( SV115 = SY601 ) ) ) )
= $true )
| ( ( ~ ! [SY464: $i] :
~ ~ ( ~ ( SV31 @ SY464 )
| ~ ! [SY465: $i] :
( ~ ( SV31 @ SY465 )
| ( SY464 = SY465 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(443,plain,
! [SV78: $i,SV32: $i > $i > $o] :
( ( ( ~ ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
| ~ ! [SY602: $i] :
~ ~ ( ~ ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SY602 )
| ~ ! [SY603: $i] :
( ~ ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SY603 )
| ( SY602 = SY603 ) ) ) )
= $false )
| ( ( ~ ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[387]) ).
thf(444,plain,
! [SV79: $i > $o,SV33: $i] :
( ( ( ~ ! [SY554: $i] :
~ ~ ( ~ ( in @ SY554 @ SV33 )
| ~ ( SV79 @ SY554 ) ) )
= $true )
| ( ( ! [SY555: $i] :
( ~ ( in @ SY555 @ SV33 )
| ~ ( SV79 @ SY555 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(445,plain,
! [SV34: $i,SV80: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 )
| ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 ) )
| ~ ( ~ ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 )
| ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 ) ) ) )
= $false )
| ( ( SV34 = SV80 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[389]) ).
thf(446,plain,
! [SV116: $i,SV36: $i > $o] :
( ( ( ~ ~ ( ~ ( SV36 @ SV116 )
| ~ ! [SY604: $i] :
( ~ ( SV36 @ SY604 )
| ( SV116 = SY604 ) ) ) )
= $true )
| ( ( ~ ! [SY481: $i] :
~ ( SV36 @ SY481 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(447,plain,
! [SV37: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ SV37 ) )
= $true )
| ( ( SV37 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(448,plain,
! [SV38: $i] :
( ( ( ! [SY483: $i] :
~ ( in @ SY483 @ SV38 ) )
= $false )
| ( ( SV38 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(449,plain,
! [SV40: $i,SV82: $i] :
( ( ~ ( in @ SV82 @ ( powerset @ SV40 ) )
| ! [SY557: $i] :
( ~ ( in @ SY557 @ SV82 )
| ( in @ SY557 @ SV40 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(450,plain,
! [SV40: $i,SV82: $i] :
( ( ~ ! [SY558: $i] :
( ~ ( in @ SY558 @ SV82 )
| ( in @ SY558 @ SV40 ) )
| ( in @ SV82 @ ( powerset @ SV40 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(451,plain,
! [SV86: $i,SV43: $i,SV105: $i] :
( ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false )
| ( ( ! [SY593: $o] :
( ~ ( ( SV105 != SV43 )
| SY593 )
| ~ ( ~ ( in @ SV105 @ SV86 )
| SY593 )
| SY593 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(452,plain,
! [SV87: $i > $o,SV44: $i] :
( ( ( ! [SY561: $i] :
~ ~ ( ~ ( in @ SY561 @ SV44 )
| ~ ~ ( SV87 @ SY561 ) ) )
= $true )
| ( ( ~ ! [SY562: $i] :
( ~ ( in @ SY562 @ SV44 )
| ( SV87 @ SY562 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(453,plain,
! [SV88: $i,SV45: $i] :
( ( ( SV45 = SV88 )
= $true )
| ( ( ~ ( in @ SV88 @ ( setadjoin @ SV45 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(454,plain,
! [SV46: $i] :
( ( ( ~ ( in @ emptyset @ SV46 ) )
= $true )
| ( ( ~ ! [SY496: $i] :
( ~ ~ ( ~ ( in @ SY496 @ omega )
| ~ ( in @ SY496 @ SV46 ) )
| ( in @ ( setadjoin @ SY496 @ SY496 ) @ SV46 ) ) )
= $true )
| ( ( ! [SY497: $i] :
( ~ ( in @ SY497 @ omega )
| ( in @ SY497 @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(455,plain,
! [SV89: $i,SV47: $i,SV106: $i] :
( ( ( in @ SV106 @ ( setadjoin @ SV47 @ ( setadjoin @ SV89 @ emptyset ) ) )
= $false )
| ( ( ( SV106 = SV47 )
| ( SV106 = SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(456,plain,
! [SV90: $i > $o,SV49: $i,SV107: $i] :
( ( ( in @ SV107 @ SV49 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV107
@ ( dsetconstr @ SV49
@ ^ [SY565: $i] : ( SV90 @ SY565 ) ) )
| ( SV90 @ SV107 ) )
| ~ ( ~ ( SV90 @ SV107 )
| ( in @ SV107
@ ( dsetconstr @ SV49
@ ^ [SY566: $i] : ( SV90 @ SY566 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(457,plain,
! [SV50: $i,SV91: $i] :
( ( ~ ( in @ SV91 @ ( setunion @ SV50 ) )
| ~ ! [SY567: $i] :
~ ~ ( ~ ( in @ SV91 @ SY567 )
| ~ ( in @ SY567 @ SV50 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[405]) ).
thf(458,plain,
! [SV50: $i,SV91: $i] :
( ( ~ ~ ! [SY568: $i] :
~ ~ ( ~ ( in @ SV91 @ SY568 )
| ~ ( in @ SY568 @ SV50 ) )
| ( in @ SV91 @ ( setunion @ SV50 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(459,plain,
! [SV94: $i > $o,SV53: $i,SV108: $i] :
( ( ( in @ SV108
@ ( dsetconstr @ SV53
@ ^ [SY570: $i] : ( SV94 @ SY570 ) ) )
= $false )
| ( ( SV94 @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(460,plain,
! [SV54: $i] :
( ( ( in @ ( sK3_SY512 @ SV54 ) @ SV54 )
= $true )
| ( ( SV54 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[410]) ).
thf(461,plain,
! [SV55: $i] :
( ( ( in @ ( sK4_SY513 @ SV55 ) @ SV55 )
= $true )
| ( ( SV55 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(462,plain,
! [SV56: $i,SV95: $i] :
( ( ( ~ ( in @ ( sK9_SY571 @ SV95 @ SV56 ) @ SV56 )
| ( in @ ( sK9_SY571 @ SV95 @ SV56 ) @ SV95 ) )
= $false )
| ( ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV95 )
| ( in @ SY572 @ SV56 ) )
| ( SV56 = SV95 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[412]) ).
thf(463,plain,
! [SV110: $o,SV9: $i,SV62: $i] :
( ( ( ~ ! [SY597: $i] :
( ~ ( in @ SV62 @ SY597 )
| ~ ( in @ SY597 @ SV9 )
| SV110 ) )
= $true )
| ( SV110 = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(464,plain,
! [SV9: $i,SV62: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV62 @ SX0 )
| ~ ( in @ SX0 @ SV9 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(465,plain,
! [SV9: $i,SV62: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV62 @ SX0 )
| ~ ( in @ SX0 @ SV9 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(466,plain,
( ( ~ ~ ( ~ ( sK1_SX0 @ sK10_SY521 )
| ~ ! [SY605: $i] :
( ~ ( sK1_SX0 @ SY605 )
| ( sK10_SY521 = SY605 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[420]) ).
thf(467,plain,
! [SV111: $i] :
( ( ~ ( ~ ( sK1_SX0 @ SV111 )
| ~ ! [SY598: $i] :
( ~ ( sK1_SX0 @ SY598 )
| ( SV111 = SY598 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(468,plain,
! [SV10: $i,SV63: $i,SV97: $i] :
( ( ( ~ ( in @ SV97 @ SV63 ) )
= $true )
| ( ( in @ SV97 @ SV10 )
= $true )
| ( ( in @ SV63 @ ( powerset @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(469,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK11_SY398 @ SV11 ) @ SV11 )
| ~ $true ) )
= $false )
| ( ( SV11 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[423]) ).
thf(470,plain,
! [SV64: $i > $o,SV12: $i,SV118: $i] :
( ( ( ~ ( in @ SV118 @ SV12 )
| ( SV64 @ SV118 ) )
= $true )
| ( ( ~ ! [SY527: $i] :
~ ~ ( ~ ( in @ SY527 @ SV12 )
| ~ ~ ( SV64 @ SY527 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(471,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ ( sK2_SY402 @ SV13 ) )
| ! [SY404: $i] :
( ~ ( in @ SY404 @ SY573 )
| ( in @ SY404 @ SV13 ) ) )
| ~ ! [SY575: $i,SY576: $i] :
( ~ ~ ( ~ ( in @ SY575 @ SV13 )
| ~ ( in @ SY576 @ SV13 ) )
| ~ ! [SY577: $i] :
( ~ ( in @ SY577 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY575 @ SY577 )
| ( in @ SY576 @ SY577 ) )
| ~ ( ~ ( in @ SY576 @ SY577 )
| ( in @ SY575 @ SY577 ) ) ) )
| ( SY575 = SY576 ) ) )
| ~ ! [SY578: $i,SY579: $i] :
( ~ ~ ( ~ ( in @ SY578 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY579 @ ( sK2_SY402 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY578 )
| ( in @ SX4 @ SY579 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY579 )
| ( in @ SX4 @ SY578 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(472,plain,
! [SV13: $i] :
( ( ~ ! [SY582: $i] :
( ~ ~ ( ~ ! [SY413: $i] :
( ~ ( in @ SY413 @ SY582 )
| ( in @ SY413 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY582 ) )
| ~ ! [SY585: $i] :
~ ~ ! [SY586: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY585 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY586 @ SY582 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY585 )
| ~ ( in @ SX5 @ SY582 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY585 ) )
| ( in @ SY586 @ SY588 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(473,plain,
! [SV66: $i,SV16: $i,SV99: $i] :
( ( ( SV99 = SV16 )
= $true )
| ( ( in @ SV99 @ SV66 )
= $true )
| ( ( in @ SV99 @ ( setadjoin @ SV16 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(474,plain,
! [SV112: $i,SV17: $i > $o] :
( ( ( ~ ( ~ ( SV17 @ SV112 )
| ~ ! [SY599: $i] :
( ~ ( SV17 @ SY599 )
| ( SV112 = SY599 ) ) ) )
= $false )
| ( ( SV17
@ ( descr
@ ^ [SY426: $i] : ( SV17 @ SY426 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(475,plain,
! [SV18: $i,SV100: $i,SV67: $i > $o] :
( ( ( ~ ( SV67 @ SV100 ) )
= $true )
| ( ( ( dsetconstr @ SV18
@ ^ [SY531: $i] : ( SV67 @ SY531 ) )
!= emptyset )
= $true )
| ( ( in @ SV100 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(476,plain,
! [SV19: $i,SV68: $i > $o] :
( ( ( ~ ( in @ ( sK5_SY532 @ SV68 @ SV19 ) @ SV19 ) )
= $false )
| ( ( ~ ~ ! [SY533: $i] :
~ ~ ( ~ ( in @ SY533 @ SV19 )
| ~ ( SV68 @ SY533 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(477,plain,
! [SV19: $i,SV68: $i > $o] :
( ( ( ~ ( SV68 @ ( sK5_SY532 @ SV68 @ SV19 ) ) )
= $false )
| ( ( ~ ~ ! [SY533: $i] :
~ ~ ( ~ ( in @ SY533 @ SV19 )
| ~ ( SV68 @ SY533 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(478,plain,
! [SV69: $i,SV20: $i] :
( ( ( ~ ( in @ ( sK6_SY534 @ SV20 @ SV69 ) @ SV69 ) )
= $false )
| ( ( in @ SV69 @ ( powerset @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(479,plain,
! [SV69: $i,SV20: $i] :
( ( ( in @ ( sK6_SY534 @ SV20 @ SV69 ) @ SV20 )
= $false )
| ( ( in @ SV69 @ ( powerset @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(480,plain,
! [SV70: $i > $o,SV21: $i,SV119: $i] :
( ( ( ~ ( in @ SV119 @ SV21 )
| ( SV70 @ SV119 ) )
= $true )
| ( ( ~ ! [SY536: $i] :
~ ~ ( ~ ( in @ SY536 @ SV21 )
| ~ ~ ( SV70 @ SY536 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(481,plain,
! [SV71: $i > $o,SV22: $i] :
( ( ( ! [SY537: $i] :
~ ~ ( ~ ( in @ SY537 @ SV22 )
| ~ ( SV71 @ SY537 ) ) )
= $false )
| ( ( ! [SY538: $i] :
( ~ ( in @ SY538 @ SV22 )
| ~ ( SV71 @ SY538 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(482,plain,
! [SV72: $i,SV23: $i,SV101: $i] :
( ( ~ ( in @ SV101 @ ( setadjoin @ SV23 @ SV72 ) )
| ( SV101 = SV23 )
| ( in @ SV101 @ SV72 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(483,plain,
! [SV72: $i,SV23: $i,SV101: $i] :
( ( ~ ( ( SV101 = SV23 )
| ( in @ SV101 @ SV72 ) )
| ( in @ SV101 @ ( setadjoin @ SV23 @ SV72 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(484,plain,
! [SV73: $i > $o,SV24: $i,SV120: $i] :
( ( ( ~ ~ ( ~ ( in @ SV120 @ SV24 )
| ~ ( SV73 @ SV120 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV24
@ ^ [SY541: $i] : ( SV73 @ SY541 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(485,plain,
! [SV113: $i,SV27: $i > $o] :
( ( ( ~ ( ~ ( SV27 @ SV113 )
| ~ ! [SY600: $i] :
( ~ ( SV27 @ SY600 )
| ( SV113 = SY600 ) ) ) )
= $false )
| ( ( ~ ! [SY452: $i] :
~ ! [SY453: $i] :
~ ( ~ ( ~ ( SV27 @ SY453 )
| ( SY453 = SY452 ) )
| ~ ( ( SY453 != SY452 )
| ( SV27 @ SY453 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(486,plain,
! [SV28: $i,SV103: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ SV103 ) )
= $true )
| ( ( in @ SV103
@ ( dsetconstr @ SV28
@ ^ [SY545: $i] : ( SV76 @ SY545 ) ) )
= $true )
| ( ( in @ SV103 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(487,plain,
! [SV77: $i,SV29: $i,SV104: $i] :
( ( ( ~ ( in @ SV104 @ SV29 ) )
= $true )
| ( ( in @ SV77 @ ( setunion @ SV29 ) )
= $true )
| ( ( in @ SV77 @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(488,plain,
! [SV30: $i,SV114: $i] :
( ( ( in @ SV114 @ SV30 )
= $false )
| ( ( ~ ! [SY460: $i] :
~ ~ ( ~ ( in @ SY460 @ SV30 )
| ~ ~ ~ ! [SY461: $i] :
~ ~ ( ~ ( in @ SY461 @ SY460 )
| ~ ( in @ SY461 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(489,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ~ ( ~ ( SV31 @ SV115 )
| ~ ! [SY601: $i] :
( ~ ( SV31 @ SY601 )
| ( SV115 = SY601 ) ) ) )
= $false )
| ( ( ~ ! [SY464: $i] :
~ ~ ( ~ ( SV31 @ SY464 )
| ~ ! [SY465: $i] :
( ~ ( SV31 @ SY465 )
| ( SY464 = SY465 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(490,plain,
! [SV78: $i,SV32: $i > $i > $o] :
( ( ( ~ ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 ) )
= $false )
| ( ( ~ ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(491,plain,
! [SV78: $i,SV32: $i > $i > $o] :
( ( ( ~ ! [SY602: $i] :
~ ~ ( ~ ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SY602 )
| ~ ! [SY603: $i] :
( ~ ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SY603 )
| ( SY602 = SY603 ) ) ) )
= $false )
| ( ( ~ ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(492,plain,
! [SV79: $i > $o,SV33: $i] :
( ( ( ! [SY554: $i] :
~ ~ ( ~ ( in @ SY554 @ SV33 )
| ~ ( SV79 @ SY554 ) ) )
= $false )
| ( ( ! [SY555: $i] :
( ~ ( in @ SY555 @ SV33 )
| ~ ( SV79 @ SY555 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(493,plain,
! [SV34: $i,SV80: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 )
| ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 ) )
| ~ ( ~ ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 )
| ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 ) ) )
= $true )
| ( ( SV34 = SV80 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(494,plain,
! [SV116: $i,SV36: $i > $o] :
( ( ( ~ ( ~ ( SV36 @ SV116 )
| ~ ! [SY604: $i] :
( ~ ( SV36 @ SY604 )
| ( SV116 = SY604 ) ) ) )
= $false )
| ( ( ~ ! [SY481: $i] :
~ ( SV36 @ SY481 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(495,plain,
! [SV37: $i,SV117: $i] :
( ( ( in @ SV117 @ SV37 )
= $false )
| ( ( SV37 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(496,plain,
! [SV38: $i] :
( ( ( ~ ( in @ ( sK12_SY483 @ SV38 ) @ SV38 ) )
= $false )
| ( ( SV38 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[448]) ).
thf(497,plain,
! [SV40: $i,SV82: $i] :
( ( ( ~ ( in @ SV82 @ ( powerset @ SV40 ) ) )
= $true )
| ( ( ! [SY557: $i] :
( ~ ( in @ SY557 @ SV82 )
| ( in @ SY557 @ SV40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(498,plain,
! [SV40: $i,SV82: $i] :
( ( ( ~ ! [SY558: $i] :
( ~ ( in @ SY558 @ SV82 )
| ( in @ SY558 @ SV40 ) ) )
= $true )
| ( ( in @ SV82 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(499,plain,
! [SV86: $i,SV121: $o,SV43: $i,SV105: $i] :
( ( ( ~ ( ( SV105 != SV43 )
| SV121 )
| ~ ( ~ ( in @ SV105 @ SV86 )
| SV121 )
| SV121 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[451]) ).
thf(500,plain,
! [SV86: $i,SV43: $i,SV105: $i] :
( ( ( ~ ( ( SV105 != SV43 )
| $true )
| ~ ( ~ ( in @ SV105 @ SV86 )
| $true )
| $true )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[451]) ).
thf(501,plain,
! [SV86: $i,SV43: $i,SV105: $i] :
( ( ( ~ ( ( SV105 != SV43 )
| $false )
| ~ ( ~ ( in @ SV105 @ SV86 )
| $false )
| $false )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[451]) ).
thf(502,plain,
! [SV87: $i > $o,SV44: $i,SV122: $i] :
( ( ( ~ ~ ( ~ ( in @ SV122 @ SV44 )
| ~ ~ ( SV87 @ SV122 ) ) )
= $true )
| ( ( ~ ! [SY562: $i] :
( ~ ( in @ SY562 @ SV44 )
| ( SV87 @ SY562 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(503,plain,
! [SV45: $i,SV88: $i] :
( ( ( in @ SV88 @ ( setadjoin @ SV45 @ emptyset ) )
= $false )
| ( ( SV45 = SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(504,plain,
! [SV46: $i] :
( ( ( in @ emptyset @ SV46 )
= $false )
| ( ( ~ ! [SY496: $i] :
( ~ ~ ( ~ ( in @ SY496 @ omega )
| ~ ( in @ SY496 @ SV46 ) )
| ( in @ ( setadjoin @ SY496 @ SY496 ) @ SV46 ) ) )
= $true )
| ( ( ! [SY497: $i] :
( ~ ( in @ SY497 @ omega )
| ( in @ SY497 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(505,plain,
! [SV89: $i,SV47: $i,SV106: $i] :
( ( ( SV106 = SV47 )
= $true )
| ( ( SV106 = SV89 )
= $true )
| ( ( in @ SV106 @ ( setadjoin @ SV47 @ ( setadjoin @ SV89 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(506,plain,
! [SV90: $i > $o,SV49: $i,SV107: $i] :
( ( ( ~ ( ~ ( in @ SV107
@ ( dsetconstr @ SV49
@ ^ [SY565: $i] : ( SV90 @ SY565 ) ) )
| ( SV90 @ SV107 ) )
| ~ ( ~ ( SV90 @ SV107 )
| ( in @ SV107
@ ( dsetconstr @ SV49
@ ^ [SY566: $i] : ( SV90 @ SY566 ) ) ) ) )
= $false )
| ( ( in @ SV107 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(507,plain,
! [SV50: $i,SV91: $i] :
( ( ( ~ ( in @ SV91 @ ( setunion @ SV50 ) ) )
= $true )
| ( ( ~ ! [SY567: $i] :
~ ~ ( ~ ( in @ SV91 @ SY567 )
| ~ ( in @ SY567 @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(508,plain,
! [SV50: $i,SV91: $i] :
( ( ( ~ ~ ! [SY568: $i] :
~ ~ ( ~ ( in @ SV91 @ SY568 )
| ~ ( in @ SY568 @ SV50 ) ) )
= $true )
| ( ( in @ SV91 @ ( setunion @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(509,plain,
! [SV56: $i,SV95: $i] :
( ( ( ~ ( in @ ( sK9_SY571 @ SV95 @ SV56 ) @ SV56 ) )
= $false )
| ( ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV95 )
| ( in @ SY572 @ SV56 ) )
| ( SV56 = SV95 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(510,plain,
! [SV56: $i,SV95: $i] :
( ( ( in @ ( sK9_SY571 @ SV95 @ SV56 ) @ SV95 )
= $false )
| ( ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV95 )
| ( in @ SY572 @ SV56 ) )
| ( SV56 = SV95 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(511,plain,
! [SV110: $o,SV9: $i,SV62: $i] :
( ( ( ! [SY597: $i] :
( ~ ( in @ SV62 @ SY597 )
| ~ ( in @ SY597 @ SV9 )
| SV110 ) )
= $false )
| ( SV110 = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(512,plain,
! [SV9: $i,SV62: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV62 @ SX0 )
| ~ ( in @ SX0 @ SV9 )
| $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(513,plain,
! [SV9: $i,SV62: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV62 @ SX0 )
| ~ ( in @ SX0 @ SV9 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(514,plain,
( ( ~ ( ~ ( sK1_SX0 @ sK10_SY521 )
| ~ ! [SY605: $i] :
( ~ ( sK1_SX0 @ SY605 )
| ( sK10_SY521 = SY605 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(515,plain,
! [SV111: $i] :
( ( ~ ( sK1_SX0 @ SV111 )
| ~ ! [SY598: $i] :
( ~ ( sK1_SX0 @ SY598 )
| ( SV111 = SY598 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[467]) ).
thf(516,plain,
! [SV10: $i,SV63: $i,SV97: $i] :
( ( ( in @ SV97 @ SV63 )
= $false )
| ( ( in @ SV97 @ SV10 )
= $true )
| ( ( in @ SV63 @ ( powerset @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(517,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY398 @ SV11 ) @ SV11 )
| ~ $true ) )
= $true )
| ( ( SV11 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[469]) ).
thf(518,plain,
! [SV64: $i > $o,SV12: $i,SV118: $i] :
( ( ( ~ ( in @ SV118 @ SV12 ) )
= $true )
| ( ( SV64 @ SV118 )
= $true )
| ( ( ~ ! [SY527: $i] :
~ ~ ( ~ ( in @ SY527 @ SV12 )
| ~ ~ ( SV64 @ SY527 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(519,plain,
! [SV13: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ ( sK2_SY402 @ SV13 ) )
| ! [SY404: $i] :
( ~ ( in @ SY404 @ SY573 )
| ( in @ SY404 @ SV13 ) ) )
| ~ ! [SY575: $i,SY576: $i] :
( ~ ~ ( ~ ( in @ SY575 @ SV13 )
| ~ ( in @ SY576 @ SV13 ) )
| ~ ! [SY577: $i] :
( ~ ( in @ SY577 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY575 @ SY577 )
| ( in @ SY576 @ SY577 ) )
| ~ ( ~ ( in @ SY576 @ SY577 )
| ( in @ SY575 @ SY577 ) ) ) )
| ( SY575 = SY576 ) ) )
| ~ ! [SY578: $i,SY579: $i] :
( ~ ~ ( ~ ( in @ SY578 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY579 @ ( sK2_SY402 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY578 )
| ( in @ SX4 @ SY579 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY579 )
| ( in @ SX4 @ SY578 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[471]) ).
thf(520,plain,
! [SV13: $i] :
( ( ! [SY582: $i] :
( ~ ~ ( ~ ! [SY413: $i] :
( ~ ( in @ SY413 @ SY582 )
| ( in @ SY413 @ SV13 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY582 ) )
| ~ ! [SY585: $i] :
~ ~ ! [SY586: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY585 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY586 @ SY582 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY585 )
| ~ ( in @ SX5 @ SY582 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY585 ) )
| ( in @ SY586 @ SY588 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(521,plain,
! [SV112: $i,SV17: $i > $o] :
( ( ( ~ ( SV17 @ SV112 )
| ~ ! [SY599: $i] :
( ~ ( SV17 @ SY599 )
| ( SV112 = SY599 ) ) )
= $true )
| ( ( SV17
@ ( descr
@ ^ [SY426: $i] : ( SV17 @ SY426 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(522,plain,
! [SV18: $i,SV100: $i,SV67: $i > $o] :
( ( ( SV67 @ SV100 )
= $false )
| ( ( ( dsetconstr @ SV18
@ ^ [SY531: $i] : ( SV67 @ SY531 ) )
!= emptyset )
= $true )
| ( ( in @ SV100 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(523,plain,
! [SV19: $i,SV68: $i > $o] :
( ( ( in @ ( sK5_SY532 @ SV68 @ SV19 ) @ SV19 )
= $true )
| ( ( ~ ~ ! [SY533: $i] :
~ ~ ( ~ ( in @ SY533 @ SV19 )
| ~ ( SV68 @ SY533 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(524,plain,
! [SV19: $i,SV68: $i > $o] :
( ( ( SV68 @ ( sK5_SY532 @ SV68 @ SV19 ) )
= $true )
| ( ( ~ ~ ! [SY533: $i] :
~ ~ ( ~ ( in @ SY533 @ SV19 )
| ~ ( SV68 @ SY533 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(525,plain,
! [SV69: $i,SV20: $i] :
( ( ( in @ ( sK6_SY534 @ SV20 @ SV69 ) @ SV69 )
= $true )
| ( ( in @ SV69 @ ( powerset @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(526,plain,
! [SV70: $i > $o,SV21: $i,SV119: $i] :
( ( ( ~ ( in @ SV119 @ SV21 ) )
= $true )
| ( ( SV70 @ SV119 )
= $true )
| ( ( ~ ! [SY536: $i] :
~ ~ ( ~ ( in @ SY536 @ SV21 )
| ~ ~ ( SV70 @ SY536 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(527,plain,
! [SV22: $i,SV71: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY537 @ SV71 @ SV22 ) @ SV22 )
| ~ ( SV71 @ ( sK13_SY537 @ SV71 @ SV22 ) ) ) )
= $false )
| ( ( ! [SY538: $i] :
( ~ ( in @ SY538 @ SV22 )
| ~ ( SV71 @ SY538 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[481]) ).
thf(528,plain,
! [SV72: $i,SV23: $i,SV101: $i] :
( ( ( ~ ( in @ SV101 @ ( setadjoin @ SV23 @ SV72 ) ) )
= $true )
| ( ( ( SV101 = SV23 )
| ( in @ SV101 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(529,plain,
! [SV72: $i,SV23: $i,SV101: $i] :
( ( ( ~ ( ( SV101 = SV23 )
| ( in @ SV101 @ SV72 ) ) )
= $true )
| ( ( in @ SV101 @ ( setadjoin @ SV23 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(530,plain,
! [SV73: $i > $o,SV24: $i,SV120: $i] :
( ( ( ~ ( ~ ( in @ SV120 @ SV24 )
| ~ ( SV73 @ SV120 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV24
@ ^ [SY541: $i] : ( SV73 @ SY541 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(531,plain,
! [SV113: $i,SV27: $i > $o] :
( ( ( ~ ( SV27 @ SV113 )
| ~ ! [SY600: $i] :
( ~ ( SV27 @ SY600 )
| ( SV113 = SY600 ) ) )
= $true )
| ( ( ~ ! [SY452: $i] :
~ ! [SY453: $i] :
~ ( ~ ( ~ ( SV27 @ SY453 )
| ( SY453 = SY452 ) )
| ~ ( ( SY453 != SY452 )
| ( SV27 @ SY453 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[485]) ).
thf(532,plain,
! [SV28: $i,SV103: $i,SV76: $i > $o] :
( ( ( SV76 @ SV103 )
= $false )
| ( ( in @ SV103
@ ( dsetconstr @ SV28
@ ^ [SY545: $i] : ( SV76 @ SY545 ) ) )
= $true )
| ( ( in @ SV103 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(533,plain,
! [SV77: $i,SV29: $i,SV104: $i] :
( ( ( in @ SV104 @ SV29 )
= $false )
| ( ( in @ SV77 @ ( setunion @ SV29 ) )
= $true )
| ( ( in @ SV77 @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(534,plain,
! [SV114: $i,SV30: $i] :
( ( ( ! [SY460: $i] :
~ ~ ( ~ ( in @ SY460 @ SV30 )
| ~ ~ ~ ! [SY461: $i] :
~ ~ ( ~ ( in @ SY461 @ SY460 )
| ~ ( in @ SY461 @ SV30 ) ) ) )
= $false )
| ( ( in @ SV114 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(535,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ~ ( SV31 @ SV115 )
| ~ ! [SY601: $i] :
( ~ ( SV31 @ SY601 )
| ( SV115 = SY601 ) ) )
= $true )
| ( ( ~ ! [SY464: $i] :
~ ~ ( ~ ( SV31 @ SY464 )
| ~ ! [SY465: $i] :
( ~ ( SV31 @ SY465 )
| ( SY464 = SY465 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[489]) ).
thf(536,plain,
! [SV78: $i,SV32: $i > $i > $o] :
( ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true )
| ( ( ~ ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[490]) ).
thf(537,plain,
! [SV78: $i,SV32: $i > $i > $o] :
( ( ( ! [SY602: $i] :
~ ~ ( ~ ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SY602 )
| ~ ! [SY603: $i] :
( ~ ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SY603 )
| ( SY602 = SY603 ) ) ) )
= $true )
| ( ( ~ ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(538,plain,
! [SV33: $i,SV79: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_SY554 @ SV79 @ SV33 ) @ SV33 )
| ~ ( SV79 @ ( sK14_SY554 @ SV79 @ SV33 ) ) ) )
= $false )
| ( ( ! [SY555: $i] :
( ~ ( in @ SY555 @ SV33 )
| ~ ( SV79 @ SY555 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[492]) ).
thf(539,plain,
! [SV34: $i,SV80: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 )
| ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 )
| ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 ) ) )
= $true )
| ( ( SV34 = SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(540,plain,
! [SV116: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ SV116 )
| ~ ! [SY604: $i] :
( ~ ( SV36 @ SY604 )
| ( SV116 = SY604 ) ) )
= $true )
| ( ( ~ ! [SY481: $i] :
~ ( SV36 @ SY481 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(541,plain,
! [SV117: $i,SV37: $i] :
( ( ( SV37 = emptyset )
= $false )
| ( ( in @ SV117 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(542,plain,
! [SV38: $i] :
( ( ( in @ ( sK12_SY483 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[496]) ).
thf(543,plain,
! [SV40: $i,SV82: $i] :
( ( ( in @ SV82 @ ( powerset @ SV40 ) )
= $false )
| ( ( ! [SY557: $i] :
( ~ ( in @ SY557 @ SV82 )
| ( in @ SY557 @ SV40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(544,plain,
! [SV40: $i,SV82: $i] :
( ( ( ! [SY558: $i] :
( ~ ( in @ SY558 @ SV82 )
| ( in @ SY558 @ SV40 ) ) )
= $false )
| ( ( in @ SV82 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(545,plain,
! [SV86: $i,SV121: $o,SV43: $i,SV105: $i] :
( ( ( ~ ( ( SV105 != SV43 )
| SV121 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| SV121 )
| SV121 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(546,plain,
! [SV86: $i,SV43: $i,SV105: $i] :
( ( ( ~ ( ( SV105 != SV43 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| $true )
| $true )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(547,plain,
! [SV86: $i,SV43: $i,SV105: $i] :
( ( ( ~ ( ( SV105 != SV43 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| $false )
| $false )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[501]) ).
thf(548,plain,
! [SV87: $i > $o,SV44: $i,SV122: $i] :
( ( ( ~ ( ~ ( in @ SV122 @ SV44 )
| ~ ~ ( SV87 @ SV122 ) ) )
= $false )
| ( ( ~ ! [SY562: $i] :
( ~ ( in @ SY562 @ SV44 )
| ( SV87 @ SY562 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(549,plain,
! [SV46: $i] :
( ( ( ! [SY496: $i] :
( ~ ~ ( ~ ( in @ SY496 @ omega )
| ~ ( in @ SY496 @ SV46 ) )
| ( in @ ( setadjoin @ SY496 @ SY496 ) @ SV46 ) ) )
= $false )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( ! [SY497: $i] :
( ~ ( in @ SY497 @ omega )
| ( in @ SY497 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(550,plain,
! [SV90: $i > $o,SV49: $i,SV107: $i] :
( ( ( ~ ( ~ ( in @ SV107
@ ( dsetconstr @ SV49
@ ^ [SY565: $i] : ( SV90 @ SY565 ) ) )
| ( SV90 @ SV107 ) ) )
= $false )
| ( ( in @ SV107 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[506]) ).
thf(551,plain,
! [SV49: $i,SV107: $i,SV90: $i > $o] :
( ( ( ~ ( ~ ( SV90 @ SV107 )
| ( in @ SV107
@ ( dsetconstr @ SV49
@ ^ [SY566: $i] : ( SV90 @ SY566 ) ) ) ) )
= $false )
| ( ( in @ SV107 @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[506]) ).
thf(552,plain,
! [SV50: $i,SV91: $i] :
( ( ( in @ SV91 @ ( setunion @ SV50 ) )
= $false )
| ( ( ~ ! [SY567: $i] :
~ ~ ( ~ ( in @ SV91 @ SY567 )
| ~ ( in @ SY567 @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(553,plain,
! [SV50: $i,SV91: $i] :
( ( ( ~ ! [SY568: $i] :
~ ~ ( ~ ( in @ SV91 @ SY568 )
| ~ ( in @ SY568 @ SV50 ) ) )
= $false )
| ( ( in @ SV91 @ ( setunion @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(554,plain,
! [SV56: $i,SV95: $i] :
( ( ( in @ ( sK9_SY571 @ SV95 @ SV56 ) @ SV56 )
= $true )
| ( ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV95 )
| ( in @ SY572 @ SV56 ) )
| ( SV56 = SV95 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(555,plain,
! [SV56: $i,SV95: $i] :
( ( ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV95 )
| ( in @ SY572 @ SV56 ) ) )
= $true )
| ( ( SV56 = SV95 )
= $true )
| ( ( in @ ( sK9_SY571 @ SV95 @ SV56 ) @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(556,plain,
! [SV9: $i,SV110: $o,SV62: $i] :
( ( ( ~ ( in @ SV62 @ ( sK15_SY597 @ SV110 @ SV9 @ SV62 ) )
| ~ ( in @ ( sK15_SY597 @ SV110 @ SV9 @ SV62 ) @ SV9 )
| SV110 )
= $false )
| ( SV110 = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[511]) ).
thf(557,plain,
! [SV9: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ ( sK16_SX0 @ SV9 @ SV62 ) )
| ~ ( in @ ( sK16_SX0 @ SV9 @ SV62 ) @ SV9 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[512]) ).
thf(558,plain,
! [SV9: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ ( sK17_SX0 @ SV9 @ SV62 ) )
| ~ ( in @ ( sK17_SX0 @ SV9 @ SV62 ) @ SV9 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[513]) ).
thf(559,plain,
( ( ~ ( sK1_SX0 @ sK10_SY521 )
| ~ ! [SY605: $i] :
( ~ ( sK1_SX0 @ SY605 )
| ( sK10_SY521 = SY605 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(560,plain,
! [SV111: $i] :
( ( ( ~ ( sK1_SX0 @ SV111 ) )
= $true )
| ( ( ~ ! [SY598: $i] :
( ~ ( sK1_SX0 @ SY598 )
| ( SV111 = SY598 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(561,plain,
! [SV11: $i] :
( ( ( ~ ( in @ ( sK11_SY398 @ SV11 ) @ SV11 )
| ~ $true )
= $false )
| ( ( SV11 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(562,plain,
! [SV64: $i > $o,SV12: $i,SV118: $i] :
( ( ( in @ SV118 @ SV12 )
= $false )
| ( ( SV64 @ SV118 )
= $true )
| ( ( ~ ! [SY527: $i] :
~ ~ ( ~ ( in @ SY527 @ SV12 )
| ~ ~ ( SV64 @ SY527 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(563,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ ( sK2_SY402 @ SV13 ) )
| ! [SY404: $i] :
( ~ ( in @ SY404 @ SY573 )
| ( in @ SY404 @ SV13 ) ) )
| ~ ! [SY575: $i,SY576: $i] :
( ~ ~ ( ~ ( in @ SY575 @ SV13 )
| ~ ( in @ SY576 @ SV13 ) )
| ~ ! [SY577: $i] :
( ~ ( in @ SY577 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY575 @ SY577 )
| ( in @ SY576 @ SY577 ) )
| ~ ( ~ ( in @ SY576 @ SY577 )
| ( in @ SY575 @ SY577 ) ) ) )
| ( SY575 = SY576 ) ) )
| ~ ! [SY578: $i,SY579: $i] :
( ~ ~ ( ~ ( in @ SY578 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY579 @ ( sK2_SY402 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY578 )
| ( in @ SX4 @ SY579 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY579 )
| ( in @ SX4 @ SY578 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(564,plain,
! [SV13: $i,SV123: $i] :
( ( ~ ~ ( ~ ! [SY606: $i] :
( ~ ( in @ SY606 @ SV123 )
| ( in @ SY606 @ SV13 ) )
| ~ ~ ! [SY607: $i] :
~ ( in @ SY607 @ SV123 ) )
| ~ ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(565,plain,
! [SV112: $i,SV17: $i > $o] :
( ( ( ~ ( SV17 @ SV112 ) )
= $true )
| ( ( ~ ! [SY599: $i] :
( ~ ( SV17 @ SY599 )
| ( SV112 = SY599 ) ) )
= $true )
| ( ( SV17
@ ( descr
@ ^ [SY426: $i] : ( SV17 @ SY426 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(566,plain,
! [SV100: $i,SV67: $i > $o,SV18: $i] :
( ( ( ( dsetconstr @ SV18
@ ^ [SY531: $i] : ( SV67 @ SY531 ) )
= emptyset )
= $false )
| ( ( SV67 @ SV100 )
= $false )
| ( ( in @ SV100 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(567,plain,
! [SV68: $i > $o,SV19: $i] :
( ( ( ~ ! [SY533: $i] :
~ ~ ( ~ ( in @ SY533 @ SV19 )
| ~ ( SV68 @ SY533 ) ) )
= $false )
| ( ( in @ ( sK5_SY532 @ SV68 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(568,plain,
! [SV68: $i > $o,SV19: $i] :
( ( ( ~ ! [SY533: $i] :
~ ~ ( ~ ( in @ SY533 @ SV19 )
| ~ ( SV68 @ SY533 ) ) )
= $false )
| ( ( SV68 @ ( sK5_SY532 @ SV68 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(569,plain,
! [SV70: $i > $o,SV21: $i,SV119: $i] :
( ( ( in @ SV119 @ SV21 )
= $false )
| ( ( SV70 @ SV119 )
= $true )
| ( ( ~ ! [SY536: $i] :
~ ~ ( ~ ( in @ SY536 @ SV21 )
| ~ ~ ( SV70 @ SY536 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(570,plain,
! [SV22: $i,SV71: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK13_SY537 @ SV71 @ SV22 ) @ SV22 )
| ~ ( SV71 @ ( sK13_SY537 @ SV71 @ SV22 ) ) ) )
= $true )
| ( ( ! [SY538: $i] :
( ~ ( in @ SY538 @ SV22 )
| ~ ( SV71 @ SY538 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(571,plain,
! [SV72: $i,SV23: $i,SV101: $i] :
( ( ( in @ SV101 @ ( setadjoin @ SV23 @ SV72 ) )
= $false )
| ( ( ( SV101 = SV23 )
| ( in @ SV101 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(572,plain,
! [SV72: $i,SV23: $i,SV101: $i] :
( ( ( ( SV101 = SV23 )
| ( in @ SV101 @ SV72 ) )
= $false )
| ( ( in @ SV101 @ ( setadjoin @ SV23 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(573,plain,
! [SV73: $i > $o,SV24: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV24 )
| ~ ( SV73 @ SV120 ) )
= $true )
| ( ( ( ( dsetconstr @ SV24
@ ^ [SY541: $i] : ( SV73 @ SY541 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(574,plain,
! [SV113: $i,SV27: $i > $o] :
( ( ( ~ ( SV27 @ SV113 ) )
= $true )
| ( ( ~ ! [SY600: $i] :
( ~ ( SV27 @ SY600 )
| ( SV113 = SY600 ) ) )
= $true )
| ( ( ~ ! [SY452: $i] :
~ ! [SY453: $i] :
~ ( ~ ( ~ ( SV27 @ SY453 )
| ( SY453 = SY452 ) )
| ~ ( ( SY453 != SY452 )
| ( SV27 @ SY453 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[531]) ).
thf(575,plain,
! [SV30: $i,SV114: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY460 @ SV114 @ SV30 ) @ SV30 )
| ~ ~ ~ ! [SY613: $i] :
~ ~ ( ~ ( in @ SY613 @ ( sK18_SY460 @ SV114 @ SV30 ) )
| ~ ( in @ SY613 @ SV30 ) ) ) )
= $false )
| ( ( in @ SV114 @ SV30 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[534]) ).
thf(576,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ~ ( SV31 @ SV115 ) )
= $true )
| ( ( ~ ! [SY601: $i] :
( ~ ( SV31 @ SY601 )
| ( SV115 = SY601 ) ) )
= $true )
| ( ( ~ ! [SY464: $i] :
~ ~ ( ~ ( SV31 @ SY464 )
| ~ ! [SY465: $i] :
( ~ ( SV31 @ SY465 )
| ( SY464 = SY465 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(577,plain,
! [SV32: $i > $i > $o,SV78: $i] :
( ( ( ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $false )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(578,plain,
! [SV124: $i,SV78: $i,SV32: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
| ~ ! [SY614: $i] :
( ~ ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SY614 )
| ( SV124 = SY614 ) ) ) )
= $true )
| ( ( ~ ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(579,plain,
! [SV33: $i,SV79: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK14_SY554 @ SV79 @ SV33 ) @ SV33 )
| ~ ( SV79 @ ( sK14_SY554 @ SV79 @ SV33 ) ) ) )
= $true )
| ( ( ! [SY555: $i] :
( ~ ( in @ SY555 @ SV33 )
| ~ ( SV79 @ SY555 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(580,plain,
! [SV34: $i,SV80: $i] :
( ( ( ~ ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 )
| ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 )
| ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 ) ) )
= $true )
| ( ( SV34 = SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(581,plain,
! [SV116: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ SV116 ) )
= $true )
| ( ( ~ ! [SY604: $i] :
( ~ ( SV36 @ SY604 )
| ( SV116 = SY604 ) ) )
= $true )
| ( ( ~ ! [SY481: $i] :
~ ( SV36 @ SY481 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[540]) ).
thf(582,plain,
! [SV40: $i,SV82: $i,SV125: $i] :
( ( ( ~ ( in @ SV125 @ SV82 )
| ( in @ SV125 @ SV40 ) )
= $true )
| ( ( in @ SV82 @ ( powerset @ SV40 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(583,plain,
! [SV82: $i,SV40: $i] :
( ( ( ~ ( in @ ( sK19_SY558 @ SV40 @ SV82 ) @ SV82 )
| ( in @ ( sK19_SY558 @ SV40 @ SV82 ) @ SV40 ) )
= $false )
| ( ( in @ SV82 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[544]) ).
thf(584,plain,
! [SV86: $i,SV121: $o,SV43: $i,SV105: $i] :
( ( ( ( SV105 != SV43 )
| SV121 )
= $false )
| ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| SV121 )
| SV121 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(585,plain,
! [SV86: $i,SV43: $i,SV105: $i] :
( ( ( ( SV105 != SV43 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| $true )
| $true )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(586,plain,
! [SV86: $i,SV43: $i,SV105: $i] :
( ( ( ( SV105 != SV43 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| $false )
| $false )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(587,plain,
! [SV87: $i > $o,SV44: $i,SV122: $i] :
( ( ( ~ ( in @ SV122 @ SV44 )
| ~ ~ ( SV87 @ SV122 ) )
= $true )
| ( ( ~ ! [SY562: $i] :
( ~ ( in @ SY562 @ SV44 )
| ( SV87 @ SY562 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(588,plain,
! [SV46: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY496 @ SV46 ) @ omega )
| ~ ( in @ ( sK20_SY496 @ SV46 ) @ SV46 ) )
| ( in @ ( setadjoin @ ( sK20_SY496 @ SV46 ) @ ( sK20_SY496 @ SV46 ) ) @ SV46 ) )
= $false )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( ! [SY497: $i] :
( ~ ( in @ SY497 @ omega )
| ( in @ SY497 @ SV46 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[549]) ).
thf(589,plain,
! [SV90: $i > $o,SV49: $i,SV107: $i] :
( ( ( ~ ( in @ SV107
@ ( dsetconstr @ SV49
@ ^ [SY565: $i] : ( SV90 @ SY565 ) ) )
| ( SV90 @ SV107 ) )
= $true )
| ( ( in @ SV107 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(590,plain,
! [SV49: $i,SV107: $i,SV90: $i > $o] :
( ( ( ~ ( SV90 @ SV107 )
| ( in @ SV107
@ ( dsetconstr @ SV49
@ ^ [SY566: $i] : ( SV90 @ SY566 ) ) ) )
= $true )
| ( ( in @ SV107 @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(591,plain,
! [SV50: $i,SV91: $i] :
( ( ( ! [SY567: $i] :
~ ~ ( ~ ( in @ SV91 @ SY567 )
| ~ ( in @ SY567 @ SV50 ) ) )
= $false )
| ( ( in @ SV91 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(592,plain,
! [SV50: $i,SV91: $i] :
( ( ( ! [SY568: $i] :
~ ~ ( ~ ( in @ SV91 @ SY568 )
| ~ ( in @ SY568 @ SV50 ) ) )
= $true )
| ( ( in @ SV91 @ ( setunion @ SV50 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(593,plain,
! [SV56: $i,SV95: $i] :
( ( ( ~ ! [SY572: $i] :
( ~ ( in @ SY572 @ SV95 )
| ( in @ SY572 @ SV56 ) ) )
= $true )
| ( ( SV56 = SV95 )
= $true )
| ( ( in @ ( sK9_SY571 @ SV95 @ SV56 ) @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(594,plain,
! [SV56: $i,SV95: $i] :
( ( ( ! [SY572: $i] :
( ~ ( in @ SY572 @ SV95 )
| ( in @ SY572 @ SV56 ) ) )
= $false )
| ( ( SV56 = SV95 )
= $true )
| ( ( in @ ( sK9_SY571 @ SV95 @ SV56 ) @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(595,plain,
! [SV9: $i,SV110: $o,SV62: $i] :
( ( ( ~ ( in @ SV62 @ ( sK15_SY597 @ SV110 @ SV9 @ SV62 ) ) )
= $false )
| ( SV110 = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[556]) ).
thf(596,plain,
! [SV62: $i,SV9: $i,SV110: $o] :
( ( ( ~ ( in @ ( sK15_SY597 @ SV110 @ SV9 @ SV62 ) @ SV9 )
| SV110 )
= $false )
| ( SV110 = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[556]) ).
thf(597,plain,
! [SV9: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ ( sK16_SX0 @ SV9 @ SV62 ) ) )
= $false )
| ( $true = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[557]) ).
thf(598,plain,
! [SV62: $i,SV9: $i] :
( ( ( ~ ( in @ ( sK16_SX0 @ SV9 @ SV62 ) @ SV9 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[557]) ).
thf(599,plain,
! [SV9: $i,SV62: $i] :
( ( ( ~ ( in @ SV62 @ ( sK17_SX0 @ SV9 @ SV62 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[558]) ).
thf(600,plain,
! [SV62: $i,SV9: $i] :
( ( ( ~ ( in @ ( sK17_SX0 @ SV9 @ SV62 ) @ SV9 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[558]) ).
thf(601,plain,
( ( ~ ( sK1_SX0 @ sK10_SY521 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[559]) ).
thf(602,plain,
( ( ~ ! [SY605: $i] :
( ~ ( sK1_SX0 @ SY605 )
| ( sK10_SY521 = SY605 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[559]) ).
thf(603,plain,
! [SV111: $i] :
( ( ( sK1_SX0 @ SV111 )
= $false )
| ( ( ~ ! [SY598: $i] :
( ~ ( sK1_SX0 @ SY598 )
| ( SV111 = SY598 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(604,plain,
! [SV11: $i] :
( ( ( ~ ( in @ ( sK11_SY398 @ SV11 ) @ SV11 ) )
= $false )
| ( ( SV11 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[561]) ).
thf(605,plain,
! [SV11: $i] :
( ( ( ~ $true ) = $false )
| ( ( SV11 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[561]) ).
thf(606,plain,
! [SV118: $i,SV64: $i > $o,SV12: $i] :
( ( ( ! [SY527: $i] :
~ ~ ( ~ ( in @ SY527 @ SV12 )
| ~ ~ ( SV64 @ SY527 ) ) )
= $false )
| ( ( SV64 @ SV118 )
= $true )
| ( ( in @ SV118 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(607,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ ( sK2_SY402 @ SV13 ) )
| ! [SY404: $i] :
( ~ ( in @ SY404 @ SY573 )
| ( in @ SY404 @ SV13 ) ) )
| ~ ! [SY575: $i,SY576: $i] :
( ~ ~ ( ~ ( in @ SY575 @ SV13 )
| ~ ( in @ SY576 @ SV13 ) )
| ~ ! [SY577: $i] :
( ~ ( in @ SY577 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY575 @ SY577 )
| ( in @ SY576 @ SY577 ) )
| ~ ( ~ ( in @ SY576 @ SY577 )
| ( in @ SY575 @ SY577 ) ) ) )
| ( SY575 = SY576 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[563]) ).
thf(608,plain,
! [SV13: $i] :
( ( ~ ! [SY578: $i,SY579: $i] :
( ~ ~ ( ~ ( in @ SY578 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY579 @ ( sK2_SY402 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY578 )
| ( in @ SX4 @ SY579 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY579 )
| ( in @ SX4 @ SY578 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[563]) ).
thf(609,plain,
! [SV13: $i,SV123: $i] :
( ( ( ~ ~ ( ~ ! [SY606: $i] :
( ~ ( in @ SY606 @ SV123 )
| ( in @ SY606 @ SV13 ) )
| ~ ~ ! [SY607: $i] :
~ ( in @ SY607 @ SV123 ) ) )
= $true )
| ( ( ~ ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(610,plain,
! [SV112: $i,SV17: $i > $o] :
( ( ( SV17 @ SV112 )
= $false )
| ( ( ~ ! [SY599: $i] :
( ~ ( SV17 @ SY599 )
| ( SV112 = SY599 ) ) )
= $true )
| ( ( SV17
@ ( descr
@ ^ [SY426: $i] : ( SV17 @ SY426 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(611,plain,
! [SV68: $i > $o,SV19: $i] :
( ( ( ! [SY533: $i] :
~ ~ ( ~ ( in @ SY533 @ SV19 )
| ~ ( SV68 @ SY533 ) ) )
= $true )
| ( ( in @ ( sK5_SY532 @ SV68 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(612,plain,
! [SV68: $i > $o,SV19: $i] :
( ( ( ! [SY533: $i] :
~ ~ ( ~ ( in @ SY533 @ SV19 )
| ~ ( SV68 @ SY533 ) ) )
= $true )
| ( ( SV68 @ ( sK5_SY532 @ SV68 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[568]) ).
thf(613,plain,
! [SV119: $i,SV70: $i > $o,SV21: $i] :
( ( ( ! [SY536: $i] :
~ ~ ( ~ ( in @ SY536 @ SV21 )
| ~ ~ ( SV70 @ SY536 ) ) )
= $false )
| ( ( SV70 @ SV119 )
= $true )
| ( ( in @ SV119 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(614,plain,
! [SV22: $i,SV71: $i > $o] :
( ( ( ~ ( in @ ( sK13_SY537 @ SV71 @ SV22 ) @ SV22 )
| ~ ( SV71 @ ( sK13_SY537 @ SV71 @ SV22 ) ) )
= $false )
| ( ( ! [SY538: $i] :
( ~ ( in @ SY538 @ SV22 )
| ~ ( SV71 @ SY538 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(615,plain,
! [SV72: $i,SV23: $i,SV101: $i] :
( ( ( SV101 = SV23 )
= $true )
| ( ( in @ SV101 @ SV72 )
= $true )
| ( ( in @ SV101 @ ( setadjoin @ SV23 @ SV72 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(616,plain,
! [SV72: $i,SV23: $i,SV101: $i] :
( ( ( SV101 = SV23 )
= $false )
| ( ( in @ SV101 @ ( setadjoin @ SV23 @ SV72 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[572]) ).
thf(617,plain,
! [SV23: $i,SV72: $i,SV101: $i] :
( ( ( in @ SV101 @ SV72 )
= $false )
| ( ( in @ SV101 @ ( setadjoin @ SV23 @ SV72 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[572]) ).
thf(618,plain,
! [SV73: $i > $o,SV24: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV24 ) )
= $true )
| ( ( ~ ( SV73 @ SV120 ) )
= $true )
| ( ( ( ( dsetconstr @ SV24
@ ^ [SY541: $i] : ( SV73 @ SY541 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(619,plain,
! [SV113: $i,SV27: $i > $o] :
( ( ( SV27 @ SV113 )
= $false )
| ( ( ~ ! [SY600: $i] :
( ~ ( SV27 @ SY600 )
| ( SV113 = SY600 ) ) )
= $true )
| ( ( ~ ! [SY452: $i] :
~ ! [SY453: $i] :
~ ( ~ ( ~ ( SV27 @ SY453 )
| ( SY453 = SY452 ) )
| ~ ( ( SY453 != SY452 )
| ( SV27 @ SY453 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(620,plain,
! [SV30: $i,SV114: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY460 @ SV114 @ SV30 ) @ SV30 )
| ~ ~ ~ ! [SY613: $i] :
~ ~ ( ~ ( in @ SY613 @ ( sK18_SY460 @ SV114 @ SV30 ) )
| ~ ( in @ SY613 @ SV30 ) ) ) )
= $true )
| ( ( in @ SV114 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(621,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( SV31 @ SV115 )
= $false )
| ( ( ~ ! [SY601: $i] :
( ~ ( SV31 @ SY601 )
| ( SV115 = SY601 ) ) )
= $true )
| ( ( ~ ! [SY464: $i] :
~ ~ ( ~ ( SV31 @ SY464 )
| ~ ! [SY465: $i] :
( ~ ( SV31 @ SY465 )
| ( SY464 = SY465 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(622,plain,
! [SV78: $i,SV32: $i > $i > $o] :
( ( ( ~ ! [SY615: $i] :
~ ( ~ ( ~ ( in @ SY615 @ ( sK21_SY550 @ SV32 @ SV78 ) )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY615 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY615 ) )
| ( in @ SY615 @ ( sK21_SY550 @ SV32 @ SV78 ) ) ) ) )
= $false )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[577]) ).
thf(623,plain,
! [SV124: $i,SV78: $i,SV32: $i > $i > $o] :
( ( ( ~ ( ~ ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
| ~ ! [SY614: $i] :
( ~ ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SY614 )
| ( SV124 = SY614 ) ) ) )
= $false )
| ( ( ~ ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(624,plain,
! [SV33: $i,SV79: $i > $o] :
( ( ( ~ ( in @ ( sK14_SY554 @ SV79 @ SV33 ) @ SV33 )
| ~ ( SV79 @ ( sK14_SY554 @ SV79 @ SV33 ) ) )
= $false )
| ( ( ! [SY555: $i] :
( ~ ( in @ SY555 @ SV33 )
| ~ ( SV79 @ SY555 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(625,plain,
! [SV34: $i,SV80: $i] :
( ( ( ~ ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 )
| ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 ) ) )
= $true )
| ( ( SV34 = SV80 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[580]) ).
thf(626,plain,
! [SV34: $i,SV80: $i] :
( ( ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 )
| ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 ) ) )
= $true )
| ( ( SV34 = SV80 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[580]) ).
thf(627,plain,
! [SV116: $i,SV36: $i > $o] :
( ( ( SV36 @ SV116 )
= $false )
| ( ( ~ ! [SY604: $i] :
( ~ ( SV36 @ SY604 )
| ( SV116 = SY604 ) ) )
= $true )
| ( ( ~ ! [SY481: $i] :
~ ( SV36 @ SY481 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(628,plain,
! [SV40: $i,SV82: $i,SV125: $i] :
( ( ( ~ ( in @ SV125 @ SV82 ) )
= $true )
| ( ( in @ SV125 @ SV40 )
= $true )
| ( ( in @ SV82 @ ( powerset @ SV40 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[582]) ).
thf(629,plain,
! [SV82: $i,SV40: $i] :
( ( ( ~ ( in @ ( sK19_SY558 @ SV40 @ SV82 ) @ SV82 ) )
= $false )
| ( ( in @ SV82 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(630,plain,
! [SV82: $i,SV40: $i] :
( ( ( in @ ( sK19_SY558 @ SV40 @ SV82 ) @ SV40 )
= $false )
| ( ( in @ SV82 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(631,plain,
! [SV121: $o,SV86: $i,SV43: $i,SV105: $i] :
( ( ( SV105 != SV43 )
= $false )
| ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| SV121 )
| SV121 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[584]) ).
thf(632,plain,
! [SV43: $i,SV86: $i,SV105: $i,SV121: $o] :
( ( SV121 = $false )
| ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| SV121 )
| SV121 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[584]) ).
thf(633,plain,
! [SV86: $i,SV43: $i,SV105: $i] :
( ( ( SV105 != SV43 )
= $false )
| ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| $true )
| $true )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[585]) ).
thf(634,plain,
! [SV43: $i,SV86: $i,SV105: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| $true )
| $true )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[585]) ).
thf(635,plain,
! [SV86: $i,SV43: $i,SV105: $i] :
( ( ( SV105 != SV43 )
= $false )
| ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| $false )
| $false )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[586]) ).
thf(636,plain,
! [SV43: $i,SV86: $i,SV105: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| $false )
| $false )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[586]) ).
thf(637,plain,
! [SV87: $i > $o,SV44: $i,SV122: $i] :
( ( ( ~ ( in @ SV122 @ SV44 ) )
= $true )
| ( ( ~ ~ ( SV87 @ SV122 ) )
= $true )
| ( ( ~ ! [SY562: $i] :
( ~ ( in @ SY562 @ SV44 )
| ( SV87 @ SY562 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(638,plain,
! [SV46: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY496 @ SV46 ) @ omega )
| ~ ( in @ ( sK20_SY496 @ SV46 ) @ SV46 ) ) )
= $false )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( ! [SY497: $i] :
( ~ ( in @ SY497 @ omega )
| ( in @ SY497 @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[588]) ).
thf(639,plain,
! [SV46: $i] :
( ( ( in @ ( setadjoin @ ( sK20_SY496 @ SV46 ) @ ( sK20_SY496 @ SV46 ) ) @ SV46 )
= $false )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( ! [SY497: $i] :
( ~ ( in @ SY497 @ omega )
| ( in @ SY497 @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[588]) ).
thf(640,plain,
! [SV90: $i > $o,SV49: $i,SV107: $i] :
( ( ( ~ ( in @ SV107
@ ( dsetconstr @ SV49
@ ^ [SY565: $i] : ( SV90 @ SY565 ) ) ) )
= $true )
| ( ( SV90 @ SV107 )
= $true )
| ( ( in @ SV107 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[589]) ).
thf(641,plain,
! [SV49: $i,SV107: $i,SV90: $i > $o] :
( ( ( ~ ( SV90 @ SV107 ) )
= $true )
| ( ( in @ SV107
@ ( dsetconstr @ SV49
@ ^ [SY566: $i] : ( SV90 @ SY566 ) ) )
= $true )
| ( ( in @ SV107 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(642,plain,
! [SV50: $i,SV91: $i] :
( ( ( ~ ~ ( ~ ( in @ SV91 @ ( sK22_SY567 @ SV50 @ SV91 ) )
| ~ ( in @ ( sK22_SY567 @ SV50 @ SV91 ) @ SV50 ) ) )
= $false )
| ( ( in @ SV91 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[591]) ).
thf(643,plain,
! [SV50: $i,SV126: $i,SV91: $i] :
( ( ( ~ ~ ( ~ ( in @ SV91 @ SV126 )
| ~ ( in @ SV126 @ SV50 ) ) )
= $true )
| ( ( in @ SV91 @ ( setunion @ SV50 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(644,plain,
! [SV56: $i,SV95: $i] :
( ( ( ! [SY572: $i] :
( ~ ( in @ SY572 @ SV95 )
| ( in @ SY572 @ SV56 ) ) )
= $false )
| ( ( SV56 = SV95 )
= $true )
| ( ( in @ ( sK9_SY571 @ SV95 @ SV56 ) @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(645,plain,
! [SV95: $i,SV56: $i] :
( ( ( ~ ( in @ ( sK23_SY572 @ SV56 @ SV95 ) @ SV95 )
| ( in @ ( sK23_SY572 @ SV56 @ SV95 ) @ SV56 ) )
= $false )
| ( ( SV56 = SV95 )
= $true )
| ( ( in @ ( sK9_SY571 @ SV95 @ SV56 ) @ SV95 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[594]) ).
thf(646,plain,
! [SV9: $i,SV110: $o,SV62: $i] :
( ( ( in @ SV62 @ ( sK15_SY597 @ SV110 @ SV9 @ SV62 ) )
= $true )
| ( SV110 = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(647,plain,
! [SV62: $i,SV9: $i,SV110: $o] :
( ( ( ~ ( in @ ( sK15_SY597 @ SV110 @ SV9 @ SV62 ) @ SV9 ) )
= $false )
| ( SV110 = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[596]) ).
thf(648,plain,
! [SV9: $i,SV62: $i,SV110: $o] :
( ( SV110 = $false )
| ( SV110 = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[596]) ).
thf(649,plain,
! [SV9: $i,SV62: $i] :
( ( ( in @ SV62 @ ( sK16_SX0 @ SV9 @ SV62 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[597]) ).
thf(650,plain,
! [SV62: $i,SV9: $i] :
( ( ( ~ ( in @ ( sK16_SX0 @ SV9 @ SV62 ) @ SV9 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[598]) ).
thf(651,plain,
! [SV9: $i,SV62: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[598]) ).
thf(652,plain,
! [SV9: $i,SV62: $i] :
( ( ( in @ SV62 @ ( sK17_SX0 @ SV9 @ SV62 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[599]) ).
thf(653,plain,
! [SV62: $i,SV9: $i] :
( ( ( ~ ( in @ ( sK17_SX0 @ SV9 @ SV62 ) @ SV9 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[600]) ).
thf(654,plain,
! [SV9: $i,SV62: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[600]) ).
thf(655,plain,
( ( sK1_SX0 @ sK10_SY521 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[601]) ).
thf(656,plain,
( ( ! [SY605: $i] :
( ~ ( sK1_SX0 @ SY605 )
| ( sK10_SY521 = SY605 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[602]) ).
thf(657,plain,
! [SV111: $i] :
( ( ( ! [SY598: $i] :
( ~ ( sK1_SX0 @ SY598 )
| ( SV111 = SY598 ) ) )
= $false )
| ( ( sK1_SX0 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(658,plain,
! [SV11: $i] :
( ( ( in @ ( sK11_SY398 @ SV11 ) @ SV11 )
= $true )
| ( ( SV11 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[604]) ).
thf(659,plain,
! [SV11: $i] :
( ( $true = $true )
| ( ( SV11 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[605]) ).
thf(660,plain,
! [SV12: $i,SV64: $i > $o,SV118: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY527 @ SV118 @ SV64 @ SV12 ) @ SV12 )
| ~ ~ ( SV64 @ ( sK24_SY527 @ SV118 @ SV64 @ SV12 ) ) ) )
= $false )
| ( ( SV64 @ SV118 )
= $true )
| ( ( in @ SV118 @ SV12 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[606]) ).
thf(661,plain,
! [SV13: $i] :
( ( ~ ( ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ ( sK2_SY402 @ SV13 ) )
| ! [SY404: $i] :
( ~ ( in @ SY404 @ SY573 )
| ( in @ SY404 @ SV13 ) ) )
| ~ ! [SY575: $i,SY576: $i] :
( ~ ~ ( ~ ( in @ SY575 @ SV13 )
| ~ ( in @ SY576 @ SV13 ) )
| ~ ! [SY577: $i] :
( ~ ( in @ SY577 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY575 @ SY577 )
| ( in @ SY576 @ SY577 ) )
| ~ ( ~ ( in @ SY576 @ SY577 )
| ( in @ SY575 @ SY577 ) ) ) )
| ( SY575 = SY576 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(662,plain,
! [SV13: $i] :
( ( ! [SY578: $i,SY579: $i] :
( ~ ~ ( ~ ( in @ SY578 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY579 @ ( sK2_SY402 @ SV13 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY578 )
| ( in @ SX4 @ SY579 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY579 )
| ( in @ SX4 @ SY578 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[608]) ).
thf(663,plain,
! [SV13: $i,SV123: $i] :
( ( ( ~ ( ~ ! [SY606: $i] :
( ~ ( in @ SY606 @ SV123 )
| ( in @ SY606 @ SV13 ) )
| ~ ~ ! [SY607: $i] :
~ ( in @ SY607 @ SV123 ) ) )
= $false )
| ( ( ~ ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(664,plain,
! [SV112: $i,SV17: $i > $o] :
( ( ( ! [SY599: $i] :
( ~ ( SV17 @ SY599 )
| ( SV112 = SY599 ) ) )
= $false )
| ( ( SV17 @ SV112 )
= $false )
| ( ( SV17
@ ( descr
@ ^ [SY426: $i] : ( SV17 @ SY426 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(665,plain,
! [SV68: $i > $o,SV19: $i,SV127: $i] :
( ( ( ~ ~ ( ~ ( in @ SV127 @ SV19 )
| ~ ( SV68 @ SV127 ) ) )
= $true )
| ( ( in @ ( sK5_SY532 @ SV68 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(666,plain,
! [SV68: $i > $o,SV19: $i,SV128: $i] :
( ( ( ~ ~ ( ~ ( in @ SV128 @ SV19 )
| ~ ( SV68 @ SV128 ) ) )
= $true )
| ( ( SV68 @ ( sK5_SY532 @ SV68 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(667,plain,
! [SV21: $i,SV70: $i > $o,SV119: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK25_SY536 @ SV119 @ SV70 @ SV21 ) @ SV21 )
| ~ ~ ( SV70 @ ( sK25_SY536 @ SV119 @ SV70 @ SV21 ) ) ) )
= $false )
| ( ( SV70 @ SV119 )
= $true )
| ( ( in @ SV119 @ SV21 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[613]) ).
thf(668,plain,
! [SV22: $i,SV71: $i > $o] :
( ( ( ~ ( in @ ( sK13_SY537 @ SV71 @ SV22 ) @ SV22 ) )
= $false )
| ( ( ! [SY538: $i] :
( ~ ( in @ SY538 @ SV22 )
| ~ ( SV71 @ SY538 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[614]) ).
thf(669,plain,
! [SV22: $i,SV71: $i > $o] :
( ( ( ~ ( SV71 @ ( sK13_SY537 @ SV71 @ SV22 ) ) )
= $false )
| ( ( ! [SY538: $i] :
( ~ ( in @ SY538 @ SV22 )
| ~ ( SV71 @ SY538 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[614]) ).
thf(670,plain,
! [SV73: $i > $o,SV24: $i,SV120: $i] :
( ( ( in @ SV120 @ SV24 )
= $false )
| ( ( ~ ( SV73 @ SV120 ) )
= $true )
| ( ( ( ( dsetconstr @ SV24
@ ^ [SY541: $i] : ( SV73 @ SY541 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(671,plain,
! [SV113: $i,SV27: $i > $o] :
( ( ( ! [SY600: $i] :
( ~ ( SV27 @ SY600 )
| ( SV113 = SY600 ) ) )
= $false )
| ( ( SV27 @ SV113 )
= $false )
| ( ( ~ ! [SY452: $i] :
~ ! [SY453: $i] :
~ ( ~ ( ~ ( SV27 @ SY453 )
| ( SY453 = SY452 ) )
| ~ ( ( SY453 != SY452 )
| ( SV27 @ SY453 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(672,plain,
! [SV30: $i,SV114: $i] :
( ( ( ~ ( in @ ( sK18_SY460 @ SV114 @ SV30 ) @ SV30 )
| ~ ~ ~ ! [SY613: $i] :
~ ~ ( ~ ( in @ SY613 @ ( sK18_SY460 @ SV114 @ SV30 ) )
| ~ ( in @ SY613 @ SV30 ) ) )
= $false )
| ( ( in @ SV114 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(673,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ! [SY601: $i] :
( ~ ( SV31 @ SY601 )
| ( SV115 = SY601 ) ) )
= $false )
| ( ( SV31 @ SV115 )
= $false )
| ( ( ~ ! [SY464: $i] :
~ ~ ( ~ ( SV31 @ SY464 )
| ~ ! [SY465: $i] :
( ~ ( SV31 @ SY465 )
| ( SY464 = SY465 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(674,plain,
! [SV78: $i,SV32: $i > $i > $o] :
( ( ( ! [SY615: $i] :
~ ( ~ ( ~ ( in @ SY615 @ ( sK21_SY550 @ SV32 @ SV78 ) )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY615 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY615 ) )
| ( in @ SY615 @ ( sK21_SY550 @ SV32 @ SV78 ) ) ) ) )
= $true )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(675,plain,
! [SV124: $i,SV78: $i,SV32: $i > $i > $o] :
( ( ( ~ ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
| ~ ! [SY614: $i] :
( ~ ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SY614 )
| ( SV124 = SY614 ) ) )
= $true )
| ( ( ~ ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[623]) ).
thf(676,plain,
! [SV33: $i,SV79: $i > $o] :
( ( ( ~ ( in @ ( sK14_SY554 @ SV79 @ SV33 ) @ SV33 ) )
= $false )
| ( ( ! [SY555: $i] :
( ~ ( in @ SY555 @ SV33 )
| ~ ( SV79 @ SY555 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[624]) ).
thf(677,plain,
! [SV33: $i,SV79: $i > $o] :
( ( ( ~ ( SV79 @ ( sK14_SY554 @ SV79 @ SV33 ) ) )
= $false )
| ( ( ! [SY555: $i] :
( ~ ( in @ SY555 @ SV33 )
| ~ ( SV79 @ SY555 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[624]) ).
thf(678,plain,
! [SV34: $i,SV80: $i] :
( ( ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 )
| ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 ) ) )
= $true )
| ( ( SV34 = SV80 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[625]) ).
thf(679,plain,
! [SV34: $i,SV80: $i] :
( ( ( ~ ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 )
| ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 ) )
= $false )
| ( ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 )
= $false )
| ( ( SV34 = SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(680,plain,
! [SV116: $i,SV36: $i > $o] :
( ( ( ! [SY604: $i] :
( ~ ( SV36 @ SY604 )
| ( SV116 = SY604 ) ) )
= $false )
| ( ( SV36 @ SV116 )
= $false )
| ( ( ~ ! [SY481: $i] :
~ ( SV36 @ SY481 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(681,plain,
! [SV40: $i,SV82: $i,SV125: $i] :
( ( ( in @ SV125 @ SV82 )
= $false )
| ( ( in @ SV125 @ SV40 )
= $true )
| ( ( in @ SV82 @ ( powerset @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(682,plain,
! [SV82: $i,SV40: $i] :
( ( ( in @ ( sK19_SY558 @ SV40 @ SV82 ) @ SV82 )
= $true )
| ( ( in @ SV82 @ ( powerset @ SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[629]) ).
thf(683,plain,
! [SV121: $o,SV86: $i,SV43: $i,SV105: $i] :
( ( ( SV105 = SV43 )
= $true )
| ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| SV121 )
| SV121 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[631]) ).
thf(684,plain,
! [SV43: $i,SV121: $o,SV86: $i,SV105: $i] :
( ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| SV121 ) )
= $true )
| ( SV121 = $true )
| ( SV121 = $false )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[632]) ).
thf(685,plain,
! [SV86: $i,SV43: $i,SV105: $i] :
( ( ( SV105 = SV43 )
= $true )
| ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| $true )
| $true )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[633]) ).
thf(686,plain,
! [SV43: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[634]) ).
thf(687,plain,
! [SV86: $i,SV43: $i,SV105: $i] :
( ( ( SV105 = SV43 )
= $true )
| ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| $false )
| $false )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[635]) ).
thf(688,plain,
! [SV43: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(689,plain,
! [SV87: $i > $o,SV44: $i,SV122: $i] :
( ( ( in @ SV122 @ SV44 )
= $false )
| ( ( ~ ~ ( SV87 @ SV122 ) )
= $true )
| ( ( ~ ! [SY562: $i] :
( ~ ( in @ SY562 @ SV44 )
| ( SV87 @ SY562 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(690,plain,
! [SV46: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY496 @ SV46 ) @ omega )
| ~ ( in @ ( sK20_SY496 @ SV46 ) @ SV46 ) ) )
= $true )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( ! [SY497: $i] :
( ~ ( in @ SY497 @ omega )
| ( in @ SY497 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[638]) ).
thf(691,plain,
! [SV46: $i,SV129: $i] :
( ( ( ~ ( in @ SV129 @ omega )
| ( in @ SV129 @ SV46 ) )
= $true )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( in @ ( setadjoin @ ( sK20_SY496 @ SV46 ) @ ( sK20_SY496 @ SV46 ) ) @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(692,plain,
! [SV90: $i > $o,SV49: $i,SV107: $i] :
( ( ( in @ SV107
@ ( dsetconstr @ SV49
@ ^ [SY565: $i] : ( SV90 @ SY565 ) ) )
= $false )
| ( ( SV90 @ SV107 )
= $true )
| ( ( in @ SV107 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(693,plain,
! [SV49: $i,SV107: $i,SV90: $i > $o] :
( ( ( SV90 @ SV107 )
= $false )
| ( ( in @ SV107
@ ( dsetconstr @ SV49
@ ^ [SY566: $i] : ( SV90 @ SY566 ) ) )
= $true )
| ( ( in @ SV107 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(694,plain,
! [SV50: $i,SV91: $i] :
( ( ( ~ ( ~ ( in @ SV91 @ ( sK22_SY567 @ SV50 @ SV91 ) )
| ~ ( in @ ( sK22_SY567 @ SV50 @ SV91 ) @ SV50 ) ) )
= $true )
| ( ( in @ SV91 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[642]) ).
thf(695,plain,
! [SV50: $i,SV126: $i,SV91: $i] :
( ( ( ~ ( ~ ( in @ SV91 @ SV126 )
| ~ ( in @ SV126 @ SV50 ) ) )
= $false )
| ( ( in @ SV91 @ ( setunion @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(696,plain,
! [SV95: $i,SV56: $i] :
( ( ( ~ ( in @ ( sK26_SY572 @ SV56 @ SV95 ) @ SV95 )
| ( in @ ( sK26_SY572 @ SV56 @ SV95 ) @ SV56 ) )
= $false )
| ( ( SV56 = SV95 )
= $true )
| ( ( in @ ( sK9_SY571 @ SV95 @ SV56 ) @ SV56 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[644]) ).
thf(697,plain,
! [SV95: $i,SV56: $i] :
( ( ( ~ ( in @ ( sK23_SY572 @ SV56 @ SV95 ) @ SV95 ) )
= $false )
| ( ( SV56 = SV95 )
= $true )
| ( ( in @ ( sK9_SY571 @ SV95 @ SV56 ) @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[645]) ).
thf(698,plain,
! [SV95: $i,SV56: $i] :
( ( ( in @ ( sK23_SY572 @ SV56 @ SV95 ) @ SV56 )
= $false )
| ( ( SV56 = SV95 )
= $true )
| ( ( in @ ( sK9_SY571 @ SV95 @ SV56 ) @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[645]) ).
thf(699,plain,
! [SV62: $i,SV9: $i,SV110: $o] :
( ( ( in @ ( sK15_SY597 @ SV110 @ SV9 @ SV62 ) @ SV9 )
= $true )
| ( SV110 = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[647]) ).
thf(700,plain,
! [SV62: $i,SV9: $i] :
( ( ( in @ ( sK16_SX0 @ SV9 @ SV62 ) @ SV9 )
= $true )
| ( $true = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(701,plain,
! [SV62: $i,SV9: $i] :
( ( ( in @ ( sK17_SX0 @ SV9 @ SV62 ) @ SV9 )
= $true )
| ( $false = $true )
| ( ( in @ SV62 @ ( setunion @ SV9 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[653]) ).
thf(702,plain,
! [SV130: $i] :
( ( ~ ( sK1_SX0 @ SV130 )
| ( sK10_SY521 = SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(703,plain,
! [SV111: $i] :
( ( ( ~ ( sK1_SX0 @ ( sK27_SY598 @ SV111 ) )
| ( SV111
= ( sK27_SY598 @ SV111 ) ) )
= $false )
| ( ( sK1_SX0 @ SV111 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[657]) ).
thf(704,plain,
! [SV12: $i,SV64: $i > $o,SV118: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY527 @ SV118 @ SV64 @ SV12 ) @ SV12 )
| ~ ~ ( SV64 @ ( sK24_SY527 @ SV118 @ SV64 @ SV12 ) ) ) )
= $true )
| ( ( SV64 @ SV118 )
= $true )
| ( ( in @ SV118 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[660]) ).
thf(705,plain,
! [SV13: $i] :
( ( ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ ( sK2_SY402 @ SV13 ) )
| ! [SY404: $i] :
( ~ ( in @ SY404 @ SY573 )
| ( in @ SY404 @ SV13 ) ) )
| ~ ! [SY575: $i,SY576: $i] :
( ~ ~ ( ~ ( in @ SY575 @ SV13 )
| ~ ( in @ SY576 @ SV13 ) )
| ~ ! [SY577: $i] :
( ~ ( in @ SY577 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY575 @ SY577 )
| ( in @ SY576 @ SY577 ) )
| ~ ( ~ ( in @ SY576 @ SY577 )
| ( in @ SY575 @ SY577 ) ) ) )
| ( SY575 = SY576 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(706,plain,
! [SV13: $i,SV131: $i] :
( ( ! [SY618: $i] :
( ~ ~ ( ~ ( in @ SV131 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY618 @ ( sK2_SY402 @ SV13 ) ) )
| ! [SY619: $i] :
( ~ ( in @ SY619 @ SV131 )
| ( in @ SY619 @ SY618 ) )
| ! [SY620: $i] :
( ~ ( in @ SY620 @ SY618 )
| ( in @ SY620 @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(707,plain,
! [SV13: $i,SV123: $i] :
( ( ( ~ ! [SY606: $i] :
( ~ ( in @ SY606 @ SV123 )
| ( in @ SY606 @ SV13 ) )
| ~ ~ ! [SY607: $i] :
~ ( in @ SY607 @ SV123 ) )
= $true )
| ( ( ~ ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[663]) ).
thf(708,plain,
! [SV112: $i,SV17: $i > $o] :
( ( ( ~ ( SV17 @ ( sK28_SY599 @ SV112 @ SV17 ) )
| ( SV112
= ( sK28_SY599 @ SV112 @ SV17 ) ) )
= $false )
| ( ( SV17 @ SV112 )
= $false )
| ( ( SV17
@ ( descr
@ ^ [SY426: $i] : ( SV17 @ SY426 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[664]) ).
thf(709,plain,
! [SV68: $i > $o,SV19: $i,SV127: $i] :
( ( ( ~ ( ~ ( in @ SV127 @ SV19 )
| ~ ( SV68 @ SV127 ) ) )
= $false )
| ( ( in @ ( sK5_SY532 @ SV68 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(710,plain,
! [SV68: $i > $o,SV19: $i,SV128: $i] :
( ( ( ~ ( ~ ( in @ SV128 @ SV19 )
| ~ ( SV68 @ SV128 ) ) )
= $false )
| ( ( SV68 @ ( sK5_SY532 @ SV68 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(711,plain,
! [SV21: $i,SV70: $i > $o,SV119: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY536 @ SV119 @ SV70 @ SV21 ) @ SV21 )
| ~ ~ ( SV70 @ ( sK25_SY536 @ SV119 @ SV70 @ SV21 ) ) ) )
= $true )
| ( ( SV70 @ SV119 )
= $true )
| ( ( in @ SV119 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[667]) ).
thf(712,plain,
! [SV22: $i,SV71: $i > $o] :
( ( ( in @ ( sK13_SY537 @ SV71 @ SV22 ) @ SV22 )
= $true )
| ( ( ! [SY538: $i] :
( ~ ( in @ SY538 @ SV22 )
| ~ ( SV71 @ SY538 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[668]) ).
thf(713,plain,
! [SV22: $i,SV71: $i > $o] :
( ( ( SV71 @ ( sK13_SY537 @ SV71 @ SV22 ) )
= $true )
| ( ( ! [SY538: $i] :
( ~ ( in @ SY538 @ SV22 )
| ~ ( SV71 @ SY538 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[669]) ).
thf(714,plain,
! [SV24: $i,SV120: $i,SV73: $i > $o] :
( ( ( SV73 @ SV120 )
= $false )
| ( ( in @ SV120 @ SV24 )
= $false )
| ( ( ( ( dsetconstr @ SV24
@ ^ [SY541: $i] : ( SV73 @ SY541 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(715,plain,
! [SV113: $i,SV27: $i > $o] :
( ( ( ~ ( SV27 @ ( sK29_SY600 @ SV113 @ SV27 ) )
| ( SV113
= ( sK29_SY600 @ SV113 @ SV27 ) ) )
= $false )
| ( ( SV27 @ SV113 )
= $false )
| ( ( ~ ! [SY452: $i] :
~ ! [SY453: $i] :
~ ( ~ ( ~ ( SV27 @ SY453 )
| ( SY453 = SY452 ) )
| ~ ( ( SY453 != SY452 )
| ( SV27 @ SY453 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[671]) ).
thf(716,plain,
! [SV30: $i,SV114: $i] :
( ( ( ~ ( in @ ( sK18_SY460 @ SV114 @ SV30 ) @ SV30 ) )
= $false )
| ( ( in @ SV114 @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[672]) ).
thf(717,plain,
! [SV30: $i,SV114: $i] :
( ( ( ~ ~ ~ ! [SY613: $i] :
~ ~ ( ~ ( in @ SY613 @ ( sK18_SY460 @ SV114 @ SV30 ) )
| ~ ( in @ SY613 @ SV30 ) ) )
= $false )
| ( ( in @ SV114 @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[672]) ).
thf(718,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ~ ( SV31 @ ( sK30_SY601 @ SV115 @ SV31 ) )
| ( SV115
= ( sK30_SY601 @ SV115 @ SV31 ) ) )
= $false )
| ( ( SV31 @ SV115 )
= $false )
| ( ( ~ ! [SY464: $i] :
~ ~ ( ~ ( SV31 @ SY464 )
| ~ ! [SY465: $i] :
( ~ ( SV31 @ SY465 )
| ( SY464 = SY465 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[673]) ).
thf(719,plain,
! [SV78: $i,SV32: $i > $i > $o,SV132: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
| ~ ! [SY621: $i] :
~ ~ ( ~ ( in @ SY621 @ SV78 )
| ~ ( SV32 @ SY621 @ SV132 ) ) )
| ~ ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ SY622 @ SV78 )
| ~ ( SV32 @ SY622 @ SV132 ) )
| ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) ) ) ) )
= $true )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(720,plain,
! [SV124: $i,SV78: $i,SV32: $i > $i > $o] :
( ( ( ~ ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 ) )
= $true )
| ( ( ~ ! [SY614: $i] :
( ~ ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SY614 )
| ( SV124 = SY614 ) ) )
= $true )
| ( ( ~ ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(721,plain,
! [SV33: $i,SV79: $i > $o] :
( ( ( in @ ( sK14_SY554 @ SV79 @ SV33 ) @ SV33 )
= $true )
| ( ( ! [SY555: $i] :
( ~ ( in @ SY555 @ SV33 )
| ~ ( SV79 @ SY555 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[676]) ).
thf(722,plain,
! [SV33: $i,SV79: $i > $o] :
( ( ( SV79 @ ( sK14_SY554 @ SV79 @ SV33 ) )
= $true )
| ( ( ! [SY555: $i] :
( ~ ( in @ SY555 @ SV33 )
| ~ ( SV79 @ SY555 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[677]) ).
thf(723,plain,
! [SV34: $i,SV80: $i] :
( ( ( ~ ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 )
| ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 ) )
= $false )
| ( ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 )
= $true )
| ( ( SV34 = SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(724,plain,
! [SV34: $i,SV80: $i] :
( ( ( ~ ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 ) )
= $false )
| ( ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 )
= $false )
| ( ( SV34 = SV80 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(725,plain,
! [SV34: $i,SV80: $i] :
( ( ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 )
= $false )
| ( ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 )
= $false )
| ( ( SV34 = SV80 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(726,plain,
! [SV116: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ ( sK31_SY604 @ SV116 @ SV36 ) )
| ( SV116
= ( sK31_SY604 @ SV116 @ SV36 ) ) )
= $false )
| ( ( SV36 @ SV116 )
= $false )
| ( ( ~ ! [SY481: $i] :
~ ( SV36 @ SY481 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[680]) ).
thf(727,plain,
! [SV43: $i,SV121: $o,SV86: $i,SV105: $i] :
( ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| SV121 ) )
= $true )
| ( SV121 = $true )
| ( ( SV105 = SV43 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(728,plain,
! [SV43: $i,SV121: $o,SV86: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ SV86 )
| SV121 )
= $false )
| ( SV121 = $true )
| ( SV121 = $false )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(729,plain,
! [SV43: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( SV105 = SV43 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[685]) ).
thf(730,plain,
! [SV43: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ SV86 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(731,plain,
! [SV43: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( ~ ( in @ SV105 @ SV86 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( SV105 = SV43 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(732,plain,
! [SV43: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ SV86 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(733,plain,
! [SV44: $i,SV122: $i,SV87: $i > $o] :
( ( ( ~ ( SV87 @ SV122 ) )
= $false )
| ( ( in @ SV122 @ SV44 )
= $false )
| ( ( ~ ! [SY562: $i] :
( ~ ( in @ SY562 @ SV44 )
| ( SV87 @ SY562 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(734,plain,
! [SV46: $i] :
( ( ( ~ ( in @ ( sK20_SY496 @ SV46 ) @ omega )
| ~ ( in @ ( sK20_SY496 @ SV46 ) @ SV46 ) )
= $false )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( ! [SY497: $i] :
( ~ ( in @ SY497 @ omega )
| ( in @ SY497 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(735,plain,
! [SV46: $i,SV129: $i] :
( ( ( ~ ( in @ SV129 @ omega ) )
= $true )
| ( ( in @ SV129 @ SV46 )
= $true )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( in @ ( setadjoin @ ( sK20_SY496 @ SV46 ) @ ( sK20_SY496 @ SV46 ) ) @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(736,plain,
! [SV50: $i,SV91: $i] :
( ( ( ~ ( in @ SV91 @ ( sK22_SY567 @ SV50 @ SV91 ) )
| ~ ( in @ ( sK22_SY567 @ SV50 @ SV91 ) @ SV50 ) )
= $false )
| ( ( in @ SV91 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(737,plain,
! [SV50: $i,SV126: $i,SV91: $i] :
( ( ( ~ ( in @ SV91 @ SV126 )
| ~ ( in @ SV126 @ SV50 ) )
= $true )
| ( ( in @ SV91 @ ( setunion @ SV50 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[695]) ).
thf(738,plain,
! [SV95: $i,SV56: $i] :
( ( ( ~ ( in @ ( sK26_SY572 @ SV56 @ SV95 ) @ SV95 ) )
= $false )
| ( ( SV56 = SV95 )
= $true )
| ( ( in @ ( sK9_SY571 @ SV95 @ SV56 ) @ SV56 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(739,plain,
! [SV95: $i,SV56: $i] :
( ( ( in @ ( sK26_SY572 @ SV56 @ SV95 ) @ SV56 )
= $false )
| ( ( SV56 = SV95 )
= $true )
| ( ( in @ ( sK9_SY571 @ SV95 @ SV56 ) @ SV56 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(740,plain,
! [SV95: $i,SV56: $i] :
( ( ( in @ ( sK23_SY572 @ SV56 @ SV95 ) @ SV95 )
= $true )
| ( ( SV56 = SV95 )
= $true )
| ( ( in @ ( sK9_SY571 @ SV95 @ SV56 ) @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[697]) ).
thf(741,plain,
! [SV130: $i] :
( ( ( ~ ( sK1_SX0 @ SV130 ) )
= $true )
| ( ( sK10_SY521 = SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[702]) ).
thf(742,plain,
! [SV111: $i] :
( ( ( ~ ( sK1_SX0 @ ( sK27_SY598 @ SV111 ) ) )
= $false )
| ( ( sK1_SX0 @ SV111 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(743,plain,
! [SV111: $i] :
( ( ( SV111
= ( sK27_SY598 @ SV111 ) )
= $false )
| ( ( sK1_SX0 @ SV111 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(744,plain,
! [SV12: $i,SV64: $i > $o,SV118: $i] :
( ( ( ~ ( in @ ( sK24_SY527 @ SV118 @ SV64 @ SV12 ) @ SV12 )
| ~ ~ ( SV64 @ ( sK24_SY527 @ SV118 @ SV64 @ SV12 ) ) )
= $false )
| ( ( SV64 @ SV118 )
= $true )
| ( ( in @ SV118 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(745,plain,
! [SV13: $i] :
( ( ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ ( sK2_SY402 @ SV13 ) )
| ! [SY404: $i] :
( ~ ( in @ SY404 @ SY573 )
| ( in @ SY404 @ SV13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(746,plain,
! [SV13: $i] :
( ( ~ ! [SY575: $i,SY576: $i] :
( ~ ~ ( ~ ( in @ SY575 @ SV13 )
| ~ ( in @ SY576 @ SV13 ) )
| ~ ! [SY577: $i] :
( ~ ( in @ SY577 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY575 @ SY577 )
| ( in @ SY576 @ SY577 ) )
| ~ ( ~ ( in @ SY576 @ SY577 )
| ( in @ SY575 @ SY577 ) ) ) )
| ( SY575 = SY576 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(747,plain,
! [SV133: $i,SV13: $i,SV131: $i] :
( ( ~ ~ ( ~ ( in @ SV131 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SV133 @ ( sK2_SY402 @ SV13 ) ) )
| ! [SY623: $i] :
( ~ ( in @ SY623 @ SV131 )
| ( in @ SY623 @ SV133 ) )
| ! [SY624: $i] :
( ~ ( in @ SY624 @ SV133 )
| ( in @ SY624 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(748,plain,
! [SV13: $i,SV123: $i] :
( ( ( ~ ! [SY606: $i] :
( ~ ( in @ SY606 @ SV123 )
| ( in @ SY606 @ SV13 ) ) )
= $true )
| ( ( ~ ~ ! [SY607: $i] :
~ ( in @ SY607 @ SV123 ) )
= $true )
| ( ( ~ ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[707]) ).
thf(749,plain,
! [SV112: $i,SV17: $i > $o] :
( ( ( ~ ( SV17 @ ( sK28_SY599 @ SV112 @ SV17 ) ) )
= $false )
| ( ( SV17 @ SV112 )
= $false )
| ( ( SV17
@ ( descr
@ ^ [SY426: $i] : ( SV17 @ SY426 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[708]) ).
thf(750,plain,
! [SV17: $i > $o,SV112: $i] :
( ( ( SV112
= ( sK28_SY599 @ SV112 @ SV17 ) )
= $false )
| ( ( SV17 @ SV112 )
= $false )
| ( ( SV17
@ ( descr
@ ^ [SY426: $i] : ( SV17 @ SY426 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[708]) ).
thf(751,plain,
! [SV68: $i > $o,SV19: $i,SV127: $i] :
( ( ( ~ ( in @ SV127 @ SV19 )
| ~ ( SV68 @ SV127 ) )
= $true )
| ( ( in @ ( sK5_SY532 @ SV68 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(752,plain,
! [SV68: $i > $o,SV19: $i,SV128: $i] :
( ( ( ~ ( in @ SV128 @ SV19 )
| ~ ( SV68 @ SV128 ) )
= $true )
| ( ( SV68 @ ( sK5_SY532 @ SV68 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[710]) ).
thf(753,plain,
! [SV21: $i,SV70: $i > $o,SV119: $i] :
( ( ( ~ ( in @ ( sK25_SY536 @ SV119 @ SV70 @ SV21 ) @ SV21 )
| ~ ~ ( SV70 @ ( sK25_SY536 @ SV119 @ SV70 @ SV21 ) ) )
= $false )
| ( ( SV70 @ SV119 )
= $true )
| ( ( in @ SV119 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(754,plain,
! [SV71: $i > $o,SV22: $i,SV134: $i] :
( ( ( ~ ( in @ SV134 @ SV22 )
| ~ ( SV71 @ SV134 ) )
= $true )
| ( ( in @ ( sK13_SY537 @ SV71 @ SV22 ) @ SV22 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(755,plain,
! [SV71: $i > $o,SV22: $i,SV135: $i] :
( ( ( ~ ( in @ SV135 @ SV22 )
| ~ ( SV71 @ SV135 ) )
= $true )
| ( ( SV71 @ ( sK13_SY537 @ SV71 @ SV22 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(756,plain,
! [SV120: $i,SV73: $i > $o,SV24: $i] :
( ( ( ( dsetconstr @ SV24
@ ^ [SY541: $i] : ( SV73 @ SY541 ) )
!= emptyset )
= $true )
| ( $false = $true )
| ( ( in @ SV120 @ SV24 )
= $false )
| ( ( SV73 @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(757,plain,
! [SV113: $i,SV27: $i > $o] :
( ( ( ~ ( SV27 @ ( sK29_SY600 @ SV113 @ SV27 ) ) )
= $false )
| ( ( SV27 @ SV113 )
= $false )
| ( ( ~ ! [SY452: $i] :
~ ! [SY453: $i] :
~ ( ~ ( ~ ( SV27 @ SY453 )
| ( SY453 = SY452 ) )
| ~ ( ( SY453 != SY452 )
| ( SV27 @ SY453 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[715]) ).
thf(758,plain,
! [SV27: $i > $o,SV113: $i] :
( ( ( SV113
= ( sK29_SY600 @ SV113 @ SV27 ) )
= $false )
| ( ( SV27 @ SV113 )
= $false )
| ( ( ~ ! [SY452: $i] :
~ ! [SY453: $i] :
~ ( ~ ( ~ ( SV27 @ SY453 )
| ( SY453 = SY452 ) )
| ~ ( ( SY453 != SY452 )
| ( SV27 @ SY453 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[715]) ).
thf(759,plain,
! [SV30: $i,SV114: $i] :
( ( ( in @ ( sK18_SY460 @ SV114 @ SV30 ) @ SV30 )
= $true )
| ( ( in @ SV114 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[716]) ).
thf(760,plain,
! [SV30: $i,SV114: $i] :
( ( ( ~ ~ ! [SY613: $i] :
~ ~ ( ~ ( in @ SY613 @ ( sK18_SY460 @ SV114 @ SV30 ) )
| ~ ( in @ SY613 @ SV30 ) ) )
= $true )
| ( ( in @ SV114 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[717]) ).
thf(761,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ~ ( SV31 @ ( sK30_SY601 @ SV115 @ SV31 ) ) )
= $false )
| ( ( SV31 @ SV115 )
= $false )
| ( ( ~ ! [SY464: $i] :
~ ~ ( ~ ( SV31 @ SY464 )
| ~ ! [SY465: $i] :
( ~ ( SV31 @ SY465 )
| ( SY464 = SY465 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[718]) ).
thf(762,plain,
! [SV31: $i > $o,SV115: $i] :
( ( ( SV115
= ( sK30_SY601 @ SV115 @ SV31 ) )
= $false )
| ( ( SV31 @ SV115 )
= $false )
| ( ( ~ ! [SY464: $i] :
~ ~ ( ~ ( SV31 @ SY464 )
| ~ ! [SY465: $i] :
( ~ ( SV31 @ SY465 )
| ( SY464 = SY465 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[718]) ).
thf(763,plain,
! [SV78: $i,SV32: $i > $i > $o,SV132: $i] :
( ( ( ~ ( ~ ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
| ~ ! [SY621: $i] :
~ ~ ( ~ ( in @ SY621 @ SV78 )
| ~ ( SV32 @ SY621 @ SV132 ) ) )
| ~ ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ SY622 @ SV78 )
| ~ ( SV32 @ SY622 @ SV132 ) )
| ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) ) ) )
= $false )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(764,plain,
! [SV124: $i,SV78: $i,SV32: $i > $i > $o] :
( ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( ~ ! [SY614: $i] :
( ~ ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SY614 )
| ( SV124 = SY614 ) ) )
= $true )
| ( ( ~ ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(765,plain,
! [SV79: $i > $o,SV33: $i,SV136: $i] :
( ( ( ~ ( in @ SV136 @ SV33 )
| ~ ( SV79 @ SV136 ) )
= $true )
| ( ( in @ ( sK14_SY554 @ SV79 @ SV33 ) @ SV33 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(766,plain,
! [SV79: $i > $o,SV33: $i,SV137: $i] :
( ( ( ~ ( in @ SV137 @ SV33 )
| ~ ( SV79 @ SV137 ) )
= $true )
| ( ( SV79 @ ( sK14_SY554 @ SV79 @ SV33 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(767,plain,
! [SV34: $i,SV80: $i] :
( ( ( ~ ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 ) )
= $false )
| ( ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 )
= $true )
| ( ( SV34 = SV80 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[723]) ).
thf(768,plain,
! [SV34: $i,SV80: $i] :
( ( ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 )
= $false )
| ( ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 )
= $true )
| ( ( SV34 = SV80 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[723]) ).
thf(769,plain,
! [SV34: $i,SV80: $i] :
( ( ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 )
= $true )
| ( ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 )
= $false )
| ( ( SV34 = SV80 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[724]) ).
thf(770,plain,
! [SV116: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ ( sK31_SY604 @ SV116 @ SV36 ) ) )
= $false )
| ( ( SV36 @ SV116 )
= $false )
| ( ( ~ ! [SY481: $i] :
~ ( SV36 @ SY481 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[726]) ).
thf(771,plain,
! [SV36: $i > $o,SV116: $i] :
( ( ( SV116
= ( sK31_SY604 @ SV116 @ SV36 ) )
= $false )
| ( ( SV36 @ SV116 )
= $false )
| ( ( ~ ! [SY481: $i] :
~ ( SV36 @ SY481 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[726]) ).
thf(772,plain,
! [SV43: $i,SV121: $o,SV86: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ SV86 )
| SV121 )
= $false )
| ( SV121 = $true )
| ( ( SV105 = SV43 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(773,plain,
! [SV43: $i,SV121: $o,SV86: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ SV86 ) )
= $false )
| ( SV121 = $true )
| ( SV121 = $false )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(774,plain,
! [SV86: $i,SV43: $i,SV105: $i,SV121: $o] :
( ( SV121 = $false )
| ( SV121 = $true )
| ( SV121 = $false )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(775,plain,
! [SV43: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ SV86 )
| $true )
= $false )
| ( $true = $true )
| ( ( SV105 = SV43 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(776,plain,
! [SV43: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ SV86 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[730]) ).
thf(777,plain,
! [SV86: $i,SV43: $i,SV105: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[730]) ).
thf(778,plain,
! [SV43: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ SV86 )
| $false )
= $false )
| ( $false = $true )
| ( ( SV105 = SV43 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(779,plain,
! [SV43: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ SV86 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(780,plain,
! [SV86: $i,SV43: $i,SV105: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(781,plain,
! [SV44: $i,SV122: $i,SV87: $i > $o] :
( ( ( SV87 @ SV122 )
= $true )
| ( ( in @ SV122 @ SV44 )
= $false )
| ( ( ~ ! [SY562: $i] :
( ~ ( in @ SY562 @ SV44 )
| ( SV87 @ SY562 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[733]) ).
thf(782,plain,
! [SV46: $i] :
( ( ( ~ ( in @ ( sK20_SY496 @ SV46 ) @ omega ) )
= $false )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( ! [SY497: $i] :
( ~ ( in @ SY497 @ omega )
| ( in @ SY497 @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[734]) ).
thf(783,plain,
! [SV46: $i] :
( ( ( ~ ( in @ ( sK20_SY496 @ SV46 ) @ SV46 ) )
= $false )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( ! [SY497: $i] :
( ~ ( in @ SY497 @ omega )
| ( in @ SY497 @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[734]) ).
thf(784,plain,
! [SV46: $i,SV129: $i] :
( ( ( in @ SV129 @ omega )
= $false )
| ( ( in @ SV129 @ SV46 )
= $true )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( in @ ( setadjoin @ ( sK20_SY496 @ SV46 ) @ ( sK20_SY496 @ SV46 ) ) @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(785,plain,
! [SV50: $i,SV91: $i] :
( ( ( ~ ( in @ SV91 @ ( sK22_SY567 @ SV50 @ SV91 ) ) )
= $false )
| ( ( in @ SV91 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[736]) ).
thf(786,plain,
! [SV91: $i,SV50: $i] :
( ( ( ~ ( in @ ( sK22_SY567 @ SV50 @ SV91 ) @ SV50 ) )
= $false )
| ( ( in @ SV91 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[736]) ).
thf(787,plain,
! [SV50: $i,SV126: $i,SV91: $i] :
( ( ( ~ ( in @ SV91 @ SV126 ) )
= $true )
| ( ( ~ ( in @ SV126 @ SV50 ) )
= $true )
| ( ( in @ SV91 @ ( setunion @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(788,plain,
! [SV95: $i,SV56: $i] :
( ( ( in @ ( sK26_SY572 @ SV56 @ SV95 ) @ SV95 )
= $true )
| ( ( SV56 = SV95 )
= $true )
| ( ( in @ ( sK9_SY571 @ SV95 @ SV56 ) @ SV56 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[738]) ).
thf(789,plain,
! [SV130: $i] :
( ( ( sK1_SX0 @ SV130 )
= $false )
| ( ( sK10_SY521 = SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(790,plain,
! [SV111: $i] :
( ( ( sK1_SX0 @ ( sK27_SY598 @ SV111 ) )
= $true )
| ( ( sK1_SX0 @ SV111 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[742]) ).
thf(791,plain,
! [SV12: $i,SV64: $i > $o,SV118: $i] :
( ( ( ~ ( in @ ( sK24_SY527 @ SV118 @ SV64 @ SV12 ) @ SV12 ) )
= $false )
| ( ( SV64 @ SV118 )
= $true )
| ( ( in @ SV118 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[744]) ).
thf(792,plain,
! [SV12: $i,SV118: $i,SV64: $i > $o] :
( ( ( ~ ~ ( SV64 @ ( sK24_SY527 @ SV118 @ SV64 @ SV12 ) ) )
= $false )
| ( ( SV64 @ SV118 )
= $true )
| ( ( in @ SV118 @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[744]) ).
thf(793,plain,
! [SV13: $i] :
( ( ! [SY573: $i] :
( ~ ( in @ SY573 @ ( sK2_SY402 @ SV13 ) )
| ! [SY404: $i] :
( ~ ( in @ SY404 @ SY573 )
| ( in @ SY404 @ SV13 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[745]) ).
thf(794,plain,
! [SV13: $i] :
( ( ! [SY575: $i,SY576: $i] :
( ~ ~ ( ~ ( in @ SY575 @ SV13 )
| ~ ( in @ SY576 @ SV13 ) )
| ~ ! [SY577: $i] :
( ~ ( in @ SY577 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SY575 @ SY577 )
| ( in @ SY576 @ SY577 ) )
| ~ ( ~ ( in @ SY576 @ SY577 )
| ( in @ SY575 @ SY577 ) ) ) )
| ( SY575 = SY576 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[746]) ).
thf(795,plain,
! [SV133: $i,SV13: $i,SV131: $i] :
( ( ( ~ ~ ( ~ ( in @ SV131 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SV133 @ ( sK2_SY402 @ SV13 ) ) ) )
= $true )
| ( ( ! [SY623: $i] :
( ~ ( in @ SY623 @ SV131 )
| ( in @ SY623 @ SV133 ) )
| ! [SY624: $i] :
( ~ ( in @ SY624 @ SV133 )
| ( in @ SY624 @ SV131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[747]) ).
thf(796,plain,
! [SV13: $i,SV123: $i] :
( ( ( ! [SY606: $i] :
( ~ ( in @ SY606 @ SV123 )
| ( in @ SY606 @ SV13 ) ) )
= $false )
| ( ( ~ ~ ! [SY607: $i] :
~ ( in @ SY607 @ SV123 ) )
= $true )
| ( ( ~ ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(797,plain,
! [SV112: $i,SV17: $i > $o] :
( ( ( SV17 @ ( sK28_SY599 @ SV112 @ SV17 ) )
= $true )
| ( ( SV17 @ SV112 )
= $false )
| ( ( SV17
@ ( descr
@ ^ [SY426: $i] : ( SV17 @ SY426 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[749]) ).
thf(798,plain,
! [SV68: $i > $o,SV19: $i,SV127: $i] :
( ( ( ~ ( in @ SV127 @ SV19 ) )
= $true )
| ( ( ~ ( SV68 @ SV127 ) )
= $true )
| ( ( in @ ( sK5_SY532 @ SV68 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(799,plain,
! [SV68: $i > $o,SV19: $i,SV128: $i] :
( ( ( ~ ( in @ SV128 @ SV19 ) )
= $true )
| ( ( ~ ( SV68 @ SV128 ) )
= $true )
| ( ( SV68 @ ( sK5_SY532 @ SV68 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[752]) ).
thf(800,plain,
! [SV21: $i,SV70: $i > $o,SV119: $i] :
( ( ( ~ ( in @ ( sK25_SY536 @ SV119 @ SV70 @ SV21 ) @ SV21 ) )
= $false )
| ( ( SV70 @ SV119 )
= $true )
| ( ( in @ SV119 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[753]) ).
thf(801,plain,
! [SV21: $i,SV119: $i,SV70: $i > $o] :
( ( ( ~ ~ ( SV70 @ ( sK25_SY536 @ SV119 @ SV70 @ SV21 ) ) )
= $false )
| ( ( SV70 @ SV119 )
= $true )
| ( ( in @ SV119 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[753]) ).
thf(802,plain,
! [SV71: $i > $o,SV22: $i,SV134: $i] :
( ( ( ~ ( in @ SV134 @ SV22 ) )
= $true )
| ( ( ~ ( SV71 @ SV134 ) )
= $true )
| ( ( in @ ( sK13_SY537 @ SV71 @ SV22 ) @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(803,plain,
! [SV71: $i > $o,SV22: $i,SV135: $i] :
( ( ( ~ ( in @ SV135 @ SV22 ) )
= $true )
| ( ( ~ ( SV71 @ SV135 ) )
= $true )
| ( ( SV71 @ ( sK13_SY537 @ SV71 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(804,plain,
! [SV120: $i,SV73: $i > $o,SV24: $i] :
( ( ( ( dsetconstr @ SV24
@ ^ [SY541: $i] : ( SV73 @ SY541 ) )
= emptyset )
= $false )
| ( $false = $true )
| ( ( in @ SV120 @ SV24 )
= $false )
| ( ( SV73 @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(805,plain,
! [SV113: $i,SV27: $i > $o] :
( ( ( SV27 @ ( sK29_SY600 @ SV113 @ SV27 ) )
= $true )
| ( ( SV27 @ SV113 )
= $false )
| ( ( ~ ! [SY452: $i] :
~ ! [SY453: $i] :
~ ( ~ ( ~ ( SV27 @ SY453 )
| ( SY453 = SY452 ) )
| ~ ( ( SY453 != SY452 )
| ( SV27 @ SY453 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[757]) ).
thf(806,plain,
! [SV113: $i,SV27: $i > $o] :
( ( ( ! [SY452: $i] :
~ ! [SY453: $i] :
~ ( ~ ( ~ ( SV27 @ SY453 )
| ( SY453 = SY452 ) )
| ~ ( ( SY453 != SY452 )
| ( SV27 @ SY453 ) ) ) )
= $false )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV113
= ( sK29_SY600 @ SV113 @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(807,plain,
! [SV30: $i,SV114: $i] :
( ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( in @ SY613 @ ( sK18_SY460 @ SV114 @ SV30 ) )
| ~ ( in @ SY613 @ SV30 ) ) )
= $false )
| ( ( in @ SV114 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[760]) ).
thf(808,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( SV31 @ ( sK30_SY601 @ SV115 @ SV31 ) )
= $true )
| ( ( SV31 @ SV115 )
= $false )
| ( ( ~ ! [SY464: $i] :
~ ~ ( ~ ( SV31 @ SY464 )
| ~ ! [SY465: $i] :
( ~ ( SV31 @ SY465 )
| ( SY464 = SY465 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[761]) ).
thf(809,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ! [SY464: $i] :
~ ~ ( ~ ( SV31 @ SY464 )
| ~ ! [SY465: $i] :
( ~ ( SV31 @ SY465 )
| ( SY464 = SY465 ) ) ) )
= $false )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV115
= ( sK30_SY601 @ SV115 @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(810,plain,
! [SV78: $i,SV32: $i > $i > $o,SV132: $i] :
( ( ( ~ ( ~ ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
| ~ ! [SY621: $i] :
~ ~ ( ~ ( in @ SY621 @ SV78 )
| ~ ( SV32 @ SY621 @ SV132 ) ) ) )
= $false )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[763]) ).
thf(811,plain,
! [SV132: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ~ ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ SY622 @ SV78 )
| ~ ( SV32 @ SY622 @ SV132 ) )
| ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) ) ) )
= $false )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[763]) ).
thf(812,plain,
! [SV124: $i,SV78: $i,SV32: $i > $i > $o] :
( ( ( ! [SY614: $i] :
( ~ ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SY614 )
| ( SV124 = SY614 ) ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( ~ ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(813,plain,
! [SV79: $i > $o,SV33: $i,SV136: $i] :
( ( ( ~ ( in @ SV136 @ SV33 ) )
= $true )
| ( ( ~ ( SV79 @ SV136 ) )
= $true )
| ( ( in @ ( sK14_SY554 @ SV79 @ SV33 ) @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(814,plain,
! [SV79: $i > $o,SV33: $i,SV137: $i] :
( ( ( ~ ( in @ SV137 @ SV33 ) )
= $true )
| ( ( ~ ( SV79 @ SV137 ) )
= $true )
| ( ( SV79 @ ( sK14_SY554 @ SV79 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(815,plain,
! [SV34: $i,SV80: $i] :
( ( ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV80 )
= $true )
| ( ( in @ ( sK8_SY556 @ SV80 @ SV34 ) @ SV34 )
= $true )
| ( ( SV34 = SV80 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[767]) ).
thf(816,plain,
! [SV116: $i,SV36: $i > $o] :
( ( ( SV36 @ ( sK31_SY604 @ SV116 @ SV36 ) )
= $true )
| ( ( SV36 @ SV116 )
= $false )
| ( ( ~ ! [SY481: $i] :
~ ( SV36 @ SY481 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[770]) ).
thf(817,plain,
! [SV116: $i,SV36: $i > $o] :
( ( ( ! [SY481: $i] :
~ ( SV36 @ SY481 ) )
= $false )
| ( ( SV36 @ SV116 )
= $false )
| ( ( SV116
= ( sK31_SY604 @ SV116 @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(818,plain,
! [SV43: $i,SV121: $o,SV86: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ SV86 ) )
= $false )
| ( SV121 = $true )
| ( ( SV105 = SV43 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[772]) ).
thf(819,plain,
! [SV86: $i,SV43: $i,SV105: $i,SV121: $o] :
( ( SV121 = $false )
| ( SV121 = $true )
| ( ( SV105 = SV43 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[772]) ).
thf(820,plain,
! [SV43: $i,SV121: $o,SV86: $i,SV105: $i] :
( ( ( in @ SV105 @ SV86 )
= $true )
| ( SV121 = $true )
| ( SV121 = $false )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[773]) ).
thf(821,plain,
! [SV43: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ SV86 ) )
= $false )
| ( $true = $true )
| ( ( SV105 = SV43 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[775]) ).
thf(822,plain,
! [SV86: $i,SV43: $i,SV105: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( SV105 = SV43 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[775]) ).
thf(823,plain,
! [SV43: $i,SV86: $i,SV105: $i] :
( ( ( in @ SV105 @ SV86 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[776]) ).
thf(824,plain,
! [SV43: $i,SV86: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ SV86 ) )
= $false )
| ( $false = $true )
| ( ( SV105 = SV43 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[778]) ).
thf(825,plain,
! [SV86: $i,SV43: $i,SV105: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( SV105 = SV43 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[778]) ).
thf(826,plain,
! [SV43: $i,SV86: $i,SV105: $i] :
( ( ( in @ SV105 @ SV86 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[779]) ).
thf(827,plain,
! [SV122: $i,SV87: $i > $o,SV44: $i] :
( ( ( ! [SY562: $i] :
( ~ ( in @ SY562 @ SV44 )
| ( SV87 @ SY562 ) ) )
= $false )
| ( ( in @ SV122 @ SV44 )
= $false )
| ( ( SV87 @ SV122 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(828,plain,
! [SV46: $i] :
( ( ( in @ ( sK20_SY496 @ SV46 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( ! [SY497: $i] :
( ~ ( in @ SY497 @ omega )
| ( in @ SY497 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[782]) ).
thf(829,plain,
! [SV46: $i] :
( ( ( in @ ( sK20_SY496 @ SV46 ) @ SV46 )
= $true )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( ! [SY497: $i] :
( ~ ( in @ SY497 @ omega )
| ( in @ SY497 @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[783]) ).
thf(830,plain,
! [SV50: $i,SV91: $i] :
( ( ( in @ SV91 @ ( sK22_SY567 @ SV50 @ SV91 ) )
= $true )
| ( ( in @ SV91 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[785]) ).
thf(831,plain,
! [SV91: $i,SV50: $i] :
( ( ( in @ ( sK22_SY567 @ SV50 @ SV91 ) @ SV50 )
= $true )
| ( ( in @ SV91 @ ( setunion @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[786]) ).
thf(832,plain,
! [SV50: $i,SV126: $i,SV91: $i] :
( ( ( in @ SV91 @ SV126 )
= $false )
| ( ( ~ ( in @ SV126 @ SV50 ) )
= $true )
| ( ( in @ SV91 @ ( setunion @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(833,plain,
! [SV12: $i,SV64: $i > $o,SV118: $i] :
( ( ( in @ ( sK24_SY527 @ SV118 @ SV64 @ SV12 ) @ SV12 )
= $true )
| ( ( SV64 @ SV118 )
= $true )
| ( ( in @ SV118 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[791]) ).
thf(834,plain,
! [SV12: $i,SV118: $i,SV64: $i > $o] :
( ( ( ~ ( SV64 @ ( sK24_SY527 @ SV118 @ SV64 @ SV12 ) ) )
= $true )
| ( ( SV64 @ SV118 )
= $true )
| ( ( in @ SV118 @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(835,plain,
! [SV13: $i,SV138: $i] :
( ( ~ ( in @ SV138 @ ( sK2_SY402 @ SV13 ) )
| ! [SY625: $i] :
( ~ ( in @ SY625 @ SV138 )
| ( in @ SY625 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(836,plain,
! [SV13: $i,SV139: $i] :
( ( ! [SY626: $i] :
( ~ ~ ( ~ ( in @ SV139 @ SV13 )
| ~ ( in @ SY626 @ SV13 ) )
| ~ ! [SY627: $i] :
( ~ ( in @ SY627 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV139 @ SY627 )
| ( in @ SY626 @ SY627 ) )
| ~ ( ~ ( in @ SY626 @ SY627 )
| ( in @ SV139 @ SY627 ) ) ) )
| ( SV139 = SY626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(837,plain,
! [SV133: $i,SV13: $i,SV131: $i] :
( ( ( ~ ( ~ ( in @ SV131 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SV133 @ ( sK2_SY402 @ SV13 ) ) ) )
= $false )
| ( ( ! [SY623: $i] :
( ~ ( in @ SY623 @ SV131 )
| ( in @ SY623 @ SV133 ) )
| ! [SY624: $i] :
( ~ ( in @ SY624 @ SV133 )
| ( in @ SY624 @ SV131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(838,plain,
! [SV123: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
| ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 ) )
= $false )
| ( ( ~ ~ ! [SY607: $i] :
~ ( in @ SY607 @ SV123 ) )
= $true )
| ( ( ~ ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[796]) ).
thf(839,plain,
! [SV68: $i > $o,SV19: $i,SV127: $i] :
( ( ( in @ SV127 @ SV19 )
= $false )
| ( ( ~ ( SV68 @ SV127 ) )
= $true )
| ( ( in @ ( sK5_SY532 @ SV68 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[798]) ).
thf(840,plain,
! [SV68: $i > $o,SV19: $i,SV128: $i] :
( ( ( in @ SV128 @ SV19 )
= $false )
| ( ( ~ ( SV68 @ SV128 ) )
= $true )
| ( ( SV68 @ ( sK5_SY532 @ SV68 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(841,plain,
! [SV21: $i,SV70: $i > $o,SV119: $i] :
( ( ( in @ ( sK25_SY536 @ SV119 @ SV70 @ SV21 ) @ SV21 )
= $true )
| ( ( SV70 @ SV119 )
= $true )
| ( ( in @ SV119 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(842,plain,
! [SV21: $i,SV119: $i,SV70: $i > $o] :
( ( ( ~ ( SV70 @ ( sK25_SY536 @ SV119 @ SV70 @ SV21 ) ) )
= $true )
| ( ( SV70 @ SV119 )
= $true )
| ( ( in @ SV119 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(843,plain,
! [SV71: $i > $o,SV22: $i,SV134: $i] :
( ( ( in @ SV134 @ SV22 )
= $false )
| ( ( ~ ( SV71 @ SV134 ) )
= $true )
| ( ( in @ ( sK13_SY537 @ SV71 @ SV22 ) @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(844,plain,
! [SV71: $i > $o,SV22: $i,SV135: $i] :
( ( ( in @ SV135 @ SV22 )
= $false )
| ( ( ~ ( SV71 @ SV135 ) )
= $true )
| ( ( SV71 @ ( sK13_SY537 @ SV71 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(845,plain,
! [SV113: $i,SV27: $i > $o] :
( ( ( ! [SY452: $i] :
~ ! [SY453: $i] :
~ ( ~ ( ~ ( SV27 @ SY453 )
| ( SY453 = SY452 ) )
| ~ ( ( SY453 != SY452 )
| ( SV27 @ SY453 ) ) ) )
= $false )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV27 @ ( sK29_SY600 @ SV113 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(846,plain,
! [SV113: $i,SV27: $i > $o] :
( ( ( ~ ! [SY628: $i] :
~ ( ~ ( ~ ( SV27 @ SY628 )
| ( SY628
= ( sK33_SY452 @ SV113 @ SV27 ) ) )
| ~ ( ( SY628
!= ( sK33_SY452 @ SV113 @ SV27 ) )
| ( SV27 @ SY628 ) ) ) )
= $false )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV113
= ( sK29_SY600 @ SV113 @ SV27 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[806]) ).
thf(847,plain,
! [SV30: $i,SV114: $i] :
( ( ( ! [SY613: $i] :
~ ~ ( ~ ( in @ SY613 @ ( sK18_SY460 @ SV114 @ SV30 ) )
| ~ ( in @ SY613 @ SV30 ) ) )
= $true )
| ( ( in @ SV114 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(848,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ! [SY464: $i] :
~ ~ ( ~ ( SV31 @ SY464 )
| ~ ! [SY465: $i] :
( ~ ( SV31 @ SY465 )
| ( SY464 = SY465 ) ) ) )
= $false )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV31 @ ( sK30_SY601 @ SV115 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(849,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ~ ~ ( ~ ( SV31 @ ( sK34_SY464 @ SV115 @ SV31 ) )
| ~ ! [SY629: $i] :
( ~ ( SV31 @ SY629 )
| ( ( sK34_SY464 @ SV115 @ SV31 )
= SY629 ) ) ) )
= $false )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV115
= ( sK30_SY601 @ SV115 @ SV31 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[809]) ).
thf(850,plain,
! [SV78: $i,SV32: $i > $i > $o,SV132: $i] :
( ( ( ~ ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
| ~ ! [SY621: $i] :
~ ~ ( ~ ( in @ SY621 @ SV78 )
| ~ ( SV32 @ SY621 @ SV132 ) ) )
= $true )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(851,plain,
! [SV132: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ SY622 @ SV78 )
| ~ ( SV32 @ SY622 @ SV132 ) )
| ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) ) )
= $true )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[811]) ).
thf(852,plain,
! [SV124: $i,SV78: $i,SV32: $i > $i > $o] :
( ( ( ~ ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
| ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( ~ ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[812]) ).
thf(853,plain,
! [SV79: $i > $o,SV33: $i,SV136: $i] :
( ( ( in @ SV136 @ SV33 )
= $false )
| ( ( ~ ( SV79 @ SV136 ) )
= $true )
| ( ( in @ ( sK14_SY554 @ SV79 @ SV33 ) @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(854,plain,
! [SV79: $i > $o,SV33: $i,SV137: $i] :
( ( ( in @ SV137 @ SV33 )
= $false )
| ( ( ~ ( SV79 @ SV137 ) )
= $true )
| ( ( SV79 @ ( sK14_SY554 @ SV79 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(855,plain,
! [SV116: $i,SV36: $i > $o] :
( ( ( ! [SY481: $i] :
~ ( SV36 @ SY481 ) )
= $false )
| ( ( SV36 @ SV116 )
= $false )
| ( ( SV36 @ ( sK31_SY604 @ SV116 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(856,plain,
! [SV116: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ ( sK36_SY481 @ SV116 @ SV36 ) ) )
= $false )
| ( ( SV36 @ SV116 )
= $false )
| ( ( SV116
= ( sK31_SY604 @ SV116 @ SV36 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[817]) ).
thf(857,plain,
! [SV43: $i,SV121: $o,SV86: $i,SV105: $i] :
( ( ( in @ SV105 @ SV86 )
= $true )
| ( SV121 = $true )
| ( ( SV105 = SV43 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[818]) ).
thf(858,plain,
! [SV43: $i,SV86: $i,SV105: $i] :
( ( ( in @ SV105 @ SV86 )
= $true )
| ( $true = $true )
| ( ( SV105 = SV43 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(859,plain,
! [SV43: $i,SV86: $i,SV105: $i] :
( ( ( in @ SV105 @ SV86 )
= $true )
| ( $false = $true )
| ( ( SV105 = SV43 )
= $true )
| ( ( in @ SV105 @ ( setadjoin @ SV43 @ SV86 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[824]) ).
thf(860,plain,
! [SV44: $i,SV87: $i > $o,SV122: $i] :
( ( ( ~ ( in @ ( sK37_SY562 @ SV122 @ SV87 @ SV44 ) @ SV44 )
| ( SV87 @ ( sK37_SY562 @ SV122 @ SV87 @ SV44 ) ) )
= $false )
| ( ( in @ SV122 @ SV44 )
= $false )
| ( ( SV87 @ SV122 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[827]) ).
thf(861,plain,
! [SV46: $i,SV140: $i] :
( ( ( ~ ( in @ SV140 @ omega )
| ( in @ SV140 @ SV46 ) )
= $true )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( in @ ( sK20_SY496 @ SV46 ) @ omega )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(862,plain,
! [SV46: $i,SV141: $i] :
( ( ( ~ ( in @ SV141 @ omega )
| ( in @ SV141 @ SV46 ) )
= $true )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( in @ ( sK20_SY496 @ SV46 ) @ SV46 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(863,plain,
! [SV91: $i,SV50: $i,SV126: $i] :
( ( ( in @ SV126 @ SV50 )
= $false )
| ( ( in @ SV91 @ SV126 )
= $false )
| ( ( in @ SV91 @ ( setunion @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(864,plain,
! [SV12: $i,SV118: $i,SV64: $i > $o] :
( ( ( SV64 @ ( sK24_SY527 @ SV118 @ SV64 @ SV12 ) )
= $false )
| ( ( SV64 @ SV118 )
= $true )
| ( ( in @ SV118 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(865,plain,
! [SV13: $i,SV138: $i] :
( ( ( ~ ( in @ SV138 @ ( sK2_SY402 @ SV13 ) ) )
= $true )
| ( ( ! [SY625: $i] :
( ~ ( in @ SY625 @ SV138 )
| ( in @ SY625 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(866,plain,
! [SV142: $i,SV13: $i,SV139: $i] :
( ( ~ ~ ( ~ ( in @ SV139 @ SV13 )
| ~ ( in @ SV142 @ SV13 ) )
| ~ ! [SY630: $i] :
( ~ ( in @ SY630 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV139 @ SY630 )
| ( in @ SV142 @ SY630 ) )
| ~ ( ~ ( in @ SV142 @ SY630 )
| ( in @ SV139 @ SY630 ) ) ) )
| ( SV139 = SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(867,plain,
! [SV133: $i,SV13: $i,SV131: $i] :
( ( ( ~ ( in @ SV131 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SV133 @ ( sK2_SY402 @ SV13 ) ) )
= $true )
| ( ( ! [SY623: $i] :
( ~ ( in @ SY623 @ SV131 )
| ( in @ SY623 @ SV133 ) )
| ! [SY624: $i] :
( ~ ( in @ SY624 @ SV133 )
| ( in @ SY624 @ SV131 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[837]) ).
thf(868,plain,
! [SV123: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 ) )
= $false )
| ( ( ~ ~ ! [SY607: $i] :
~ ( in @ SY607 @ SV123 ) )
= $true )
| ( ( ~ ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[838]) ).
thf(869,plain,
! [SV123: $i,SV13: $i] :
( ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( ~ ~ ! [SY607: $i] :
~ ( in @ SY607 @ SV123 ) )
= $true )
| ( ( ~ ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[838]) ).
thf(870,plain,
! [SV19: $i,SV127: $i,SV68: $i > $o] :
( ( ( SV68 @ SV127 )
= $false )
| ( ( in @ SV127 @ SV19 )
= $false )
| ( ( in @ ( sK5_SY532 @ SV68 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[839]) ).
thf(871,plain,
! [SV19: $i,SV128: $i,SV68: $i > $o] :
( ( ( SV68 @ SV128 )
= $false )
| ( ( in @ SV128 @ SV19 )
= $false )
| ( ( SV68 @ ( sK5_SY532 @ SV68 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[840]) ).
thf(872,plain,
! [SV21: $i,SV119: $i,SV70: $i > $o] :
( ( ( SV70 @ ( sK25_SY536 @ SV119 @ SV70 @ SV21 ) )
= $false )
| ( ( SV70 @ SV119 )
= $true )
| ( ( in @ SV119 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(873,plain,
! [SV22: $i,SV134: $i,SV71: $i > $o] :
( ( ( SV71 @ SV134 )
= $false )
| ( ( in @ SV134 @ SV22 )
= $false )
| ( ( in @ ( sK13_SY537 @ SV71 @ SV22 ) @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(874,plain,
! [SV22: $i,SV135: $i,SV71: $i > $o] :
( ( ( SV71 @ SV135 )
= $false )
| ( ( in @ SV135 @ SV22 )
= $false )
| ( ( SV71 @ ( sK13_SY537 @ SV71 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(875,plain,
! [SV113: $i,SV27: $i > $o] :
( ( ( ~ ! [SY631: $i] :
~ ( ~ ( ~ ( SV27 @ SY631 )
| ( SY631
= ( sK38_SY452 @ SV113 @ SV27 ) ) )
| ~ ( ( SY631
!= ( sK38_SY452 @ SV113 @ SV27 ) )
| ( SV27 @ SY631 ) ) ) )
= $false )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV27 @ ( sK29_SY600 @ SV113 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[845]) ).
thf(876,plain,
! [SV113: $i,SV27: $i > $o] :
( ( ( ! [SY628: $i] :
~ ( ~ ( ~ ( SV27 @ SY628 )
| ( SY628
= ( sK33_SY452 @ SV113 @ SV27 ) ) )
| ~ ( ( SY628
!= ( sK33_SY452 @ SV113 @ SV27 ) )
| ( SV27 @ SY628 ) ) ) )
= $true )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV113
= ( sK29_SY600 @ SV113 @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[846]) ).
thf(877,plain,
! [SV30: $i,SV114: $i,SV143: $i] :
( ( ( ~ ~ ( ~ ( in @ SV143 @ ( sK18_SY460 @ SV114 @ SV30 ) )
| ~ ( in @ SV143 @ SV30 ) ) )
= $true )
| ( ( in @ SV114 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(878,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ~ ~ ( ~ ( SV31 @ ( sK39_SY464 @ SV115 @ SV31 ) )
| ~ ! [SY632: $i] :
( ~ ( SV31 @ SY632 )
| ( ( sK39_SY464 @ SV115 @ SV31 )
= SY632 ) ) ) )
= $false )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV31 @ ( sK30_SY601 @ SV115 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[848]) ).
thf(879,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ~ ( ~ ( SV31 @ ( sK34_SY464 @ SV115 @ SV31 ) )
| ~ ! [SY629: $i] :
( ~ ( SV31 @ SY629 )
| ( ( sK34_SY464 @ SV115 @ SV31 )
= SY629 ) ) ) )
= $true )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV115
= ( sK30_SY601 @ SV115 @ SV31 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[849]) ).
thf(880,plain,
! [SV78: $i,SV32: $i > $i > $o,SV132: $i] :
( ( ( ~ ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) ) )
= $true )
| ( ( ~ ! [SY621: $i] :
~ ~ ( ~ ( in @ SY621 @ SV78 )
| ~ ( SV32 @ SY621 @ SV132 ) ) )
= $true )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(881,plain,
! [SV132: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ~ ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ SY622 @ SV78 )
| ~ ( SV32 @ SY622 @ SV132 ) ) )
= $true )
| ( ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
= $true )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(882,plain,
! [SV124: $i,SV78: $i,SV32: $i > $i > $o] :
( ( ( ~ ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( ~ ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(883,plain,
! [SV32: $i > $i > $o,SV78: $i,SV124: $i] :
( ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( ~ ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(884,plain,
! [SV33: $i,SV136: $i,SV79: $i > $o] :
( ( ( SV79 @ SV136 )
= $false )
| ( ( in @ SV136 @ SV33 )
= $false )
| ( ( in @ ( sK14_SY554 @ SV79 @ SV33 ) @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[853]) ).
thf(885,plain,
! [SV33: $i,SV137: $i,SV79: $i > $o] :
( ( ( SV79 @ SV137 )
= $false )
| ( ( in @ SV137 @ SV33 )
= $false )
| ( ( SV79 @ ( sK14_SY554 @ SV79 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(886,plain,
! [SV116: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ ( sK40_SY481 @ SV116 @ SV36 ) ) )
= $false )
| ( ( SV36 @ SV116 )
= $false )
| ( ( SV36 @ ( sK31_SY604 @ SV116 @ SV36 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[855]) ).
thf(887,plain,
! [SV116: $i,SV36: $i > $o] :
( ( ( SV36 @ ( sK36_SY481 @ SV116 @ SV36 ) )
= $true )
| ( ( SV36 @ SV116 )
= $false )
| ( ( SV116
= ( sK31_SY604 @ SV116 @ SV36 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[856]) ).
thf(888,plain,
! [SV44: $i,SV87: $i > $o,SV122: $i] :
( ( ( ~ ( in @ ( sK37_SY562 @ SV122 @ SV87 @ SV44 ) @ SV44 ) )
= $false )
| ( ( in @ SV122 @ SV44 )
= $false )
| ( ( SV87 @ SV122 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[860]) ).
thf(889,plain,
! [SV44: $i,SV122: $i,SV87: $i > $o] :
( ( ( SV87 @ ( sK37_SY562 @ SV122 @ SV87 @ SV44 ) )
= $false )
| ( ( in @ SV122 @ SV44 )
= $false )
| ( ( SV87 @ SV122 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[860]) ).
thf(890,plain,
! [SV46: $i,SV140: $i] :
( ( ( ~ ( in @ SV140 @ omega ) )
= $true )
| ( ( in @ SV140 @ SV46 )
= $true )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( in @ ( sK20_SY496 @ SV46 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[861]) ).
thf(891,plain,
! [SV46: $i,SV141: $i] :
( ( ( ~ ( in @ SV141 @ omega ) )
= $true )
| ( ( in @ SV141 @ SV46 )
= $true )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( in @ ( sK20_SY496 @ SV46 ) @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(892,plain,
! [SV13: $i,SV138: $i] :
( ( ( in @ SV138 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( ! [SY625: $i] :
( ~ ( in @ SY625 @ SV138 )
| ( in @ SY625 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(893,plain,
! [SV142: $i,SV13: $i,SV139: $i] :
( ( ( ~ ~ ( ~ ( in @ SV139 @ SV13 )
| ~ ( in @ SV142 @ SV13 ) ) )
= $true )
| ( ( ~ ! [SY630: $i] :
( ~ ( in @ SY630 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV139 @ SY630 )
| ( in @ SV142 @ SY630 ) )
| ~ ( ~ ( in @ SV142 @ SY630 )
| ( in @ SV139 @ SY630 ) ) ) )
| ( SV139 = SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(894,plain,
! [SV133: $i,SV13: $i,SV131: $i] :
( ( ( ~ ( in @ SV131 @ ( sK2_SY402 @ SV13 ) ) )
= $true )
| ( ( ~ ( in @ SV133 @ ( sK2_SY402 @ SV13 ) ) )
= $true )
| ( ( ! [SY623: $i] :
( ~ ( in @ SY623 @ SV131 )
| ( in @ SY623 @ SV133 ) )
| ! [SY624: $i] :
( ~ ( in @ SY624 @ SV133 )
| ( in @ SY624 @ SV131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(895,plain,
! [SV123: $i,SV13: $i] :
( ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( ~ ~ ! [SY607: $i] :
~ ( in @ SY607 @ SV123 ) )
= $true )
| ( ( ~ ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(896,plain,
! [SV13: $i,SV123: $i] :
( ( ( ~ ! [SY607: $i] :
~ ( in @ SY607 @ SV123 ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( ~ ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(897,plain,
! [SV113: $i,SV27: $i > $o] :
( ( ( ! [SY631: $i] :
~ ( ~ ( ~ ( SV27 @ SY631 )
| ( SY631
= ( sK38_SY452 @ SV113 @ SV27 ) ) )
| ~ ( ( SY631
!= ( sK38_SY452 @ SV113 @ SV27 ) )
| ( SV27 @ SY631 ) ) ) )
= $true )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV27 @ ( sK29_SY600 @ SV113 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[875]) ).
thf(898,plain,
! [SV113: $i,SV144: $i,SV27: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV27 @ SV144 )
| ( SV144
= ( sK33_SY452 @ SV113 @ SV27 ) ) )
| ~ ( ( SV144
!= ( sK33_SY452 @ SV113 @ SV27 ) )
| ( SV27 @ SV144 ) ) ) )
= $true )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV113
= ( sK29_SY600 @ SV113 @ SV27 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(899,plain,
! [SV30: $i,SV114: $i,SV143: $i] :
( ( ( ~ ( ~ ( in @ SV143 @ ( sK18_SY460 @ SV114 @ SV30 ) )
| ~ ( in @ SV143 @ SV30 ) ) )
= $false )
| ( ( in @ SV114 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(900,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ~ ( ~ ( SV31 @ ( sK39_SY464 @ SV115 @ SV31 ) )
| ~ ! [SY632: $i] :
( ~ ( SV31 @ SY632 )
| ( ( sK39_SY464 @ SV115 @ SV31 )
= SY632 ) ) ) )
= $true )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV31 @ ( sK30_SY601 @ SV115 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[878]) ).
thf(901,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ~ ( SV31 @ ( sK34_SY464 @ SV115 @ SV31 ) )
| ~ ! [SY629: $i] :
( ~ ( SV31 @ SY629 )
| ( ( sK34_SY464 @ SV115 @ SV31 )
= SY629 ) ) )
= $false )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV115
= ( sK30_SY601 @ SV115 @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(902,plain,
! [SV78: $i,SV32: $i > $i > $o,SV132: $i] :
( ( ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
= $false )
| ( ( ~ ! [SY621: $i] :
~ ~ ( ~ ( in @ SY621 @ SV78 )
| ~ ( SV32 @ SY621 @ SV132 ) ) )
= $true )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[880]) ).
thf(903,plain,
! [SV132: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ~ ! [SY622: $i] :
~ ~ ( ~ ( in @ SY622 @ SV78 )
| ~ ( SV32 @ SY622 @ SV132 ) ) )
= $false )
| ( ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
= $true )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(904,plain,
! [SV124: $i,SV78: $i,SV32: $i > $i > $o] :
( ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( ~ ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[882]) ).
thf(905,plain,
! [SV124: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(906,plain,
! [SV116: $i,SV36: $i > $o] :
( ( ( SV36 @ ( sK40_SY481 @ SV116 @ SV36 ) )
= $true )
| ( ( SV36 @ SV116 )
= $false )
| ( ( SV36 @ ( sK31_SY604 @ SV116 @ SV36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[886]) ).
thf(907,plain,
! [SV44: $i,SV87: $i > $o,SV122: $i] :
( ( ( in @ ( sK37_SY562 @ SV122 @ SV87 @ SV44 ) @ SV44 )
= $true )
| ( ( in @ SV122 @ SV44 )
= $false )
| ( ( SV87 @ SV122 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[888]) ).
thf(908,plain,
! [SV46: $i,SV140: $i] :
( ( ( in @ SV140 @ omega )
= $false )
| ( ( in @ SV140 @ SV46 )
= $true )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( in @ ( sK20_SY496 @ SV46 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(909,plain,
! [SV46: $i,SV141: $i] :
( ( ( in @ SV141 @ omega )
= $false )
| ( ( in @ SV141 @ SV46 )
= $true )
| ( ( in @ emptyset @ SV46 )
= $false )
| ( ( in @ ( sK20_SY496 @ SV46 ) @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(910,plain,
! [SV13: $i,SV138: $i,SV145: $i] :
( ( ( ~ ( in @ SV145 @ SV138 )
| ( in @ SV145 @ SV13 ) )
= $true )
| ( ( in @ SV138 @ ( sK2_SY402 @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(911,plain,
! [SV142: $i,SV13: $i,SV139: $i] :
( ( ( ~ ( ~ ( in @ SV139 @ SV13 )
| ~ ( in @ SV142 @ SV13 ) ) )
= $false )
| ( ( ~ ! [SY630: $i] :
( ~ ( in @ SY630 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV139 @ SY630 )
| ( in @ SV142 @ SY630 ) )
| ~ ( ~ ( in @ SV142 @ SY630 )
| ( in @ SV139 @ SY630 ) ) ) )
| ( SV139 = SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(912,plain,
! [SV133: $i,SV13: $i,SV131: $i] :
( ( ( in @ SV131 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( ~ ( in @ SV133 @ ( sK2_SY402 @ SV13 ) ) )
= $true )
| ( ( ! [SY623: $i] :
( ~ ( in @ SY623 @ SV131 )
| ( in @ SY623 @ SV133 ) )
| ! [SY624: $i] :
( ~ ( in @ SY624 @ SV133 )
| ( in @ SY624 @ SV131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(913,plain,
! [SV13: $i,SV123: $i] :
( ( ( ~ ! [SY607: $i] :
~ ( in @ SY607 @ SV123 ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( ~ ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(914,plain,
! [SV13: $i,SV123: $i] :
( ( ( ! [SY607: $i] :
~ ( in @ SY607 @ SV123 ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( ~ ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[896]) ).
thf(915,plain,
! [SV113: $i,SV146: $i,SV27: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV27 @ SV146 )
| ( SV146
= ( sK38_SY452 @ SV113 @ SV27 ) ) )
| ~ ( ( SV146
!= ( sK38_SY452 @ SV113 @ SV27 ) )
| ( SV27 @ SV146 ) ) ) )
= $true )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV27 @ ( sK29_SY600 @ SV113 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(916,plain,
! [SV113: $i,SV144: $i,SV27: $i > $o] :
( ( ( ~ ( ~ ( SV27 @ SV144 )
| ( SV144
= ( sK33_SY452 @ SV113 @ SV27 ) ) )
| ~ ( ( SV144
!= ( sK33_SY452 @ SV113 @ SV27 ) )
| ( SV27 @ SV144 ) ) )
= $false )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV113
= ( sK29_SY600 @ SV113 @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(917,plain,
! [SV30: $i,SV114: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ ( sK18_SY460 @ SV114 @ SV30 ) )
| ~ ( in @ SV143 @ SV30 ) )
= $true )
| ( ( in @ SV114 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[899]) ).
thf(918,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ~ ( SV31 @ ( sK39_SY464 @ SV115 @ SV31 ) )
| ~ ! [SY632: $i] :
( ~ ( SV31 @ SY632 )
| ( ( sK39_SY464 @ SV115 @ SV31 )
= SY632 ) ) )
= $false )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV31 @ ( sK30_SY601 @ SV115 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(919,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ~ ( SV31 @ ( sK34_SY464 @ SV115 @ SV31 ) ) )
= $false )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV115
= ( sK30_SY601 @ SV115 @ SV31 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[901]) ).
thf(920,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ~ ! [SY629: $i] :
( ~ ( SV31 @ SY629 )
| ( ( sK34_SY464 @ SV115 @ SV31 )
= SY629 ) ) )
= $false )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV115
= ( sK30_SY601 @ SV115 @ SV31 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[901]) ).
thf(921,plain,
! [SV132: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ! [SY621: $i] :
~ ~ ( ~ ( in @ SY621 @ SV78 )
| ~ ( SV32 @ SY621 @ SV132 ) ) )
= $false )
| ( ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
= $false )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(922,plain,
! [SV132: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ! [SY622: $i] :
~ ~ ( ~ ( in @ SY622 @ SV78 )
| ~ ( SV32 @ SY622 @ SV132 ) ) )
= $true )
| ( ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
= $true )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[903]) ).
thf(923,plain,
! [SV124: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ! [SY550: $i] :
~ ! [SY551: $i] :
~ ( ~ ( ~ ( in @ SY551 @ SY550 )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY551 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY551 ) )
| ( in @ SY551 @ SY550 ) ) ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(924,plain,
! [SV78: $i,SV32: $i > $i > $o,SV124: $i] :
( ( ( ~ ! [SY633: $i] :
~ ( ~ ( ~ ( in @ SY633 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY633 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY633 ) )
| ( in @ SY633 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) ) ) ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[905]) ).
thf(925,plain,
! [SV13: $i,SV138: $i,SV145: $i] :
( ( ( ~ ( in @ SV145 @ SV138 ) )
= $true )
| ( ( in @ SV145 @ SV13 )
= $true )
| ( ( in @ SV138 @ ( sK2_SY402 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(926,plain,
! [SV142: $i,SV13: $i,SV139: $i] :
( ( ( ~ ( in @ SV139 @ SV13 )
| ~ ( in @ SV142 @ SV13 ) )
= $true )
| ( ( ~ ! [SY630: $i] :
( ~ ( in @ SY630 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV139 @ SY630 )
| ( in @ SV142 @ SY630 ) )
| ~ ( ~ ( in @ SV142 @ SY630 )
| ( in @ SV139 @ SY630 ) ) ) )
| ( SV139 = SV142 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[911]) ).
thf(927,plain,
! [SV131: $i,SV13: $i,SV133: $i] :
( ( ( in @ SV133 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( in @ SV131 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( ! [SY623: $i] :
( ~ ( in @ SY623 @ SV131 )
| ( in @ SY623 @ SV133 ) )
| ! [SY624: $i] :
( ~ ( in @ SY624 @ SV133 )
| ( in @ SY624 @ SV131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(928,plain,
! [SV13: $i,SV123: $i] :
( ( ( ! [SY607: $i] :
~ ( in @ SY607 @ SV123 ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( ~ ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[913]) ).
thf(929,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( ~ ( in @ SV147 @ SV123 ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( ~ ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(930,plain,
! [SV113: $i,SV146: $i,SV27: $i > $o] :
( ( ( ~ ( ~ ( SV27 @ SV146 )
| ( SV146
= ( sK38_SY452 @ SV113 @ SV27 ) ) )
| ~ ( ( SV146
!= ( sK38_SY452 @ SV113 @ SV27 ) )
| ( SV27 @ SV146 ) ) )
= $false )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV27 @ ( sK29_SY600 @ SV113 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(931,plain,
! [SV113: $i,SV144: $i,SV27: $i > $o] :
( ( ( ~ ( ~ ( SV27 @ SV144 )
| ( SV144
= ( sK33_SY452 @ SV113 @ SV27 ) ) ) )
= $false )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV113
= ( sK29_SY600 @ SV113 @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[916]) ).
thf(932,plain,
! [SV27: $i > $o,SV113: $i,SV144: $i] :
( ( ( ~ ( ( SV144
!= ( sK33_SY452 @ SV113 @ SV27 ) )
| ( SV27 @ SV144 ) ) )
= $false )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV113
= ( sK29_SY600 @ SV113 @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[916]) ).
thf(933,plain,
! [SV30: $i,SV114: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ ( sK18_SY460 @ SV114 @ SV30 ) ) )
= $true )
| ( ( ~ ( in @ SV143 @ SV30 ) )
= $true )
| ( ( in @ SV114 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(934,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ~ ( SV31 @ ( sK39_SY464 @ SV115 @ SV31 ) ) )
= $false )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV31 @ ( sK30_SY601 @ SV115 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[918]) ).
thf(935,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ~ ! [SY632: $i] :
( ~ ( SV31 @ SY632 )
| ( ( sK39_SY464 @ SV115 @ SV31 )
= SY632 ) ) )
= $false )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV31 @ ( sK30_SY601 @ SV115 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[918]) ).
thf(936,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( SV31 @ ( sK34_SY464 @ SV115 @ SV31 ) )
= $true )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV115
= ( sK30_SY601 @ SV115 @ SV31 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[919]) ).
thf(937,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ! [SY629: $i] :
( ~ ( SV31 @ SY629 )
| ( ( sK34_SY464 @ SV115 @ SV31 )
= SY629 ) ) )
= $true )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV115
= ( sK30_SY601 @ SV115 @ SV31 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[920]) ).
thf(938,plain,
! [SV78: $i,SV32: $i > $i > $o,SV132: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK42_SY621 @ SV132 @ SV32 @ SV78 ) @ SV78 )
| ~ ( SV32 @ ( sK42_SY621 @ SV132 @ SV32 @ SV78 ) @ SV132 ) ) )
= $false )
| ( ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
= $false )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[921]) ).
thf(939,plain,
! [SV132: $i,SV32: $i > $i > $o,SV78: $i,SV148: $i] :
( ( ( ~ ~ ( ~ ( in @ SV148 @ SV78 )
| ~ ( SV32 @ SV148 @ SV132 ) ) )
= $true )
| ( ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
= $true )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(940,plain,
! [SV78: $i,SV32: $i > $i > $o,SV124: $i] :
( ( ( ~ ! [SY636: $i] :
~ ( ~ ( ~ ( in @ SY636 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY636 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY636 ) )
| ( in @ SY636 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) ) ) ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[923]) ).
thf(941,plain,
! [SV78: $i,SV32: $i > $i > $o,SV124: $i] :
( ( ( ! [SY633: $i] :
~ ( ~ ( ~ ( in @ SY633 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY633 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY633 ) )
| ( in @ SY633 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) ) ) ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[924]) ).
thf(942,plain,
! [SV13: $i,SV138: $i,SV145: $i] :
( ( ( in @ SV145 @ SV138 )
= $false )
| ( ( in @ SV145 @ SV13 )
= $true )
| ( ( in @ SV138 @ ( sK2_SY402 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(943,plain,
! [SV142: $i,SV13: $i,SV139: $i] :
( ( ( ~ ( in @ SV139 @ SV13 ) )
= $true )
| ( ( ~ ( in @ SV142 @ SV13 ) )
= $true )
| ( ( ~ ! [SY630: $i] :
( ~ ( in @ SY630 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV139 @ SY630 )
| ( in @ SV142 @ SY630 ) )
| ~ ( ~ ( in @ SV142 @ SY630 )
| ( in @ SV139 @ SY630 ) ) ) )
| ( SV139 = SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(944,plain,
! [SV13: $i,SV133: $i,SV131: $i] :
( ( ( ! [SY623: $i] :
( ~ ( in @ SY623 @ SV131 )
| ( in @ SY623 @ SV133 ) ) )
= $true )
| ( ( ! [SY624: $i] :
( ~ ( in @ SY624 @ SV133 )
| ( in @ SY624 @ SV131 ) ) )
= $true )
| ( ( in @ SV131 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( in @ SV133 @ ( sK2_SY402 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[927]) ).
thf(945,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( ~ ( in @ SV149 @ SV123 ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( ~ ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(946,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( in @ SV147 @ SV123 )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( ~ ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[929]) ).
thf(947,plain,
! [SV113: $i,SV146: $i,SV27: $i > $o] :
( ( ( ~ ( ~ ( SV27 @ SV146 )
| ( SV146
= ( sK38_SY452 @ SV113 @ SV27 ) ) ) )
= $false )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV27 @ ( sK29_SY600 @ SV113 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[930]) ).
thf(948,plain,
! [SV27: $i > $o,SV113: $i,SV146: $i] :
( ( ( ~ ( ( SV146
!= ( sK38_SY452 @ SV113 @ SV27 ) )
| ( SV27 @ SV146 ) ) )
= $false )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV27 @ ( sK29_SY600 @ SV113 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[930]) ).
thf(949,plain,
! [SV113: $i,SV144: $i,SV27: $i > $o] :
( ( ( ~ ( SV27 @ SV144 )
| ( SV144
= ( sK33_SY452 @ SV113 @ SV27 ) ) )
= $true )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV113
= ( sK29_SY600 @ SV113 @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[931]) ).
thf(950,plain,
! [SV27: $i > $o,SV113: $i,SV144: $i] :
( ( ( ( SV144
!= ( sK33_SY452 @ SV113 @ SV27 ) )
| ( SV27 @ SV144 ) )
= $true )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV113
= ( sK29_SY600 @ SV113 @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[932]) ).
thf(951,plain,
! [SV30: $i,SV114: $i,SV143: $i] :
( ( ( in @ SV143 @ ( sK18_SY460 @ SV114 @ SV30 ) )
= $false )
| ( ( ~ ( in @ SV143 @ SV30 ) )
= $true )
| ( ( in @ SV114 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(952,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( SV31 @ ( sK39_SY464 @ SV115 @ SV31 ) )
= $true )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV31 @ ( sK30_SY601 @ SV115 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[934]) ).
thf(953,plain,
! [SV115: $i,SV31: $i > $o] :
( ( ( ! [SY632: $i] :
( ~ ( SV31 @ SY632 )
| ( ( sK39_SY464 @ SV115 @ SV31 )
= SY632 ) ) )
= $true )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV31 @ ( sK30_SY601 @ SV115 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[935]) ).
thf(954,plain,
! [SV115: $i,SV150: $i,SV31: $i > $o] :
( ( ( ~ ( SV31 @ SV150 )
| ( ( sK34_SY464 @ SV115 @ SV31 )
= SV150 ) )
= $true )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV115
= ( sK30_SY601 @ SV115 @ SV31 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(955,plain,
! [SV78: $i,SV32: $i > $i > $o,SV132: $i] :
( ( ( ~ ( ~ ( in @ ( sK42_SY621 @ SV132 @ SV32 @ SV78 ) @ SV78 )
| ~ ( SV32 @ ( sK42_SY621 @ SV132 @ SV32 @ SV78 ) @ SV132 ) ) )
= $true )
| ( ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
= $false )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[938]) ).
thf(956,plain,
! [SV132: $i,SV32: $i > $i > $o,SV78: $i,SV148: $i] :
( ( ( ~ ( ~ ( in @ SV148 @ SV78 )
| ~ ( SV32 @ SV148 @ SV132 ) ) )
= $false )
| ( ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
= $true )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(957,plain,
! [SV78: $i,SV32: $i > $i > $o,SV124: $i] :
( ( ( ! [SY636: $i] :
~ ( ~ ( ~ ( in @ SY636 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
| ~ ! [SY552: $i] :
~ ~ ( ~ ( in @ SY552 @ SV78 )
| ~ ( SV32 @ SY552 @ SY636 ) ) )
| ~ ( ~ ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV78 )
| ~ ( SV32 @ SY553 @ SY636 ) )
| ( in @ SY636 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) ) ) ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[940]) ).
thf(958,plain,
! [SV78: $i,SV32: $i > $i > $o,SV124: $i,SV151: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
| ~ ! [SY639: $i] :
~ ~ ( ~ ( in @ SY639 @ SV78 )
| ~ ( SV32 @ SY639 @ SV151 ) ) )
| ~ ( ~ ~ ! [SY640: $i] :
~ ~ ( ~ ( in @ SY640 @ SV78 )
| ~ ( SV32 @ SY640 @ SV151 ) )
| ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) ) ) ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(959,plain,
! [SV142: $i,SV13: $i,SV139: $i] :
( ( ( in @ SV139 @ SV13 )
= $false )
| ( ( ~ ( in @ SV142 @ SV13 ) )
= $true )
| ( ( ~ ! [SY630: $i] :
( ~ ( in @ SY630 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV139 @ SY630 )
| ( in @ SV142 @ SY630 ) )
| ~ ( ~ ( in @ SV142 @ SY630 )
| ( in @ SV139 @ SY630 ) ) ) )
| ( SV139 = SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(960,plain,
! [SV13: $i,SV133: $i,SV131: $i,SV152: $i] :
( ( ( ~ ( in @ SV152 @ SV131 )
| ( in @ SV152 @ SV133 ) )
= $true )
| ( ( ! [SY624: $i] :
( ~ ( in @ SY624 @ SV133 )
| ( in @ SY624 @ SV131 ) ) )
= $true )
| ( ( in @ SV131 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( in @ SV133 @ ( sK2_SY402 @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(961,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( in @ SV149 @ SV123 )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( ~ ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(962,plain,
! [SV147: $i,SV123: $i,SV13: $i] :
( ( ( ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[946]) ).
thf(963,plain,
! [SV113: $i,SV146: $i,SV27: $i > $o] :
( ( ( ~ ( SV27 @ SV146 )
| ( SV146
= ( sK38_SY452 @ SV113 @ SV27 ) ) )
= $true )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV27 @ ( sK29_SY600 @ SV113 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[947]) ).
thf(964,plain,
! [SV27: $i > $o,SV113: $i,SV146: $i] :
( ( ( ( SV146
!= ( sK38_SY452 @ SV113 @ SV27 ) )
| ( SV27 @ SV146 ) )
= $true )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV27 @ ( sK29_SY600 @ SV113 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[948]) ).
thf(965,plain,
! [SV113: $i,SV144: $i,SV27: $i > $o] :
( ( ( ~ ( SV27 @ SV144 ) )
= $true )
| ( ( SV144
= ( sK33_SY452 @ SV113 @ SV27 ) )
= $true )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV113
= ( sK29_SY600 @ SV113 @ SV27 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(966,plain,
! [SV27: $i > $o,SV113: $i,SV144: $i] :
( ( ( SV144
!= ( sK33_SY452 @ SV113 @ SV27 ) )
= $true )
| ( ( SV27 @ SV144 )
= $true )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV113
= ( sK29_SY600 @ SV113 @ SV27 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[950]) ).
thf(967,plain,
! [SV114: $i,SV30: $i,SV143: $i] :
( ( ( in @ SV143 @ SV30 )
= $false )
| ( ( in @ SV143 @ ( sK18_SY460 @ SV114 @ SV30 ) )
= $false )
| ( ( in @ SV114 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(968,plain,
! [SV115: $i,SV153: $i,SV31: $i > $o] :
( ( ( ~ ( SV31 @ SV153 )
| ( ( sK39_SY464 @ SV115 @ SV31 )
= SV153 ) )
= $true )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV31 @ ( sK30_SY601 @ SV115 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(969,plain,
! [SV115: $i,SV150: $i,SV31: $i > $o] :
( ( ( ~ ( SV31 @ SV150 ) )
= $true )
| ( ( ( sK34_SY464 @ SV115 @ SV31 )
= SV150 )
= $true )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV115
= ( sK30_SY601 @ SV115 @ SV31 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[954]) ).
thf(970,plain,
! [SV78: $i,SV32: $i > $i > $o,SV132: $i] :
( ( ( ~ ( in @ ( sK42_SY621 @ SV132 @ SV32 @ SV78 ) @ SV78 )
| ~ ( SV32 @ ( sK42_SY621 @ SV132 @ SV32 @ SV78 ) @ SV132 ) )
= $false )
| ( ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
= $false )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(971,plain,
! [SV132: $i,SV32: $i > $i > $o,SV78: $i,SV148: $i] :
( ( ( ~ ( in @ SV148 @ SV78 )
| ~ ( SV32 @ SV148 @ SV132 ) )
= $true )
| ( ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
= $true )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[956]) ).
thf(972,plain,
! [SV78: $i,SV32: $i > $i > $o,SV124: $i,SV154: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
| ~ ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV78 )
| ~ ( SV32 @ SY641 @ SV154 ) ) )
| ~ ( ~ ~ ! [SY642: $i] :
~ ~ ( ~ ( in @ SY642 @ SV78 )
| ~ ( SV32 @ SY642 @ SV154 ) )
| ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) ) ) ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(973,plain,
! [SV78: $i,SV32: $i > $i > $o,SV124: $i,SV151: $i] :
( ( ( ~ ( ~ ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
| ~ ! [SY639: $i] :
~ ~ ( ~ ( in @ SY639 @ SV78 )
| ~ ( SV32 @ SY639 @ SV151 ) ) )
| ~ ( ~ ~ ! [SY640: $i] :
~ ~ ( ~ ( in @ SY640 @ SV78 )
| ~ ( SV32 @ SY640 @ SV151 ) )
| ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) ) ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(974,plain,
! [SV139: $i,SV13: $i,SV142: $i] :
( ( ( in @ SV142 @ SV13 )
= $false )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( ~ ! [SY630: $i] :
( ~ ( in @ SY630 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV139 @ SY630 )
| ( in @ SV142 @ SY630 ) )
| ~ ( ~ ( in @ SV142 @ SY630 )
| ( in @ SV139 @ SY630 ) ) ) )
| ( SV139 = SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(975,plain,
! [SV13: $i,SV133: $i,SV131: $i,SV152: $i] :
( ( ( ~ ( in @ SV152 @ SV131 ) )
= $true )
| ( ( in @ SV152 @ SV133 )
= $true )
| ( ( ! [SY624: $i] :
( ~ ( in @ SY624 @ SV133 )
| ( in @ SY624 @ SV131 ) ) )
= $true )
| ( ( in @ SV131 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( in @ SV133 @ ( sK2_SY402 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[960]) ).
thf(976,plain,
! [SV149: $i,SV123: $i,SV13: $i] :
( ( ( ! [SY608: $i] :
~ ~ ! [SY609: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY608 @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY609 @ SV123 ) )
| ~ ~ ~ ! [SY610: $i] :
~ ~ ( ~ ( in @ SY610 @ SY608 )
| ~ ( in @ SY610 @ SV123 ) ) )
| ~ ! [SY588: $i] :
( ~ ( in @ SY588 @ ( sK2_SY402 @ SV13 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY588 )
| ( in @ SX6 @ SY608 ) )
| ( in @ SY609 @ SY588 ) ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(977,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( ~ ~ ! [SY643: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY643 @ SV123 ) )
| ~ ~ ~ ! [SY644: $i] :
~ ~ ( ~ ( in @ SY644 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
| ~ ( in @ SY644 @ SV123 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK2_SY402 @ SV13 ) )
| ! [SY646: $i] :
( ~ ( in @ SY646 @ SY645 )
| ( in @ SY646 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) ) )
| ( in @ SY643 @ SY645 ) ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[962]) ).
thf(978,plain,
! [SV113: $i,SV146: $i,SV27: $i > $o] :
( ( ( ~ ( SV27 @ SV146 ) )
= $true )
| ( ( SV146
= ( sK38_SY452 @ SV113 @ SV27 ) )
= $true )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV27 @ ( sK29_SY600 @ SV113 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(979,plain,
! [SV27: $i > $o,SV113: $i,SV146: $i] :
( ( ( SV146
!= ( sK38_SY452 @ SV113 @ SV27 ) )
= $true )
| ( ( SV27 @ SV146 )
= $true )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV27 @ ( sK29_SY600 @ SV113 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(980,plain,
! [SV113: $i,SV144: $i,SV27: $i > $o] :
( ( ( SV27 @ SV144 )
= $false )
| ( ( SV144
= ( sK33_SY452 @ SV113 @ SV27 ) )
= $true )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV113
= ( sK29_SY600 @ SV113 @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(981,plain,
! [SV27: $i > $o,SV113: $i,SV144: $i] :
( ( ( SV144
= ( sK33_SY452 @ SV113 @ SV27 ) )
= $false )
| ( ( SV27 @ SV144 )
= $true )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV113
= ( sK29_SY600 @ SV113 @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(982,plain,
! [SV115: $i,SV153: $i,SV31: $i > $o] :
( ( ( ~ ( SV31 @ SV153 ) )
= $true )
| ( ( ( sK39_SY464 @ SV115 @ SV31 )
= SV153 )
= $true )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV31 @ ( sK30_SY601 @ SV115 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[968]) ).
thf(983,plain,
! [SV115: $i,SV150: $i,SV31: $i > $o] :
( ( ( SV31 @ SV150 )
= $false )
| ( ( ( sK34_SY464 @ SV115 @ SV31 )
= SV150 )
= $true )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV115
= ( sK30_SY601 @ SV115 @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[969]) ).
thf(984,plain,
! [SV78: $i,SV32: $i > $i > $o,SV132: $i] :
( ( ( ~ ( in @ ( sK42_SY621 @ SV132 @ SV32 @ SV78 ) @ SV78 ) )
= $false )
| ( ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
= $false )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[970]) ).
thf(985,plain,
! [SV78: $i,SV132: $i,SV32: $i > $i > $o] :
( ( ( ~ ( SV32 @ ( sK42_SY621 @ SV132 @ SV32 @ SV78 ) @ SV132 ) )
= $false )
| ( ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
= $false )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[970]) ).
thf(986,plain,
! [SV132: $i,SV32: $i > $i > $o,SV78: $i,SV148: $i] :
( ( ( ~ ( in @ SV148 @ SV78 ) )
= $true )
| ( ( ~ ( SV32 @ SV148 @ SV132 ) )
= $true )
| ( ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
= $true )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(987,plain,
! [SV78: $i,SV32: $i > $i > $o,SV124: $i,SV154: $i] :
( ( ( ~ ( ~ ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
| ~ ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV78 )
| ~ ( SV32 @ SY641 @ SV154 ) ) )
| ~ ( ~ ~ ! [SY642: $i] :
~ ~ ( ~ ( in @ SY642 @ SV78 )
| ~ ( SV32 @ SY642 @ SV154 ) )
| ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) ) ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(988,plain,
! [SV78: $i,SV32: $i > $i > $o,SV124: $i,SV151: $i] :
( ( ( ~ ( ~ ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
| ~ ! [SY639: $i] :
~ ~ ( ~ ( in @ SY639 @ SV78 )
| ~ ( SV32 @ SY639 @ SV151 ) ) ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(989,plain,
! [SV124: $i,SV151: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ~ ( ~ ~ ! [SY640: $i] :
~ ~ ( ~ ( in @ SY640 @ SV78 )
| ~ ( SV32 @ SY640 @ SV151 ) )
| ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) ) ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(990,plain,
! [SV142: $i,SV139: $i,SV13: $i] :
( ( ( ~ ! [SY630: $i] :
( ~ ( in @ SY630 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV139 @ SY630 )
| ( in @ SV142 @ SY630 ) )
| ~ ( ~ ( in @ SV142 @ SY630 )
| ( in @ SV139 @ SY630 ) ) ) ) )
= $true )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[974]) ).
thf(991,plain,
! [SV13: $i,SV133: $i,SV131: $i,SV152: $i] :
( ( ( in @ SV152 @ SV131 )
= $false )
| ( ( in @ SV152 @ SV133 )
= $true )
| ( ( ! [SY624: $i] :
( ~ ( in @ SY624 @ SV133 )
| ( in @ SY624 @ SV131 ) ) )
= $true )
| ( ( in @ SV131 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( in @ SV133 @ ( sK2_SY402 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[975]) ).
thf(992,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( ~ ~ ! [SY647: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY647 @ SV123 ) )
| ~ ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( in @ SY648 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
| ~ ( in @ SY648 @ SV123 ) ) )
| ~ ! [SY649: $i] :
( ~ ( in @ SY649 @ ( sK2_SY402 @ SV13 ) )
| ! [SY650: $i] :
( ~ ( in @ SY650 @ SY649 )
| ( in @ SY650 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) ) )
| ( in @ SY647 @ SY649 ) ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[976]) ).
thf(993,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( ~ ! [SY643: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY643 @ SV123 ) )
| ~ ~ ~ ! [SY644: $i] :
~ ~ ( ~ ( in @ SY644 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
| ~ ( in @ SY644 @ SV123 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK2_SY402 @ SV13 ) )
| ! [SY646: $i] :
( ~ ( in @ SY646 @ SY645 )
| ( in @ SY646 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) ) )
| ( in @ SY643 @ SY645 ) ) ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[977]) ).
thf(994,plain,
! [SV113: $i,SV146: $i,SV27: $i > $o] :
( ( ( SV27 @ SV146 )
= $false )
| ( ( SV146
= ( sK38_SY452 @ SV113 @ SV27 ) )
= $true )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV27 @ ( sK29_SY600 @ SV113 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(995,plain,
! [SV27: $i > $o,SV113: $i,SV146: $i] :
( ( ( SV146
= ( sK38_SY452 @ SV113 @ SV27 ) )
= $false )
| ( ( SV27 @ SV146 )
= $true )
| ( ( SV27 @ SV113 )
= $false )
| ( ( SV27 @ ( sK29_SY600 @ SV113 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[979]) ).
thf(996,plain,
! [SV115: $i,SV153: $i,SV31: $i > $o] :
( ( ( SV31 @ SV153 )
= $false )
| ( ( ( sK39_SY464 @ SV115 @ SV31 )
= SV153 )
= $true )
| ( ( SV31 @ SV115 )
= $false )
| ( ( SV31 @ ( sK30_SY601 @ SV115 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(997,plain,
! [SV78: $i,SV32: $i > $i > $o,SV132: $i] :
( ( ( in @ ( sK42_SY621 @ SV132 @ SV32 @ SV78 ) @ SV78 )
= $true )
| ( ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
= $false )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(998,plain,
! [SV78: $i,SV132: $i,SV32: $i > $i > $o] :
( ( ( SV32 @ ( sK42_SY621 @ SV132 @ SV32 @ SV78 ) @ SV132 )
= $true )
| ( ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
= $false )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(999,plain,
! [SV132: $i,SV32: $i > $i > $o,SV78: $i,SV148: $i] :
( ( ( in @ SV148 @ SV78 )
= $false )
| ( ( ~ ( SV32 @ SV148 @ SV132 ) )
= $true )
| ( ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
= $true )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(1000,plain,
! [SV78: $i,SV32: $i > $i > $o,SV124: $i,SV154: $i] :
( ( ( ~ ( ~ ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
| ~ ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV78 )
| ~ ( SV32 @ SY641 @ SV154 ) ) ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[987]) ).
thf(1001,plain,
! [SV124: $i,SV154: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ~ ( ~ ~ ! [SY642: $i] :
~ ~ ( ~ ( in @ SY642 @ SV78 )
| ~ ( SV32 @ SY642 @ SV154 ) )
| ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) ) ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[987]) ).
thf(1002,plain,
! [SV78: $i,SV32: $i > $i > $o,SV124: $i,SV151: $i] :
( ( ( ~ ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
| ~ ! [SY639: $i] :
~ ~ ( ~ ( in @ SY639 @ SV78 )
| ~ ( SV32 @ SY639 @ SV151 ) ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[988]) ).
thf(1003,plain,
! [SV124: $i,SV151: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ~ ~ ! [SY640: $i] :
~ ~ ( ~ ( in @ SY640 @ SV78 )
| ~ ( SV32 @ SY640 @ SV151 ) )
| ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[989]) ).
thf(1004,plain,
! [SV142: $i,SV139: $i,SV13: $i] :
( ( ( ! [SY630: $i] :
( ~ ( in @ SY630 @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV139 @ SY630 )
| ( in @ SV142 @ SY630 ) )
| ~ ( ~ ( in @ SV142 @ SY630 )
| ( in @ SV139 @ SY630 ) ) ) ) )
= $false )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1005,plain,
! [SV13: $i,SV152: $i,SV131: $i,SV133: $i,SV155: $i] :
( ( ( ~ ( in @ SV155 @ SV133 )
| ( in @ SV155 @ SV131 ) )
= $true )
| ( ( in @ SV152 @ SV133 )
= $true )
| ( ( in @ SV152 @ SV131 )
= $false )
| ( ( in @ SV131 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( in @ SV133 @ ( sK2_SY402 @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1006,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( ~ ! [SY647: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY647 @ SV123 ) )
| ~ ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( in @ SY648 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
| ~ ( in @ SY648 @ SV123 ) ) )
| ~ ! [SY649: $i] :
( ~ ( in @ SY649 @ ( sK2_SY402 @ SV13 ) )
| ! [SY650: $i] :
( ~ ( in @ SY650 @ SY649 )
| ( in @ SY650 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) ) )
| ( in @ SY647 @ SY649 ) ) ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1007,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( ! [SY643: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY643 @ SV123 ) )
| ~ ~ ~ ! [SY644: $i] :
~ ~ ( ~ ( in @ SY644 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
| ~ ( in @ SY644 @ SV123 ) ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ ( sK2_SY402 @ SV13 ) )
| ! [SY646: $i] :
( ~ ( in @ SY646 @ SY645 )
| ( in @ SY646 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) ) )
| ( in @ SY643 @ SY645 ) ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1008,plain,
! [SV78: $i,SV132: $i,SV148: $i,SV32: $i > $i > $o] :
( ( ( SV32 @ SV148 @ SV132 )
= $false )
| ( ( in @ SV148 @ SV78 )
= $false )
| ( ( in @ SV132 @ ( sK21_SY550 @ SV32 @ SV78 ) )
= $true )
| ( ( in @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1009,plain,
! [SV78: $i,SV32: $i > $i > $o,SV124: $i,SV154: $i] :
( ( ( ~ ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
| ~ ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV78 )
| ~ ( SV32 @ SY641 @ SV154 ) ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1010,plain,
! [SV124: $i,SV154: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ~ ~ ! [SY642: $i] :
~ ~ ( ~ ( in @ SY642 @ SV78 )
| ~ ( SV32 @ SY642 @ SV154 ) )
| ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1001]) ).
thf(1011,plain,
! [SV78: $i,SV32: $i > $i > $o,SV124: $i,SV151: $i] :
( ( ( ~ ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) ) )
= $true )
| ( ( ~ ! [SY639: $i] :
~ ~ ( ~ ( in @ SY639 @ SV78 )
| ~ ( SV32 @ SY639 @ SV151 ) ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1002]) ).
thf(1012,plain,
! [SV124: $i,SV151: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ~ ~ ! [SY640: $i] :
~ ~ ( ~ ( in @ SY640 @ SV78 )
| ~ ( SV32 @ SY640 @ SV151 ) ) )
= $true )
| ( ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1013,plain,
! [SV13: $i,SV139: $i,SV142: $i] :
( ( ( ~ ( in @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( ~ ( ~ ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
| ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) ) )
| ~ ( ~ ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
| ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) ) ) ) )
= $false )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1004]) ).
thf(1014,plain,
! [SV13: $i,SV152: $i,SV131: $i,SV133: $i,SV155: $i] :
( ( ( ~ ( in @ SV155 @ SV133 ) )
= $true )
| ( ( in @ SV155 @ SV131 )
= $true )
| ( ( in @ SV152 @ SV133 )
= $true )
| ( ( in @ SV152 @ SV131 )
= $false )
| ( ( in @ SV131 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( in @ SV133 @ ( sK2_SY402 @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1015,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( ! [SY647: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ SY647 @ SV123 ) )
| ~ ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( in @ SY648 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
| ~ ( in @ SY648 @ SV123 ) ) )
| ~ ! [SY649: $i] :
( ~ ( in @ SY649 @ ( sK2_SY402 @ SV13 ) )
| ! [SY650: $i] :
( ~ ( in @ SY650 @ SY649 )
| ( in @ SY650 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) ) )
| ( in @ SY647 @ SY649 ) ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1016,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SV123 ) )
| ~ ~ ~ ! [SY644: $i] :
~ ~ ( ~ ( in @ SY644 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
| ~ ( in @ SY644 @ SV123 ) ) )
| ~ ! [SY652: $i] :
( ~ ( in @ SY652 @ ( sK2_SY402 @ SV13 ) )
| ! [SY646: $i] :
( ~ ( in @ SY646 @ SY652 )
| ( in @ SY646 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) ) )
| ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SY652 ) ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1007]) ).
thf(1017,plain,
! [SV78: $i,SV32: $i > $i > $o,SV124: $i,SV154: $i] :
( ( ( ~ ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) ) )
= $true )
| ( ( ~ ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV78 )
| ~ ( SV32 @ SY641 @ SV154 ) ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1018,plain,
! [SV124: $i,SV154: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ~ ~ ! [SY642: $i] :
~ ~ ( ~ ( in @ SY642 @ SV78 )
| ~ ( SV32 @ SY642 @ SV154 ) ) )
= $true )
| ( ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1010]) ).
thf(1019,plain,
! [SV78: $i,SV32: $i > $i > $o,SV124: $i,SV151: $i] :
( ( ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
= $false )
| ( ( ~ ! [SY639: $i] :
~ ~ ( ~ ( in @ SY639 @ SV78 )
| ~ ( SV32 @ SY639 @ SV151 ) ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1020,plain,
! [SV124: $i,SV151: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ~ ! [SY640: $i] :
~ ~ ( ~ ( in @ SY640 @ SV78 )
| ~ ( SV32 @ SY640 @ SV151 ) ) )
= $false )
| ( ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1021,plain,
! [SV13: $i,SV139: $i,SV142: $i] :
( ( ( ~ ( in @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) @ ( sK2_SY402 @ SV13 ) ) )
= $false )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1013]) ).
thf(1022,plain,
! [SV13: $i,SV142: $i,SV139: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
| ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) ) )
| ~ ( ~ ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
| ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) ) ) ) )
= $false )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1013]) ).
thf(1023,plain,
! [SV13: $i,SV152: $i,SV131: $i,SV133: $i,SV155: $i] :
( ( ( in @ SV155 @ SV133 )
= $false )
| ( ( in @ SV155 @ SV131 )
= $true )
| ( ( in @ SV152 @ SV133 )
= $true )
| ( ( in @ SV152 @ SV131 )
= $false )
| ( ( in @ SV131 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( in @ SV133 @ ( sK2_SY402 @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1024,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SV123 ) )
| ~ ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( in @ SY648 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
| ~ ( in @ SY648 @ SV123 ) ) )
| ~ ! [SY655: $i] :
( ~ ( in @ SY655 @ ( sK2_SY402 @ SV13 ) )
| ! [SY650: $i] :
( ~ ( in @ SY650 @ SY655 )
| ( in @ SY650 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) ) )
| ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SY655 ) ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1015]) ).
thf(1025,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SV123 ) )
| ~ ~ ~ ! [SY644: $i] :
~ ~ ( ~ ( in @ SY644 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
| ~ ( in @ SY644 @ SV123 ) ) )
| ~ ! [SY652: $i] :
( ~ ( in @ SY652 @ ( sK2_SY402 @ SV13 ) )
| ! [SY646: $i] :
( ~ ( in @ SY646 @ SY652 )
| ( in @ SY646 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) ) )
| ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SY652 ) ) ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1016]) ).
thf(1026,plain,
! [SV78: $i,SV32: $i > $i > $o,SV124: $i,SV154: $i] :
( ( ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
= $false )
| ( ( ~ ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV78 )
| ~ ( SV32 @ SY641 @ SV154 ) ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1027,plain,
! [SV124: $i,SV154: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ~ ! [SY642: $i] :
~ ~ ( ~ ( in @ SY642 @ SV78 )
| ~ ( SV32 @ SY642 @ SV154 ) ) )
= $false )
| ( ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1028,plain,
! [SV124: $i,SV151: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ! [SY639: $i] :
~ ~ ( ~ ( in @ SY639 @ SV78 )
| ~ ( SV32 @ SY639 @ SV151 ) ) )
= $false )
| ( ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1029,plain,
! [SV124: $i,SV151: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ! [SY640: $i] :
~ ~ ( ~ ( in @ SY640 @ SV78 )
| ~ ( SV32 @ SY640 @ SV151 ) ) )
= $true )
| ( ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1020]) ).
thf(1030,plain,
! [SV13: $i,SV139: $i,SV142: $i] :
( ( ( in @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
= $true )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1021]) ).
thf(1031,plain,
! [SV13: $i,SV142: $i,SV139: $i] :
( ( ( ~ ( ~ ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
| ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) ) )
| ~ ( ~ ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
| ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) ) ) )
= $true )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1022]) ).
thf(1032,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SV123 ) )
| ~ ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( in @ SY648 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
| ~ ( in @ SY648 @ SV123 ) ) )
| ~ ! [SY655: $i] :
( ~ ( in @ SY655 @ ( sK2_SY402 @ SV13 ) )
| ! [SY650: $i] :
( ~ ( in @ SY650 @ SY655 )
| ( in @ SY650 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) ) )
| ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SY655 ) ) ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1024]) ).
thf(1033,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SV123 ) )
| ~ ~ ~ ! [SY644: $i] :
~ ~ ( ~ ( in @ SY644 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
| ~ ( in @ SY644 @ SV123 ) ) )
| ~ ! [SY652: $i] :
( ~ ( in @ SY652 @ ( sK2_SY402 @ SV13 ) )
| ! [SY646: $i] :
( ~ ( in @ SY646 @ SY652 )
| ( in @ SY646 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) ) )
| ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SY652 ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1034,plain,
! [SV124: $i,SV154: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV78 )
| ~ ( SV32 @ SY641 @ SV154 ) ) )
= $false )
| ( ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1035,plain,
! [SV124: $i,SV154: $i,SV32: $i > $i > $o,SV78: $i] :
( ( ( ! [SY642: $i] :
~ ~ ( ~ ( in @ SY642 @ SV78 )
| ~ ( SV32 @ SY642 @ SV154 ) ) )
= $true )
| ( ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1027]) ).
thf(1036,plain,
! [SV78: $i,SV32: $i > $i > $o,SV151: $i,SV124: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK49_SY639 @ SV124 @ SV151 @ SV32 @ SV78 ) @ SV78 )
| ~ ( SV32 @ ( sK49_SY639 @ SV124 @ SV151 @ SV32 @ SV78 ) @ SV151 ) ) )
= $false )
| ( ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1028]) ).
thf(1037,plain,
! [SV124: $i,SV151: $i,SV32: $i > $i > $o,SV78: $i,SV156: $i] :
( ( ( ~ ~ ( ~ ( in @ SV156 @ SV78 )
| ~ ( SV32 @ SV156 @ SV151 ) ) )
= $true )
| ( ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1038,plain,
! [SV13: $i,SV142: $i,SV139: $i] :
( ( ( ~ ( ~ ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
| ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
| ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) ) ) )
= $true )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1039,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SV123 ) )
| ~ ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( in @ SY648 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
| ~ ( in @ SY648 @ SV123 ) ) )
| ~ ! [SY655: $i] :
( ~ ( in @ SY655 @ ( sK2_SY402 @ SV13 ) )
| ! [SY650: $i] :
( ~ ( in @ SY650 @ SY655 )
| ( in @ SY650 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) ) )
| ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SY655 ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1040,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SV123 ) )
| ~ ~ ~ ! [SY644: $i] :
~ ~ ( ~ ( in @ SY644 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
| ~ ( in @ SY644 @ SV123 ) ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1033]) ).
thf(1041,plain,
! [SV123: $i,SV147: $i,SV13: $i] :
( ( ( ~ ! [SY652: $i] :
( ~ ( in @ SY652 @ ( sK2_SY402 @ SV13 ) )
| ! [SY646: $i] :
( ~ ( in @ SY646 @ SY652 )
| ( in @ SY646 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) ) )
| ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SY652 ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1033]) ).
thf(1042,plain,
! [SV78: $i,SV32: $i > $i > $o,SV154: $i,SV124: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK50_SY641 @ SV124 @ SV154 @ SV32 @ SV78 ) @ SV78 )
| ~ ( SV32 @ ( sK50_SY641 @ SV124 @ SV154 @ SV32 @ SV78 ) @ SV154 ) ) )
= $false )
| ( ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1034]) ).
thf(1043,plain,
! [SV124: $i,SV154: $i,SV32: $i > $i > $o,SV78: $i,SV157: $i] :
( ( ( ~ ~ ( ~ ( in @ SV157 @ SV78 )
| ~ ( SV32 @ SV157 @ SV154 ) ) )
= $true )
| ( ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1044,plain,
! [SV78: $i,SV32: $i > $i > $o,SV151: $i,SV124: $i] :
( ( ( ~ ( ~ ( in @ ( sK49_SY639 @ SV124 @ SV151 @ SV32 @ SV78 ) @ SV78 )
| ~ ( SV32 @ ( sK49_SY639 @ SV124 @ SV151 @ SV32 @ SV78 ) @ SV151 ) ) )
= $true )
| ( ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1036]) ).
thf(1045,plain,
! [SV124: $i,SV151: $i,SV32: $i > $i > $o,SV78: $i,SV156: $i] :
( ( ( ~ ( ~ ( in @ SV156 @ SV78 )
| ~ ( SV32 @ SV156 @ SV151 ) ) )
= $false )
| ( ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1046,plain,
! [SV13: $i,SV142: $i,SV139: $i] :
( ( ( ~ ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
| ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
| ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) ) ) )
= $true )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1047,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SV123 ) )
| ~ ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( in @ SY648 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
| ~ ( in @ SY648 @ SV123 ) ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1039]) ).
thf(1048,plain,
! [SV123: $i,SV149: $i,SV13: $i] :
( ( ( ~ ! [SY655: $i] :
( ~ ( in @ SY655 @ ( sK2_SY402 @ SV13 ) )
| ! [SY650: $i] :
( ~ ( in @ SY650 @ SY655 )
| ( in @ SY650 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) ) )
| ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SY655 ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1039]) ).
thf(1049,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SV123 ) )
| ~ ~ ~ ! [SY644: $i] :
~ ~ ( ~ ( in @ SY644 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
| ~ ( in @ SY644 @ SV123 ) ) ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1040]) ).
thf(1050,plain,
! [SV123: $i,SV147: $i,SV13: $i] :
( ( ( ! [SY652: $i] :
( ~ ( in @ SY652 @ ( sK2_SY402 @ SV13 ) )
| ! [SY646: $i] :
( ~ ( in @ SY646 @ SY652 )
| ( in @ SY646 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) ) )
| ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SY652 ) ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1051,plain,
! [SV78: $i,SV32: $i > $i > $o,SV154: $i,SV124: $i] :
( ( ( ~ ( ~ ( in @ ( sK50_SY641 @ SV124 @ SV154 @ SV32 @ SV78 ) @ SV78 )
| ~ ( SV32 @ ( sK50_SY641 @ SV124 @ SV154 @ SV32 @ SV78 ) @ SV154 ) ) )
= $true )
| ( ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1042]) ).
thf(1052,plain,
! [SV124: $i,SV154: $i,SV32: $i > $i > $o,SV78: $i,SV157: $i] :
( ( ( ~ ( ~ ( in @ SV157 @ SV78 )
| ~ ( SV32 @ SV157 @ SV154 ) ) )
= $false )
| ( ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1053,plain,
! [SV78: $i,SV32: $i > $i > $o,SV151: $i,SV124: $i] :
( ( ( ~ ( in @ ( sK49_SY639 @ SV124 @ SV151 @ SV32 @ SV78 ) @ SV78 )
| ~ ( SV32 @ ( sK49_SY639 @ SV124 @ SV151 @ SV32 @ SV78 ) @ SV151 ) )
= $false )
| ( ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1054,plain,
! [SV124: $i,SV151: $i,SV32: $i > $i > $o,SV78: $i,SV156: $i] :
( ( ( ~ ( in @ SV156 @ SV78 )
| ~ ( SV32 @ SV156 @ SV151 ) )
= $true )
| ( ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1045]) ).
thf(1055,plain,
! [SV13: $i,SV142: $i,SV139: $i] :
( ( ( ~ ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
| ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) ) ) )
= $true )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1056,plain,
! [SV13: $i,SV139: $i,SV142: $i] :
( ( ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
| ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) ) ) )
= $true )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1057,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SV123 ) )
| ~ ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( in @ SY648 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
| ~ ( in @ SY648 @ SV123 ) ) ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1047]) ).
thf(1058,plain,
! [SV123: $i,SV149: $i,SV13: $i] :
( ( ( ! [SY655: $i] :
( ~ ( in @ SY655 @ ( sK2_SY402 @ SV13 ) )
| ! [SY650: $i] :
( ~ ( in @ SY650 @ SY655 )
| ( in @ SY650 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) ) )
| ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SY655 ) ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1048]) ).
thf(1059,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SV123 ) )
| ~ ~ ~ ! [SY644: $i] :
~ ~ ( ~ ( in @ SY644 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
| ~ ( in @ SY644 @ SV123 ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1060,plain,
! [SV123: $i,SV147: $i,SV13: $i,SV158: $i] :
( ( ( ~ ( in @ SV158 @ ( sK2_SY402 @ SV13 ) )
| ! [SY657: $i] :
( ~ ( in @ SY657 @ SV158 )
| ( in @ SY657 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) ) )
| ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SV158 ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1061,plain,
! [SV78: $i,SV32: $i > $i > $o,SV154: $i,SV124: $i] :
( ( ( ~ ( in @ ( sK50_SY641 @ SV124 @ SV154 @ SV32 @ SV78 ) @ SV78 )
| ~ ( SV32 @ ( sK50_SY641 @ SV124 @ SV154 @ SV32 @ SV78 ) @ SV154 ) )
= $false )
| ( ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1062,plain,
! [SV124: $i,SV154: $i,SV32: $i > $i > $o,SV78: $i,SV157: $i] :
( ( ( ~ ( in @ SV157 @ SV78 )
| ~ ( SV32 @ SV157 @ SV154 ) )
= $true )
| ( ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1052]) ).
thf(1063,plain,
! [SV78: $i,SV32: $i > $i > $o,SV151: $i,SV124: $i] :
( ( ( ~ ( in @ ( sK49_SY639 @ SV124 @ SV151 @ SV32 @ SV78 ) @ SV78 ) )
= $false )
| ( ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1064,plain,
! [SV78: $i,SV151: $i,SV124: $i,SV32: $i > $i > $o] :
( ( ( ~ ( SV32 @ ( sK49_SY639 @ SV124 @ SV151 @ SV32 @ SV78 ) @ SV151 ) )
= $false )
| ( ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1065,plain,
! [SV124: $i,SV151: $i,SV32: $i > $i > $o,SV78: $i,SV156: $i] :
( ( ( ~ ( in @ SV156 @ SV78 ) )
= $true )
| ( ( ~ ( SV32 @ SV156 @ SV151 ) )
= $true )
| ( ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1054]) ).
thf(1066,plain,
! [SV13: $i,SV142: $i,SV139: $i] :
( ( ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
| ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) ) ) )
= $true )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1055]) ).
thf(1067,plain,
! [SV13: $i,SV139: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
| ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) ) )
= $false )
| ( ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
= $false )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1056]) ).
thf(1068,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SV123 ) )
| ~ ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( in @ SY648 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
| ~ ( in @ SY648 @ SV123 ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1069,plain,
! [SV123: $i,SV149: $i,SV13: $i,SV159: $i] :
( ( ( ~ ( in @ SV159 @ ( sK2_SY402 @ SV13 ) )
| ! [SY658: $i] :
( ~ ( in @ SY658 @ SV159 )
| ( in @ SY658 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) ) )
| ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SV159 ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1070,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SV123 ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1071,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( ~ ~ ~ ! [SY644: $i] :
~ ~ ( ~ ( in @ SY644 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
| ~ ( in @ SY644 @ SV123 ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1072,plain,
! [SV123: $i,SV147: $i,SV13: $i,SV158: $i] :
( ( ( ~ ( in @ SV158 @ ( sK2_SY402 @ SV13 ) ) )
= $true )
| ( ( ! [SY657: $i] :
( ~ ( in @ SY657 @ SV158 )
| ( in @ SY657 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) ) )
| ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SV158 ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1073,plain,
! [SV78: $i,SV32: $i > $i > $o,SV154: $i,SV124: $i] :
( ( ( ~ ( in @ ( sK50_SY641 @ SV124 @ SV154 @ SV32 @ SV78 ) @ SV78 ) )
= $false )
| ( ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1074,plain,
! [SV78: $i,SV154: $i,SV124: $i,SV32: $i > $i > $o] :
( ( ( ~ ( SV32 @ ( sK50_SY641 @ SV124 @ SV154 @ SV32 @ SV78 ) @ SV154 ) )
= $false )
| ( ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1075,plain,
! [SV124: $i,SV154: $i,SV32: $i > $i > $o,SV78: $i,SV157: $i] :
( ( ( ~ ( in @ SV157 @ SV78 ) )
= $true )
| ( ( ~ ( SV32 @ SV157 @ SV154 ) )
= $true )
| ( ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1076,plain,
! [SV78: $i,SV32: $i > $i > $o,SV151: $i,SV124: $i] :
( ( ( in @ ( sK49_SY639 @ SV124 @ SV151 @ SV32 @ SV78 ) @ SV78 )
= $true )
| ( ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1063]) ).
thf(1077,plain,
! [SV78: $i,SV151: $i,SV124: $i,SV32: $i > $i > $o] :
( ( ( SV32 @ ( sK49_SY639 @ SV124 @ SV151 @ SV32 @ SV78 ) @ SV151 )
= $true )
| ( ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1064]) ).
thf(1078,plain,
! [SV124: $i,SV151: $i,SV32: $i > $i > $o,SV78: $i,SV156: $i] :
( ( ( in @ SV156 @ SV78 )
= $false )
| ( ( ~ ( SV32 @ SV156 @ SV151 ) )
= $true )
| ( ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1079,plain,
! [SV13: $i,SV139: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
| ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) ) )
= $false )
| ( ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
= $true )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1080,plain,
! [SV13: $i,SV139: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) ) )
= $false )
| ( ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
= $false )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1067]) ).
thf(1081,plain,
! [SV13: $i,SV142: $i,SV139: $i] :
( ( ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
= $false )
| ( ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
= $false )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1067]) ).
thf(1082,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SV123 ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1068]) ).
thf(1083,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( ~ ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( in @ SY648 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
| ~ ( in @ SY648 @ SV123 ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1068]) ).
thf(1084,plain,
! [SV123: $i,SV149: $i,SV13: $i,SV159: $i] :
( ( ( ~ ( in @ SV159 @ ( sK2_SY402 @ SV13 ) ) )
= $true )
| ( ( ! [SY658: $i] :
( ~ ( in @ SY658 @ SV159 )
| ( in @ SY658 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) ) )
| ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SV159 ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1085,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( ~ ( ~ ( in @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SV123 ) ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1070]) ).
thf(1086,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( ~ ~ ! [SY644: $i] :
~ ~ ( ~ ( in @ SY644 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
| ~ ( in @ SY644 @ SV123 ) ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1071]) ).
thf(1087,plain,
! [SV123: $i,SV147: $i,SV13: $i,SV158: $i] :
( ( ( in @ SV158 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( ! [SY657: $i] :
( ~ ( in @ SY657 @ SV158 )
| ( in @ SY657 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) ) )
| ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SV158 ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1088,plain,
! [SV78: $i,SV32: $i > $i > $o,SV154: $i,SV124: $i] :
( ( ( in @ ( sK50_SY641 @ SV124 @ SV154 @ SV32 @ SV78 ) @ SV78 )
= $true )
| ( ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1073]) ).
thf(1089,plain,
! [SV78: $i,SV154: $i,SV124: $i,SV32: $i > $i > $o] :
( ( ( SV32 @ ( sK50_SY641 @ SV124 @ SV154 @ SV32 @ SV78 ) @ SV154 )
= $true )
| ( ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1090,plain,
! [SV124: $i,SV154: $i,SV32: $i > $i > $o,SV78: $i,SV157: $i] :
( ( ( in @ SV157 @ SV78 )
= $false )
| ( ( ~ ( SV32 @ SV157 @ SV154 ) )
= $true )
| ( ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1091,plain,
! [SV124: $i,SV78: $i,SV151: $i,SV156: $i,SV32: $i > $i > $o] :
( ( ( SV32 @ SV156 @ SV151 )
= $false )
| ( ( in @ SV156 @ SV78 )
= $false )
| ( ( in @ SV151 @ ( sK41_SY550 @ SV124 @ SV32 @ SV78 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV124
= ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1092,plain,
! [SV13: $i,SV139: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) ) )
= $false )
| ( ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
= $true )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1079]) ).
thf(1093,plain,
! [SV13: $i,SV142: $i,SV139: $i] :
( ( ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
= $false )
| ( ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
= $true )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1079]) ).
thf(1094,plain,
! [SV13: $i,SV139: $i,SV142: $i] :
( ( ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
= $true )
| ( ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
= $false )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1080]) ).
thf(1095,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( ~ ( ~ ( in @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SV123 ) ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1096,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( in @ SY648 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
| ~ ( in @ SY648 @ SV123 ) ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1083]) ).
thf(1097,plain,
! [SV123: $i,SV149: $i,SV13: $i,SV159: $i] :
( ( ( in @ SV159 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( ! [SY658: $i] :
( ~ ( in @ SY658 @ SV159 )
| ( in @ SY658 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) ) )
| ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SV159 ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1098,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( ~ ( in @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SV123 ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1099,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( ~ ! [SY644: $i] :
~ ~ ( ~ ( in @ SY644 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
| ~ ( in @ SY644 @ SV123 ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1100,plain,
! [SV13: $i,SV123: $i,SV147: $i,SV158: $i] :
( ( ( ! [SY657: $i] :
( ~ ( in @ SY657 @ SV158 )
| ( in @ SY657 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) ) ) )
= $true )
| ( ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SV158 )
= $true )
| ( ( in @ SV158 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1101,plain,
! [SV124: $i,SV78: $i,SV154: $i,SV157: $i,SV32: $i > $i > $o] :
( ( ( SV32 @ SV157 @ SV154 )
= $false )
| ( ( in @ SV157 @ SV78 )
= $false )
| ( ( in @ SV154 @ ( sK43_SY550 @ SV124 @ SV32 @ SV78 ) )
= $true )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ SV124 )
= $false )
| ( ( SV32 @ ( sK7_SY547 @ SV32 @ SV78 ) @ ( sK35_SY614 @ SV124 @ SV78 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1102,plain,
! [SV13: $i,SV139: $i,SV142: $i] :
( ( ( in @ SV142 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
= $true )
| ( ( in @ SV139 @ ( sK46_SY630 @ SV142 @ SV139 @ SV13 ) )
= $true )
| ( ( SV139 = SV142 )
= $true )
| ( ( in @ SV139 @ SV13 )
= $false )
| ( ( in @ SV142 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1092]) ).
thf(1103,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( ~ ( in @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
| ~ ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SV123 ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1104,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( ~ ! [SY648: $i] :
~ ~ ( ~ ( in @ SY648 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
| ~ ( in @ SY648 @ SV123 ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1105,plain,
! [SV13: $i,SV123: $i,SV149: $i,SV159: $i] :
( ( ( ! [SY658: $i] :
( ~ ( in @ SY658 @ SV159 )
| ( in @ SY658 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) ) ) )
= $true )
| ( ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SV159 )
= $true )
| ( ( in @ SV159 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1097]) ).
thf(1106,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( ~ ( in @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1098]) ).
thf(1107,plain,
! [SV147: $i,SV123: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SV123 ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1098]) ).
thf(1108,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( ! [SY644: $i] :
~ ~ ( ~ ( in @ SY644 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
| ~ ( in @ SY644 @ SV123 ) ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1099]) ).
thf(1109,plain,
! [SV13: $i,SV123: $i,SV147: $i,SV158: $i,SV160: $i] :
( ( ( ~ ( in @ SV160 @ SV158 )
| ( in @ SV160 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) ) )
= $true )
| ( ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SV158 )
= $true )
| ( ( in @ SV158 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1110,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( ~ ( in @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1111,plain,
! [SV149: $i,SV123: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SV123 ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1112,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( ! [SY648: $i] :
~ ~ ( ~ ( in @ SY648 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
| ~ ( in @ SY648 @ SV123 ) ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1104]) ).
thf(1113,plain,
! [SV13: $i,SV123: $i,SV149: $i,SV159: $i,SV161: $i] :
( ( ( ~ ( in @ SV161 @ SV159 )
| ( in @ SV161 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) ) )
= $true )
| ( ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SV159 )
= $true )
| ( ( in @ SV159 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1114,plain,
! [SV13: $i,SV123: $i,SV147: $i] :
( ( ( in @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1106]) ).
thf(1115,plain,
! [SV147: $i,SV123: $i,SV13: $i] :
( ( ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SV123 )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1107]) ).
thf(1116,plain,
! [SV13: $i,SV123: $i,SV147: $i,SV162: $i] :
( ( ( ~ ~ ( ~ ( in @ SV162 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
| ~ ( in @ SV162 @ SV123 ) ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1117,plain,
! [SV13: $i,SV123: $i,SV147: $i,SV158: $i,SV160: $i] :
( ( ( ~ ( in @ SV160 @ SV158 ) )
= $true )
| ( ( in @ SV160 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
= $true )
| ( ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SV158 )
= $true )
| ( ( in @ SV158 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1118,plain,
! [SV13: $i,SV123: $i,SV149: $i] :
( ( ( in @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) @ ( sK2_SY402 @ SV13 ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1110]) ).
thf(1119,plain,
! [SV149: $i,SV123: $i,SV13: $i] :
( ( ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SV123 )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1120,plain,
! [SV13: $i,SV123: $i,SV149: $i,SV163: $i] :
( ( ( ~ ~ ( ~ ( in @ SV163 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
| ~ ( in @ SV163 @ SV123 ) ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1121,plain,
! [SV13: $i,SV123: $i,SV149: $i,SV159: $i,SV161: $i] :
( ( ( ~ ( in @ SV161 @ SV159 ) )
= $true )
| ( ( in @ SV161 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
= $true )
| ( ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SV159 )
= $true )
| ( ( in @ SV159 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1113]) ).
thf(1122,plain,
! [SV13: $i,SV123: $i,SV147: $i,SV162: $i] :
( ( ( ~ ( ~ ( in @ SV162 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
| ~ ( in @ SV162 @ SV123 ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1123,plain,
! [SV13: $i,SV123: $i,SV147: $i,SV158: $i,SV160: $i] :
( ( ( in @ SV160 @ SV158 )
= $false )
| ( ( in @ SV160 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
= $true )
| ( ( in @ ( sK47_SY643 @ SV13 @ SV123 @ SV147 ) @ SV158 )
= $true )
| ( ( in @ SV158 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1124,plain,
! [SV13: $i,SV123: $i,SV149: $i,SV163: $i] :
( ( ( ~ ( ~ ( in @ SV163 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
| ~ ( in @ SV163 @ SV123 ) ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1125,plain,
! [SV13: $i,SV123: $i,SV149: $i,SV159: $i,SV161: $i] :
( ( ( in @ SV161 @ SV159 )
= $false )
| ( ( in @ SV161 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
= $true )
| ( ( in @ ( sK48_SY647 @ SV13 @ SV123 @ SV149 ) @ SV159 )
= $true )
| ( ( in @ SV159 @ ( sK2_SY402 @ SV13 ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1126,plain,
! [SV13: $i,SV123: $i,SV147: $i,SV162: $i] :
( ( ( ~ ( in @ SV162 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
| ~ ( in @ SV162 @ SV123 ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1122]) ).
thf(1127,plain,
! [SV13: $i,SV123: $i,SV149: $i,SV163: $i] :
( ( ( ~ ( in @ SV163 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
| ~ ( in @ SV163 @ SV123 ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1124]) ).
thf(1128,plain,
! [SV13: $i,SV123: $i,SV147: $i,SV162: $i] :
( ( ( ~ ( in @ SV162 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) ) )
= $true )
| ( ( ~ ( in @ SV162 @ SV123 ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1129,plain,
! [SV13: $i,SV123: $i,SV149: $i,SV163: $i] :
( ( ( ~ ( in @ SV163 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) ) )
= $true )
| ( ( ~ ( in @ SV163 @ SV123 ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1127]) ).
thf(1130,plain,
! [SV13: $i,SV123: $i,SV147: $i,SV162: $i] :
( ( ( in @ SV162 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
= $false )
| ( ( ~ ( in @ SV162 @ SV123 ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1131,plain,
! [SV13: $i,SV123: $i,SV149: $i,SV163: $i] :
( ( ( in @ SV163 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
= $false )
| ( ( ~ ( in @ SV163 @ SV123 ) )
= $true )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1132,plain,
! [SV13: $i,SV147: $i,SV123: $i,SV162: $i] :
( ( ( in @ SV162 @ SV123 )
= $false )
| ( ( in @ SV162 @ ( sK44_SY608 @ SV147 @ SV123 @ SV13 ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV13 )
= $false )
| ( ( in @ SV147 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1133,plain,
! [SV13: $i,SV149: $i,SV123: $i,SV163: $i] :
( ( ( in @ SV163 @ SV123 )
= $false )
| ( ( in @ SV163 @ ( sK45_SY608 @ SV149 @ SV123 @ SV13 ) )
= $false )
| ( ( in @ ( sK32_SY606 @ SV13 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV149 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1134,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[96,1133,1132,1125,1123,1119,1118,1115,1114,1102,1101,1094,1093,1091,1089,1088,1081,1077,1076,1030,1023,1008,998,997,996,995,994,983,981,980,967,952,942,936,909,908,907,906,889,887,885,884,874,873,872,871,870,864,863,859,858,857,841,833,831,830,826,825,823,822,820,819,815,804,797,790,789,788,784,780,777,774,769,768,759,750,743,740,739,725,701,700,699,698,693,692,682,681,659,658,655,654,652,651,649,648,646,630,617,616,615,566,542,541,533,532,525,516,505,503,479,473,461,460,459,437,426,416,415,414,413,408,407,398,397,396,393,381,352,351,350,341,340,339,333,313,247,246,245,244,243,182,181,180,120]) ).
thf(1135,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU544^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.17 % Computer : n020.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Oct 6 15:28:36 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.15/0.79
% 3.15/0.79 No.of.Axioms: 0
% 3.15/0.79
% 3.15/0.79 Length.of.Defs: 12650
% 3.15/0.79
% 3.15/0.79 Contains.Choice.Funs: true
% 3.15/0.79 ..........................................
% 3.15/0.79
% 3.15/0.79 ********************************
% 3.15/0.79 * All subproblems solved! *
% 3.15/0.79 ********************************
% 3.15/0.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:60,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1134,loop_count:0,foatp_calls:1,translation:fof_full)
% 3.15/0.79
% 3.15/0.79 %**** Beginning of derivation protocol ****
% 3.15/0.79 % SZS output start CNFRefutation
% See solution above
% 3.15/0.79
% 3.15/0.79 %**** End of derivation protocol ****
% 3.15/0.79 %**** no. of clauses in derivation: 1135 ****
% 3.15/0.79 %**** clause counter: 1134 ****
% 3.15/0.79
% 3.15/0.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:60,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1134,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------