%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU556^1 : 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 : n003.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 10:45:03 AM UTC 2026
% Result : Theorem 9.10s 1.75s
% Output : CNFRefutation 9.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 75
% Syntax : Number of formulae : 1857 ( 479 unt; 0 typ; 74 def)
% Number of atoms : 15737 (6948 equ; 0 cnn)
% Maximal formula atoms : 74 ( 8 avg)
% Number of connectives : 34562 (8602 ~;6776 |; 142 &;18298 @)
% ( 48 <=>; 696 =>; 0 <=; 0 <~>)
% Maximal formula depth : 80 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1596 (1596 >; 0 *; 0 +; 0 <<)
% Number of symbols : 184 ( 181 usr; 79 con; 0-4 aty)
% Number of variables : 7347 ( 128 ^;7073 !; 146 ?;7347 :)
% 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_emptyset__Cong,type,
emptyset__Cong: $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_exuE3u,type,
exuE3u: $o ).
thf(tp_exuI1,type,
exuI1: $o ).
thf(tp_exuI2,type,
exuI2: $o ).
thf(tp_exuI3,type,
exuI3: $o ).
thf(tp_exu__Cong,type,
exu__Cong: $o ).
thf(tp_foundationAx,type,
foundationAx: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_inCongP,type,
inCongP: $o ).
thf(tp_in__Cong,type,
in__Cong: $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_omega__Cong,type,
omega__Cong: $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_powerset__Cong,type,
powerset__Cong: $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_SY694,type,
sK10_SY694: ( $i > $o ) > $i > $i ).
thf(tp_sK11_SY748,type,
sK11_SY748: $i ).
thf(tp_sK12_SY714,type,
sK12_SY714: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK13_SY750,type,
sK13_SY750: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK14_SY557,type,
sK14_SY557: $i > $i ).
thf(tp_sK15_SY702,type,
sK15_SY702: $i ).
thf(tp_sK16_SY637,type,
sK16_SY637: $i > $i ).
thf(tp_sK17_SY668,type,
sK17_SY668: ( $i > $o ) > $i > $i ).
thf(tp_sK18_SY674,type,
sK18_SY674: ( $i > $o ) > $i > $i ).
thf(tp_sK19_SY759,type,
sK19_SY759: $i > ( $i > $o ) > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i > $o ).
thf(tp_sK20_SY752,type,
sK20_SY752: $o > $i > $i > $i ).
thf(tp_sK21_SX0,type,
sK21_SX0: $i > $i > $i ).
thf(tp_sK22_SX0,type,
sK22_SX0: $i > $i > $i ).
thf(tp_sK23_SY685,type,
sK23_SY685: $i > $i > $i ).
thf(tp_sK24_SY618,type,
sK24_SY618: $i > $i ).
thf(tp_sK25_SY635,type,
sK25_SY635: $i > $i > $i ).
thf(tp_sK26_SY689,type,
sK26_SY689: $i > $i > $i ).
thf(tp_sK27_SY597,type,
sK27_SY597: $i > ( $i > $o ) > $i ).
thf(tp_sK28_SY717,type,
sK28_SY717: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK29_SY721,type,
sK29_SY721: $i > $i > $i ).
thf(tp_sK2_SY521,type,
sK2_SY521: $i > $i ).
thf(tp_sK30_SY673,type,
sK30_SY673: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK31_SY683,type,
sK31_SY683: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK32_SY689,type,
sK32_SY689: $i > $i > $i ).
thf(tp_sK33_SY773,type,
sK33_SY773: $i > ( $i > $o ) > $i ).
thf(tp_sK34_SY751,type,
sK34_SY751: $i > ( $i > $o ) > $i ).
thf(tp_sK35_SY753,type,
sK35_SY753: $i > ( $i > $o ) > $i ).
thf(tp_sK36_SY755,type,
sK36_SY755: $i > ( $i > $o ) > $i ).
thf(tp_sK37_SY756,type,
sK37_SY756: $i > ( $i > $o ) > $i ).
thf(tp_sK38_SY757,type,
sK38_SY757: $i > ( $i > $o ) > $i ).
thf(tp_sK39_SY758,type,
sK39_SY758: $i > ( $i > $o ) > $i ).
thf(tp_sK3_SY595,type,
sK3_SY595: $i > $i ).
thf(tp_sK40_SY764,type,
sK40_SY764: $i > $i > $i ).
thf(tp_sK41_SY687,type,
sK41_SY687: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK42_SY565,type,
sK42_SY565: $i > ( $i > $o ) > $i ).
thf(tp_sK43_SY582,type,
sK43_SY582: $i > ( $i > $o ) > $i ).
thf(tp_sK44_SY590,type,
sK44_SY590: $i > ( $i > $o ) > $i ).
thf(tp_sK45_SY594,type,
sK45_SY594: $i > ( $i > $o ) > $i ).
thf(tp_sK46_SY599,type,
sK46_SY599: $i > ( $i > $o ) > $i ).
thf(tp_sK47_SY599,type,
sK47_SY599: $i > ( $i > $o ) > $i ).
thf(tp_sK48_SY772,type,
sK48_SY772: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK49_SY565,type,
sK49_SY565: $i > ( $i > $o ) > $i ).
thf(tp_sK4_SY606,type,
sK4_SY606: $i > $i ).
thf(tp_sK50_SY582,type,
sK50_SY582: $i > ( $i > $o ) > $i ).
thf(tp_sK51_SY590,type,
sK51_SY590: $i > ( $i > $o ) > $i ).
thf(tp_sK52_SY594,type,
sK52_SY594: $i > ( $i > $o ) > $i ).
thf(tp_sK53_SY599,type,
sK53_SY599: $i > ( $i > $o ) > $i ).
thf(tp_sK54_SY613,type,
sK54_SY613: $i > ( $i > $o ) > $i ).
thf(tp_sK55_SY613,type,
sK55_SY613: $i > ( $i > $o ) > $i ).
thf(tp_sK56_SY613,type,
sK56_SY613: $i > ( $i > $o ) > $i ).
thf(tp_sK57_SY613,type,
sK57_SY613: $i > ( $i > $o ) > $i ).
thf(tp_sK58_SY717,type,
sK58_SY717: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK59_SY780,type,
sK59_SY780: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK5_SY704,type,
sK5_SY704: $i ).
thf(tp_sK60_SY717,type,
sK60_SY717: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK61_SY794,type,
sK61_SY794: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK62_SY795,type,
sK62_SY795: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK63_SY766,type,
sK63_SY766: $i > $i > $i > $i ).
thf(tp_sK64_SY766,type,
sK64_SY766: $i > $i > $i > $i ).
thf(tp_sK65_SY660,type,
sK65_SY660: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK66_SY501,type,
sK66_SY501: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK67_SY796,type,
sK67_SY796: $i > $i > $i > $i ).
thf(tp_sK68_SY821,type,
sK68_SY821: $i > $i > $i > $i ).
thf(tp_sK69_SY660,type,
sK69_SY660: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK6_SY656,type,
sK6_SY656: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK70_SY501,type,
sK70_SY501: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK71_SY827,type,
sK71_SY827: $i > $i > $i > $i ).
thf(tp_sK72_SY813,type,
sK72_SY813: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK73_SY814,type,
sK73_SY814: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK74_SY811,type,
sK74_SY811: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK75_SY817,type,
sK75_SY817: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK76_SY818,type,
sK76_SY818: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK77_SY819,type,
sK77_SY819: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK78_SY820,type,
sK78_SY820: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK79_SY815,type,
sK79_SY815: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK7_SY666,type,
sK7_SY666: $i > $i > $i ).
thf(tp_sK80_SY825,type,
sK80_SY825: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK81_SY826,type,
sK81_SY826: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK82_SY660,type,
sK82_SY660: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK83_SY501,type,
sK83_SY501: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK84_SY660,type,
sK84_SY660: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK85_SY501,type,
sK85_SY501: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK86_SY660,type,
sK86_SY660: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK87_SY501,type,
sK87_SY501: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK88_SY660,type,
sK88_SY660: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK89_SY501,type,
sK89_SY501: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK8_SY667,type,
sK8_SY667: $i > $i > $i ).
thf(tp_sK90_SY660,type,
sK90_SY660: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK91_SY501,type,
sK91_SY501: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK92_SY660,type,
sK92_SY660: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK93_SY501,type,
sK93_SY501: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK94_SY660,type,
sK94_SY660: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK95_SY501,type,
sK95_SY501: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK96_SY660,type,
sK96_SY660: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK97_SY501,type,
sK97_SY501: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK9_SY688,type,
sK9_SY688: $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_setadjoin__Cong,type,
setadjoin__Cong: $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_setunion__Cong,type,
setunion__Cong: $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(emptyset__Cong,definition,
( emptyset__Cong
= ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
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(exuE3u,definition,
( exuE3u
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exuI1,definition,
( exuI1
= ( ! [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(exuI2,definition,
( exuI2
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,definition,
( exuI3
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] : ( Xphi @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exu__Cong,definition,
( exu__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
<=> ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
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(inCongP,definition,
( inCongP
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(in__Cong,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
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(omega__Cong,definition,
( omega__Cong
= ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
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(powerset__Cong,definition,
( powerset__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
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(setadjoin__Cong,definition,
( setadjoin__Cong
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
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(setunion__Cong,definition,
( setunion__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
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
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
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
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $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 ) ) )
=> ( ! [SY195: $i > $o] :
( ? [Xx: $i] :
( ( SY195 @ Xx )
& ! [Xy: $i] :
( ( SY195 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY199: $i] :
( ( SY195 @ SY199 )
& ! [SY200: $i] :
( ( SY195 @ SY200 )
=> ( SY199 = SY200 ) ) ) )
=> ( ! [SY201: $i > $o] :
( ? [Xx: $i] : ( SY201 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY201 @ Xx )
=> ( ( SY201 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY206: $i] :
( ( SY201 @ SY206 )
& ! [SY207: $i] :
( ( SY201 @ SY207 )
=> ( SY206 = SY207 ) ) ) ) )
=> ( ! [SY208: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY208 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY212: $i] :
( ( SY208 @ SY212 )
& ! [SY213: $i] :
( ( SY208 @ SY213 )
=> ( SY212 = SY213 ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) )
=> ( ! [SY222: $i > $o] :
( ? [SY224: $i] :
( ( SY222 @ SY224 )
& ! [SY225: $i] :
( ( SY222 @ SY225 )
=> ( SY224 = SY225 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY222 @ Xx )
=> ( ( SY222 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY228: $i > $o,SY229: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY228 @ Xx )
<=> ( SY229 @ Xy ) ) )
=> ( ? [SY233: $i] :
( ( SY228 @ SY233 )
& ! [SY234: $i] :
( ( SY228 @ SY234 )
=> ( SY233 = SY234 ) ) )
<=> ? [SY236: $i] :
( ( SY229 @ SY236 )
& ! [SY237: $i] :
( ( SY229 @ SY237 )
=> ( SY236 = SY237 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) )
=> ( ( omega = omega )
=> ! [SY0: $i > $o] :
( ? [SY2: $i] :
( ( SY0 @ SY2 )
& ! [SY3: $i] :
( ( SY0 @ SY3 )
=> ( SY2 = SY3 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY0 @ Xx )
=> ( ( SY0 @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,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,
( ( ! [SY195: $i > $o] :
( ? [Xx: $i] :
( ( SY195 @ Xx )
& ! [Xy: $i] :
( ( SY195 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY199: $i] :
( ( SY195 @ SY199 )
& ! [SY200: $i] :
( ( SY195 @ SY200 )
=> ( SY199 = SY200 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(65,plain,
( ( ! [SY201: $i > $o] :
( ? [Xx: $i] : ( SY201 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY201 @ Xx )
=> ( ( SY201 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY206: $i] :
( ( SY201 @ SY206 )
& ! [SY207: $i] :
( ( SY201 @ SY207 )
=> ( SY206 = SY207 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(66,plain,
( ( ! [SY208: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY208 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY212: $i] :
( ( SY208 @ SY212 )
& ! [SY213: $i] :
( ( SY208 @ SY213 )
=> ( SY212 = SY213 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(68,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(69,plain,
( ( ! [SY222: $i > $o] :
( ? [SY224: $i] :
( ( SY222 @ SY224 )
& ! [SY225: $i] :
( ( SY222 @ SY225 )
=> ( SY224 = SY225 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY222 @ Xx )
=> ( ( SY222 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(70,plain,
( ( ! [SY228: $i > $o,SY229: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY228 @ Xx )
<=> ( SY229 @ Xy ) ) )
=> ( ? [SY233: $i] :
( ( SY228 @ SY233 )
& ! [SY234: $i] :
( ( SY228 @ SY234 )
=> ( SY233 = SY234 ) ) )
<=> ? [SY236: $i] :
( ( SY229 @ SY236 )
& ! [SY237: $i] :
( ( SY229 @ SY237 )
=> ( SY236 = SY237 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(71,plain,
( ( emptyset = emptyset )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(72,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(73,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(74,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(75,plain,
( ( omega = omega )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(76,plain,
( ( ! [SY0: $i > $o] :
( ? [SY2: $i] :
( ( SY0 @ SY2 )
& ! [SY3: $i] :
( ( SY0 @ SY3 )
=> ( SY2 = SY3 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY0 @ Xx )
=> ( ( SY0 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(77,plain,
( ( ~ ! [SY0: $i > $o] :
( ? [SY2: $i] :
( ( SY0 @ SY2 )
& ! [SY3: $i] :
( ( SY0 @ SY3 )
=> ( SY2 = SY3 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY0 @ Xx )
=> ( ( SY0 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[76]) ).
thf(78,plain,
( ( omega = omega )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(81,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(82,plain,
( ( emptyset = emptyset )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(83,plain,
( ( ! [SY228: $i > $o,SY229: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY228 @ Xx )
<=> ( SY229 @ Xy ) ) )
=> ( ? [SY233: $i] :
( ( SY228 @ SY233 )
& ! [SY234: $i] :
( ( SY228 @ SY234 )
=> ( SY233 = SY234 ) ) )
<=> ? [SY236: $i] :
( ( SY229 @ SY236 )
& ! [SY237: $i] :
( ( SY229 @ SY237 )
=> ( SY236 = SY237 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(84,plain,
( ( ! [SY222: $i > $o] :
( ? [SY224: $i] :
( ( SY222 @ SY224 )
& ! [SY225: $i] :
( ( SY222 @ SY225 )
=> ( SY224 = SY225 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY222 @ Xx )
=> ( ( SY222 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(85,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(86,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(87,plain,
( ( ! [SY208: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY208 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY212: $i] :
( ( SY208 @ SY212 )
& ! [SY213: $i] :
( ( SY208 @ SY213 )
=> ( SY212 = SY213 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(88,plain,
( ( ! [SY201: $i > $o] :
( ? [Xx: $i] : ( SY201 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY201 @ Xx )
=> ( ( SY201 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY206: $i] :
( ( SY201 @ SY206 )
& ! [SY207: $i] :
( ( SY201 @ SY207 )
=> ( SY206 = SY207 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(89,plain,
( ( ! [SY195: $i > $o] :
( ? [Xx: $i] :
( ( SY195 @ Xx )
& ! [Xy: $i] :
( ( SY195 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY199: $i] :
( ( SY195 @ SY199 )
& ! [SY200: $i] :
( ( SY195 @ SY200 )
=> ( SY199 = SY200 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(90,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(91,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(92,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(93,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(94,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(95,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(96,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(97,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(98,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(99,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(100,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(101,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(102,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(103,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(104,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(105,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(106,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(107,plain,
( ( ! [SY146: $i] :
( ( SY146 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY146 )
& $true ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(108,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(109,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(110,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(111,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(112,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(113,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(114,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(115,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(116,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(117,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(118,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(119,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(120,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(121,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(122,plain,
( ( ! [SY107: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY107 )
=> ( SY107 != emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(123,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(124,plain,
( ( ! [SY101: $i] :
( ( SY101 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY101 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(125,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(126,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(127,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(128,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(129,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(130,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(131,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(132,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(133,plain,
( ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(134,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(135,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(136,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(137,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(138,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(139,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(140,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(141,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(142,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(143,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(144,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(145,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(146,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(147,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(148,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(149,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(150,plain,
( ( ~ ! [SY0: $i > $o] :
( ? [SY2: $i] :
( ( SY0 @ SY2 )
& ! [SY3: $i] :
( ( SY0 @ SY3 )
=> ( SY2 = SY3 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY0 @ Xx )
=> ( ( SY0 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(151,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(152,plain,
( ( ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( ~ ( ~ ( SX0 @ SX2 )
| ( SX1 @ SX3 ) )
| ~ ( ~ ( SX1 @ SX3 )
| ( SX0 @ SX2 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SX0 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SX0 @ SX3 )
| ( SX2 = SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(153,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(154,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)],[149,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(155,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)],[95,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(156,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)],[99,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(157,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)],[97,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(158,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)],[91,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(159,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)],[147,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(160,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)],[139,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(161,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)],[123,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(162,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(163,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)],[138,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(164,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)],[110,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(165,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| ! [SX1: $o] : SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[132,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(166,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)],[90,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(167,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)],[146,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(168,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(169,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ( in @ SX1 @ emptyset )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(170,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(171,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)],[94,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(172,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)],[134,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(173,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)],[128,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(174,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ( ( setadjoin @ SX0 @ SX2 )
= ( setadjoin @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(175,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)],[118,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(176,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)],[96,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(177,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setunion @ SX0 )
= ( setunion @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(178,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)],[89,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(179,plain,
( ( ! [SX0: $o,SX1: $i] :
( ~ ( in @ SX1 @ ( prop2set @ SX0 ) )
| SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[133,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(180,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(181,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(182,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)],[108,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(183,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(184,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(185,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ( SX0 @ SX1 )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(186,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)],[136,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(187,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( set2prop @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(188,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(189,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( in @ emptyset @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(190,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(191,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ! [SX1: $i,SX2: $i] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(192,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ( ~ ( ~ ( SX0 @ SX2 )
| ( SX2 = SX1 ) )
| ~ ( ( SX2 != SX1 )
| ( SX0 @ SX2 ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(193,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)],[137,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(194,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)],[142,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(195,plain,
( ( ~ ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ! [SX1: $i,SX2: $i] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(196,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(197,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(198,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)],[125,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(199,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(200,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(201,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( in @ SX3 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(202,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 != emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(203,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[131,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(204,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)],[140,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(205,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(206,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)],[141,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(207,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)],[145,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(208,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(209,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(210,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(211,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( powerset @ SX0 )
= ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notinemptyset,notinsingleton,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetI,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoin__Cong,setbeta,setext,setextAx,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(212,plain,
! [SV1: $i] :
( ( ! [SY485: $i] : ( in @ SY485 @ ( setadjoin @ SV1 @ ( setadjoin @ SY485 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(213,plain,
! [SV2: $i] :
( ( ! [SY486: $i] : ( in @ SV2 @ ( setadjoin @ SV2 @ ( setadjoin @ SY486 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(214,plain,
! [SV3: $i] :
( ( in @ emptyset @ ( powerset @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(215,plain,
! [SV4: $i] :
( ( in @ emptyset @ ( powerset @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(216,plain,
! [SV5: $i] :
( ( ( dsetconstr @ SV5
@ ^ [Xx: $i] : $true )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(217,plain,
! [SV6: $i] :
( ( ! [SY488: $i] : ( in @ SV6 @ ( setadjoin @ SV6 @ SY488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(218,plain,
! [SV7: $i] :
( ( ~ ( in @ SV7 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(219,plain,
! [SV8: $i] :
( ( ~ ( in @ SV8 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(220,plain,
! [SV9: $i] :
( ( ! [SY489: $i] :
( ( SV9 != SY489 )
| ! [SY490: $i,SY491: $i] :
( ( SY490 != SY491 )
| ~ ( in @ SY490 @ SV9 )
| ( in @ SY491 @ SY489 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(221,plain,
! [SV10: $i > $o] :
( ( ! [SY492: $i > $o] :
( ~ ! [SY493: $i,SY494: $i] :
( ( SY493 != SY494 )
| ~ ( ~ ( ~ ( SV10 @ SY493 )
| ( SY492 @ SY494 ) )
| ~ ( ~ ( SY492 @ SY494 )
| ( SV10 @ SY493 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SY492 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY492 @ SX3 )
| ( SX2 = SX3 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY492 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY492 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(222,plain,
! [SV11: $i] :
( ( ! [SY503: $i] :
( ~ ! [SY504: $i] :
( ~ ( in @ SY504 @ SY503 )
| ( in @ SY504 @ SV11 ) )
| ( in @ SY503 @ ( powerset @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(223,plain,
! [SV12: $i] :
( ( ! [SY505: $i] :
( ~ ! [SY506: $i] :
~ ( ~ ( ~ ( in @ SY506 @ SV12 )
| ( in @ SY506 @ SY505 ) )
| ~ ( ~ ( in @ SY506 @ SY505 )
| ( in @ SY506 @ SV12 ) ) )
| ( SV12 = SY505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(224,plain,
! [SV13: $i] :
( ( ! [SY507: $i > $o] :
( ~ ~ ~ ! [SY508: $i] :
~ ~ ( ~ ( in @ SY508 @ SV13 )
| ~ ( SY507 @ SY508 ) )
| ! [SY509: $i] :
( ~ ( in @ SY509 @ SV13 )
| ~ ( SY507 @ SY509 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(225,plain,
! [SV14: $i] :
( ( ! [SY510: $i > $o] :
( ~ ~ ! [SY511: $i] :
~ ~ ( ~ ( in @ SY511 @ SV14 )
| ~ ( SY510 @ SY511 ) )
| ( ( dsetconstr @ SV14
@ ^ [SX2: $i] : ( SY510 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(226,plain,
! [SV15: $i] :
( ( ! [SY513: $i > $o] :
( ~ ~ ! [SY514: $i] :
( ~ ( in @ SY514 @ SV15 )
| ( SY513 @ SY514 ) )
| ~ ! [SY515: $i] :
~ ~ ( ~ ( in @ SY515 @ SV15 )
| ~ ~ ( SY513 @ SY515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(227,plain,
! [SV16: $i] :
( ( ! [SY516: $i > $o] :
( ~ ~ ~ ! [SY517: $i] :
~ ~ ( ~ ( in @ SY517 @ SV16 )
| ~ ( SY516 @ SY517 ) )
| ! [SY518: $i] :
( ~ ( in @ SY518 @ SV16 )
| ~ ( SY516 @ SY518 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(228,plain,
! [SV17: $i] :
( ( ! [SY519: $i,SY520: $i] :
~ ( ~ ( ~ ( in @ SY520 @ ( setadjoin @ SV17 @ SY519 ) )
| ( SY520 = SV17 )
| ( in @ SY520 @ SY519 ) )
| ~ ( ~ ( ( SY520 = SV17 )
| ( in @ SY520 @ SY519 ) )
| ( in @ SY520 @ ( setadjoin @ SV17 @ SY519 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(229,plain,
! [SV18: $i] :
( ( ~ ! [SY521: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY522: $i] :
( ~ ( in @ SY522 @ SY521 )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY522 )
| ( in @ SY523 @ SV18 ) ) )
| ~ ! [SY524: $i,SY525: $i] :
( ~ ~ ( ~ ( in @ SY524 @ SV18 )
| ~ ( in @ SY525 @ SV18 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY521 )
| ~ ( ~ ( ~ ( in @ SY524 @ SX4 )
| ( in @ SY525 @ SX4 ) )
| ~ ( ~ ( in @ SY525 @ SX4 )
| ( in @ SY524 @ SX4 ) ) ) )
| ( SY524 = SY525 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY521 )
| ~ ( in @ SX3 @ SY521 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY531: $i] :
( ~ ~ ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SY531 )
| ( in @ SY532 @ SV18 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY531 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY521 )
| ~ ( in @ SX4 @ SY531 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY531 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY521 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(230,plain,
! [SV19: $i] :
( ( ! [SY539: $i > $o,SY540: $i] :
( ~ ( in @ SY540 @ SV19 )
| ~ ( SY539 @ SY540 )
| ( ( dsetconstr @ SV19
@ ^ [SX3: $i] : ( SY539 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(231,plain,
! [SV20: $i] :
( ( ! [SY542: $i,SY543: $i] :
( ~ ( in @ SY542 @ ( powerset @ SV20 ) )
| ~ ( in @ SY543 @ SY542 )
| ( in @ SY543 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(232,plain,
! [SV21: $i > $o] :
( ( ~ ~ ! [SY544: $i] :
~ ~ ( ~ ( SV21 @ SY544 )
| ~ ! [SY545: $i] :
( ~ ( SV21 @ SY545 )
| ( SY544 = SY545 ) ) )
| ( SV21
@ ( descr
@ ^ [SY546: $i] : ( SV21 @ SY546 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(233,plain,
! [SV22: $i] :
( ( ! [SY547: $i] :
( ~ ( in @ SY547 @ ( setunion @ SV22 ) )
| ! [SY548: $o] :
( ~ ! [SY549: $i] :
( ~ ( in @ SY547 @ SY549 )
| ~ ( in @ SY549 @ SV22 )
| SY548 )
| SY548 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(234,plain,
! [SV23: $i] :
( ( ~ ( in @ SV23 @ emptyset )
| ! [SX1: $o] : SX1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(235,plain,
! [SV24: $i] :
( ( ! [SY551: $i > $o] :
( ~ ~ ! [SY552: $i] :
( ~ ( in @ SY552 @ SV24 )
| ( SY551 @ SY552 ) )
| ~ ! [SY553: $i] :
~ ~ ( ~ ( in @ SY553 @ SV24 )
| ~ ~ ( SY551 @ SY553 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(236,plain,
! [SV25: $i] :
( ( ! [SY554: $i] :
~ ( ~ ( ~ ( in @ SY554 @ ( powerset @ SV25 ) )
| ! [SY555: $i] :
( ~ ( in @ SY555 @ SY554 )
| ( in @ SY555 @ SV25 ) ) )
| ~ ( ~ ! [SY556: $i] :
( ~ ( in @ SY556 @ SY554 )
| ( in @ SY556 @ SV25 ) )
| ( in @ SY554 @ ( powerset @ SV25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(237,plain,
! [SV26: $i] :
( ( ~ ( ( SV26 != emptyset ) )
| ~ ! [SY557: $i] :
~ ~ ( ~ ( in @ SY557 @ SV26 )
| ~ $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(238,plain,
! [SV27: $i > $o] :
( ( ! [SY558: $i] :
( ~ ( in @ SY558 @ emptyset )
| ( SV27 @ SY558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(239,plain,
! [SV28: $i] :
( ( ! [SY559: $i] :
( ~ ( in @ SY559 @ SV28 )
| ( in @ SY559 @ ( powerset @ ( setunion @ SV28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(240,plain,
! [SV29: $i] :
( ( ! [SY560: $i > $o] :
( ~ ~ ! [SY561: $i] :
~ ~ ( ~ ( in @ SY561 @ SV29 )
| ~ ~ ( SY560 @ SY561 ) )
| ~ ! [SY562: $i] :
( ~ ( in @ SY562 @ SV29 )
| ( SY560 @ SY562 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(241,plain,
! [SV30: $i > $o] :
( ( ~ ~ ! [SY563: $i] :
~ ~ ( ~ ( SV30 @ SY563 )
| ~ ! [SY564: $i] :
( ~ ( SV30 @ SY564 )
| ( SY563 = SY564 ) ) )
| ~ ! [SY565: $i] :
~ ~ ( ~ ( SV30 @ SY565 )
| ~ ! [SY566: $i] :
( ~ ( SV30 @ SY566 )
| ( SY565 = SY566 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(242,plain,
! [SV31: $i] :
( ( ! [SY567: $i] :
( ~ ! [SY568: $i] :
( ~ ( in @ SY568 @ SV31 )
| ( in @ SY568 @ SY567 ) )
| ~ ! [SY569: $i] :
( ~ ( in @ SY569 @ SY567 )
| ( in @ SY569 @ SV31 ) )
| ( SV31 = SY567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(243,plain,
! [SV32: $i] :
( ( ! [SY570: $i] :
( ( SV32 != SY570 )
| ! [SY571: $i,SY572: $i] :
( ( SY571 != SY572 )
| ( ( setadjoin @ SV32 @ SY571 )
= ( setadjoin @ SY570 @ SY572 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(244,plain,
! [SV33: $i] :
( ( ! [SY573: $i,SY574: $i] :
( ~ ( in @ SY574 @ ( setadjoin @ SV33 @ SY573 ) )
| ! [SY575: $o] :
( ~ ( ( SY574 != SV33 )
| SY575 )
| ~ ( ~ ( in @ SY574 @ SY573 )
| SY575 )
| SY575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(245,plain,
! [SV34: $i] :
( ( ! [SY576: $i > $o] :
( ~ ! [SY577: $i] :
( ~ ( in @ SY577 @ SV34 )
| ~ ( SY576 @ SY577 ) )
| ~ ~ ! [SY578: $i] :
~ ~ ( ~ ( in @ SY578 @ SV34 )
| ~ ( SY576 @ SY578 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(246,plain,
! [SV35: $i] :
( ( ! [SY579: $i] :
( ( SV35 != SY579 )
| ( ( setunion @ SV35 )
= ( setunion @ SY579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(247,plain,
! [SV36: $i > $o] :
( ( ~ ~ ! [SY580: $i] :
~ ~ ( ~ ( SV36 @ SY580 )
| ~ ! [SY581: $i] :
( ~ ( SV36 @ SY581 )
| ( SY580 = SY581 ) ) )
| ~ ! [SY582: $i] :
~ ~ ( ~ ( SV36 @ SY582 )
| ~ ! [SY583: $i] :
( ~ ( SV36 @ SY583 )
| ( SY582 = SY583 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(248,plain,
! [SV37: $o] :
( ( ! [SY584: $i] :
( ~ ( in @ SY584 @ ( prop2set @ SV37 ) )
| SV37 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[179]) ).
thf(249,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $true ) )
| $true ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[179]) ).
thf(250,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $false ) )
| $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[179]) ).
thf(251,plain,
! [SV38: $i] :
( ( ! [SY585: $i,SY586: $i] :
( ~ ( in @ SY585 @ SY586 )
| ~ ( in @ SY586 @ SV38 )
| ( in @ SY585 @ ( setunion @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(252,plain,
! [SV39: $i] :
( ( ! [SY587: $i] :
( ~ ( in @ SV39 @ ( setadjoin @ SY587 @ emptyset ) )
| ( SV39 = SY587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(253,plain,
! [SV40: $i > $o] :
( ( ~ ~ ! [SY588: $i] :
~ ~ ( ~ ( SV40 @ SY588 )
| ~ ! [SY589: $i] :
( ~ ( SV40 @ SY589 )
| ( SY588 = SY589 ) ) )
| ~ ! [SY590: $i] :
~ ! [SY591: $i] :
~ ( ~ ( ~ ( SV40 @ SY591 )
| ( SY591 = SY590 ) )
| ~ ( ( SY591 != SY590 )
| ( SV40 @ SY591 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(254,plain,
! [SV41: $i > $o] :
( ( ~ ~ ! [SY592: $i] :
~ ~ ( ~ ( SV41 @ SY592 )
| ~ ! [SY593: $i] :
( ~ ( SV41 @ SY593 )
| ( SY592 = SY593 ) ) )
| ~ ! [SY594: $i] :
~ ( SV41 @ SY594 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(255,plain,
! [SV42: $i] :
( ( ~ ! [SY595: $i] :
~ ( in @ SY595 @ SV42 )
| ( SV42 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(256,plain,
! [SV43: $i > $o] :
( ( ~ ~ ! [SY596: $i] :
~ ( SV43 @ SY596 )
| ~ ! [SY597: $i,SY598: $i] :
( ~ ( SV43 @ SY597 )
| ~ ( SV43 @ SY598 )
| ( SY597 = SY598 ) )
| ~ ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(257,plain,
! [SV44: $i] :
( ( ! [SY601: $i > $o,SY602: $i] :
( ~ ( in @ SY602
@ ( dsetconstr @ SV44
@ ^ [SX3: $i] : ( SY601 @ SX3 ) ) )
| ( in @ SY602 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(258,plain,
! [SV45: $o] :
( ( ~ SV45
| ( set2prop @ ( prop2set @ SV45 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[187]) ).
thf(259,plain,
( ( ~ $true
| ( set2prop @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[187]) ).
thf(260,plain,
( ( ~ $false
| ( set2prop @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[187]) ).
thf(261,plain,
! [SV46: $i] :
( ( ! [SY604: $i,SY605: $i] :
( ~ ( in @ SY605 @ SY604 )
| ( in @ SY605 @ ( setadjoin @ SV46 @ SY604 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(262,plain,
! [SV47: $o] :
( ( ~ SV47
| ( in @ emptyset @ ( prop2set @ SV47 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[189]) ).
thf(263,plain,
( ( ~ $true
| ( in @ emptyset @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[189]) ).
thf(264,plain,
( ( ~ $false
| ( in @ emptyset @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[189]) ).
thf(265,plain,
! [SV48: $i] :
( ( ~ ! [SY606: $i] :
~ ( in @ SY606 @ SV48 )
| ( SV48 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(266,plain,
! [SV49: $i > $o] :
( ( ~ ~ ! [SY607: $i] :
~ ~ ( ~ ( SV49 @ SY607 )
| ~ ! [SY608: $i] :
( ~ ( SV49 @ SY608 )
| ( SY607 = SY608 ) ) )
| ! [SY609: $i,SY610: $i] :
( ~ ( SV49 @ SY609 )
| ~ ( SV49 @ SY610 )
| ( SY609 = SY610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(267,plain,
! [SV50: $i > $o] :
( ( ~ ~ ! [SY611: $i] :
~ ! [SY612: $i] :
~ ( ~ ( ~ ( SV50 @ SY612 )
| ( SY612 = SY611 ) )
| ~ ( ( SY612 != SY611 )
| ( SV50 @ SY612 ) ) )
| ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(268,plain,
! [SV51: $i] :
( ( ! [SY615: $i > $o,SY616: $i] :
( ~ ( in @ SY616 @ SV51 )
| ~ ( SY615 @ SY616 )
| ( in @ SY616
@ ( dsetconstr @ SV51
@ ^ [SX3: $i] : ( SY615 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(269,plain,
! [SV52: $i] :
( ( ~ ~ ( ~ ( in @ emptyset @ SV52 )
| ~ ! [SY618: $i] :
( ~ ~ ( ~ ( in @ SY618 @ omega )
| ~ ( in @ SY618 @ SV52 ) )
| ( in @ ( setadjoin @ SY618 @ SY618 ) @ SV52 ) ) )
| ! [SY619: $i] :
( ~ ( in @ SY619 @ omega )
| ( in @ SY619 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(270,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ! [SX1: $i,SX2: $i] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(271,plain,
! [SV53: $i] :
( ( ! [SY620: $i,SY621: $i] :
( ~ ( in @ SY621 @ ( setadjoin @ SV53 @ SY620 ) )
| ( SY621 = SV53 )
| ( in @ SY621 @ SY620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(272,plain,
! [SV54: $i] :
( ( ~ ( in @ SV54 @ omega )
| ( in @ ( setadjoin @ SV54 @ SV54 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(273,plain,
! [SV55: $i] :
( ( ! [SY622: $i > $o,SY623: $i] :
( ~ ( in @ SY623 @ SV55 )
| ~ ( ~ ( ~ ( in @ SY623
@ ( dsetconstr @ SV55
@ ^ [SX3: $i] : ( SY622 @ SX3 ) ) )
| ( SY622 @ SY623 ) )
| ~ ( ~ ( SY622 @ SY623 )
| ( in @ SY623
@ ( dsetconstr @ SV55
@ ^ [SX3: $i] : ( SY622 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(274,plain,
! [SV56: $i] :
( ( ! [SY626: $i > $o,SY627: $i] :
( ~ ( in @ SY627
@ ( dsetconstr @ SV56
@ ^ [SX3: $i] : ( SY626 @ SX3 ) ) )
| ( SY626 @ SY627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(275,plain,
! [SV57: $i] :
( ( ! [SY629: $i] :
( ~ ( ( SV57 != SY629 ) )
| ~ ( in @ SY629 @ ( setadjoin @ SV57 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(276,plain,
! [SV58: $i] :
( ( ! [SY630: $i] :
( ( SV58 != SY630 )
| ! [SY631: $i,SY632: $i] :
( ( SY631 != SY632 )
| ~ ( ~ ( ~ ( in @ SY631 @ SV58 )
| ( in @ SY632 @ SY630 ) )
| ~ ( ~ ( in @ SY632 @ SY630 )
| ( in @ SY631 @ SV58 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(277,plain,
! [SV59: $i] :
( ( ~ ~ ! [SY633: $i] :
~ ( in @ SY633 @ SV59 )
| ( SV59 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(278,plain,
! [SV60: $i] :
( ( ~ ( in @ SV60 @ emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(279,plain,
! [SV61: $i] :
( ( ~ ~ ! [SY634: $i] :
~ ( in @ SY634 @ SV61 )
| ~ ! [SY635: $i] :
~ ~ ( ~ ( in @ SY635 @ SV61 )
| ~ ~ ~ ! [SY636: $i] :
~ ~ ( ~ ( in @ SY636 @ SY635 )
| ~ ( in @ SY636 @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(280,plain,
! [SV62: $i] :
( ( ~ ( ( SV62 != emptyset ) )
| ~ ! [SY637: $i] :
~ ( in @ SY637 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(281,plain,
! [SV63: $i > $i > $o] :
( ( ! [SY638: $i] :
( ~ ! [SY639: $i] :
( ~ ( in @ SY639 @ SY638 )
| ~ ! [SY640: $i] :
~ ~ ( ~ ( SV63 @ SY639 @ SY640 )
| ~ ! [SY641: $i] :
( ~ ( SV63 @ SY639 @ SY641 )
| ( SY640 = SY641 ) ) ) )
| ~ ! [SY642: $i] :
~ ! [SY643: $i] :
~ ( ~ ( ~ ( in @ SY643 @ SY642 )
| ~ ! [SY644: $i] :
~ ~ ( ~ ( in @ SY644 @ SY638 )
| ~ ( SV63 @ SY644 @ SY643 ) ) )
| ~ ( ~ ~ ! [SY645: $i] :
~ ~ ( ~ ( in @ SY645 @ SY638 )
| ~ ( SV63 @ SY645 @ SY643 ) )
| ( in @ SY643 @ SY642 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(282,plain,
! [SV64: $i] :
( ( ! [SY646: $i] :
~ ( ~ ( ~ ( in @ SY646 @ ( setunion @ SV64 ) )
| ~ ! [SY647: $i] :
~ ~ ( ~ ( in @ SY646 @ SY647 )
| ~ ( in @ SY647 @ SV64 ) ) )
| ~ ( ~ ~ ! [SY648: $i] :
~ ~ ( ~ ( in @ SY646 @ SY648 )
| ~ ( in @ SY648 @ SV64 ) )
| ( in @ SY646 @ ( setunion @ SV64 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(283,plain,
! [SV65: $i] :
( ( ! [SY649: $i,SY650: $i] :
( ~ ( in @ SY650 @ ( setadjoin @ SV65 @ ( setadjoin @ SY649 @ emptyset ) ) )
| ( SY650 = SV65 )
| ( SY650 = SY649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(284,plain,
! [SV66: $i] :
( ( ! [SY651: $i] :
( ~ ( in @ SV66 @ ( setadjoin @ SY651 @ emptyset ) )
| ( in @ SY651 @ ( setadjoin @ SV66 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(285,plain,
! [SV67: $i] :
( ( ! [SY652: $i] :
( ( SV67 != SY652 )
| ( in @ SV67 @ ( setadjoin @ SY652 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(286,plain,
! [SV68: $i] :
( ( ! [SY653: $i] :
( ( SV68 != SY653 )
| ( ( powerset @ SV68 )
= ( powerset @ SY653 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(287,plain,
! [SV1: $i,SV69: $i] :
( ( in @ SV69 @ ( setadjoin @ SV1 @ ( setadjoin @ SV69 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(288,plain,
! [SV70: $i,SV2: $i] :
( ( in @ SV2 @ ( setadjoin @ SV2 @ ( setadjoin @ SV70 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(289,plain,
! [SV71: $i,SV6: $i] :
( ( in @ SV6 @ ( setadjoin @ SV6 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(290,plain,
! [SV7: $i] :
( ( in @ SV7 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(291,plain,
! [SV8: $i] :
( ( in @ SV8 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(292,plain,
! [SV72: $i,SV9: $i] :
( ( ( SV9 != SV72 )
| ! [SY654: $i,SY655: $i] :
( ( SY654 != SY655 )
| ~ ( in @ SY654 @ SV9 )
| ( in @ SY655 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(293,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ~ ! [SY656: $i,SY657: $i] :
( ( SY656 != SY657 )
| ~ ( ~ ( ~ ( SV10 @ SY656 )
| ( SV73 @ SY657 ) )
| ~ ( ~ ( SV73 @ SY657 )
| ( SV10 @ SY656 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(294,plain,
! [SV11: $i,SV74: $i] :
( ( ~ ! [SY666: $i] :
( ~ ( in @ SY666 @ SV74 )
| ( in @ SY666 @ SV11 ) )
| ( in @ SV74 @ ( powerset @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(295,plain,
! [SV75: $i,SV12: $i] :
( ( ~ ! [SY667: $i] :
~ ( ~ ( ~ ( in @ SY667 @ SV12 )
| ( in @ SY667 @ SV75 ) )
| ~ ( ~ ( in @ SY667 @ SV75 )
| ( in @ SY667 @ SV12 ) ) )
| ( SV12 = SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(296,plain,
! [SV76: $i > $o,SV13: $i] :
( ( ~ ~ ~ ! [SY668: $i] :
~ ~ ( ~ ( in @ SY668 @ SV13 )
| ~ ( SV76 @ SY668 ) )
| ! [SY669: $i] :
( ~ ( in @ SY669 @ SV13 )
| ~ ( SV76 @ SY669 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(297,plain,
! [SV77: $i > $o,SV14: $i] :
( ( ~ ~ ! [SY670: $i] :
~ ~ ( ~ ( in @ SY670 @ SV14 )
| ~ ( SV77 @ SY670 ) )
| ( ( dsetconstr @ SV14
@ ^ [SY671: $i] : ( SV77 @ SY671 ) )
!= emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(298,plain,
! [SV78: $i > $o,SV15: $i] :
( ( ~ ~ ! [SY672: $i] :
( ~ ( in @ SY672 @ SV15 )
| ( SV78 @ SY672 ) )
| ~ ! [SY673: $i] :
~ ~ ( ~ ( in @ SY673 @ SV15 )
| ~ ~ ( SV78 @ SY673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(299,plain,
! [SV79: $i > $o,SV16: $i] :
( ( ~ ~ ~ ! [SY674: $i] :
~ ~ ( ~ ( in @ SY674 @ SV16 )
| ~ ( SV79 @ SY674 ) )
| ! [SY675: $i] :
( ~ ( in @ SY675 @ SV16 )
| ~ ( SV79 @ SY675 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(300,plain,
! [SV80: $i,SV17: $i] :
( ( ! [SY676: $i] :
~ ( ~ ( ~ ( in @ SY676 @ ( setadjoin @ SV17 @ SV80 ) )
| ( SY676 = SV17 )
| ( in @ SY676 @ SV80 ) )
| ~ ( ~ ( ( SY676 = SV17 )
| ( in @ SY676 @ SV80 ) )
| ( in @ SY676 @ ( setadjoin @ SV17 @ SV80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(301,plain,
! [SV18: $i] :
( ( ! [SY521: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY522: $i] :
( ~ ( in @ SY522 @ SY521 )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY522 )
| ( in @ SY523 @ SV18 ) ) )
| ~ ! [SY524: $i,SY525: $i] :
( ~ ~ ( ~ ( in @ SY524 @ SV18 )
| ~ ( in @ SY525 @ SV18 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY521 )
| ~ ( ~ ( ~ ( in @ SY524 @ SX4 )
| ( in @ SY525 @ SX4 ) )
| ~ ( ~ ( in @ SY525 @ SX4 )
| ( in @ SY524 @ SX4 ) ) ) )
| ( SY524 = SY525 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY521 )
| ~ ( in @ SX3 @ SY521 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY531: $i] :
( ~ ~ ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SY531 )
| ( in @ SY532 @ SV18 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY531 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY521 )
| ~ ( in @ SX4 @ SY531 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY531 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY521 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(302,plain,
! [SV81: $i > $o,SV19: $i] :
( ( ! [SY677: $i] :
( ~ ( in @ SY677 @ SV19 )
| ~ ( SV81 @ SY677 )
| ( ( dsetconstr @ SV19
@ ^ [SY678: $i] : ( SV81 @ SY678 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(303,plain,
! [SV20: $i,SV82: $i] :
( ( ! [SY679: $i] :
( ~ ( in @ SV82 @ ( powerset @ SV20 ) )
| ~ ( in @ SY679 @ SV82 )
| ( in @ SY679 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(304,plain,
! [SV21: $i > $o] :
( ( ( ~ ~ ! [SY544: $i] :
~ ~ ( ~ ( SV21 @ SY544 )
| ~ ! [SY545: $i] :
( ~ ( SV21 @ SY545 )
| ( SY544 = SY545 ) ) ) )
= $true )
| ( ( SV21
@ ( descr
@ ^ [SY546: $i] : ( SV21 @ SY546 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(305,plain,
! [SV22: $i,SV83: $i] :
( ( ~ ( in @ SV83 @ ( setunion @ SV22 ) )
| ! [SY680: $o] :
( ~ ! [SY681: $i] :
( ~ ( in @ SV83 @ SY681 )
| ~ ( in @ SY681 @ SV22 )
| SY680 )
| SY680 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(306,plain,
! [SV23: $i] :
( ( ( ~ ( in @ SV23 @ emptyset ) )
= $true )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(307,plain,
! [SV84: $i > $o,SV24: $i] :
( ( ~ ~ ! [SY682: $i] :
( ~ ( in @ SY682 @ SV24 )
| ( SV84 @ SY682 ) )
| ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ SY683 @ SV24 )
| ~ ~ ( SV84 @ SY683 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(308,plain,
! [SV25: $i,SV85: $i] :
( ( ~ ( ~ ( ~ ( in @ SV85 @ ( powerset @ SV25 ) )
| ! [SY684: $i] :
( ~ ( in @ SY684 @ SV85 )
| ( in @ SY684 @ SV25 ) ) )
| ~ ( ~ ! [SY685: $i] :
( ~ ( in @ SY685 @ SV85 )
| ( in @ SY685 @ SV25 ) )
| ( in @ SV85 @ ( powerset @ SV25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(309,plain,
! [SV26: $i] :
( ( ( ~ ( ( SV26 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY557: $i] :
~ ~ ( ~ ( in @ SY557 @ SV26 )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(310,plain,
! [SV27: $i > $o,SV86: $i] :
( ( ~ ( in @ SV86 @ emptyset )
| ( SV27 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(311,plain,
! [SV28: $i,SV87: $i] :
( ( ~ ( in @ SV87 @ SV28 )
| ( in @ SV87 @ ( powerset @ ( setunion @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(312,plain,
! [SV88: $i > $o,SV29: $i] :
( ( ~ ~ ! [SY686: $i] :
~ ~ ( ~ ( in @ SY686 @ SV29 )
| ~ ~ ( SV88 @ SY686 ) )
| ~ ! [SY687: $i] :
( ~ ( in @ SY687 @ SV29 )
| ( SV88 @ SY687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(313,plain,
! [SV30: $i > $o] :
( ( ( ~ ~ ! [SY563: $i] :
~ ~ ( ~ ( SV30 @ SY563 )
| ~ ! [SY564: $i] :
( ~ ( SV30 @ SY564 )
| ( SY563 = SY564 ) ) ) )
= $true )
| ( ( ~ ! [SY565: $i] :
~ ~ ( ~ ( SV30 @ SY565 )
| ~ ! [SY566: $i] :
( ~ ( SV30 @ SY566 )
| ( SY565 = SY566 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(314,plain,
! [SV89: $i,SV31: $i] :
( ( ~ ! [SY688: $i] :
( ~ ( in @ SY688 @ SV31 )
| ( in @ SY688 @ SV89 ) )
| ~ ! [SY689: $i] :
( ~ ( in @ SY689 @ SV89 )
| ( in @ SY689 @ SV31 ) )
| ( SV31 = SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(315,plain,
! [SV90: $i,SV32: $i] :
( ( ( SV32 != SV90 )
| ! [SY690: $i,SY691: $i] :
( ( SY690 != SY691 )
| ( ( setadjoin @ SV32 @ SY690 )
= ( setadjoin @ SV90 @ SY691 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(316,plain,
! [SV91: $i,SV33: $i] :
( ( ! [SY692: $i] :
( ~ ( in @ SY692 @ ( setadjoin @ SV33 @ SV91 ) )
| ! [SY693: $o] :
( ~ ( ( SY692 != SV33 )
| SY693 )
| ~ ( ~ ( in @ SY692 @ SV91 )
| SY693 )
| SY693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(317,plain,
! [SV92: $i > $o,SV34: $i] :
( ( ~ ! [SY694: $i] :
( ~ ( in @ SY694 @ SV34 )
| ~ ( SV92 @ SY694 ) )
| ~ ~ ! [SY695: $i] :
~ ~ ( ~ ( in @ SY695 @ SV34 )
| ~ ( SV92 @ SY695 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(318,plain,
! [SV93: $i,SV35: $i] :
( ( ( SV35 != SV93 )
| ( ( setunion @ SV35 )
= ( setunion @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(319,plain,
! [SV36: $i > $o] :
( ( ( ~ ~ ! [SY580: $i] :
~ ~ ( ~ ( SV36 @ SY580 )
| ~ ! [SY581: $i] :
( ~ ( SV36 @ SY581 )
| ( SY580 = SY581 ) ) ) )
= $true )
| ( ( ~ ! [SY582: $i] :
~ ~ ( ~ ( SV36 @ SY582 )
| ~ ! [SY583: $i] :
( ~ ( SV36 @ SY583 )
| ( SY582 = SY583 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(320,plain,
! [SV37: $o,SV94: $i] :
( ( ~ ( in @ SV94 @ ( prop2set @ SV37 ) )
| SV37 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(321,plain,
! [SV95: $i] :
( ( ~ ( in @ SV95 @ ( prop2set @ $true ) )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(322,plain,
! [SV96: $i] :
( ( ~ ( in @ SV96 @ ( prop2set @ $false ) )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(323,plain,
! [SV38: $i,SV97: $i] :
( ( ! [SY696: $i] :
( ~ ( in @ SV97 @ SY696 )
| ~ ( in @ SY696 @ SV38 )
| ( in @ SV97 @ ( setunion @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(324,plain,
! [SV98: $i,SV39: $i] :
( ( ~ ( in @ SV39 @ ( setadjoin @ SV98 @ emptyset ) )
| ( SV39 = SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(325,plain,
! [SV40: $i > $o] :
( ( ( ~ ~ ! [SY588: $i] :
~ ~ ( ~ ( SV40 @ SY588 )
| ~ ! [SY589: $i] :
( ~ ( SV40 @ SY589 )
| ( SY588 = SY589 ) ) ) )
= $true )
| ( ( ~ ! [SY590: $i] :
~ ! [SY591: $i] :
~ ( ~ ( ~ ( SV40 @ SY591 )
| ( SY591 = SY590 ) )
| ~ ( ( SY591 != SY590 )
| ( SV40 @ SY591 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(326,plain,
! [SV41: $i > $o] :
( ( ( ~ ~ ! [SY592: $i] :
~ ~ ( ~ ( SV41 @ SY592 )
| ~ ! [SY593: $i] :
( ~ ( SV41 @ SY593 )
| ( SY592 = SY593 ) ) ) )
= $true )
| ( ( ~ ! [SY594: $i] :
~ ( SV41 @ SY594 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(327,plain,
! [SV42: $i] :
( ( ( ~ ! [SY595: $i] :
~ ( in @ SY595 @ SV42 ) )
= $true )
| ( ( SV42 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(328,plain,
! [SV43: $i > $o] :
( ( ( ~ ~ ! [SY596: $i] :
~ ( SV43 @ SY596 ) )
= $true )
| ( ( ~ ! [SY597: $i,SY598: $i] :
( ~ ( SV43 @ SY597 )
| ~ ( SV43 @ SY598 )
| ( SY597 = SY598 ) )
| ~ ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(329,plain,
! [SV99: $i > $o,SV44: $i] :
( ( ! [SY697: $i] :
( ~ ( in @ SY697
@ ( dsetconstr @ SV44
@ ^ [SY698: $i] : ( SV99 @ SY698 ) ) )
| ( in @ SY697 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(330,plain,
! [SV45: $o] :
( ( ( ~ SV45 ) = $true )
| ( ( set2prop @ ( prop2set @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(331,plain,
( ( ( ~ $true ) = $true )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(332,plain,
( ( ( ~ $false ) = $true )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(333,plain,
! [SV46: $i,SV100: $i] :
( ( ! [SY699: $i] :
( ~ ( in @ SY699 @ SV100 )
| ( in @ SY699 @ ( setadjoin @ SV46 @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(334,plain,
! [SV47: $o] :
( ( ( ~ SV47 ) = $true )
| ( ( in @ emptyset @ ( prop2set @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(335,plain,
( ( ( ~ $true ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(336,plain,
( ( ( ~ $false ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(337,plain,
! [SV48: $i] :
( ( ( ~ ! [SY606: $i] :
~ ( in @ SY606 @ SV48 ) )
= $true )
| ( ( SV48 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(338,plain,
! [SV49: $i > $o] :
( ( ( ~ ~ ! [SY607: $i] :
~ ~ ( ~ ( SV49 @ SY607 )
| ~ ! [SY608: $i] :
( ~ ( SV49 @ SY608 )
| ( SY607 = SY608 ) ) ) )
= $true )
| ( ( ! [SY609: $i,SY610: $i] :
( ~ ( SV49 @ SY609 )
| ~ ( SV49 @ SY610 )
| ( SY609 = SY610 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(339,plain,
! [SV50: $i > $o] :
( ( ( ~ ~ ! [SY611: $i] :
~ ! [SY612: $i] :
~ ( ~ ( ~ ( SV50 @ SY612 )
| ( SY612 = SY611 ) )
| ~ ( ( SY612 != SY611 )
| ( SV50 @ SY612 ) ) ) )
= $true )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(340,plain,
! [SV101: $i > $o,SV51: $i] :
( ( ! [SY700: $i] :
( ~ ( in @ SY700 @ SV51 )
| ~ ( SV101 @ SY700 )
| ( in @ SY700
@ ( dsetconstr @ SV51
@ ^ [SY701: $i] : ( SV101 @ SY701 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(341,plain,
! [SV52: $i] :
( ( ( ~ ~ ( ~ ( in @ emptyset @ SV52 )
| ~ ! [SY618: $i] :
( ~ ~ ( ~ ( in @ SY618 @ omega )
| ~ ( in @ SY618 @ SV52 ) )
| ( in @ ( setadjoin @ SY618 @ SY618 ) @ SV52 ) ) ) )
= $true )
| ( ( ! [SY619: $i] :
( ~ ( in @ SY619 @ omega )
| ( in @ SY619 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(342,plain,
( ( ~ ~ ! [SY702: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY702 )
| ~ ! [SY703: $i] :
( ~ ( sK1_SX0 @ SY703 )
| ( SY702 = SY703 ) ) )
| ! [SY704: $i,SY705: $i] :
( ~ ( sK1_SX0 @ SY704 )
| ~ ( sK1_SX0 @ SY705 )
| ( SY704 = SY705 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[270]) ).
thf(343,plain,
! [SV102: $i,SV53: $i] :
( ( ! [SY706: $i] :
( ~ ( in @ SY706 @ ( setadjoin @ SV53 @ SV102 ) )
| ( SY706 = SV53 )
| ( in @ SY706 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(344,plain,
! [SV54: $i] :
( ( ( ~ ( in @ SV54 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV54 @ SV54 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(345,plain,
! [SV103: $i > $o,SV55: $i] :
( ( ! [SY707: $i] :
( ~ ( in @ SY707 @ SV55 )
| ~ ( ~ ( ~ ( in @ SY707
@ ( dsetconstr @ SV55
@ ^ [SY708: $i] : ( SV103 @ SY708 ) ) )
| ( SV103 @ SY707 ) )
| ~ ( ~ ( SV103 @ SY707 )
| ( in @ SY707
@ ( dsetconstr @ SV55
@ ^ [SY709: $i] : ( SV103 @ SY709 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(346,plain,
! [SV104: $i > $o,SV56: $i] :
( ( ! [SY710: $i] :
( ~ ( in @ SY710
@ ( dsetconstr @ SV56
@ ^ [SY711: $i] : ( SV104 @ SY711 ) ) )
| ( SV104 @ SY710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(347,plain,
! [SV105: $i,SV57: $i] :
( ( ~ ( ( SV57 != SV105 ) )
| ~ ( in @ SV105 @ ( setadjoin @ SV57 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(348,plain,
! [SV106: $i,SV58: $i] :
( ( ( SV58 != SV106 )
| ! [SY712: $i,SY713: $i] :
( ( SY712 != SY713 )
| ~ ( ~ ( ~ ( in @ SY712 @ SV58 )
| ( in @ SY713 @ SV106 ) )
| ~ ( ~ ( in @ SY713 @ SV106 )
| ( in @ SY712 @ SV58 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(349,plain,
! [SV59: $i] :
( ( ( ~ ~ ! [SY633: $i] :
~ ( in @ SY633 @ SV59 ) )
= $true )
| ( ( SV59 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(350,plain,
! [SV60: $i] :
( ( ( ~ ( in @ SV60 @ emptyset ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(351,plain,
! [SV61: $i] :
( ( ( ~ ~ ! [SY634: $i] :
~ ( in @ SY634 @ SV61 ) )
= $true )
| ( ( ~ ! [SY635: $i] :
~ ~ ( ~ ( in @ SY635 @ SV61 )
| ~ ~ ~ ! [SY636: $i] :
~ ~ ( ~ ( in @ SY636 @ SY635 )
| ~ ( in @ SY636 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(352,plain,
! [SV62: $i] :
( ( ( ~ ( ( SV62 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY637: $i] :
~ ( in @ SY637 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(353,plain,
! [SV63: $i > $i > $o,SV107: $i] :
( ( ~ ! [SY714: $i] :
( ~ ( in @ SY714 @ SV107 )
| ~ ! [SY640: $i] :
~ ~ ( ~ ( SV63 @ SY714 @ SY640 )
| ~ ! [SY641: $i] :
( ~ ( SV63 @ SY714 @ SY641 )
| ( SY640 = SY641 ) ) ) )
| ~ ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(354,plain,
! [SV64: $i,SV108: $i] :
( ( ~ ( ~ ( ~ ( in @ SV108 @ ( setunion @ SV64 ) )
| ~ ! [SY721: $i] :
~ ~ ( ~ ( in @ SV108 @ SY721 )
| ~ ( in @ SY721 @ SV64 ) ) )
| ~ ( ~ ~ ! [SY722: $i] :
~ ~ ( ~ ( in @ SV108 @ SY722 )
| ~ ( in @ SY722 @ SV64 ) )
| ( in @ SV108 @ ( setunion @ SV64 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(355,plain,
! [SV109: $i,SV65: $i] :
( ( ! [SY723: $i] :
( ~ ( in @ SY723 @ ( setadjoin @ SV65 @ ( setadjoin @ SV109 @ emptyset ) ) )
| ( SY723 = SV65 )
| ( SY723 = SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(356,plain,
! [SV110: $i,SV66: $i] :
( ( ~ ( in @ SV66 @ ( setadjoin @ SV110 @ emptyset ) )
| ( in @ SV110 @ ( setadjoin @ SV66 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(357,plain,
! [SV111: $i,SV67: $i] :
( ( ( SV67 != SV111 )
| ( in @ SV67 @ ( setadjoin @ SV111 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(358,plain,
! [SV112: $i,SV68: $i] :
( ( ( SV68 != SV112 )
| ( ( powerset @ SV68 )
= ( powerset @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(359,plain,
! [SV72: $i,SV9: $i] :
( ( ( SV9 != SV72 )
= $true )
| ( ( ! [SY654: $i,SY655: $i] :
( ( SY654 != SY655 )
| ~ ( in @ SY654 @ SV9 )
| ( in @ SY655 @ SV72 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(360,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ! [SY656: $i,SY657: $i] :
( ( SY656 != SY657 )
| ~ ( ~ ( ~ ( SV10 @ SY656 )
| ( SV73 @ SY657 ) )
| ~ ( ~ ( SV73 @ SY657 )
| ( SV10 @ SY656 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(361,plain,
! [SV11: $i,SV74: $i] :
( ( ( ~ ! [SY666: $i] :
( ~ ( in @ SY666 @ SV74 )
| ( in @ SY666 @ SV11 ) ) )
= $true )
| ( ( in @ SV74 @ ( powerset @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(362,plain,
! [SV75: $i,SV12: $i] :
( ( ( ~ ! [SY667: $i] :
~ ( ~ ( ~ ( in @ SY667 @ SV12 )
| ( in @ SY667 @ SV75 ) )
| ~ ( ~ ( in @ SY667 @ SV75 )
| ( in @ SY667 @ SV12 ) ) ) )
= $true )
| ( ( SV12 = SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(363,plain,
! [SV76: $i > $o,SV13: $i] :
( ( ( ~ ~ ~ ! [SY668: $i] :
~ ~ ( ~ ( in @ SY668 @ SV13 )
| ~ ( SV76 @ SY668 ) ) )
= $true )
| ( ( ! [SY669: $i] :
( ~ ( in @ SY669 @ SV13 )
| ~ ( SV76 @ SY669 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(364,plain,
! [SV77: $i > $o,SV14: $i] :
( ( ( ~ ~ ! [SY670: $i] :
~ ~ ( ~ ( in @ SY670 @ SV14 )
| ~ ( SV77 @ SY670 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV14
@ ^ [SY671: $i] : ( SV77 @ SY671 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(365,plain,
! [SV78: $i > $o,SV15: $i] :
( ( ( ~ ~ ! [SY672: $i] :
( ~ ( in @ SY672 @ SV15 )
| ( SV78 @ SY672 ) ) )
= $true )
| ( ( ~ ! [SY673: $i] :
~ ~ ( ~ ( in @ SY673 @ SV15 )
| ~ ~ ( SV78 @ SY673 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(366,plain,
! [SV79: $i > $o,SV16: $i] :
( ( ( ~ ~ ~ ! [SY674: $i] :
~ ~ ( ~ ( in @ SY674 @ SV16 )
| ~ ( SV79 @ SY674 ) ) )
= $true )
| ( ( ! [SY675: $i] :
( ~ ( in @ SY675 @ SV16 )
| ~ ( SV79 @ SY675 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(367,plain,
! [SV80: $i,SV17: $i,SV113: $i] :
( ( ~ ( ~ ( ~ ( in @ SV113 @ ( setadjoin @ SV17 @ SV80 ) )
| ( SV113 = SV17 )
| ( in @ SV113 @ SV80 ) )
| ~ ( ~ ( ( SV113 = SV17 )
| ( in @ SV113 @ SV80 ) )
| ( in @ SV113 @ ( setadjoin @ SV17 @ SV80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(368,plain,
! [SV18: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY724: $i] :
( ~ ( in @ SY724 @ ( sK2_SY521 @ SV18 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY724 )
| ( in @ SY523 @ SV18 ) ) )
| ~ ! [SY726: $i,SY727: $i] :
( ~ ~ ( ~ ( in @ SY726 @ SV18 )
| ~ ( in @ SY727 @ SV18 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SY726 @ SY728 )
| ( in @ SY727 @ SY728 ) )
| ~ ( ~ ( in @ SY727 @ SY728 )
| ( in @ SY726 @ SY728 ) ) ) )
| ( SY726 = SY727 ) ) )
| ~ ! [SY729: $i,SY730: $i] :
( ~ ~ ( ~ ( in @ SY729 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY730 @ ( sK2_SY521 @ SV18 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY729 )
| ( in @ SX4 @ SY730 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY730 )
| ( in @ SX4 @ SY729 ) ) ) )
| ~ ! [SY733: $i] :
( ~ ~ ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SY733 )
| ( in @ SY532 @ SV18 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY733 ) )
| ~ ! [SY736: $i] :
~ ~ ! [SY737: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY736 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY737 @ SY733 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY736 )
| ~ ( in @ SX5 @ SY733 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY736 ) )
| ( in @ SY737 @ SY739 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[301]) ).
thf(369,plain,
! [SV81: $i > $o,SV19: $i,SV114: $i] :
( ( ~ ( in @ SV114 @ SV19 )
| ~ ( SV81 @ SV114 )
| ( ( dsetconstr @ SV19
@ ^ [SY678: $i] : ( SV81 @ SY678 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(370,plain,
! [SV115: $i,SV20: $i,SV82: $i] :
( ( ~ ( in @ SV82 @ ( powerset @ SV20 ) )
| ~ ( in @ SV115 @ SV82 )
| ( in @ SV115 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(371,plain,
! [SV21: $i > $o] :
( ( ( ~ ! [SY544: $i] :
~ ~ ( ~ ( SV21 @ SY544 )
| ~ ! [SY545: $i] :
( ~ ( SV21 @ SY545 )
| ( SY544 = SY545 ) ) ) )
= $false )
| ( ( SV21
@ ( descr
@ ^ [SY546: $i] : ( SV21 @ SY546 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(372,plain,
! [SV22: $i,SV83: $i] :
( ( ( ~ ( in @ SV83 @ ( setunion @ SV22 ) ) )
= $true )
| ( ( ! [SY680: $o] :
( ~ ! [SY681: $i] :
( ~ ( in @ SV83 @ SY681 )
| ~ ( in @ SY681 @ SV22 )
| SY680 )
| SY680 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(373,plain,
! [SV23: $i] :
( ( ( in @ SV23 @ emptyset )
= $false )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(374,plain,
! [SV84: $i > $o,SV24: $i] :
( ( ( ~ ~ ! [SY682: $i] :
( ~ ( in @ SY682 @ SV24 )
| ( SV84 @ SY682 ) ) )
= $true )
| ( ( ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ SY683 @ SV24 )
| ~ ~ ( SV84 @ SY683 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(375,plain,
! [SV25: $i,SV85: $i] :
( ( ~ ( ~ ( in @ SV85 @ ( powerset @ SV25 ) )
| ! [SY684: $i] :
( ~ ( in @ SY684 @ SV85 )
| ( in @ SY684 @ SV25 ) ) )
| ~ ( ~ ! [SY685: $i] :
( ~ ( in @ SY685 @ SV85 )
| ( in @ SY685 @ SV25 ) )
| ( in @ SV85 @ ( powerset @ SV25 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(376,plain,
! [SV26: $i] :
( ( ( SV26 != emptyset )
= $false )
| ( ( ~ ! [SY557: $i] :
~ ~ ( ~ ( in @ SY557 @ SV26 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(377,plain,
! [SV27: $i > $o,SV86: $i] :
( ( ( ~ ( in @ SV86 @ emptyset ) )
= $true )
| ( ( SV27 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(378,plain,
! [SV28: $i,SV87: $i] :
( ( ( ~ ( in @ SV87 @ SV28 ) )
= $true )
| ( ( in @ SV87 @ ( powerset @ ( setunion @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(379,plain,
! [SV88: $i > $o,SV29: $i] :
( ( ( ~ ~ ! [SY686: $i] :
~ ~ ( ~ ( in @ SY686 @ SV29 )
| ~ ~ ( SV88 @ SY686 ) ) )
= $true )
| ( ( ~ ! [SY687: $i] :
( ~ ( in @ SY687 @ SV29 )
| ( SV88 @ SY687 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(380,plain,
! [SV30: $i > $o] :
( ( ( ~ ! [SY563: $i] :
~ ~ ( ~ ( SV30 @ SY563 )
| ~ ! [SY564: $i] :
( ~ ( SV30 @ SY564 )
| ( SY563 = SY564 ) ) ) )
= $false )
| ( ( ~ ! [SY565: $i] :
~ ~ ( ~ ( SV30 @ SY565 )
| ~ ! [SY566: $i] :
( ~ ( SV30 @ SY566 )
| ( SY565 = SY566 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(381,plain,
! [SV89: $i,SV31: $i] :
( ( ( ~ ! [SY688: $i] :
( ~ ( in @ SY688 @ SV31 )
| ( in @ SY688 @ SV89 ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
( ~ ( in @ SY689 @ SV89 )
| ( in @ SY689 @ SV31 ) )
| ( SV31 = SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(382,plain,
! [SV90: $i,SV32: $i] :
( ( ( SV32 != SV90 )
= $true )
| ( ( ! [SY690: $i,SY691: $i] :
( ( SY690 != SY691 )
| ( ( setadjoin @ SV32 @ SY690 )
= ( setadjoin @ SV90 @ SY691 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(383,plain,
! [SV91: $i,SV33: $i,SV116: $i] :
( ( ~ ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
| ! [SY742: $o] :
( ~ ( ( SV116 != SV33 )
| SY742 )
| ~ ( ~ ( in @ SV116 @ SV91 )
| SY742 )
| SY742 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(384,plain,
! [SV92: $i > $o,SV34: $i] :
( ( ( ~ ! [SY694: $i] :
( ~ ( in @ SY694 @ SV34 )
| ~ ( SV92 @ SY694 ) ) )
= $true )
| ( ( ~ ~ ! [SY695: $i] :
~ ~ ( ~ ( in @ SY695 @ SV34 )
| ~ ( SV92 @ SY695 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(385,plain,
! [SV93: $i,SV35: $i] :
( ( ( SV35 != SV93 )
= $true )
| ( ( ( setunion @ SV35 )
= ( setunion @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(386,plain,
! [SV36: $i > $o] :
( ( ( ~ ! [SY580: $i] :
~ ~ ( ~ ( SV36 @ SY580 )
| ~ ! [SY581: $i] :
( ~ ( SV36 @ SY581 )
| ( SY580 = SY581 ) ) ) )
= $false )
| ( ( ~ ! [SY582: $i] :
~ ~ ( ~ ( SV36 @ SY582 )
| ~ ! [SY583: $i] :
( ~ ( SV36 @ SY583 )
| ( SY582 = SY583 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(387,plain,
! [SV37: $o,SV94: $i] :
( ( ( ~ ( in @ SV94 @ ( prop2set @ SV37 ) ) )
= $true )
| ( SV37 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(388,plain,
! [SV95: $i] :
( ( ( ~ ( in @ SV95 @ ( prop2set @ $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(389,plain,
! [SV96: $i] :
( ( ( ~ ( in @ SV96 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(390,plain,
! [SV38: $i,SV117: $i,SV97: $i] :
( ( ~ ( in @ SV97 @ SV117 )
| ~ ( in @ SV117 @ SV38 )
| ( in @ SV97 @ ( setunion @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(391,plain,
! [SV98: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ ( setadjoin @ SV98 @ emptyset ) ) )
= $true )
| ( ( SV39 = SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(392,plain,
! [SV40: $i > $o] :
( ( ( ~ ! [SY588: $i] :
~ ~ ( ~ ( SV40 @ SY588 )
| ~ ! [SY589: $i] :
( ~ ( SV40 @ SY589 )
| ( SY588 = SY589 ) ) ) )
= $false )
| ( ( ~ ! [SY590: $i] :
~ ! [SY591: $i] :
~ ( ~ ( ~ ( SV40 @ SY591 )
| ( SY591 = SY590 ) )
| ~ ( ( SY591 != SY590 )
| ( SV40 @ SY591 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(393,plain,
! [SV41: $i > $o] :
( ( ( ~ ! [SY592: $i] :
~ ~ ( ~ ( SV41 @ SY592 )
| ~ ! [SY593: $i] :
( ~ ( SV41 @ SY593 )
| ( SY592 = SY593 ) ) ) )
= $false )
| ( ( ~ ! [SY594: $i] :
~ ( SV41 @ SY594 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(394,plain,
! [SV42: $i] :
( ( ( ! [SY595: $i] :
~ ( in @ SY595 @ SV42 ) )
= $false )
| ( ( SV42 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(395,plain,
! [SV43: $i > $o] :
( ( ( ~ ! [SY596: $i] :
~ ( SV43 @ SY596 ) )
= $false )
| ( ( ~ ! [SY597: $i,SY598: $i] :
( ~ ( SV43 @ SY597 )
| ~ ( SV43 @ SY598 )
| ( SY597 = SY598 ) )
| ~ ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(396,plain,
! [SV99: $i > $o,SV44: $i,SV118: $i] :
( ( ~ ( in @ SV118
@ ( dsetconstr @ SV44
@ ^ [SY698: $i] : ( SV99 @ SY698 ) ) )
| ( in @ SV118 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(397,plain,
! [SV45: $o] :
( ( SV45 = $false )
| ( ( set2prop @ ( prop2set @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(398,plain,
( ( $true = $false )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(399,plain,
( ( $false = $false )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(400,plain,
! [SV46: $i,SV100: $i,SV119: $i] :
( ( ~ ( in @ SV119 @ SV100 )
| ( in @ SV119 @ ( setadjoin @ SV46 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(401,plain,
! [SV47: $o] :
( ( SV47 = $false )
| ( ( in @ emptyset @ ( prop2set @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(402,plain,
( ( $true = $false )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(403,plain,
( ( $false = $false )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(404,plain,
! [SV48: $i] :
( ( ( ! [SY606: $i] :
~ ( in @ SY606 @ SV48 ) )
= $false )
| ( ( SV48 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(405,plain,
! [SV49: $i > $o] :
( ( ( ~ ! [SY607: $i] :
~ ~ ( ~ ( SV49 @ SY607 )
| ~ ! [SY608: $i] :
( ~ ( SV49 @ SY608 )
| ( SY607 = SY608 ) ) ) )
= $false )
| ( ( ! [SY609: $i,SY610: $i] :
( ~ ( SV49 @ SY609 )
| ~ ( SV49 @ SY610 )
| ( SY609 = SY610 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(406,plain,
! [SV50: $i > $o] :
( ( ( ~ ! [SY611: $i] :
~ ! [SY612: $i] :
~ ( ~ ( ~ ( SV50 @ SY612 )
| ( SY612 = SY611 ) )
| ~ ( ( SY612 != SY611 )
| ( SV50 @ SY612 ) ) ) )
= $false )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(407,plain,
! [SV101: $i > $o,SV51: $i,SV120: $i] :
( ( ~ ( in @ SV120 @ SV51 )
| ~ ( SV101 @ SV120 )
| ( in @ SV120
@ ( dsetconstr @ SV51
@ ^ [SY701: $i] : ( SV101 @ SY701 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(408,plain,
! [SV52: $i] :
( ( ( ~ ( ~ ( in @ emptyset @ SV52 )
| ~ ! [SY618: $i] :
( ~ ~ ( ~ ( in @ SY618 @ omega )
| ~ ( in @ SY618 @ SV52 ) )
| ( in @ ( setadjoin @ SY618 @ SY618 ) @ SV52 ) ) ) )
= $false )
| ( ( ! [SY619: $i] :
( ~ ( in @ SY619 @ omega )
| ( in @ SY619 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(409,plain,
( ( ~ ~ ! [SY702: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY702 )
| ~ ! [SY703: $i] :
( ~ ( sK1_SX0 @ SY703 )
| ( SY702 = SY703 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[342]) ).
thf(410,plain,
( ( ! [SY704: $i,SY705: $i] :
( ~ ( sK1_SX0 @ SY704 )
| ~ ( sK1_SX0 @ SY705 )
| ( SY704 = SY705 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[342]) ).
thf(411,plain,
! [SV102: $i,SV53: $i,SV121: $i] :
( ( ~ ( in @ SV121 @ ( setadjoin @ SV53 @ SV102 ) )
| ( SV121 = SV53 )
| ( in @ SV121 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(412,plain,
! [SV54: $i] :
( ( ( in @ SV54 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV54 @ SV54 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(413,plain,
! [SV103: $i > $o,SV55: $i,SV122: $i] :
( ( ~ ( in @ SV122 @ SV55 )
| ~ ( ~ ( ~ ( in @ SV122
@ ( dsetconstr @ SV55
@ ^ [SY708: $i] : ( SV103 @ SY708 ) ) )
| ( SV103 @ SV122 ) )
| ~ ( ~ ( SV103 @ SV122 )
| ( in @ SV122
@ ( dsetconstr @ SV55
@ ^ [SY709: $i] : ( SV103 @ SY709 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(414,plain,
! [SV104: $i > $o,SV56: $i,SV123: $i] :
( ( ~ ( in @ SV123
@ ( dsetconstr @ SV56
@ ^ [SY711: $i] : ( SV104 @ SY711 ) ) )
| ( SV104 @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(415,plain,
! [SV105: $i,SV57: $i] :
( ( ( ~ ( ( SV57 != SV105 ) ) )
= $true )
| ( ( ~ ( in @ SV105 @ ( setadjoin @ SV57 @ emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(416,plain,
! [SV106: $i,SV58: $i] :
( ( ( SV58 != SV106 )
= $true )
| ( ( ! [SY712: $i,SY713: $i] :
( ( SY712 != SY713 )
| ~ ( ~ ( ~ ( in @ SY712 @ SV58 )
| ( in @ SY713 @ SV106 ) )
| ~ ( ~ ( in @ SY713 @ SV106 )
| ( in @ SY712 @ SV58 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(417,plain,
! [SV59: $i] :
( ( ( ~ ! [SY633: $i] :
~ ( in @ SY633 @ SV59 ) )
= $false )
| ( ( SV59 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(418,plain,
! [SV60: $i] :
( ( ( in @ SV60 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(419,plain,
! [SV61: $i] :
( ( ( ~ ! [SY634: $i] :
~ ( in @ SY634 @ SV61 ) )
= $false )
| ( ( ~ ! [SY635: $i] :
~ ~ ( ~ ( in @ SY635 @ SV61 )
| ~ ~ ~ ! [SY636: $i] :
~ ~ ( ~ ( in @ SY636 @ SY635 )
| ~ ( in @ SY636 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(420,plain,
! [SV62: $i] :
( ( ( SV62 != emptyset )
= $false )
| ( ( ~ ! [SY637: $i] :
~ ( in @ SY637 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(421,plain,
! [SV63: $i > $i > $o,SV107: $i] :
( ( ( ~ ! [SY714: $i] :
( ~ ( in @ SY714 @ SV107 )
| ~ ! [SY640: $i] :
~ ~ ( ~ ( SV63 @ SY714 @ SY640 )
| ~ ! [SY641: $i] :
( ~ ( SV63 @ SY714 @ SY641 )
| ( SY640 = SY641 ) ) ) ) )
= $true )
| ( ( ~ ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(422,plain,
! [SV64: $i,SV108: $i] :
( ( ~ ( ~ ( in @ SV108 @ ( setunion @ SV64 ) )
| ~ ! [SY721: $i] :
~ ~ ( ~ ( in @ SV108 @ SY721 )
| ~ ( in @ SY721 @ SV64 ) ) )
| ~ ( ~ ~ ! [SY722: $i] :
~ ~ ( ~ ( in @ SV108 @ SY722 )
| ~ ( in @ SY722 @ SV64 ) )
| ( in @ SV108 @ ( setunion @ SV64 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(423,plain,
! [SV109: $i,SV65: $i,SV124: $i] :
( ( ~ ( in @ SV124 @ ( setadjoin @ SV65 @ ( setadjoin @ SV109 @ emptyset ) ) )
| ( SV124 = SV65 )
| ( SV124 = SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(424,plain,
! [SV110: $i,SV66: $i] :
( ( ( ~ ( in @ SV66 @ ( setadjoin @ SV110 @ emptyset ) ) )
= $true )
| ( ( in @ SV110 @ ( setadjoin @ SV66 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(425,plain,
! [SV111: $i,SV67: $i] :
( ( ( SV67 != SV111 )
= $true )
| ( ( in @ SV67 @ ( setadjoin @ SV111 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(426,plain,
! [SV112: $i,SV68: $i] :
( ( ( SV68 != SV112 )
= $true )
| ( ( ( powerset @ SV68 )
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(427,plain,
! [SV72: $i,SV9: $i] :
( ( ( SV9 = SV72 )
= $false )
| ( ( ! [SY654: $i,SY655: $i] :
( ( SY654 != SY655 )
| ~ ( in @ SY654 @ SV9 )
| ( in @ SY655 @ SV72 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(428,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ! [SY656: $i,SY657: $i] :
( ( SY656 != SY657 )
| ~ ( ~ ( ~ ( SV10 @ SY656 )
| ( SV73 @ SY657 ) )
| ~ ( ~ ( SV73 @ SY657 )
| ( SV10 @ SY656 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(429,plain,
! [SV11: $i,SV74: $i] :
( ( ( ! [SY666: $i] :
( ~ ( in @ SY666 @ SV74 )
| ( in @ SY666 @ SV11 ) ) )
= $false )
| ( ( in @ SV74 @ ( powerset @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(430,plain,
! [SV75: $i,SV12: $i] :
( ( ( ! [SY667: $i] :
~ ( ~ ( ~ ( in @ SY667 @ SV12 )
| ( in @ SY667 @ SV75 ) )
| ~ ( ~ ( in @ SY667 @ SV75 )
| ( in @ SY667 @ SV12 ) ) ) )
= $false )
| ( ( SV12 = SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(431,plain,
! [SV76: $i > $o,SV13: $i] :
( ( ( ~ ~ ! [SY668: $i] :
~ ~ ( ~ ( in @ SY668 @ SV13 )
| ~ ( SV76 @ SY668 ) ) )
= $false )
| ( ( ! [SY669: $i] :
( ~ ( in @ SY669 @ SV13 )
| ~ ( SV76 @ SY669 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(432,plain,
! [SV77: $i > $o,SV14: $i] :
( ( ( ~ ! [SY670: $i] :
~ ~ ( ~ ( in @ SY670 @ SV14 )
| ~ ( SV77 @ SY670 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV14
@ ^ [SY671: $i] : ( SV77 @ SY671 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(433,plain,
! [SV78: $i > $o,SV15: $i] :
( ( ( ~ ! [SY672: $i] :
( ~ ( in @ SY672 @ SV15 )
| ( SV78 @ SY672 ) ) )
= $false )
| ( ( ~ ! [SY673: $i] :
~ ~ ( ~ ( in @ SY673 @ SV15 )
| ~ ~ ( SV78 @ SY673 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(434,plain,
! [SV79: $i > $o,SV16: $i] :
( ( ( ~ ~ ! [SY674: $i] :
~ ~ ( ~ ( in @ SY674 @ SV16 )
| ~ ( SV79 @ SY674 ) ) )
= $false )
| ( ( ! [SY675: $i] :
( ~ ( in @ SY675 @ SV16 )
| ~ ( SV79 @ SY675 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(435,plain,
! [SV80: $i,SV17: $i,SV113: $i] :
( ( ~ ( ~ ( in @ SV113 @ ( setadjoin @ SV17 @ SV80 ) )
| ( SV113 = SV17 )
| ( in @ SV113 @ SV80 ) )
| ~ ( ~ ( ( SV113 = SV17 )
| ( in @ SV113 @ SV80 ) )
| ( in @ SV113 @ ( setadjoin @ SV17 @ SV80 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(436,plain,
! [SV18: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY724: $i] :
( ~ ( in @ SY724 @ ( sK2_SY521 @ SV18 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY724 )
| ( in @ SY523 @ SV18 ) ) )
| ~ ! [SY726: $i,SY727: $i] :
( ~ ~ ( ~ ( in @ SY726 @ SV18 )
| ~ ( in @ SY727 @ SV18 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SY726 @ SY728 )
| ( in @ SY727 @ SY728 ) )
| ~ ( ~ ( in @ SY727 @ SY728 )
| ( in @ SY726 @ SY728 ) ) ) )
| ( SY726 = SY727 ) ) )
| ~ ! [SY729: $i,SY730: $i] :
( ~ ~ ( ~ ( in @ SY729 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY730 @ ( sK2_SY521 @ SV18 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY729 )
| ( in @ SX4 @ SY730 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY730 )
| ( in @ SX4 @ SY729 ) ) ) )
| ~ ! [SY733: $i] :
( ~ ~ ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SY733 )
| ( in @ SY532 @ SV18 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY733 ) )
| ~ ! [SY736: $i] :
~ ~ ! [SY737: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY736 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY737 @ SY733 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY736 )
| ~ ( in @ SX5 @ SY733 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY736 ) )
| ( in @ SY737 @ SY739 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(437,plain,
! [SV81: $i > $o,SV19: $i,SV114: $i] :
( ( ( ~ ( in @ SV114 @ SV19 ) )
= $true )
| ( ( ~ ( SV81 @ SV114 )
| ( ( dsetconstr @ SV19
@ ^ [SY678: $i] : ( SV81 @ SY678 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(438,plain,
! [SV115: $i,SV20: $i,SV82: $i] :
( ( ( ~ ( in @ SV82 @ ( powerset @ SV20 ) ) )
= $true )
| ( ( ~ ( in @ SV115 @ SV82 )
| ( in @ SV115 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(439,plain,
! [SV21: $i > $o] :
( ( ( ! [SY544: $i] :
~ ~ ( ~ ( SV21 @ SY544 )
| ~ ! [SY545: $i] :
( ~ ( SV21 @ SY545 )
| ( SY544 = SY545 ) ) ) )
= $true )
| ( ( SV21
@ ( descr
@ ^ [SY546: $i] : ( SV21 @ SY546 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(440,plain,
! [SV22: $i,SV83: $i] :
( ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false )
| ( ( ! [SY680: $o] :
( ~ ! [SY681: $i] :
( ~ ( in @ SV83 @ SY681 )
| ~ ( in @ SY681 @ SV22 )
| SY680 )
| SY680 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(441,plain,
! [SV23: $i,SV125: $o] :
( ( SV125 = $true )
| ( ( in @ SV23 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[373]) ).
thf(442,plain,
! [SV23: $i] :
( ( $true = $true )
| ( ( in @ SV23 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[373]) ).
thf(443,plain,
! [SV23: $i] :
( ( $false = $true )
| ( ( in @ SV23 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[373]) ).
thf(444,plain,
! [SV84: $i > $o,SV24: $i] :
( ( ( ~ ! [SY682: $i] :
( ~ ( in @ SY682 @ SV24 )
| ( SV84 @ SY682 ) ) )
= $false )
| ( ( ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ SY683 @ SV24 )
| ~ ~ ( SV84 @ SY683 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(445,plain,
! [SV25: $i,SV85: $i] :
( ( ~ ( ~ ( in @ SV85 @ ( powerset @ SV25 ) )
| ! [SY684: $i] :
( ~ ( in @ SY684 @ SV85 )
| ( in @ SY684 @ SV25 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(446,plain,
! [SV25: $i,SV85: $i] :
( ( ~ ( ~ ! [SY685: $i] :
( ~ ( in @ SY685 @ SV85 )
| ( in @ SY685 @ SV25 ) )
| ( in @ SV85 @ ( powerset @ SV25 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(447,plain,
! [SV26: $i] :
( ( ( SV26 = emptyset )
= $true )
| ( ( ~ ! [SY557: $i] :
~ ~ ( ~ ( in @ SY557 @ SV26 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(448,plain,
! [SV27: $i > $o,SV86: $i] :
( ( ( in @ SV86 @ emptyset )
= $false )
| ( ( SV27 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(449,plain,
! [SV28: $i,SV87: $i] :
( ( ( in @ SV87 @ SV28 )
= $false )
| ( ( in @ SV87 @ ( powerset @ ( setunion @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(450,plain,
! [SV88: $i > $o,SV29: $i] :
( ( ( ~ ! [SY686: $i] :
~ ~ ( ~ ( in @ SY686 @ SV29 )
| ~ ~ ( SV88 @ SY686 ) ) )
= $false )
| ( ( ~ ! [SY687: $i] :
( ~ ( in @ SY687 @ SV29 )
| ( SV88 @ SY687 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(451,plain,
! [SV30: $i > $o] :
( ( ( ! [SY563: $i] :
~ ~ ( ~ ( SV30 @ SY563 )
| ~ ! [SY564: $i] :
( ~ ( SV30 @ SY564 )
| ( SY563 = SY564 ) ) ) )
= $true )
| ( ( ~ ! [SY565: $i] :
~ ~ ( ~ ( SV30 @ SY565 )
| ~ ! [SY566: $i] :
( ~ ( SV30 @ SY566 )
| ( SY565 = SY566 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(452,plain,
! [SV89: $i,SV31: $i] :
( ( ( ! [SY688: $i] :
( ~ ( in @ SY688 @ SV31 )
| ( in @ SY688 @ SV89 ) ) )
= $false )
| ( ( ~ ! [SY689: $i] :
( ~ ( in @ SY689 @ SV89 )
| ( in @ SY689 @ SV31 ) )
| ( SV31 = SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(453,plain,
! [SV90: $i,SV32: $i] :
( ( ( SV32 = SV90 )
= $false )
| ( ( ! [SY690: $i,SY691: $i] :
( ( SY690 != SY691 )
| ( ( setadjoin @ SV32 @ SY690 )
= ( setadjoin @ SV90 @ SY691 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(454,plain,
! [SV91: $i,SV33: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) ) )
= $true )
| ( ( ! [SY742: $o] :
( ~ ( ( SV116 != SV33 )
| SY742 )
| ~ ( ~ ( in @ SV116 @ SV91 )
| SY742 )
| SY742 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(455,plain,
! [SV92: $i > $o,SV34: $i] :
( ( ( ! [SY694: $i] :
( ~ ( in @ SY694 @ SV34 )
| ~ ( SV92 @ SY694 ) ) )
= $false )
| ( ( ~ ~ ! [SY695: $i] :
~ ~ ( ~ ( in @ SY695 @ SV34 )
| ~ ( SV92 @ SY695 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(456,plain,
! [SV93: $i,SV35: $i] :
( ( ( SV35 = SV93 )
= $false )
| ( ( ( setunion @ SV35 )
= ( setunion @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(457,plain,
! [SV36: $i > $o] :
( ( ( ! [SY580: $i] :
~ ~ ( ~ ( SV36 @ SY580 )
| ~ ! [SY581: $i] :
( ~ ( SV36 @ SY581 )
| ( SY580 = SY581 ) ) ) )
= $true )
| ( ( ~ ! [SY582: $i] :
~ ~ ( ~ ( SV36 @ SY582 )
| ~ ! [SY583: $i] :
( ~ ( SV36 @ SY583 )
| ( SY582 = SY583 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(458,plain,
! [SV37: $o,SV94: $i] :
( ( ( in @ SV94 @ ( prop2set @ SV37 ) )
= $false )
| ( SV37 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(459,plain,
! [SV95: $i] :
( ( ( in @ SV95 @ ( prop2set @ $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(460,plain,
! [SV96: $i] :
( ( ( in @ SV96 @ ( prop2set @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(461,plain,
! [SV38: $i,SV117: $i,SV97: $i] :
( ( ( ~ ( in @ SV97 @ SV117 ) )
= $true )
| ( ( ~ ( in @ SV117 @ SV38 )
| ( in @ SV97 @ ( setunion @ SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[390]) ).
thf(462,plain,
! [SV98: $i,SV39: $i] :
( ( ( in @ SV39 @ ( setadjoin @ SV98 @ emptyset ) )
= $false )
| ( ( SV39 = SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(463,plain,
! [SV40: $i > $o] :
( ( ( ! [SY588: $i] :
~ ~ ( ~ ( SV40 @ SY588 )
| ~ ! [SY589: $i] :
( ~ ( SV40 @ SY589 )
| ( SY588 = SY589 ) ) ) )
= $true )
| ( ( ~ ! [SY590: $i] :
~ ! [SY591: $i] :
~ ( ~ ( ~ ( SV40 @ SY591 )
| ( SY591 = SY590 ) )
| ~ ( ( SY591 != SY590 )
| ( SV40 @ SY591 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[392]) ).
thf(464,plain,
! [SV41: $i > $o] :
( ( ( ! [SY592: $i] :
~ ~ ( ~ ( SV41 @ SY592 )
| ~ ! [SY593: $i] :
( ~ ( SV41 @ SY593 )
| ( SY592 = SY593 ) ) ) )
= $true )
| ( ( ~ ! [SY594: $i] :
~ ( SV41 @ SY594 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[393]) ).
thf(465,plain,
! [SV42: $i] :
( ( ( ~ ( in @ ( sK3_SY595 @ SV42 ) @ SV42 ) )
= $false )
| ( ( SV42 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[394]) ).
thf(466,plain,
! [SV43: $i > $o] :
( ( ( ! [SY596: $i] :
~ ( SV43 @ SY596 ) )
= $true )
| ( ( ~ ! [SY597: $i,SY598: $i] :
( ~ ( SV43 @ SY597 )
| ~ ( SV43 @ SY598 )
| ( SY597 = SY598 ) )
| ~ ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(467,plain,
! [SV99: $i > $o,SV44: $i,SV118: $i] :
( ( ( ~ ( in @ SV118
@ ( dsetconstr @ SV44
@ ^ [SY698: $i] : ( SV99 @ SY698 ) ) ) )
= $true )
| ( ( in @ SV118 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(468,plain,
! [SV46: $i,SV100: $i,SV119: $i] :
( ( ( ~ ( in @ SV119 @ SV100 ) )
= $true )
| ( ( in @ SV119 @ ( setadjoin @ SV46 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(469,plain,
! [SV48: $i] :
( ( ( ~ ( in @ ( sK4_SY606 @ SV48 ) @ SV48 ) )
= $false )
| ( ( SV48 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[404]) ).
thf(470,plain,
! [SV49: $i > $o] :
( ( ( ! [SY607: $i] :
~ ~ ( ~ ( SV49 @ SY607 )
| ~ ! [SY608: $i] :
( ~ ( SV49 @ SY608 )
| ( SY607 = SY608 ) ) ) )
= $true )
| ( ( ! [SY609: $i,SY610: $i] :
( ~ ( SV49 @ SY609 )
| ~ ( SV49 @ SY610 )
| ( SY609 = SY610 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[405]) ).
thf(471,plain,
! [SV50: $i > $o] :
( ( ( ! [SY611: $i] :
~ ! [SY612: $i] :
~ ( ~ ( ~ ( SV50 @ SY612 )
| ( SY612 = SY611 ) )
| ~ ( ( SY612 != SY611 )
| ( SV50 @ SY612 ) ) ) )
= $true )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(472,plain,
! [SV101: $i > $o,SV51: $i,SV120: $i] :
( ( ( ~ ( in @ SV120 @ SV51 ) )
= $true )
| ( ( ~ ( SV101 @ SV120 )
| ( in @ SV120
@ ( dsetconstr @ SV51
@ ^ [SY701: $i] : ( SV101 @ SY701 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(473,plain,
! [SV52: $i] :
( ( ( ~ ( in @ emptyset @ SV52 )
| ~ ! [SY618: $i] :
( ~ ~ ( ~ ( in @ SY618 @ omega )
| ~ ( in @ SY618 @ SV52 ) )
| ( in @ ( setadjoin @ SY618 @ SY618 ) @ SV52 ) ) )
= $true )
| ( ( ! [SY619: $i] :
( ~ ( in @ SY619 @ omega )
| ( in @ SY619 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[408]) ).
thf(474,plain,
( ( ~ ! [SY702: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY702 )
| ~ ! [SY703: $i] :
( ~ ( sK1_SX0 @ SY703 )
| ( SY702 = SY703 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[409]) ).
thf(475,plain,
( ( ! [SY748: $i] :
( ~ ( sK1_SX0 @ sK5_SY704 )
| ~ ( sK1_SX0 @ SY748 )
| ( sK5_SY704 = SY748 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[410]) ).
thf(476,plain,
! [SV102: $i,SV53: $i,SV121: $i] :
( ( ( ~ ( in @ SV121 @ ( setadjoin @ SV53 @ SV102 ) ) )
= $true )
| ( ( ( SV121 = SV53 )
| ( in @ SV121 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(477,plain,
! [SV103: $i > $o,SV55: $i,SV122: $i] :
( ( ( ~ ( in @ SV122 @ SV55 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV122
@ ( dsetconstr @ SV55
@ ^ [SY708: $i] : ( SV103 @ SY708 ) ) )
| ( SV103 @ SV122 ) )
| ~ ( ~ ( SV103 @ SV122 )
| ( in @ SV122
@ ( dsetconstr @ SV55
@ ^ [SY709: $i] : ( SV103 @ SY709 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(478,plain,
! [SV104: $i > $o,SV56: $i,SV123: $i] :
( ( ( ~ ( in @ SV123
@ ( dsetconstr @ SV56
@ ^ [SY711: $i] : ( SV104 @ SY711 ) ) ) )
= $true )
| ( ( SV104 @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(479,plain,
! [SV105: $i,SV57: $i] :
( ( ( SV57 != SV105 )
= $false )
| ( ( ~ ( in @ SV105 @ ( setadjoin @ SV57 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(480,plain,
! [SV106: $i,SV58: $i] :
( ( ( SV58 = SV106 )
= $false )
| ( ( ! [SY712: $i,SY713: $i] :
( ( SY712 != SY713 )
| ~ ( ~ ( ~ ( in @ SY712 @ SV58 )
| ( in @ SY713 @ SV106 ) )
| ~ ( ~ ( in @ SY713 @ SV106 )
| ( in @ SY712 @ SV58 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(481,plain,
! [SV59: $i] :
( ( ( ! [SY633: $i] :
~ ( in @ SY633 @ SV59 ) )
= $true )
| ( ( SV59 != emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[417]) ).
thf(482,plain,
! [SV61: $i] :
( ( ( ! [SY634: $i] :
~ ( in @ SY634 @ SV61 ) )
= $true )
| ( ( ~ ! [SY635: $i] :
~ ~ ( ~ ( in @ SY635 @ SV61 )
| ~ ~ ~ ! [SY636: $i] :
~ ~ ( ~ ( in @ SY636 @ SY635 )
| ~ ( in @ SY636 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(483,plain,
! [SV62: $i] :
( ( ( SV62 = emptyset )
= $true )
| ( ( ~ ! [SY637: $i] :
~ ( in @ SY637 @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[420]) ).
thf(484,plain,
! [SV63: $i > $i > $o,SV107: $i] :
( ( ( ! [SY714: $i] :
( ~ ( in @ SY714 @ SV107 )
| ~ ! [SY640: $i] :
~ ~ ( ~ ( SV63 @ SY714 @ SY640 )
| ~ ! [SY641: $i] :
( ~ ( SV63 @ SY714 @ SY641 )
| ( SY640 = SY641 ) ) ) ) )
= $false )
| ( ( ~ ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(485,plain,
! [SV64: $i,SV108: $i] :
( ( ~ ( ~ ( in @ SV108 @ ( setunion @ SV64 ) )
| ~ ! [SY721: $i] :
~ ~ ( ~ ( in @ SV108 @ SY721 )
| ~ ( in @ SY721 @ SV64 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(486,plain,
! [SV64: $i,SV108: $i] :
( ( ~ ( ~ ~ ! [SY722: $i] :
~ ~ ( ~ ( in @ SV108 @ SY722 )
| ~ ( in @ SY722 @ SV64 ) )
| ( in @ SV108 @ ( setunion @ SV64 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(487,plain,
! [SV109: $i,SV65: $i,SV124: $i] :
( ( ( ~ ( in @ SV124 @ ( setadjoin @ SV65 @ ( setadjoin @ SV109 @ emptyset ) ) ) )
= $true )
| ( ( ( SV124 = SV65 )
| ( SV124 = SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(488,plain,
! [SV110: $i,SV66: $i] :
( ( ( in @ SV66 @ ( setadjoin @ SV110 @ emptyset ) )
= $false )
| ( ( in @ SV110 @ ( setadjoin @ SV66 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(489,plain,
! [SV111: $i,SV67: $i] :
( ( ( SV67 = SV111 )
= $false )
| ( ( in @ SV67 @ ( setadjoin @ SV111 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(490,plain,
! [SV112: $i,SV68: $i] :
( ( ( SV68 = SV112 )
= $false )
| ( ( ( powerset @ SV68 )
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(491,plain,
! [SV72: $i,SV9: $i,SV126: $i] :
( ( ( ! [SY749: $i] :
( ( SV126 != SY749 )
| ~ ( in @ SV126 @ SV9 )
| ( in @ SY749 @ SV72 ) ) )
= $true )
| ( ( SV9 = SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(492,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ! [SY750: $i] :
( ( ( sK6_SY656 @ SV73 @ SV10 )
!= SY750 )
| ~ ( ~ ( ~ ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
| ( SV73 @ SY750 ) )
| ~ ( ~ ( SV73 @ SY750 )
| ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[428]) ).
thf(493,plain,
! [SV74: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK7_SY666 @ SV11 @ SV74 ) @ SV74 )
| ( in @ ( sK7_SY666 @ SV11 @ SV74 ) @ SV11 ) )
= $false )
| ( ( in @ SV74 @ ( powerset @ SV11 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[429]) ).
thf(494,plain,
! [SV12: $i,SV75: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 )
| ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 ) )
| ~ ( ~ ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 )
| ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 ) ) ) )
= $false )
| ( ( SV12 = SV75 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[430]) ).
thf(495,plain,
! [SV76: $i > $o,SV13: $i] :
( ( ( ~ ! [SY668: $i] :
~ ~ ( ~ ( in @ SY668 @ SV13 )
| ~ ( SV76 @ SY668 ) ) )
= $true )
| ( ( ! [SY669: $i] :
( ~ ( in @ SY669 @ SV13 )
| ~ ( SV76 @ SY669 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(496,plain,
! [SV77: $i > $o,SV14: $i] :
( ( ( ! [SY670: $i] :
~ ~ ( ~ ( in @ SY670 @ SV14 )
| ~ ( SV77 @ SY670 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV14
@ ^ [SY671: $i] : ( SV77 @ SY671 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(497,plain,
! [SV78: $i > $o,SV15: $i] :
( ( ( ! [SY672: $i] :
( ~ ( in @ SY672 @ SV15 )
| ( SV78 @ SY672 ) ) )
= $true )
| ( ( ~ ! [SY673: $i] :
~ ~ ( ~ ( in @ SY673 @ SV15 )
| ~ ~ ( SV78 @ SY673 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(498,plain,
! [SV79: $i > $o,SV16: $i] :
( ( ( ~ ! [SY674: $i] :
~ ~ ( ~ ( in @ SY674 @ SV16 )
| ~ ( SV79 @ SY674 ) ) )
= $true )
| ( ( ! [SY675: $i] :
( ~ ( in @ SY675 @ SV16 )
| ~ ( SV79 @ SY675 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(499,plain,
! [SV80: $i,SV17: $i,SV113: $i] :
( ( ~ ( ~ ( in @ SV113 @ ( setadjoin @ SV17 @ SV80 ) )
| ( SV113 = SV17 )
| ( in @ SV113 @ SV80 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(500,plain,
! [SV80: $i,SV17: $i,SV113: $i] :
( ( ~ ( ~ ( ( SV113 = SV17 )
| ( in @ SV113 @ SV80 ) )
| ( in @ SV113 @ ( setadjoin @ SV17 @ SV80 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(501,plain,
! [SV18: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY724: $i] :
( ~ ( in @ SY724 @ ( sK2_SY521 @ SV18 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY724 )
| ( in @ SY523 @ SV18 ) ) )
| ~ ! [SY726: $i,SY727: $i] :
( ~ ~ ( ~ ( in @ SY726 @ SV18 )
| ~ ( in @ SY727 @ SV18 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SY726 @ SY728 )
| ( in @ SY727 @ SY728 ) )
| ~ ( ~ ( in @ SY727 @ SY728 )
| ( in @ SY726 @ SY728 ) ) ) )
| ( SY726 = SY727 ) ) )
| ~ ! [SY729: $i,SY730: $i] :
( ~ ~ ( ~ ( in @ SY729 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY730 @ ( sK2_SY521 @ SV18 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY729 )
| ( in @ SX4 @ SY730 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY730 )
| ( in @ SX4 @ SY729 ) ) ) )
| ~ ! [SY733: $i] :
( ~ ~ ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SY733 )
| ( in @ SY532 @ SV18 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY733 ) )
| ~ ! [SY736: $i] :
~ ~ ! [SY737: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY736 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY737 @ SY733 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY736 )
| ~ ( in @ SX5 @ SY733 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY736 ) )
| ( in @ SY737 @ SY739 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(502,plain,
! [SV81: $i > $o,SV19: $i,SV114: $i] :
( ( ( in @ SV114 @ SV19 )
= $false )
| ( ( ~ ( SV81 @ SV114 )
| ( ( dsetconstr @ SV19
@ ^ [SY678: $i] : ( SV81 @ SY678 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(503,plain,
! [SV115: $i,SV20: $i,SV82: $i] :
( ( ( in @ SV82 @ ( powerset @ SV20 ) )
= $false )
| ( ( ~ ( in @ SV115 @ SV82 )
| ( in @ SV115 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(504,plain,
! [SV127: $i,SV21: $i > $o] :
( ( ( ~ ~ ( ~ ( SV21 @ SV127 )
| ~ ! [SY751: $i] :
( ~ ( SV21 @ SY751 )
| ( SV127 = SY751 ) ) ) )
= $true )
| ( ( SV21
@ ( descr
@ ^ [SY546: $i] : ( SV21 @ SY546 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(505,plain,
! [SV128: $o,SV22: $i,SV83: $i] :
( ( ( ~ ! [SY752: $i] :
( ~ ( in @ SV83 @ SY752 )
| ~ ( in @ SY752 @ SV22 )
| SV128 )
| SV128 )
= $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[440]) ).
thf(506,plain,
! [SV22: $i,SV83: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV83 @ SX0 )
| ~ ( in @ SX0 @ SV22 )
| $true )
| $true )
= $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[440]) ).
thf(507,plain,
! [SV22: $i,SV83: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV83 @ SX0 )
| ~ ( in @ SX0 @ SV22 )
| $false )
| $false )
= $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[440]) ).
thf(508,plain,
! [SV84: $i > $o,SV24: $i] :
( ( ( ! [SY682: $i] :
( ~ ( in @ SY682 @ SV24 )
| ( SV84 @ SY682 ) ) )
= $true )
| ( ( ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ SY683 @ SV24 )
| ~ ~ ( SV84 @ SY683 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[444]) ).
thf(509,plain,
! [SV25: $i,SV85: $i] :
( ( ~ ( in @ SV85 @ ( powerset @ SV25 ) )
| ! [SY684: $i] :
( ~ ( in @ SY684 @ SV85 )
| ( in @ SY684 @ SV25 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(510,plain,
! [SV25: $i,SV85: $i] :
( ( ~ ! [SY685: $i] :
( ~ ( in @ SY685 @ SV85 )
| ( in @ SY685 @ SV25 ) )
| ( in @ SV85 @ ( powerset @ SV25 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(511,plain,
! [SV26: $i] :
( ( ( ! [SY557: $i] :
~ ~ ( ~ ( in @ SY557 @ SV26 )
| ~ $true ) )
= $false )
| ( ( SV26 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(512,plain,
! [SV88: $i > $o,SV29: $i] :
( ( ( ! [SY686: $i] :
~ ~ ( ~ ( in @ SY686 @ SV29 )
| ~ ~ ( SV88 @ SY686 ) ) )
= $true )
| ( ( ~ ! [SY687: $i] :
( ~ ( in @ SY687 @ SV29 )
| ( SV88 @ SY687 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(513,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ~ ~ ( ~ ( SV30 @ SV129 )
| ~ ! [SY753: $i] :
( ~ ( SV30 @ SY753 )
| ( SV129 = SY753 ) ) ) )
= $true )
| ( ( ~ ! [SY565: $i] :
~ ~ ( ~ ( SV30 @ SY565 )
| ~ ! [SY566: $i] :
( ~ ( SV30 @ SY566 )
| ( SY565 = SY566 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(514,plain,
! [SV31: $i,SV89: $i] :
( ( ( ~ ( in @ ( sK9_SY688 @ SV89 @ SV31 ) @ SV31 )
| ( in @ ( sK9_SY688 @ SV89 @ SV31 ) @ SV89 ) )
= $false )
| ( ( ~ ! [SY689: $i] :
( ~ ( in @ SY689 @ SV89 )
| ( in @ SY689 @ SV31 ) )
| ( SV31 = SV89 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[452]) ).
thf(515,plain,
! [SV90: $i,SV32: $i,SV130: $i] :
( ( ( ! [SY754: $i] :
( ( SV130 != SY754 )
| ( ( setadjoin @ SV32 @ SV130 )
= ( setadjoin @ SV90 @ SY754 ) ) ) )
= $true )
| ( ( SV32 = SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(516,plain,
! [SV91: $i,SV33: $i,SV116: $i] :
( ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false )
| ( ( ! [SY742: $o] :
( ~ ( ( SV116 != SV33 )
| SY742 )
| ~ ( ~ ( in @ SV116 @ SV91 )
| SY742 )
| SY742 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(517,plain,
! [SV34: $i,SV92: $i > $o] :
( ( ( ~ ( in @ ( sK10_SY694 @ SV92 @ SV34 ) @ SV34 )
| ~ ( SV92 @ ( sK10_SY694 @ SV92 @ SV34 ) ) )
= $false )
| ( ( ~ ~ ! [SY695: $i] :
~ ~ ( ~ ( in @ SY695 @ SV34 )
| ~ ( SV92 @ SY695 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[455]) ).
thf(518,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ~ ~ ( ~ ( SV36 @ SV131 )
| ~ ! [SY755: $i] :
( ~ ( SV36 @ SY755 )
| ( SV131 = SY755 ) ) ) )
= $true )
| ( ( ~ ! [SY582: $i] :
~ ~ ( ~ ( SV36 @ SY582 )
| ~ ! [SY583: $i] :
( ~ ( SV36 @ SY583 )
| ( SY582 = SY583 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(519,plain,
! [SV38: $i,SV117: $i,SV97: $i] :
( ( ( in @ SV97 @ SV117 )
= $false )
| ( ( ~ ( in @ SV117 @ SV38 )
| ( in @ SV97 @ ( setunion @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(520,plain,
! [SV132: $i,SV40: $i > $o] :
( ( ( ~ ~ ( ~ ( SV40 @ SV132 )
| ~ ! [SY756: $i] :
( ~ ( SV40 @ SY756 )
| ( SV132 = SY756 ) ) ) )
= $true )
| ( ( ~ ! [SY590: $i] :
~ ! [SY591: $i] :
~ ( ~ ( ~ ( SV40 @ SY591 )
| ( SY591 = SY590 ) )
| ~ ( ( SY591 != SY590 )
| ( SV40 @ SY591 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(521,plain,
! [SV133: $i,SV41: $i > $o] :
( ( ( ~ ~ ( ~ ( SV41 @ SV133 )
| ~ ! [SY757: $i] :
( ~ ( SV41 @ SY757 )
| ( SV133 = SY757 ) ) ) )
= $true )
| ( ( ~ ! [SY594: $i] :
~ ( SV41 @ SY594 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(522,plain,
! [SV42: $i] :
( ( ( in @ ( sK3_SY595 @ SV42 ) @ SV42 )
= $true )
| ( ( SV42 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(523,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ SV134 ) )
= $true )
| ( ( ~ ! [SY597: $i,SY598: $i] :
( ~ ( SV43 @ SY597 )
| ~ ( SV43 @ SY598 )
| ( SY597 = SY598 ) )
| ~ ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(524,plain,
! [SV99: $i > $o,SV44: $i,SV118: $i] :
( ( ( in @ SV118
@ ( dsetconstr @ SV44
@ ^ [SY698: $i] : ( SV99 @ SY698 ) ) )
= $false )
| ( ( in @ SV118 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(525,plain,
! [SV46: $i,SV100: $i,SV119: $i] :
( ( ( in @ SV119 @ SV100 )
= $false )
| ( ( in @ SV119 @ ( setadjoin @ SV46 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(526,plain,
! [SV48: $i] :
( ( ( in @ ( sK4_SY606 @ SV48 ) @ SV48 )
= $true )
| ( ( SV48 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[469]) ).
thf(527,plain,
! [SV135: $i,SV49: $i > $o] :
( ( ( ~ ~ ( ~ ( SV49 @ SV135 )
| ~ ! [SY758: $i] :
( ~ ( SV49 @ SY758 )
| ( SV135 = SY758 ) ) ) )
= $true )
| ( ( ! [SY609: $i,SY610: $i] :
( ~ ( SV49 @ SY609 )
| ~ ( SV49 @ SY610 )
| ( SY609 = SY610 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(528,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ! [SY759: $i] :
~ ( ~ ( ~ ( SV50 @ SY759 )
| ( SY759 = SV136 ) )
| ~ ( ( SY759 != SV136 )
| ( SV50 @ SY759 ) ) ) )
= $true )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(529,plain,
! [SV101: $i > $o,SV51: $i,SV120: $i] :
( ( ( in @ SV120 @ SV51 )
= $false )
| ( ( ~ ( SV101 @ SV120 )
| ( in @ SV120
@ ( dsetconstr @ SV51
@ ^ [SY701: $i] : ( SV101 @ SY701 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(530,plain,
! [SV52: $i] :
( ( ( ~ ( in @ emptyset @ SV52 ) )
= $true )
| ( ( ~ ! [SY618: $i] :
( ~ ~ ( ~ ( in @ SY618 @ omega )
| ~ ( in @ SY618 @ SV52 ) )
| ( in @ ( setadjoin @ SY618 @ SY618 ) @ SV52 ) ) )
= $true )
| ( ( ! [SY619: $i] :
( ~ ( in @ SY619 @ omega )
| ( in @ SY619 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(531,plain,
( ( ! [SY702: $i] :
~ ~ ( ~ ( sK1_SX0 @ SY702 )
| ~ ! [SY703: $i] :
( ~ ( sK1_SX0 @ SY703 )
| ( SY702 = SY703 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(532,plain,
( ( ~ ( sK1_SX0 @ sK5_SY704 )
| ~ ( sK1_SX0 @ sK11_SY748 )
| ( sK5_SY704 = sK11_SY748 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[475]) ).
thf(533,plain,
! [SV102: $i,SV53: $i,SV121: $i] :
( ( ( in @ SV121 @ ( setadjoin @ SV53 @ SV102 ) )
= $false )
| ( ( ( SV121 = SV53 )
| ( in @ SV121 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(534,plain,
! [SV103: $i > $o,SV55: $i,SV122: $i] :
( ( ( in @ SV122 @ SV55 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV122
@ ( dsetconstr @ SV55
@ ^ [SY708: $i] : ( SV103 @ SY708 ) ) )
| ( SV103 @ SV122 ) )
| ~ ( ~ ( SV103 @ SV122 )
| ( in @ SV122
@ ( dsetconstr @ SV55
@ ^ [SY709: $i] : ( SV103 @ SY709 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(535,plain,
! [SV104: $i > $o,SV56: $i,SV123: $i] :
( ( ( in @ SV123
@ ( dsetconstr @ SV56
@ ^ [SY711: $i] : ( SV104 @ SY711 ) ) )
= $false )
| ( ( SV104 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(536,plain,
! [SV105: $i,SV57: $i] :
( ( ( SV57 = SV105 )
= $true )
| ( ( ~ ( in @ SV105 @ ( setadjoin @ SV57 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(537,plain,
! [SV106: $i,SV58: $i,SV137: $i] :
( ( ( ! [SY760: $i] :
( ( SV137 != SY760 )
| ~ ( ~ ( ~ ( in @ SV137 @ SV58 )
| ( in @ SY760 @ SV106 ) )
| ~ ( ~ ( in @ SY760 @ SV106 )
| ( in @ SV137 @ SV58 ) ) ) ) )
= $true )
| ( ( SV58 = SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(538,plain,
! [SV59: $i,SV138: $i] :
( ( ( ~ ( in @ SV138 @ SV59 ) )
= $true )
| ( ( SV59 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(539,plain,
! [SV61: $i,SV139: $i] :
( ( ( ~ ( in @ SV139 @ SV61 ) )
= $true )
| ( ( ~ ! [SY635: $i] :
~ ~ ( ~ ( in @ SY635 @ SV61 )
| ~ ~ ~ ! [SY636: $i] :
~ ~ ( ~ ( in @ SY636 @ SY635 )
| ~ ( in @ SY636 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(540,plain,
! [SV62: $i] :
( ( ( ! [SY637: $i] :
~ ( in @ SY637 @ SV62 ) )
= $false )
| ( ( SV62 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(541,plain,
! [SV107: $i,SV63: $i > $i > $o] :
( ( ( ~ ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
| ~ ! [SY761: $i] :
~ ~ ( ~ ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SY761 )
| ~ ! [SY762: $i] :
( ~ ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SY762 )
| ( SY761 = SY762 ) ) ) )
= $false )
| ( ( ~ ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[484]) ).
thf(542,plain,
! [SV64: $i,SV108: $i] :
( ( ~ ( in @ SV108 @ ( setunion @ SV64 ) )
| ~ ! [SY721: $i] :
~ ~ ( ~ ( in @ SV108 @ SY721 )
| ~ ( in @ SY721 @ SV64 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[485]) ).
thf(543,plain,
! [SV64: $i,SV108: $i] :
( ( ~ ~ ! [SY722: $i] :
~ ~ ( ~ ( in @ SV108 @ SY722 )
| ~ ( in @ SY722 @ SV64 ) )
| ( in @ SV108 @ ( setunion @ SV64 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(544,plain,
! [SV109: $i,SV65: $i,SV124: $i] :
( ( ( in @ SV124 @ ( setadjoin @ SV65 @ ( setadjoin @ SV109 @ emptyset ) ) )
= $false )
| ( ( ( SV124 = SV65 )
| ( SV124 = SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(545,plain,
! [SV72: $i,SV9: $i,SV140: $i,SV126: $i] :
( ( ( ( SV126 != SV140 )
| ~ ( in @ SV126 @ SV9 )
| ( in @ SV140 @ SV72 ) )
= $true )
| ( ( SV9 = SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(546,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ( ( sK6_SY656 @ SV73 @ SV10 )
!= ( sK13_SY750 @ SV10 @ SV73 ) )
| ~ ( ~ ( ~ ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
| ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) ) )
| ~ ( ~ ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
| ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[492]) ).
thf(547,plain,
! [SV74: $i,SV11: $i] :
( ( ( ~ ( in @ ( sK7_SY666 @ SV11 @ SV74 ) @ SV74 ) )
= $false )
| ( ( in @ SV74 @ ( powerset @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(548,plain,
! [SV74: $i,SV11: $i] :
( ( ( in @ ( sK7_SY666 @ SV11 @ SV74 ) @ SV11 )
= $false )
| ( ( in @ SV74 @ ( powerset @ SV11 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[493]) ).
thf(549,plain,
! [SV12: $i,SV75: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 )
| ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 ) )
| ~ ( ~ ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 )
| ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 ) ) )
= $true )
| ( ( SV12 = SV75 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(550,plain,
! [SV76: $i > $o,SV13: $i] :
( ( ( ! [SY668: $i] :
~ ~ ( ~ ( in @ SY668 @ SV13 )
| ~ ( SV76 @ SY668 ) ) )
= $false )
| ( ( ! [SY669: $i] :
( ~ ( in @ SY669 @ SV13 )
| ~ ( SV76 @ SY669 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(551,plain,
! [SV77: $i > $o,SV14: $i,SV141: $i] :
( ( ( ~ ~ ( ~ ( in @ SV141 @ SV14 )
| ~ ( SV77 @ SV141 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV14
@ ^ [SY671: $i] : ( SV77 @ SY671 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(552,plain,
! [SV78: $i > $o,SV15: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ SV15 )
| ( SV78 @ SV142 ) )
= $true )
| ( ( ~ ! [SY673: $i] :
~ ~ ( ~ ( in @ SY673 @ SV15 )
| ~ ~ ( SV78 @ SY673 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(553,plain,
! [SV79: $i > $o,SV16: $i] :
( ( ( ! [SY674: $i] :
~ ~ ( ~ ( in @ SY674 @ SV16 )
| ~ ( SV79 @ SY674 ) ) )
= $false )
| ( ( ! [SY675: $i] :
( ~ ( in @ SY675 @ SV16 )
| ~ ( SV79 @ SY675 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(554,plain,
! [SV80: $i,SV17: $i,SV113: $i] :
( ( ~ ( in @ SV113 @ ( setadjoin @ SV17 @ SV80 ) )
| ( SV113 = SV17 )
| ( in @ SV113 @ SV80 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(555,plain,
! [SV80: $i,SV17: $i,SV113: $i] :
( ( ~ ( ( SV113 = SV17 )
| ( in @ SV113 @ SV80 ) )
| ( in @ SV113 @ ( setadjoin @ SV17 @ SV80 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(556,plain,
! [SV18: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY724: $i] :
( ~ ( in @ SY724 @ ( sK2_SY521 @ SV18 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY724 )
| ( in @ SY523 @ SV18 ) ) )
| ~ ! [SY726: $i,SY727: $i] :
( ~ ~ ( ~ ( in @ SY726 @ SV18 )
| ~ ( in @ SY727 @ SV18 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SY726 @ SY728 )
| ( in @ SY727 @ SY728 ) )
| ~ ( ~ ( in @ SY727 @ SY728 )
| ( in @ SY726 @ SY728 ) ) ) )
| ( SY726 = SY727 ) ) )
| ~ ! [SY729: $i,SY730: $i] :
( ~ ~ ( ~ ( in @ SY729 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY730 @ ( sK2_SY521 @ SV18 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY729 )
| ( in @ SX4 @ SY730 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY730 )
| ( in @ SX4 @ SY729 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(557,plain,
! [SV18: $i] :
( ( ~ ! [SY733: $i] :
( ~ ~ ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SY733 )
| ( in @ SY532 @ SV18 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY733 ) )
| ~ ! [SY736: $i] :
~ ~ ! [SY737: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY736 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY737 @ SY733 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY736 )
| ~ ( in @ SX5 @ SY733 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY736 ) )
| ( in @ SY737 @ SY739 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(558,plain,
! [SV19: $i,SV114: $i,SV81: $i > $o] :
( ( ( ~ ( SV81 @ SV114 ) )
= $true )
| ( ( ( dsetconstr @ SV19
@ ^ [SY678: $i] : ( SV81 @ SY678 ) )
!= emptyset )
= $true )
| ( ( in @ SV114 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(559,plain,
! [SV20: $i,SV82: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ SV82 ) )
= $true )
| ( ( in @ SV115 @ SV20 )
= $true )
| ( ( in @ SV82 @ ( powerset @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(560,plain,
! [SV127: $i,SV21: $i > $o] :
( ( ( ~ ( ~ ( SV21 @ SV127 )
| ~ ! [SY751: $i] :
( ~ ( SV21 @ SY751 )
| ( SV127 = SY751 ) ) ) )
= $false )
| ( ( SV21
@ ( descr
@ ^ [SY546: $i] : ( SV21 @ SY546 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(561,plain,
! [SV128: $o,SV22: $i,SV83: $i] :
( ( ( ~ ! [SY752: $i] :
( ~ ( in @ SV83 @ SY752 )
| ~ ( in @ SY752 @ SV22 )
| SV128 ) )
= $true )
| ( SV128 = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(562,plain,
! [SV22: $i,SV83: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV83 @ SX0 )
| ~ ( in @ SX0 @ SV22 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(563,plain,
! [SV22: $i,SV83: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV83 @ SX0 )
| ~ ( in @ SX0 @ SV22 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[507]) ).
thf(564,plain,
! [SV84: $i > $o,SV24: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ SV24 )
| ( SV84 @ SV143 ) )
= $true )
| ( ( ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ SY683 @ SV24 )
| ~ ~ ( SV84 @ SY683 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(565,plain,
! [SV25: $i,SV85: $i] :
( ( ( ~ ( in @ SV85 @ ( powerset @ SV25 ) ) )
= $true )
| ( ( ! [SY684: $i] :
( ~ ( in @ SY684 @ SV85 )
| ( in @ SY684 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(566,plain,
! [SV25: $i,SV85: $i] :
( ( ( ~ ! [SY685: $i] :
( ~ ( in @ SY685 @ SV85 )
| ( in @ SY685 @ SV25 ) ) )
= $true )
| ( ( in @ SV85 @ ( powerset @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(567,plain,
! [SV26: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_SY557 @ SV26 ) @ SV26 )
| ~ $true ) )
= $false )
| ( ( SV26 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[511]) ).
thf(568,plain,
! [SV88: $i > $o,SV29: $i,SV144: $i] :
( ( ( ~ ~ ( ~ ( in @ SV144 @ SV29 )
| ~ ~ ( SV88 @ SV144 ) ) )
= $true )
| ( ( ~ ! [SY687: $i] :
( ~ ( in @ SY687 @ SV29 )
| ( SV88 @ SY687 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(569,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ~ ( ~ ( SV30 @ SV129 )
| ~ ! [SY753: $i] :
( ~ ( SV30 @ SY753 )
| ( SV129 = SY753 ) ) ) )
= $false )
| ( ( ~ ! [SY565: $i] :
~ ~ ( ~ ( SV30 @ SY565 )
| ~ ! [SY566: $i] :
( ~ ( SV30 @ SY566 )
| ( SY565 = SY566 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(570,plain,
! [SV31: $i,SV89: $i] :
( ( ( ~ ( in @ ( sK9_SY688 @ SV89 @ SV31 ) @ SV31 ) )
= $false )
| ( ( ~ ! [SY689: $i] :
( ~ ( in @ SY689 @ SV89 )
| ( in @ SY689 @ SV31 ) )
| ( SV31 = SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(571,plain,
! [SV31: $i,SV89: $i] :
( ( ( in @ ( sK9_SY688 @ SV89 @ SV31 ) @ SV89 )
= $false )
| ( ( ~ ! [SY689: $i] :
( ~ ( in @ SY689 @ SV89 )
| ( in @ SY689 @ SV31 ) )
| ( SV31 = SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(572,plain,
! [SV90: $i,SV32: $i,SV145: $i,SV130: $i] :
( ( ( ( SV130 != SV145 )
| ( ( setadjoin @ SV32 @ SV130 )
= ( setadjoin @ SV90 @ SV145 ) ) )
= $true )
| ( ( SV32 = SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(573,plain,
! [SV91: $i,SV146: $o,SV33: $i,SV116: $i] :
( ( ( ~ ( ( SV116 != SV33 )
| SV146 )
| ~ ( ~ ( in @ SV116 @ SV91 )
| SV146 )
| SV146 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[516]) ).
thf(574,plain,
! [SV91: $i,SV33: $i,SV116: $i] :
( ( ( ~ ( ( SV116 != SV33 )
| $true )
| ~ ( ~ ( in @ SV116 @ SV91 )
| $true )
| $true )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[516]) ).
thf(575,plain,
! [SV91: $i,SV33: $i,SV116: $i] :
( ( ( ~ ( ( SV116 != SV33 )
| $false )
| ~ ( ~ ( in @ SV116 @ SV91 )
| $false )
| $false )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[516]) ).
thf(576,plain,
! [SV34: $i,SV92: $i > $o] :
( ( ( ~ ( in @ ( sK10_SY694 @ SV92 @ SV34 ) @ SV34 ) )
= $false )
| ( ( ~ ~ ! [SY695: $i] :
~ ~ ( ~ ( in @ SY695 @ SV34 )
| ~ ( SV92 @ SY695 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[517]) ).
thf(577,plain,
! [SV34: $i,SV92: $i > $o] :
( ( ( ~ ( SV92 @ ( sK10_SY694 @ SV92 @ SV34 ) ) )
= $false )
| ( ( ~ ~ ! [SY695: $i] :
~ ~ ( ~ ( in @ SY695 @ SV34 )
| ~ ( SV92 @ SY695 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[517]) ).
thf(578,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ~ ( ~ ( SV36 @ SV131 )
| ~ ! [SY755: $i] :
( ~ ( SV36 @ SY755 )
| ( SV131 = SY755 ) ) ) )
= $false )
| ( ( ~ ! [SY582: $i] :
~ ~ ( ~ ( SV36 @ SY582 )
| ~ ! [SY583: $i] :
( ~ ( SV36 @ SY583 )
| ( SY582 = SY583 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(579,plain,
! [SV97: $i,SV38: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ SV38 ) )
= $true )
| ( ( in @ SV97 @ ( setunion @ SV38 ) )
= $true )
| ( ( in @ SV97 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(580,plain,
! [SV132: $i,SV40: $i > $o] :
( ( ( ~ ( ~ ( SV40 @ SV132 )
| ~ ! [SY756: $i] :
( ~ ( SV40 @ SY756 )
| ( SV132 = SY756 ) ) ) )
= $false )
| ( ( ~ ! [SY590: $i] :
~ ! [SY591: $i] :
~ ( ~ ( ~ ( SV40 @ SY591 )
| ( SY591 = SY590 ) )
| ~ ( ( SY591 != SY590 )
| ( SV40 @ SY591 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(581,plain,
! [SV133: $i,SV41: $i > $o] :
( ( ( ~ ( ~ ( SV41 @ SV133 )
| ~ ! [SY757: $i] :
( ~ ( SV41 @ SY757 )
| ( SV133 = SY757 ) ) ) )
= $false )
| ( ( ~ ! [SY594: $i] :
~ ( SV41 @ SY594 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(582,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( SV43 @ SV134 )
= $false )
| ( ( ~ ! [SY597: $i,SY598: $i] :
( ~ ( SV43 @ SY597 )
| ~ ( SV43 @ SY598 )
| ( SY597 = SY598 ) )
| ~ ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(583,plain,
! [SV135: $i,SV49: $i > $o] :
( ( ( ~ ( ~ ( SV49 @ SV135 )
| ~ ! [SY758: $i] :
( ~ ( SV49 @ SY758 )
| ( SV135 = SY758 ) ) ) )
= $false )
| ( ( ! [SY609: $i,SY610: $i] :
( ~ ( SV49 @ SY609 )
| ~ ( SV49 @ SY610 )
| ( SY609 = SY610 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(584,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ! [SY759: $i] :
~ ( ~ ( ~ ( SV50 @ SY759 )
| ( SY759 = SV136 ) )
| ~ ( ( SY759 != SV136 )
| ( SV50 @ SY759 ) ) ) )
= $false )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(585,plain,
! [SV51: $i,SV120: $i,SV101: $i > $o] :
( ( ( ~ ( SV101 @ SV120 ) )
= $true )
| ( ( in @ SV120
@ ( dsetconstr @ SV51
@ ^ [SY701: $i] : ( SV101 @ SY701 ) ) )
= $true )
| ( ( in @ SV120 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(586,plain,
! [SV52: $i] :
( ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ~ ! [SY618: $i] :
( ~ ~ ( ~ ( in @ SY618 @ omega )
| ~ ( in @ SY618 @ SV52 ) )
| ( in @ ( setadjoin @ SY618 @ SY618 ) @ SV52 ) ) )
= $true )
| ( ( ! [SY619: $i] :
( ~ ( in @ SY619 @ omega )
| ( in @ SY619 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(587,plain,
( ( ~ ~ ( ~ ( sK1_SX0 @ sK15_SY702 )
| ~ ! [SY763: $i] :
( ~ ( sK1_SX0 @ SY763 )
| ( sK15_SY702 = SY763 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[531]) ).
thf(588,plain,
( ( ~ ( sK1_SX0 @ sK5_SY704 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[532]) ).
thf(589,plain,
( ( ~ ( sK1_SX0 @ sK11_SY748 )
| ( sK5_SY704 = sK11_SY748 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[532]) ).
thf(590,plain,
! [SV102: $i,SV53: $i,SV121: $i] :
( ( ( SV121 = SV53 )
= $true )
| ( ( in @ SV121 @ SV102 )
= $true )
| ( ( in @ SV121 @ ( setadjoin @ SV53 @ SV102 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[533]) ).
thf(591,plain,
! [SV103: $i > $o,SV55: $i,SV122: $i] :
( ( ( ~ ( ~ ( in @ SV122
@ ( dsetconstr @ SV55
@ ^ [SY708: $i] : ( SV103 @ SY708 ) ) )
| ( SV103 @ SV122 ) )
| ~ ( ~ ( SV103 @ SV122 )
| ( in @ SV122
@ ( dsetconstr @ SV55
@ ^ [SY709: $i] : ( SV103 @ SY709 ) ) ) ) )
= $false )
| ( ( in @ SV122 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(592,plain,
! [SV57: $i,SV105: $i] :
( ( ( in @ SV105 @ ( setadjoin @ SV57 @ emptyset ) )
= $false )
| ( ( SV57 = SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(593,plain,
! [SV106: $i,SV58: $i,SV147: $i,SV137: $i] :
( ( ( ( SV137 != SV147 )
| ~ ( ~ ( ~ ( in @ SV137 @ SV58 )
| ( in @ SV147 @ SV106 ) )
| ~ ( ~ ( in @ SV147 @ SV106 )
| ( in @ SV137 @ SV58 ) ) ) )
= $true )
| ( ( SV58 = SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(594,plain,
! [SV59: $i,SV138: $i] :
( ( ( in @ SV138 @ SV59 )
= $false )
| ( ( SV59 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(595,plain,
! [SV61: $i,SV139: $i] :
( ( ( in @ SV139 @ SV61 )
= $false )
| ( ( ~ ! [SY635: $i] :
~ ~ ( ~ ( in @ SY635 @ SV61 )
| ~ ~ ~ ! [SY636: $i] :
~ ~ ( ~ ( in @ SY636 @ SY635 )
| ~ ( in @ SY636 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(596,plain,
! [SV62: $i] :
( ( ( ~ ( in @ ( sK16_SY637 @ SV62 ) @ SV62 ) )
= $false )
| ( ( SV62 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[540]) ).
thf(597,plain,
! [SV107: $i,SV63: $i > $i > $o] :
( ( ( ~ ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 ) )
= $false )
| ( ( ~ ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[541]) ).
thf(598,plain,
! [SV107: $i,SV63: $i > $i > $o] :
( ( ( ~ ! [SY761: $i] :
~ ~ ( ~ ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SY761 )
| ~ ! [SY762: $i] :
( ~ ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SY762 )
| ( SY761 = SY762 ) ) ) )
= $false )
| ( ( ~ ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[541]) ).
thf(599,plain,
! [SV64: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ ( setunion @ SV64 ) ) )
= $true )
| ( ( ~ ! [SY721: $i] :
~ ~ ( ~ ( in @ SV108 @ SY721 )
| ~ ( in @ SY721 @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(600,plain,
! [SV64: $i,SV108: $i] :
( ( ( ~ ~ ! [SY722: $i] :
~ ~ ( ~ ( in @ SV108 @ SY722 )
| ~ ( in @ SY722 @ SV64 ) ) )
= $true )
| ( ( in @ SV108 @ ( setunion @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(601,plain,
! [SV109: $i,SV65: $i,SV124: $i] :
( ( ( SV124 = SV65 )
= $true )
| ( ( SV124 = SV109 )
= $true )
| ( ( in @ SV124 @ ( setadjoin @ SV65 @ ( setadjoin @ SV109 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(602,plain,
! [SV72: $i,SV9: $i,SV140: $i,SV126: $i] :
( ( ( SV126 != SV140 )
= $true )
| ( ( ~ ( in @ SV126 @ SV9 )
| ( in @ SV140 @ SV72 ) )
= $true )
| ( ( SV9 = SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(603,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ( sK6_SY656 @ SV73 @ SV10 )
!= ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(604,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
| ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) ) )
| ~ ( ~ ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
| ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(605,plain,
! [SV74: $i,SV11: $i] :
( ( ( in @ ( sK7_SY666 @ SV11 @ SV74 ) @ SV74 )
= $true )
| ( ( in @ SV74 @ ( powerset @ SV11 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(606,plain,
! [SV12: $i,SV75: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 )
| ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 )
| ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 ) ) )
= $true )
| ( ( SV12 = SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(607,plain,
! [SV13: $i,SV76: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_SY668 @ SV76 @ SV13 ) @ SV13 )
| ~ ( SV76 @ ( sK17_SY668 @ SV76 @ SV13 ) ) ) )
= $false )
| ( ( ! [SY669: $i] :
( ~ ( in @ SY669 @ SV13 )
| ~ ( SV76 @ SY669 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[550]) ).
thf(608,plain,
! [SV77: $i > $o,SV14: $i,SV141: $i] :
( ( ( ~ ( ~ ( in @ SV141 @ SV14 )
| ~ ( SV77 @ SV141 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV14
@ ^ [SY671: $i] : ( SV77 @ SY671 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(609,plain,
! [SV78: $i > $o,SV15: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ SV15 ) )
= $true )
| ( ( SV78 @ SV142 )
= $true )
| ( ( ~ ! [SY673: $i] :
~ ~ ( ~ ( in @ SY673 @ SV15 )
| ~ ~ ( SV78 @ SY673 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(610,plain,
! [SV16: $i,SV79: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY674 @ SV79 @ SV16 ) @ SV16 )
| ~ ( SV79 @ ( sK18_SY674 @ SV79 @ SV16 ) ) ) )
= $false )
| ( ( ! [SY675: $i] :
( ~ ( in @ SY675 @ SV16 )
| ~ ( SV79 @ SY675 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[553]) ).
thf(611,plain,
! [SV80: $i,SV17: $i,SV113: $i] :
( ( ( ~ ( in @ SV113 @ ( setadjoin @ SV17 @ SV80 ) ) )
= $true )
| ( ( ( SV113 = SV17 )
| ( in @ SV113 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(612,plain,
! [SV80: $i,SV17: $i,SV113: $i] :
( ( ( ~ ( ( SV113 = SV17 )
| ( in @ SV113 @ SV80 ) ) )
= $true )
| ( ( in @ SV113 @ ( setadjoin @ SV17 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(613,plain,
! [SV18: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY724: $i] :
( ~ ( in @ SY724 @ ( sK2_SY521 @ SV18 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY724 )
| ( in @ SY523 @ SV18 ) ) )
| ~ ! [SY726: $i,SY727: $i] :
( ~ ~ ( ~ ( in @ SY726 @ SV18 )
| ~ ( in @ SY727 @ SV18 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SY726 @ SY728 )
| ( in @ SY727 @ SY728 ) )
| ~ ( ~ ( in @ SY727 @ SY728 )
| ( in @ SY726 @ SY728 ) ) ) )
| ( SY726 = SY727 ) ) )
| ~ ! [SY729: $i,SY730: $i] :
( ~ ~ ( ~ ( in @ SY729 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY730 @ ( sK2_SY521 @ SV18 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY729 )
| ( in @ SX4 @ SY730 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY730 )
| ( in @ SX4 @ SY729 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[556]) ).
thf(614,plain,
! [SV18: $i] :
( ( ! [SY733: $i] :
( ~ ~ ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SY733 )
| ( in @ SY532 @ SV18 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY733 ) )
| ~ ! [SY736: $i] :
~ ~ ! [SY737: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY736 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY737 @ SY733 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY736 )
| ~ ( in @ SX5 @ SY733 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY736 ) )
| ( in @ SY737 @ SY739 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(615,plain,
! [SV19: $i,SV114: $i,SV81: $i > $o] :
( ( ( SV81 @ SV114 )
= $false )
| ( ( ( dsetconstr @ SV19
@ ^ [SY678: $i] : ( SV81 @ SY678 ) )
!= emptyset )
= $true )
| ( ( in @ SV114 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(616,plain,
! [SV20: $i,SV82: $i,SV115: $i] :
( ( ( in @ SV115 @ SV82 )
= $false )
| ( ( in @ SV115 @ SV20 )
= $true )
| ( ( in @ SV82 @ ( powerset @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(617,plain,
! [SV127: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ SV127 )
| ~ ! [SY751: $i] :
( ~ ( SV21 @ SY751 )
| ( SV127 = SY751 ) ) )
= $true )
| ( ( SV21
@ ( descr
@ ^ [SY546: $i] : ( SV21 @ SY546 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(618,plain,
! [SV128: $o,SV22: $i,SV83: $i] :
( ( ( ! [SY752: $i] :
( ~ ( in @ SV83 @ SY752 )
| ~ ( in @ SY752 @ SV22 )
| SV128 ) )
= $false )
| ( SV128 = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(619,plain,
! [SV22: $i,SV83: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV83 @ SX0 )
| ~ ( in @ SX0 @ SV22 )
| $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(620,plain,
! [SV22: $i,SV83: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV83 @ SX0 )
| ~ ( in @ SX0 @ SV22 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(621,plain,
! [SV84: $i > $o,SV24: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ SV24 ) )
= $true )
| ( ( SV84 @ SV143 )
= $true )
| ( ( ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ SY683 @ SV24 )
| ~ ~ ( SV84 @ SY683 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(622,plain,
! [SV25: $i,SV85: $i] :
( ( ( in @ SV85 @ ( powerset @ SV25 ) )
= $false )
| ( ( ! [SY684: $i] :
( ~ ( in @ SY684 @ SV85 )
| ( in @ SY684 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(623,plain,
! [SV25: $i,SV85: $i] :
( ( ( ! [SY685: $i] :
( ~ ( in @ SY685 @ SV85 )
| ( in @ SY685 @ SV25 ) ) )
= $false )
| ( ( in @ SV85 @ ( powerset @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(624,plain,
! [SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_SY557 @ SV26 ) @ SV26 )
| ~ $true ) )
= $true )
| ( ( SV26 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(625,plain,
! [SV88: $i > $o,SV29: $i,SV144: $i] :
( ( ( ~ ( ~ ( in @ SV144 @ SV29 )
| ~ ~ ( SV88 @ SV144 ) ) )
= $false )
| ( ( ~ ! [SY687: $i] :
( ~ ( in @ SY687 @ SV29 )
| ( SV88 @ SY687 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(626,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ~ ( SV30 @ SV129 )
| ~ ! [SY753: $i] :
( ~ ( SV30 @ SY753 )
| ( SV129 = SY753 ) ) )
= $true )
| ( ( ~ ! [SY565: $i] :
~ ~ ( ~ ( SV30 @ SY565 )
| ~ ! [SY566: $i] :
( ~ ( SV30 @ SY566 )
| ( SY565 = SY566 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[569]) ).
thf(627,plain,
! [SV31: $i,SV89: $i] :
( ( ( in @ ( sK9_SY688 @ SV89 @ SV31 ) @ SV31 )
= $true )
| ( ( ~ ! [SY689: $i] :
( ~ ( in @ SY689 @ SV89 )
| ( in @ SY689 @ SV31 ) )
| ( SV31 = SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[570]) ).
thf(628,plain,
! [SV31: $i,SV89: $i] :
( ( ( ~ ! [SY689: $i] :
( ~ ( in @ SY689 @ SV89 )
| ( in @ SY689 @ SV31 ) ) )
= $true )
| ( ( SV31 = SV89 )
= $true )
| ( ( in @ ( sK9_SY688 @ SV89 @ SV31 ) @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(629,plain,
! [SV90: $i,SV32: $i,SV145: $i,SV130: $i] :
( ( ( SV130 != SV145 )
= $true )
| ( ( ( setadjoin @ SV32 @ SV130 )
= ( setadjoin @ SV90 @ SV145 ) )
= $true )
| ( ( SV32 = SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(630,plain,
! [SV91: $i,SV146: $o,SV33: $i,SV116: $i] :
( ( ( ~ ( ( SV116 != SV33 )
| SV146 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| SV146 )
| SV146 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(631,plain,
! [SV91: $i,SV33: $i,SV116: $i] :
( ( ( ~ ( ( SV116 != SV33 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| $true )
| $true )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(632,plain,
! [SV91: $i,SV33: $i,SV116: $i] :
( ( ( ~ ( ( SV116 != SV33 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| $false )
| $false )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[575]) ).
thf(633,plain,
! [SV34: $i,SV92: $i > $o] :
( ( ( in @ ( sK10_SY694 @ SV92 @ SV34 ) @ SV34 )
= $true )
| ( ( ~ ~ ! [SY695: $i] :
~ ~ ( ~ ( in @ SY695 @ SV34 )
| ~ ( SV92 @ SY695 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[576]) ).
thf(634,plain,
! [SV34: $i,SV92: $i > $o] :
( ( ( SV92 @ ( sK10_SY694 @ SV92 @ SV34 ) )
= $true )
| ( ( ~ ~ ! [SY695: $i] :
~ ~ ( ~ ( in @ SY695 @ SV34 )
| ~ ( SV92 @ SY695 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[577]) ).
thf(635,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ SV131 )
| ~ ! [SY755: $i] :
( ~ ( SV36 @ SY755 )
| ( SV131 = SY755 ) ) )
= $true )
| ( ( ~ ! [SY582: $i] :
~ ~ ( ~ ( SV36 @ SY582 )
| ~ ! [SY583: $i] :
( ~ ( SV36 @ SY583 )
| ( SY582 = SY583 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(636,plain,
! [SV97: $i,SV38: $i,SV117: $i] :
( ( ( in @ SV117 @ SV38 )
= $false )
| ( ( in @ SV97 @ ( setunion @ SV38 ) )
= $true )
| ( ( in @ SV97 @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(637,plain,
! [SV132: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ SV132 )
| ~ ! [SY756: $i] :
( ~ ( SV40 @ SY756 )
| ( SV132 = SY756 ) ) )
= $true )
| ( ( ~ ! [SY590: $i] :
~ ! [SY591: $i] :
~ ( ~ ( ~ ( SV40 @ SY591 )
| ( SY591 = SY590 ) )
| ~ ( ( SY591 != SY590 )
| ( SV40 @ SY591 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(638,plain,
! [SV133: $i,SV41: $i > $o] :
( ( ( ~ ( SV41 @ SV133 )
| ~ ! [SY757: $i] :
( ~ ( SV41 @ SY757 )
| ( SV133 = SY757 ) ) )
= $true )
| ( ( ~ ! [SY594: $i] :
~ ( SV41 @ SY594 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(639,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ! [SY597: $i,SY598: $i] :
( ~ ( SV43 @ SY597 )
| ~ ( SV43 @ SY598 )
| ( SY597 = SY598 ) ) )
= $true )
| ( ( ~ ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[582]) ).
thf(640,plain,
! [SV135: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV135 )
| ~ ! [SY758: $i] :
( ~ ( SV49 @ SY758 )
| ( SV135 = SY758 ) ) )
= $true )
| ( ( ! [SY609: $i,SY610: $i] :
( ~ ( SV49 @ SY609 )
| ~ ( SV49 @ SY610 )
| ( SY609 = SY610 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[583]) ).
thf(641,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
| ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 ) )
| ~ ( ( ( sK19_SY759 @ SV136 @ SV50 )
!= SV136 )
| ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) ) ) ) )
= $false )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[584]) ).
thf(642,plain,
! [SV51: $i,SV120: $i,SV101: $i > $o] :
( ( ( SV101 @ SV120 )
= $false )
| ( ( in @ SV120
@ ( dsetconstr @ SV51
@ ^ [SY701: $i] : ( SV101 @ SY701 ) ) )
= $true )
| ( ( in @ SV120 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(643,plain,
! [SV52: $i] :
( ( ( ! [SY618: $i] :
( ~ ~ ( ~ ( in @ SY618 @ omega )
| ~ ( in @ SY618 @ SV52 ) )
| ( in @ ( setadjoin @ SY618 @ SY618 ) @ SV52 ) ) )
= $false )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY619: $i] :
( ~ ( in @ SY619 @ omega )
| ( in @ SY619 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(644,plain,
( ( ~ ( ~ ( sK1_SX0 @ sK15_SY702 )
| ~ ! [SY763: $i] :
( ~ ( sK1_SX0 @ SY763 )
| ( sK15_SY702 = SY763 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(645,plain,
( ( sK1_SX0 @ sK5_SY704 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(646,plain,
( ( ~ ( sK1_SX0 @ sK11_SY748 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[589]) ).
thf(647,plain,
( ( sK5_SY704 = sK11_SY748 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[589]) ).
thf(648,plain,
! [SV103: $i > $o,SV55: $i,SV122: $i] :
( ( ( ~ ( ~ ( in @ SV122
@ ( dsetconstr @ SV55
@ ^ [SY708: $i] : ( SV103 @ SY708 ) ) )
| ( SV103 @ SV122 ) ) )
= $false )
| ( ( in @ SV122 @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[591]) ).
thf(649,plain,
! [SV55: $i,SV122: $i,SV103: $i > $o] :
( ( ( ~ ( ~ ( SV103 @ SV122 )
| ( in @ SV122
@ ( dsetconstr @ SV55
@ ^ [SY709: $i] : ( SV103 @ SY709 ) ) ) ) )
= $false )
| ( ( in @ SV122 @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[591]) ).
thf(650,plain,
! [SV106: $i,SV58: $i,SV147: $i,SV137: $i] :
( ( ( SV137 != SV147 )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV137 @ SV58 )
| ( in @ SV147 @ SV106 ) )
| ~ ( ~ ( in @ SV147 @ SV106 )
| ( in @ SV137 @ SV58 ) ) ) )
= $true )
| ( ( SV58 = SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(651,plain,
! [SV138: $i,SV59: $i] :
( ( ( SV59 = emptyset )
= $false )
| ( ( in @ SV138 @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(652,plain,
! [SV139: $i,SV61: $i] :
( ( ( ! [SY635: $i] :
~ ~ ( ~ ( in @ SY635 @ SV61 )
| ~ ~ ~ ! [SY636: $i] :
~ ~ ( ~ ( in @ SY636 @ SY635 )
| ~ ( in @ SY636 @ SV61 ) ) ) )
= $false )
| ( ( in @ SV139 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(653,plain,
! [SV62: $i] :
( ( ( in @ ( sK16_SY637 @ SV62 ) @ SV62 )
= $true )
| ( ( SV62 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[596]) ).
thf(654,plain,
! [SV107: $i,SV63: $i > $i > $o] :
( ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true )
| ( ( ~ ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[597]) ).
thf(655,plain,
! [SV107: $i,SV63: $i > $i > $o] :
( ( ( ! [SY761: $i] :
~ ~ ( ~ ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SY761 )
| ~ ! [SY762: $i] :
( ~ ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SY762 )
| ( SY761 = SY762 ) ) ) )
= $true )
| ( ( ~ ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[598]) ).
thf(656,plain,
! [SV64: $i,SV108: $i] :
( ( ( in @ SV108 @ ( setunion @ SV64 ) )
= $false )
| ( ( ~ ! [SY721: $i] :
~ ~ ( ~ ( in @ SV108 @ SY721 )
| ~ ( in @ SY721 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(657,plain,
! [SV64: $i,SV108: $i] :
( ( ( ~ ! [SY722: $i] :
~ ~ ( ~ ( in @ SV108 @ SY722 )
| ~ ( in @ SY722 @ SV64 ) ) )
= $false )
| ( ( in @ SV108 @ ( setunion @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(658,plain,
! [SV72: $i,SV9: $i,SV140: $i,SV126: $i] :
( ( ( SV126 = SV140 )
= $false )
| ( ( ~ ( in @ SV126 @ SV9 )
| ( in @ SV140 @ SV72 ) )
= $true )
| ( ( SV9 = SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(659,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[603]) ).
thf(660,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
| ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) ) )
| ~ ( ~ ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
| ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[604]) ).
thf(661,plain,
! [SV12: $i,SV75: $i] :
( ( ( ~ ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 )
| ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 )
| ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 ) ) )
= $true )
| ( ( SV12 = SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(662,plain,
! [SV13: $i,SV76: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK17_SY668 @ SV76 @ SV13 ) @ SV13 )
| ~ ( SV76 @ ( sK17_SY668 @ SV76 @ SV13 ) ) ) )
= $true )
| ( ( ! [SY669: $i] :
( ~ ( in @ SY669 @ SV13 )
| ~ ( SV76 @ SY669 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(663,plain,
! [SV77: $i > $o,SV14: $i,SV141: $i] :
( ( ( ~ ( in @ SV141 @ SV14 )
| ~ ( SV77 @ SV141 ) )
= $true )
| ( ( ( ( dsetconstr @ SV14
@ ^ [SY671: $i] : ( SV77 @ SY671 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[608]) ).
thf(664,plain,
! [SV78: $i > $o,SV15: $i,SV142: $i] :
( ( ( in @ SV142 @ SV15 )
= $false )
| ( ( SV78 @ SV142 )
= $true )
| ( ( ~ ! [SY673: $i] :
~ ~ ( ~ ( in @ SY673 @ SV15 )
| ~ ~ ( SV78 @ SY673 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(665,plain,
! [SV16: $i,SV79: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK18_SY674 @ SV79 @ SV16 ) @ SV16 )
| ~ ( SV79 @ ( sK18_SY674 @ SV79 @ SV16 ) ) ) )
= $true )
| ( ( ! [SY675: $i] :
( ~ ( in @ SY675 @ SV16 )
| ~ ( SV79 @ SY675 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[610]) ).
thf(666,plain,
! [SV80: $i,SV17: $i,SV113: $i] :
( ( ( in @ SV113 @ ( setadjoin @ SV17 @ SV80 ) )
= $false )
| ( ( ( SV113 = SV17 )
| ( in @ SV113 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(667,plain,
! [SV80: $i,SV17: $i,SV113: $i] :
( ( ( ( SV113 = SV17 )
| ( in @ SV113 @ SV80 ) )
= $false )
| ( ( in @ SV113 @ ( setadjoin @ SV17 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(668,plain,
! [SV18: $i] :
( ( ~ ~ ( ~ ! [SY724: $i] :
( ~ ( in @ SY724 @ ( sK2_SY521 @ SV18 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY724 )
| ( in @ SY523 @ SV18 ) ) )
| ~ ! [SY726: $i,SY727: $i] :
( ~ ~ ( ~ ( in @ SY726 @ SV18 )
| ~ ( in @ SY727 @ SV18 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SY726 @ SY728 )
| ( in @ SY727 @ SY728 ) )
| ~ ( ~ ( in @ SY727 @ SY728 )
| ( in @ SY726 @ SY728 ) ) ) )
| ( SY726 = SY727 ) ) )
| ~ ! [SY729: $i,SY730: $i] :
( ~ ~ ( ~ ( in @ SY729 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY730 @ ( sK2_SY521 @ SV18 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY729 )
| ( in @ SX4 @ SY730 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY730 )
| ( in @ SX4 @ SY729 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(669,plain,
! [SV18: $i,SV148: $i] :
( ( ~ ~ ( ~ ! [SY764: $i] :
( ~ ( in @ SY764 @ SV148 )
| ( in @ SY764 @ SV18 ) )
| ~ ~ ! [SY765: $i] :
~ ( in @ SY765 @ SV148 ) )
| ~ ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(670,plain,
! [SV114: $i,SV81: $i > $o,SV19: $i] :
( ( ( ( dsetconstr @ SV19
@ ^ [SY678: $i] : ( SV81 @ SY678 ) )
= emptyset )
= $false )
| ( ( SV81 @ SV114 )
= $false )
| ( ( in @ SV114 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(671,plain,
! [SV127: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ SV127 ) )
= $true )
| ( ( ~ ! [SY751: $i] :
( ~ ( SV21 @ SY751 )
| ( SV127 = SY751 ) ) )
= $true )
| ( ( SV21
@ ( descr
@ ^ [SY546: $i] : ( SV21 @ SY546 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(672,plain,
! [SV22: $i,SV128: $o,SV83: $i] :
( ( ( ~ ( in @ SV83 @ ( sK20_SY752 @ SV128 @ SV22 @ SV83 ) )
| ~ ( in @ ( sK20_SY752 @ SV128 @ SV22 @ SV83 ) @ SV22 )
| SV128 )
= $false )
| ( SV128 = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[618]) ).
thf(673,plain,
! [SV22: $i,SV83: $i] :
( ( ( ~ ( in @ SV83 @ ( sK21_SX0 @ SV22 @ SV83 ) )
| ~ ( in @ ( sK21_SX0 @ SV22 @ SV83 ) @ SV22 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[619]) ).
thf(674,plain,
! [SV22: $i,SV83: $i] :
( ( ( ~ ( in @ SV83 @ ( sK22_SX0 @ SV22 @ SV83 ) )
| ~ ( in @ ( sK22_SX0 @ SV22 @ SV83 ) @ SV22 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[620]) ).
thf(675,plain,
! [SV84: $i > $o,SV24: $i,SV143: $i] :
( ( ( in @ SV143 @ SV24 )
= $false )
| ( ( SV84 @ SV143 )
= $true )
| ( ( ~ ! [SY683: $i] :
~ ~ ( ~ ( in @ SY683 @ SV24 )
| ~ ~ ( SV84 @ SY683 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(676,plain,
! [SV25: $i,SV85: $i,SV149: $i] :
( ( ( ~ ( in @ SV149 @ SV85 )
| ( in @ SV149 @ SV25 ) )
= $true )
| ( ( in @ SV85 @ ( powerset @ SV25 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(677,plain,
! [SV85: $i,SV25: $i] :
( ( ( ~ ( in @ ( sK23_SY685 @ SV25 @ SV85 ) @ SV85 )
| ( in @ ( sK23_SY685 @ SV25 @ SV85 ) @ SV25 ) )
= $false )
| ( ( in @ SV85 @ ( powerset @ SV25 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[623]) ).
thf(678,plain,
! [SV26: $i] :
( ( ( ~ ( in @ ( sK14_SY557 @ SV26 ) @ SV26 )
| ~ $true )
= $false )
| ( ( SV26 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(679,plain,
! [SV88: $i > $o,SV29: $i,SV144: $i] :
( ( ( ~ ( in @ SV144 @ SV29 )
| ~ ~ ( SV88 @ SV144 ) )
= $true )
| ( ( ~ ! [SY687: $i] :
( ~ ( in @ SY687 @ SV29 )
| ( SV88 @ SY687 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[625]) ).
thf(680,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ~ ( SV30 @ SV129 ) )
= $true )
| ( ( ~ ! [SY753: $i] :
( ~ ( SV30 @ SY753 )
| ( SV129 = SY753 ) ) )
= $true )
| ( ( ~ ! [SY565: $i] :
~ ~ ( ~ ( SV30 @ SY565 )
| ~ ! [SY566: $i] :
( ~ ( SV30 @ SY566 )
| ( SY565 = SY566 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[626]) ).
thf(681,plain,
! [SV31: $i,SV89: $i] :
( ( ( ~ ! [SY689: $i] :
( ~ ( in @ SY689 @ SV89 )
| ( in @ SY689 @ SV31 ) ) )
= $true )
| ( ( SV31 = SV89 )
= $true )
| ( ( in @ ( sK9_SY688 @ SV89 @ SV31 ) @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[627]) ).
thf(682,plain,
! [SV31: $i,SV89: $i] :
( ( ( ! [SY689: $i] :
( ~ ( in @ SY689 @ SV89 )
| ( in @ SY689 @ SV31 ) ) )
= $false )
| ( ( SV31 = SV89 )
= $true )
| ( ( in @ ( sK9_SY688 @ SV89 @ SV31 ) @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(683,plain,
! [SV90: $i,SV32: $i,SV145: $i,SV130: $i] :
( ( ( SV130 = SV145 )
= $false )
| ( ( ( setadjoin @ SV32 @ SV130 )
= ( setadjoin @ SV90 @ SV145 ) )
= $true )
| ( ( SV32 = SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(684,plain,
! [SV91: $i,SV146: $o,SV33: $i,SV116: $i] :
( ( ( ( SV116 != SV33 )
| SV146 )
= $false )
| ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| SV146 )
| SV146 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(685,plain,
! [SV91: $i,SV33: $i,SV116: $i] :
( ( ( ( SV116 != SV33 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| $true )
| $true )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(686,plain,
! [SV91: $i,SV33: $i,SV116: $i] :
( ( ( ( SV116 != SV33 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| $false )
| $false )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(687,plain,
! [SV92: $i > $o,SV34: $i] :
( ( ( ~ ! [SY695: $i] :
~ ~ ( ~ ( in @ SY695 @ SV34 )
| ~ ( SV92 @ SY695 ) ) )
= $false )
| ( ( in @ ( sK10_SY694 @ SV92 @ SV34 ) @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(688,plain,
! [SV92: $i > $o,SV34: $i] :
( ( ( ~ ! [SY695: $i] :
~ ~ ( ~ ( in @ SY695 @ SV34 )
| ~ ( SV92 @ SY695 ) ) )
= $false )
| ( ( SV92 @ ( sK10_SY694 @ SV92 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(689,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ SV131 ) )
= $true )
| ( ( ~ ! [SY755: $i] :
( ~ ( SV36 @ SY755 )
| ( SV131 = SY755 ) ) )
= $true )
| ( ( ~ ! [SY582: $i] :
~ ~ ( ~ ( SV36 @ SY582 )
| ~ ! [SY583: $i] :
( ~ ( SV36 @ SY583 )
| ( SY582 = SY583 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[635]) ).
thf(690,plain,
! [SV132: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ SV132 ) )
= $true )
| ( ( ~ ! [SY756: $i] :
( ~ ( SV40 @ SY756 )
| ( SV132 = SY756 ) ) )
= $true )
| ( ( ~ ! [SY590: $i] :
~ ! [SY591: $i] :
~ ( ~ ( ~ ( SV40 @ SY591 )
| ( SY591 = SY590 ) )
| ~ ( ( SY591 != SY590 )
| ( SV40 @ SY591 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(691,plain,
! [SV133: $i,SV41: $i > $o] :
( ( ( ~ ( SV41 @ SV133 ) )
= $true )
| ( ( ~ ! [SY757: $i] :
( ~ ( SV41 @ SY757 )
| ( SV133 = SY757 ) ) )
= $true )
| ( ( ~ ! [SY594: $i] :
~ ( SV41 @ SY594 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(692,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ! [SY597: $i,SY598: $i] :
( ~ ( SV43 @ SY597 )
| ~ ( SV43 @ SY598 )
| ( SY597 = SY598 ) ) )
= $false )
| ( ( ~ ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(693,plain,
! [SV135: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV135 ) )
= $true )
| ( ( ~ ! [SY758: $i] :
( ~ ( SV49 @ SY758 )
| ( SV135 = SY758 ) ) )
= $true )
| ( ( ! [SY609: $i,SY610: $i] :
( ~ ( SV49 @ SY609 )
| ~ ( SV49 @ SY610 )
| ( SY609 = SY610 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(694,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ( ~ ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
| ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 ) )
| ~ ( ( ( sK19_SY759 @ SV136 @ SV50 )
!= SV136 )
| ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) ) ) )
= $true )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[641]) ).
thf(695,plain,
! [SV52: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY618 @ SV52 ) @ omega )
| ~ ( in @ ( sK24_SY618 @ SV52 ) @ SV52 ) )
| ( in @ ( setadjoin @ ( sK24_SY618 @ SV52 ) @ ( sK24_SY618 @ SV52 ) ) @ SV52 ) )
= $false )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY619: $i] :
( ~ ( in @ SY619 @ omega )
| ( in @ SY619 @ SV52 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[643]) ).
thf(696,plain,
( ( ~ ( sK1_SX0 @ sK15_SY702 )
| ~ ! [SY763: $i] :
( ~ ( sK1_SX0 @ SY763 )
| ( sK15_SY702 = SY763 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[644]) ).
thf(697,plain,
( ( sK1_SX0 @ sK11_SY748 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[646]) ).
thf(698,plain,
! [SV103: $i > $o,SV55: $i,SV122: $i] :
( ( ( ~ ( in @ SV122
@ ( dsetconstr @ SV55
@ ^ [SY708: $i] : ( SV103 @ SY708 ) ) )
| ( SV103 @ SV122 ) )
= $true )
| ( ( in @ SV122 @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[648]) ).
thf(699,plain,
! [SV55: $i,SV122: $i,SV103: $i > $o] :
( ( ( ~ ( SV103 @ SV122 )
| ( in @ SV122
@ ( dsetconstr @ SV55
@ ^ [SY709: $i] : ( SV103 @ SY709 ) ) ) )
= $true )
| ( ( in @ SV122 @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[649]) ).
thf(700,plain,
! [SV106: $i,SV58: $i,SV147: $i,SV137: $i] :
( ( ( SV137 = SV147 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV137 @ SV58 )
| ( in @ SV147 @ SV106 ) )
| ~ ( ~ ( in @ SV147 @ SV106 )
| ( in @ SV137 @ SV58 ) ) ) )
= $true )
| ( ( SV58 = SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(701,plain,
! [SV61: $i,SV139: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK25_SY635 @ SV139 @ SV61 ) @ SV61 )
| ~ ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ ( sK25_SY635 @ SV139 @ SV61 ) )
| ~ ( in @ SY771 @ SV61 ) ) ) )
= $false )
| ( ( in @ SV139 @ SV61 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[652]) ).
thf(702,plain,
! [SV63: $i > $i > $o,SV107: $i] :
( ( ( ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $false )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(703,plain,
! [SV150: $i,SV107: $i,SV63: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
| ~ ! [SY772: $i] :
( ~ ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SY772 )
| ( SV150 = SY772 ) ) ) )
= $true )
| ( ( ~ ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(704,plain,
! [SV64: $i,SV108: $i] :
( ( ( ! [SY721: $i] :
~ ~ ( ~ ( in @ SV108 @ SY721 )
| ~ ( in @ SY721 @ SV64 ) ) )
= $false )
| ( ( in @ SV108 @ ( setunion @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(705,plain,
! [SV64: $i,SV108: $i] :
( ( ( ! [SY722: $i] :
~ ~ ( ~ ( in @ SV108 @ SY722 )
| ~ ( in @ SY722 @ SV64 ) ) )
= $true )
| ( ( in @ SV108 @ ( setunion @ SV64 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[657]) ).
thf(706,plain,
! [SV72: $i,SV140: $i,SV9: $i,SV126: $i] :
( ( ( ~ ( in @ SV126 @ SV9 ) )
= $true )
| ( ( in @ SV140 @ SV72 )
= $true )
| ( ( SV126 = SV140 )
= $false )
| ( ( SV9 = SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(707,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(708,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
| ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
| ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(709,plain,
! [SV12: $i,SV75: $i] :
( ( ( ~ ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 )
| ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 ) ) )
= $true )
| ( ( SV12 = SV75 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[661]) ).
thf(710,plain,
! [SV12: $i,SV75: $i] :
( ( ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 )
| ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 ) ) )
= $true )
| ( ( SV12 = SV75 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[661]) ).
thf(711,plain,
! [SV13: $i,SV76: $i > $o] :
( ( ( ~ ( in @ ( sK17_SY668 @ SV76 @ SV13 ) @ SV13 )
| ~ ( SV76 @ ( sK17_SY668 @ SV76 @ SV13 ) ) )
= $false )
| ( ( ! [SY669: $i] :
( ~ ( in @ SY669 @ SV13 )
| ~ ( SV76 @ SY669 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(712,plain,
! [SV77: $i > $o,SV14: $i,SV141: $i] :
( ( ( ~ ( in @ SV141 @ SV14 ) )
= $true )
| ( ( ~ ( SV77 @ SV141 ) )
= $true )
| ( ( ( ( dsetconstr @ SV14
@ ^ [SY671: $i] : ( SV77 @ SY671 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[663]) ).
thf(713,plain,
! [SV142: $i,SV78: $i > $o,SV15: $i] :
( ( ( ! [SY673: $i] :
~ ~ ( ~ ( in @ SY673 @ SV15 )
| ~ ~ ( SV78 @ SY673 ) ) )
= $false )
| ( ( SV78 @ SV142 )
= $true )
| ( ( in @ SV142 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(714,plain,
! [SV16: $i,SV79: $i > $o] :
( ( ( ~ ( in @ ( sK18_SY674 @ SV79 @ SV16 ) @ SV16 )
| ~ ( SV79 @ ( sK18_SY674 @ SV79 @ SV16 ) ) )
= $false )
| ( ( ! [SY675: $i] :
( ~ ( in @ SY675 @ SV16 )
| ~ ( SV79 @ SY675 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(715,plain,
! [SV80: $i,SV17: $i,SV113: $i] :
( ( ( SV113 = SV17 )
= $true )
| ( ( in @ SV113 @ SV80 )
= $true )
| ( ( in @ SV113 @ ( setadjoin @ SV17 @ SV80 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(716,plain,
! [SV80: $i,SV17: $i,SV113: $i] :
( ( ( SV113 = SV17 )
= $false )
| ( ( in @ SV113 @ ( setadjoin @ SV17 @ SV80 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[667]) ).
thf(717,plain,
! [SV17: $i,SV80: $i,SV113: $i] :
( ( ( in @ SV113 @ SV80 )
= $false )
| ( ( in @ SV113 @ ( setadjoin @ SV17 @ SV80 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[667]) ).
thf(718,plain,
! [SV18: $i] :
( ( ~ ~ ( ~ ! [SY724: $i] :
( ~ ( in @ SY724 @ ( sK2_SY521 @ SV18 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY724 )
| ( in @ SY523 @ SV18 ) ) )
| ~ ! [SY726: $i,SY727: $i] :
( ~ ~ ( ~ ( in @ SY726 @ SV18 )
| ~ ( in @ SY727 @ SV18 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SY726 @ SY728 )
| ( in @ SY727 @ SY728 ) )
| ~ ( ~ ( in @ SY727 @ SY728 )
| ( in @ SY726 @ SY728 ) ) ) )
| ( SY726 = SY727 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[668]) ).
thf(719,plain,
! [SV18: $i] :
( ( ~ ! [SY729: $i,SY730: $i] :
( ~ ~ ( ~ ( in @ SY729 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY730 @ ( sK2_SY521 @ SV18 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY729 )
| ( in @ SX4 @ SY730 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY730 )
| ( in @ SX4 @ SY729 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[668]) ).
thf(720,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ~ ( ~ ! [SY764: $i] :
( ~ ( in @ SY764 @ SV148 )
| ( in @ SY764 @ SV18 ) )
| ~ ~ ! [SY765: $i] :
~ ( in @ SY765 @ SV148 ) ) )
= $true )
| ( ( ~ ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(721,plain,
! [SV127: $i,SV21: $i > $o] :
( ( ( SV21 @ SV127 )
= $false )
| ( ( ~ ! [SY751: $i] :
( ~ ( SV21 @ SY751 )
| ( SV127 = SY751 ) ) )
= $true )
| ( ( SV21
@ ( descr
@ ^ [SY546: $i] : ( SV21 @ SY546 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(722,plain,
! [SV22: $i,SV128: $o,SV83: $i] :
( ( ( ~ ( in @ SV83 @ ( sK20_SY752 @ SV128 @ SV22 @ SV83 ) ) )
= $false )
| ( SV128 = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[672]) ).
thf(723,plain,
! [SV83: $i,SV22: $i,SV128: $o] :
( ( ( ~ ( in @ ( sK20_SY752 @ SV128 @ SV22 @ SV83 ) @ SV22 )
| SV128 )
= $false )
| ( SV128 = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[672]) ).
thf(724,plain,
! [SV22: $i,SV83: $i] :
( ( ( ~ ( in @ SV83 @ ( sK21_SX0 @ SV22 @ SV83 ) ) )
= $false )
| ( $true = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[673]) ).
thf(725,plain,
! [SV83: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK21_SX0 @ SV22 @ SV83 ) @ SV22 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[673]) ).
thf(726,plain,
! [SV22: $i,SV83: $i] :
( ( ( ~ ( in @ SV83 @ ( sK22_SX0 @ SV22 @ SV83 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(727,plain,
! [SV83: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK22_SX0 @ SV22 @ SV83 ) @ SV22 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(728,plain,
! [SV143: $i,SV84: $i > $o,SV24: $i] :
( ( ( ! [SY683: $i] :
~ ~ ( ~ ( in @ SY683 @ SV24 )
| ~ ~ ( SV84 @ SY683 ) ) )
= $false )
| ( ( SV84 @ SV143 )
= $true )
| ( ( in @ SV143 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(729,plain,
! [SV25: $i,SV85: $i,SV149: $i] :
( ( ( ~ ( in @ SV149 @ SV85 ) )
= $true )
| ( ( in @ SV149 @ SV25 )
= $true )
| ( ( in @ SV85 @ ( powerset @ SV25 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(730,plain,
! [SV85: $i,SV25: $i] :
( ( ( ~ ( in @ ( sK23_SY685 @ SV25 @ SV85 ) @ SV85 ) )
= $false )
| ( ( in @ SV85 @ ( powerset @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[677]) ).
thf(731,plain,
! [SV85: $i,SV25: $i] :
( ( ( in @ ( sK23_SY685 @ SV25 @ SV85 ) @ SV25 )
= $false )
| ( ( in @ SV85 @ ( powerset @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[677]) ).
thf(732,plain,
! [SV26: $i] :
( ( ( ~ ( in @ ( sK14_SY557 @ SV26 ) @ SV26 ) )
= $false )
| ( ( SV26 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[678]) ).
thf(733,plain,
! [SV26: $i] :
( ( ( ~ $true ) = $false )
| ( ( SV26 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[678]) ).
thf(734,plain,
! [SV88: $i > $o,SV29: $i,SV144: $i] :
( ( ( ~ ( in @ SV144 @ SV29 ) )
= $true )
| ( ( ~ ~ ( SV88 @ SV144 ) )
= $true )
| ( ( ~ ! [SY687: $i] :
( ~ ( in @ SY687 @ SV29 )
| ( SV88 @ SY687 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(735,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( SV30 @ SV129 )
= $false )
| ( ( ~ ! [SY753: $i] :
( ~ ( SV30 @ SY753 )
| ( SV129 = SY753 ) ) )
= $true )
| ( ( ~ ! [SY565: $i] :
~ ~ ( ~ ( SV30 @ SY565 )
| ~ ! [SY566: $i] :
( ~ ( SV30 @ SY566 )
| ( SY565 = SY566 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(736,plain,
! [SV31: $i,SV89: $i] :
( ( ( ! [SY689: $i] :
( ~ ( in @ SY689 @ SV89 )
| ( in @ SY689 @ SV31 ) ) )
= $false )
| ( ( SV31 = SV89 )
= $true )
| ( ( in @ ( sK9_SY688 @ SV89 @ SV31 ) @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(737,plain,
! [SV89: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK26_SY689 @ SV31 @ SV89 ) @ SV89 )
| ( in @ ( sK26_SY689 @ SV31 @ SV89 ) @ SV31 ) )
= $false )
| ( ( SV31 = SV89 )
= $true )
| ( ( in @ ( sK9_SY688 @ SV89 @ SV31 ) @ SV89 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[682]) ).
thf(738,plain,
! [SV146: $o,SV91: $i,SV33: $i,SV116: $i] :
( ( ( SV116 != SV33 )
= $false )
| ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| SV146 )
| SV146 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(739,plain,
! [SV33: $i,SV91: $i,SV116: $i,SV146: $o] :
( ( SV146 = $false )
| ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| SV146 )
| SV146 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(740,plain,
! [SV91: $i,SV33: $i,SV116: $i] :
( ( ( SV116 != SV33 )
= $false )
| ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| $true )
| $true )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(741,plain,
! [SV33: $i,SV91: $i,SV116: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| $true )
| $true )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(742,plain,
! [SV91: $i,SV33: $i,SV116: $i] :
( ( ( SV116 != SV33 )
= $false )
| ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| $false )
| $false )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(743,plain,
! [SV33: $i,SV91: $i,SV116: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| $false )
| $false )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(744,plain,
! [SV92: $i > $o,SV34: $i] :
( ( ( ! [SY695: $i] :
~ ~ ( ~ ( in @ SY695 @ SV34 )
| ~ ( SV92 @ SY695 ) ) )
= $true )
| ( ( in @ ( sK10_SY694 @ SV92 @ SV34 ) @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[687]) ).
thf(745,plain,
! [SV92: $i > $o,SV34: $i] :
( ( ( ! [SY695: $i] :
~ ~ ( ~ ( in @ SY695 @ SV34 )
| ~ ( SV92 @ SY695 ) ) )
= $true )
| ( ( SV92 @ ( sK10_SY694 @ SV92 @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[688]) ).
thf(746,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( SV36 @ SV131 )
= $false )
| ( ( ~ ! [SY755: $i] :
( ~ ( SV36 @ SY755 )
| ( SV131 = SY755 ) ) )
= $true )
| ( ( ~ ! [SY582: $i] :
~ ~ ( ~ ( SV36 @ SY582 )
| ~ ! [SY583: $i] :
( ~ ( SV36 @ SY583 )
| ( SY582 = SY583 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(747,plain,
! [SV132: $i,SV40: $i > $o] :
( ( ( SV40 @ SV132 )
= $false )
| ( ( ~ ! [SY756: $i] :
( ~ ( SV40 @ SY756 )
| ( SV132 = SY756 ) ) )
= $true )
| ( ( ~ ! [SY590: $i] :
~ ! [SY591: $i] :
~ ( ~ ( ~ ( SV40 @ SY591 )
| ( SY591 = SY590 ) )
| ~ ( ( SY591 != SY590 )
| ( SV40 @ SY591 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(748,plain,
! [SV133: $i,SV41: $i > $o] :
( ( ( SV41 @ SV133 )
= $false )
| ( ( ~ ! [SY757: $i] :
( ~ ( SV41 @ SY757 )
| ( SV133 = SY757 ) ) )
= $true )
| ( ( ~ ! [SY594: $i] :
~ ( SV41 @ SY594 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(749,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ! [SY773: $i] :
( ~ ( SV43 @ ( sK27_SY597 @ SV134 @ SV43 ) )
| ~ ( SV43 @ SY773 )
| ( ( sK27_SY597 @ SV134 @ SV43 )
= SY773 ) ) )
= $false )
| ( ( ~ ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[692]) ).
thf(750,plain,
! [SV135: $i,SV49: $i > $o] :
( ( ( SV49 @ SV135 )
= $false )
| ( ( ~ ! [SY758: $i] :
( ~ ( SV49 @ SY758 )
| ( SV135 = SY758 ) ) )
= $true )
| ( ( ! [SY609: $i,SY610: $i] :
( ~ ( SV49 @ SY609 )
| ~ ( SV49 @ SY610 )
| ( SY609 = SY610 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(751,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ( ~ ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
| ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 ) ) )
= $true )
| ( ( ~ ( ( ( sK19_SY759 @ SV136 @ SV50 )
!= SV136 )
| ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) ) ) )
= $true )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(752,plain,
! [SV52: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY618 @ SV52 ) @ omega )
| ~ ( in @ ( sK24_SY618 @ SV52 ) @ SV52 ) ) )
= $false )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY619: $i] :
( ~ ( in @ SY619 @ omega )
| ( in @ SY619 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[695]) ).
thf(753,plain,
! [SV52: $i] :
( ( ( in @ ( setadjoin @ ( sK24_SY618 @ SV52 ) @ ( sK24_SY618 @ SV52 ) ) @ SV52 )
= $false )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY619: $i] :
( ~ ( in @ SY619 @ omega )
| ( in @ SY619 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[695]) ).
thf(754,plain,
( ( ~ ( sK1_SX0 @ sK15_SY702 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(755,plain,
( ( ~ ! [SY763: $i] :
( ~ ( sK1_SX0 @ SY763 )
| ( sK15_SY702 = SY763 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(756,plain,
! [SV103: $i > $o,SV55: $i,SV122: $i] :
( ( ( ~ ( in @ SV122
@ ( dsetconstr @ SV55
@ ^ [SY708: $i] : ( SV103 @ SY708 ) ) ) )
= $true )
| ( ( SV103 @ SV122 )
= $true )
| ( ( in @ SV122 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[698]) ).
thf(757,plain,
! [SV55: $i,SV122: $i,SV103: $i > $o] :
( ( ( ~ ( SV103 @ SV122 ) )
= $true )
| ( ( in @ SV122
@ ( dsetconstr @ SV55
@ ^ [SY709: $i] : ( SV103 @ SY709 ) ) )
= $true )
| ( ( in @ SV122 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[699]) ).
thf(758,plain,
! [SV106: $i,SV147: $i,SV58: $i,SV137: $i] :
( ( ( ~ ( ~ ( in @ SV137 @ SV58 )
| ( in @ SV147 @ SV106 ) )
| ~ ( ~ ( in @ SV147 @ SV106 )
| ( in @ SV137 @ SV58 ) ) )
= $false )
| ( ( SV137 = SV147 )
= $false )
| ( ( SV58 = SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(759,plain,
! [SV61: $i,SV139: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY635 @ SV139 @ SV61 ) @ SV61 )
| ~ ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ ( sK25_SY635 @ SV139 @ SV61 ) )
| ~ ( in @ SY771 @ SV61 ) ) ) )
= $true )
| ( ( in @ SV139 @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[701]) ).
thf(760,plain,
! [SV107: $i,SV63: $i > $i > $o] :
( ( ( ~ ! [SY774: $i] :
~ ( ~ ( ~ ( in @ SY774 @ ( sK28_SY717 @ SV63 @ SV107 ) )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY774 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY774 ) )
| ( in @ SY774 @ ( sK28_SY717 @ SV63 @ SV107 ) ) ) ) )
= $false )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[702]) ).
thf(761,plain,
! [SV150: $i,SV107: $i,SV63: $i > $i > $o] :
( ( ( ~ ( ~ ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
| ~ ! [SY772: $i] :
( ~ ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SY772 )
| ( SV150 = SY772 ) ) ) )
= $false )
| ( ( ~ ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(762,plain,
! [SV64: $i,SV108: $i] :
( ( ( ~ ~ ( ~ ( in @ SV108 @ ( sK29_SY721 @ SV64 @ SV108 ) )
| ~ ( in @ ( sK29_SY721 @ SV64 @ SV108 ) @ SV64 ) ) )
= $false )
| ( ( in @ SV108 @ ( setunion @ SV64 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[704]) ).
thf(763,plain,
! [SV64: $i,SV151: $i,SV108: $i] :
( ( ( ~ ~ ( ~ ( in @ SV108 @ SV151 )
| ~ ( in @ SV151 @ SV64 ) ) )
= $true )
| ( ( in @ SV108 @ ( setunion @ SV64 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(764,plain,
! [SV72: $i,SV140: $i,SV9: $i,SV126: $i] :
( ( ( in @ SV126 @ SV9 )
= $false )
| ( ( in @ SV140 @ SV72 )
= $true )
| ( ( SV126 = SV140 )
= $false )
| ( ( SV9 = SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(765,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[707]) ).
thf(766,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[707]) ).
thf(767,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
| ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) ) )
= $false )
| ( ( ~ ( ~ ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
| ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(768,plain,
! [SV12: $i,SV75: $i] :
( ( ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 )
| ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 ) ) )
= $true )
| ( ( SV12 = SV75 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(769,plain,
! [SV12: $i,SV75: $i] :
( ( ( ~ ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 )
| ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 ) )
= $false )
| ( ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 )
= $false )
| ( ( SV12 = SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(770,plain,
! [SV13: $i,SV76: $i > $o] :
( ( ( ~ ( in @ ( sK17_SY668 @ SV76 @ SV13 ) @ SV13 ) )
= $false )
| ( ( ! [SY669: $i] :
( ~ ( in @ SY669 @ SV13 )
| ~ ( SV76 @ SY669 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(771,plain,
! [SV13: $i,SV76: $i > $o] :
( ( ( ~ ( SV76 @ ( sK17_SY668 @ SV76 @ SV13 ) ) )
= $false )
| ( ( ! [SY669: $i] :
( ~ ( in @ SY669 @ SV13 )
| ~ ( SV76 @ SY669 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(772,plain,
! [SV77: $i > $o,SV14: $i,SV141: $i] :
( ( ( in @ SV141 @ SV14 )
= $false )
| ( ( ~ ( SV77 @ SV141 ) )
= $true )
| ( ( ( ( dsetconstr @ SV14
@ ^ [SY671: $i] : ( SV77 @ SY671 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(773,plain,
! [SV15: $i,SV78: $i > $o,SV142: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK30_SY673 @ SV142 @ SV78 @ SV15 ) @ SV15 )
| ~ ~ ( SV78 @ ( sK30_SY673 @ SV142 @ SV78 @ SV15 ) ) ) )
= $false )
| ( ( SV78 @ SV142 )
= $true )
| ( ( in @ SV142 @ SV15 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[713]) ).
thf(774,plain,
! [SV16: $i,SV79: $i > $o] :
( ( ( ~ ( in @ ( sK18_SY674 @ SV79 @ SV16 ) @ SV16 ) )
= $false )
| ( ( ! [SY675: $i] :
( ~ ( in @ SY675 @ SV16 )
| ~ ( SV79 @ SY675 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[714]) ).
thf(775,plain,
! [SV16: $i,SV79: $i > $o] :
( ( ( ~ ( SV79 @ ( sK18_SY674 @ SV79 @ SV16 ) ) )
= $false )
| ( ( ! [SY675: $i] :
( ~ ( in @ SY675 @ SV16 )
| ~ ( SV79 @ SY675 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[714]) ).
thf(776,plain,
! [SV18: $i] :
( ( ~ ( ~ ! [SY724: $i] :
( ~ ( in @ SY724 @ ( sK2_SY521 @ SV18 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY724 )
| ( in @ SY523 @ SV18 ) ) )
| ~ ! [SY726: $i,SY727: $i] :
( ~ ~ ( ~ ( in @ SY726 @ SV18 )
| ~ ( in @ SY727 @ SV18 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SY726 @ SY728 )
| ( in @ SY727 @ SY728 ) )
| ~ ( ~ ( in @ SY727 @ SY728 )
| ( in @ SY726 @ SY728 ) ) ) )
| ( SY726 = SY727 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[718]) ).
thf(777,plain,
! [SV18: $i] :
( ( ! [SY729: $i,SY730: $i] :
( ~ ~ ( ~ ( in @ SY729 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY730 @ ( sK2_SY521 @ SV18 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY729 )
| ( in @ SX4 @ SY730 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY730 )
| ( in @ SX4 @ SY729 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[719]) ).
thf(778,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ( ~ ! [SY764: $i] :
( ~ ( in @ SY764 @ SV148 )
| ( in @ SY764 @ SV18 ) )
| ~ ~ ! [SY765: $i] :
~ ( in @ SY765 @ SV148 ) ) )
= $false )
| ( ( ~ ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(779,plain,
! [SV127: $i,SV21: $i > $o] :
( ( ( ! [SY751: $i] :
( ~ ( SV21 @ SY751 )
| ( SV127 = SY751 ) ) )
= $false )
| ( ( SV21 @ SV127 )
= $false )
| ( ( SV21
@ ( descr
@ ^ [SY546: $i] : ( SV21 @ SY546 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(780,plain,
! [SV22: $i,SV128: $o,SV83: $i] :
( ( ( in @ SV83 @ ( sK20_SY752 @ SV128 @ SV22 @ SV83 ) )
= $true )
| ( SV128 = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[722]) ).
thf(781,plain,
! [SV83: $i,SV22: $i,SV128: $o] :
( ( ( ~ ( in @ ( sK20_SY752 @ SV128 @ SV22 @ SV83 ) @ SV22 ) )
= $false )
| ( SV128 = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[723]) ).
thf(782,plain,
! [SV22: $i,SV83: $i,SV128: $o] :
( ( SV128 = $false )
| ( SV128 = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[723]) ).
thf(783,plain,
! [SV22: $i,SV83: $i] :
( ( ( in @ SV83 @ ( sK21_SX0 @ SV22 @ SV83 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[724]) ).
thf(784,plain,
! [SV83: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK21_SX0 @ SV22 @ SV83 ) @ SV22 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[725]) ).
thf(785,plain,
! [SV22: $i,SV83: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[725]) ).
thf(786,plain,
! [SV22: $i,SV83: $i] :
( ( ( in @ SV83 @ ( sK22_SX0 @ SV22 @ SV83 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[726]) ).
thf(787,plain,
! [SV83: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK22_SX0 @ SV22 @ SV83 ) @ SV22 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[727]) ).
thf(788,plain,
! [SV22: $i,SV83: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[727]) ).
thf(789,plain,
! [SV24: $i,SV84: $i > $o,SV143: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK31_SY683 @ SV143 @ SV84 @ SV24 ) @ SV24 )
| ~ ~ ( SV84 @ ( sK31_SY683 @ SV143 @ SV84 @ SV24 ) ) ) )
= $false )
| ( ( SV84 @ SV143 )
= $true )
| ( ( in @ SV143 @ SV24 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[728]) ).
thf(790,plain,
! [SV25: $i,SV85: $i,SV149: $i] :
( ( ( in @ SV149 @ SV85 )
= $false )
| ( ( in @ SV149 @ SV25 )
= $true )
| ( ( in @ SV85 @ ( powerset @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(791,plain,
! [SV85: $i,SV25: $i] :
( ( ( in @ ( sK23_SY685 @ SV25 @ SV85 ) @ SV85 )
= $true )
| ( ( in @ SV85 @ ( powerset @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[730]) ).
thf(792,plain,
! [SV26: $i] :
( ( ( in @ ( sK14_SY557 @ SV26 ) @ SV26 )
= $true )
| ( ( SV26 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[732]) ).
thf(793,plain,
! [SV26: $i] :
( ( $true = $true )
| ( ( SV26 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[733]) ).
thf(794,plain,
! [SV88: $i > $o,SV29: $i,SV144: $i] :
( ( ( in @ SV144 @ SV29 )
= $false )
| ( ( ~ ~ ( SV88 @ SV144 ) )
= $true )
| ( ( ~ ! [SY687: $i] :
( ~ ( in @ SY687 @ SV29 )
| ( SV88 @ SY687 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(795,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ! [SY753: $i] :
( ~ ( SV30 @ SY753 )
| ( SV129 = SY753 ) ) )
= $false )
| ( ( SV30 @ SV129 )
= $false )
| ( ( ~ ! [SY565: $i] :
~ ~ ( ~ ( SV30 @ SY565 )
| ~ ! [SY566: $i] :
( ~ ( SV30 @ SY566 )
| ( SY565 = SY566 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(796,plain,
! [SV89: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK32_SY689 @ SV31 @ SV89 ) @ SV89 )
| ( in @ ( sK32_SY689 @ SV31 @ SV89 ) @ SV31 ) )
= $false )
| ( ( SV31 = SV89 )
= $true )
| ( ( in @ ( sK9_SY688 @ SV89 @ SV31 ) @ SV31 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[736]) ).
thf(797,plain,
! [SV89: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK26_SY689 @ SV31 @ SV89 ) @ SV89 ) )
= $false )
| ( ( SV31 = SV89 )
= $true )
| ( ( in @ ( sK9_SY688 @ SV89 @ SV31 ) @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[737]) ).
thf(798,plain,
! [SV89: $i,SV31: $i] :
( ( ( in @ ( sK26_SY689 @ SV31 @ SV89 ) @ SV31 )
= $false )
| ( ( SV31 = SV89 )
= $true )
| ( ( in @ ( sK9_SY688 @ SV89 @ SV31 ) @ SV89 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[737]) ).
thf(799,plain,
! [SV146: $o,SV91: $i,SV33: $i,SV116: $i] :
( ( ( SV116 = SV33 )
= $true )
| ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| SV146 )
| SV146 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[738]) ).
thf(800,plain,
! [SV33: $i,SV146: $o,SV91: $i,SV116: $i] :
( ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| SV146 ) )
= $true )
| ( SV146 = $true )
| ( SV146 = $false )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[739]) ).
thf(801,plain,
! [SV91: $i,SV33: $i,SV116: $i] :
( ( ( SV116 = SV33 )
= $true )
| ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| $true )
| $true )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[740]) ).
thf(802,plain,
! [SV33: $i,SV91: $i,SV116: $i] :
( ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[741]) ).
thf(803,plain,
! [SV91: $i,SV33: $i,SV116: $i] :
( ( ( SV116 = SV33 )
= $true )
| ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| $false )
| $false )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[742]) ).
thf(804,plain,
! [SV33: $i,SV91: $i,SV116: $i] :
( ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(805,plain,
! [SV92: $i > $o,SV34: $i,SV152: $i] :
( ( ( ~ ~ ( ~ ( in @ SV152 @ SV34 )
| ~ ( SV92 @ SV152 ) ) )
= $true )
| ( ( in @ ( sK10_SY694 @ SV92 @ SV34 ) @ SV34 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(806,plain,
! [SV92: $i > $o,SV34: $i,SV153: $i] :
( ( ( ~ ~ ( ~ ( in @ SV153 @ SV34 )
| ~ ( SV92 @ SV153 ) ) )
= $true )
| ( ( SV92 @ ( sK10_SY694 @ SV92 @ SV34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(807,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ! [SY755: $i] :
( ~ ( SV36 @ SY755 )
| ( SV131 = SY755 ) ) )
= $false )
| ( ( SV36 @ SV131 )
= $false )
| ( ( ~ ! [SY582: $i] :
~ ~ ( ~ ( SV36 @ SY582 )
| ~ ! [SY583: $i] :
( ~ ( SV36 @ SY583 )
| ( SY582 = SY583 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(808,plain,
! [SV132: $i,SV40: $i > $o] :
( ( ( ! [SY756: $i] :
( ~ ( SV40 @ SY756 )
| ( SV132 = SY756 ) ) )
= $false )
| ( ( SV40 @ SV132 )
= $false )
| ( ( ~ ! [SY590: $i] :
~ ! [SY591: $i] :
~ ( ~ ( ~ ( SV40 @ SY591 )
| ( SY591 = SY590 ) )
| ~ ( ( SY591 != SY590 )
| ( SV40 @ SY591 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(809,plain,
! [SV133: $i,SV41: $i > $o] :
( ( ( ! [SY757: $i] :
( ~ ( SV41 @ SY757 )
| ( SV133 = SY757 ) ) )
= $false )
| ( ( SV41 @ SV133 )
= $false )
| ( ( ~ ! [SY594: $i] :
~ ( SV41 @ SY594 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(810,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ ( sK27_SY597 @ SV134 @ SV43 ) )
| ~ ( SV43 @ ( sK33_SY773 @ SV134 @ SV43 ) )
| ( ( sK27_SY597 @ SV134 @ SV43 )
= ( sK33_SY773 @ SV134 @ SV43 ) ) )
= $false )
| ( ( ~ ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[749]) ).
thf(811,plain,
! [SV135: $i,SV49: $i > $o] :
( ( ( ! [SY758: $i] :
( ~ ( SV49 @ SY758 )
| ( SV135 = SY758 ) ) )
= $false )
| ( ( SV49 @ SV135 )
= $false )
| ( ( ! [SY609: $i,SY610: $i] :
( ~ ( SV49 @ SY609 )
| ~ ( SV49 @ SY610 )
| ( SY609 = SY610 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(812,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
| ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 ) )
= $false )
| ( ( ~ ( ( ( sK19_SY759 @ SV136 @ SV50 )
!= SV136 )
| ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) ) ) )
= $true )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(813,plain,
! [SV52: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY618 @ SV52 ) @ omega )
| ~ ( in @ ( sK24_SY618 @ SV52 ) @ SV52 ) ) )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY619: $i] :
( ~ ( in @ SY619 @ omega )
| ( in @ SY619 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[752]) ).
thf(814,plain,
! [SV52: $i,SV154: $i] :
( ( ( ~ ( in @ SV154 @ omega )
| ( in @ SV154 @ SV52 ) )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( in @ ( setadjoin @ ( sK24_SY618 @ SV52 ) @ ( sK24_SY618 @ SV52 ) ) @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(815,plain,
( ( sK1_SX0 @ sK15_SY702 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[754]) ).
thf(816,plain,
( ( ! [SY763: $i] :
( ~ ( sK1_SX0 @ SY763 )
| ( sK15_SY702 = SY763 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[755]) ).
thf(817,plain,
! [SV103: $i > $o,SV55: $i,SV122: $i] :
( ( ( in @ SV122
@ ( dsetconstr @ SV55
@ ^ [SY708: $i] : ( SV103 @ SY708 ) ) )
= $false )
| ( ( SV103 @ SV122 )
= $true )
| ( ( in @ SV122 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(818,plain,
! [SV55: $i,SV122: $i,SV103: $i > $o] :
( ( ( SV103 @ SV122 )
= $false )
| ( ( in @ SV122
@ ( dsetconstr @ SV55
@ ^ [SY709: $i] : ( SV103 @ SY709 ) ) )
= $true )
| ( ( in @ SV122 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(819,plain,
! [SV106: $i,SV147: $i,SV58: $i,SV137: $i] :
( ( ( ~ ( ~ ( in @ SV137 @ SV58 )
| ( in @ SV147 @ SV106 ) ) )
= $false )
| ( ( SV137 = SV147 )
= $false )
| ( ( SV58 = SV106 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[758]) ).
thf(820,plain,
! [SV58: $i,SV137: $i,SV106: $i,SV147: $i] :
( ( ( ~ ( ~ ( in @ SV147 @ SV106 )
| ( in @ SV137 @ SV58 ) ) )
= $false )
| ( ( SV137 = SV147 )
= $false )
| ( ( SV58 = SV106 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[758]) ).
thf(821,plain,
! [SV61: $i,SV139: $i] :
( ( ( ~ ( in @ ( sK25_SY635 @ SV139 @ SV61 ) @ SV61 )
| ~ ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ ( sK25_SY635 @ SV139 @ SV61 ) )
| ~ ( in @ SY771 @ SV61 ) ) )
= $false )
| ( ( in @ SV139 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(822,plain,
! [SV107: $i,SV63: $i > $i > $o] :
( ( ( ! [SY774: $i] :
~ ( ~ ( ~ ( in @ SY774 @ ( sK28_SY717 @ SV63 @ SV107 ) )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY774 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY774 ) )
| ( in @ SY774 @ ( sK28_SY717 @ SV63 @ SV107 ) ) ) ) )
= $true )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[760]) ).
thf(823,plain,
! [SV150: $i,SV107: $i,SV63: $i > $i > $o] :
( ( ( ~ ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
| ~ ! [SY772: $i] :
( ~ ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SY772 )
| ( SV150 = SY772 ) ) )
= $true )
| ( ( ~ ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[761]) ).
thf(824,plain,
! [SV64: $i,SV108: $i] :
( ( ( ~ ( ~ ( in @ SV108 @ ( sK29_SY721 @ SV64 @ SV108 ) )
| ~ ( in @ ( sK29_SY721 @ SV64 @ SV108 ) @ SV64 ) ) )
= $true )
| ( ( in @ SV108 @ ( setunion @ SV64 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[762]) ).
thf(825,plain,
! [SV64: $i,SV151: $i,SV108: $i] :
( ( ( ~ ( ~ ( in @ SV108 @ SV151 )
| ~ ( in @ SV151 @ SV64 ) ) )
= $false )
| ( ( in @ SV108 @ ( setunion @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(826,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[765]) ).
thf(827,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[766]) ).
thf(828,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) ) )
= $false )
| ( ( ~ ( ~ ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
| ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[767]) ).
thf(829,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( ~ ( ~ ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
| ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[767]) ).
thf(830,plain,
! [SV12: $i,SV75: $i] :
( ( ( ~ ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 )
| ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 ) )
= $false )
| ( ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 )
= $true )
| ( ( SV12 = SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(831,plain,
! [SV12: $i,SV75: $i] :
( ( ( ~ ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 ) )
= $false )
| ( ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 )
= $false )
| ( ( SV12 = SV75 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[769]) ).
thf(832,plain,
! [SV12: $i,SV75: $i] :
( ( ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 )
= $false )
| ( ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 )
= $false )
| ( ( SV12 = SV75 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[769]) ).
thf(833,plain,
! [SV13: $i,SV76: $i > $o] :
( ( ( in @ ( sK17_SY668 @ SV76 @ SV13 ) @ SV13 )
= $true )
| ( ( ! [SY669: $i] :
( ~ ( in @ SY669 @ SV13 )
| ~ ( SV76 @ SY669 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[770]) ).
thf(834,plain,
! [SV13: $i,SV76: $i > $o] :
( ( ( SV76 @ ( sK17_SY668 @ SV76 @ SV13 ) )
= $true )
| ( ( ! [SY669: $i] :
( ~ ( in @ SY669 @ SV13 )
| ~ ( SV76 @ SY669 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[771]) ).
thf(835,plain,
! [SV14: $i,SV141: $i,SV77: $i > $o] :
( ( ( SV77 @ SV141 )
= $false )
| ( ( in @ SV141 @ SV14 )
= $false )
| ( ( ( ( dsetconstr @ SV14
@ ^ [SY671: $i] : ( SV77 @ SY671 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(836,plain,
! [SV15: $i,SV78: $i > $o,SV142: $i] :
( ( ( ~ ( ~ ( in @ ( sK30_SY673 @ SV142 @ SV78 @ SV15 ) @ SV15 )
| ~ ~ ( SV78 @ ( sK30_SY673 @ SV142 @ SV78 @ SV15 ) ) ) )
= $true )
| ( ( SV78 @ SV142 )
= $true )
| ( ( in @ SV142 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[773]) ).
thf(837,plain,
! [SV16: $i,SV79: $i > $o] :
( ( ( in @ ( sK18_SY674 @ SV79 @ SV16 ) @ SV16 )
= $true )
| ( ( ! [SY675: $i] :
( ~ ( in @ SY675 @ SV16 )
| ~ ( SV79 @ SY675 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[774]) ).
thf(838,plain,
! [SV16: $i,SV79: $i > $o] :
( ( ( SV79 @ ( sK18_SY674 @ SV79 @ SV16 ) )
= $true )
| ( ( ! [SY675: $i] :
( ~ ( in @ SY675 @ SV16 )
| ~ ( SV79 @ SY675 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[775]) ).
thf(839,plain,
! [SV18: $i] :
( ( ~ ! [SY724: $i] :
( ~ ( in @ SY724 @ ( sK2_SY521 @ SV18 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY724 )
| ( in @ SY523 @ SV18 ) ) )
| ~ ! [SY726: $i,SY727: $i] :
( ~ ~ ( ~ ( in @ SY726 @ SV18 )
| ~ ( in @ SY727 @ SV18 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SY726 @ SY728 )
| ( in @ SY727 @ SY728 ) )
| ~ ( ~ ( in @ SY727 @ SY728 )
| ( in @ SY726 @ SY728 ) ) ) )
| ( SY726 = SY727 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(840,plain,
! [SV18: $i,SV155: $i] :
( ( ! [SY777: $i] :
( ~ ~ ( ~ ( in @ SV155 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY777 @ ( sK2_SY521 @ SV18 ) ) )
| ! [SY778: $i] :
( ~ ( in @ SY778 @ SV155 )
| ( in @ SY778 @ SY777 ) )
| ! [SY779: $i] :
( ~ ( in @ SY779 @ SY777 )
| ( in @ SY779 @ SV155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(841,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ! [SY764: $i] :
( ~ ( in @ SY764 @ SV148 )
| ( in @ SY764 @ SV18 ) )
| ~ ~ ! [SY765: $i] :
~ ( in @ SY765 @ SV148 ) )
= $true )
| ( ( ~ ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[778]) ).
thf(842,plain,
! [SV127: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ ( sK34_SY751 @ SV127 @ SV21 ) )
| ( SV127
= ( sK34_SY751 @ SV127 @ SV21 ) ) )
= $false )
| ( ( SV21 @ SV127 )
= $false )
| ( ( SV21
@ ( descr
@ ^ [SY546: $i] : ( SV21 @ SY546 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[779]) ).
thf(843,plain,
! [SV83: $i,SV22: $i,SV128: $o] :
( ( ( in @ ( sK20_SY752 @ SV128 @ SV22 @ SV83 ) @ SV22 )
= $true )
| ( SV128 = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[781]) ).
thf(844,plain,
! [SV83: $i,SV22: $i] :
( ( ( in @ ( sK21_SX0 @ SV22 @ SV83 ) @ SV22 )
= $true )
| ( $true = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(845,plain,
! [SV83: $i,SV22: $i] :
( ( ( in @ ( sK22_SX0 @ SV22 @ SV83 ) @ SV22 )
= $true )
| ( $false = $true )
| ( ( in @ SV83 @ ( setunion @ SV22 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[787]) ).
thf(846,plain,
! [SV24: $i,SV84: $i > $o,SV143: $i] :
( ( ( ~ ( ~ ( in @ ( sK31_SY683 @ SV143 @ SV84 @ SV24 ) @ SV24 )
| ~ ~ ( SV84 @ ( sK31_SY683 @ SV143 @ SV84 @ SV24 ) ) ) )
= $true )
| ( ( SV84 @ SV143 )
= $true )
| ( ( in @ SV143 @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(847,plain,
! [SV29: $i,SV144: $i,SV88: $i > $o] :
( ( ( ~ ( SV88 @ SV144 ) )
= $false )
| ( ( in @ SV144 @ SV29 )
= $false )
| ( ( ~ ! [SY687: $i] :
( ~ ( in @ SY687 @ SV29 )
| ( SV88 @ SY687 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(848,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ~ ( SV30 @ ( sK35_SY753 @ SV129 @ SV30 ) )
| ( SV129
= ( sK35_SY753 @ SV129 @ SV30 ) ) )
= $false )
| ( ( SV30 @ SV129 )
= $false )
| ( ( ~ ! [SY565: $i] :
~ ~ ( ~ ( SV30 @ SY565 )
| ~ ! [SY566: $i] :
( ~ ( SV30 @ SY566 )
| ( SY565 = SY566 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[795]) ).
thf(849,plain,
! [SV89: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK32_SY689 @ SV31 @ SV89 ) @ SV89 ) )
= $false )
| ( ( SV31 = SV89 )
= $true )
| ( ( in @ ( sK9_SY688 @ SV89 @ SV31 ) @ SV31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[796]) ).
thf(850,plain,
! [SV89: $i,SV31: $i] :
( ( ( in @ ( sK32_SY689 @ SV31 @ SV89 ) @ SV31 )
= $false )
| ( ( SV31 = SV89 )
= $true )
| ( ( in @ ( sK9_SY688 @ SV89 @ SV31 ) @ SV31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[796]) ).
thf(851,plain,
! [SV89: $i,SV31: $i] :
( ( ( in @ ( sK26_SY689 @ SV31 @ SV89 ) @ SV89 )
= $true )
| ( ( SV31 = SV89 )
= $true )
| ( ( in @ ( sK9_SY688 @ SV89 @ SV31 ) @ SV89 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[797]) ).
thf(852,plain,
! [SV33: $i,SV146: $o,SV91: $i,SV116: $i] :
( ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| SV146 ) )
= $true )
| ( SV146 = $true )
| ( ( SV116 = SV33 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(853,plain,
! [SV33: $i,SV146: $o,SV91: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV91 )
| SV146 )
= $false )
| ( SV146 = $true )
| ( SV146 = $false )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(854,plain,
! [SV33: $i,SV91: $i,SV116: $i] :
( ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( SV116 = SV33 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[801]) ).
thf(855,plain,
! [SV33: $i,SV91: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV91 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(856,plain,
! [SV33: $i,SV91: $i,SV116: $i] :
( ( ( ~ ( ~ ( in @ SV116 @ SV91 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( SV116 = SV33 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[803]) ).
thf(857,plain,
! [SV33: $i,SV91: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV91 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(858,plain,
! [SV92: $i > $o,SV34: $i,SV152: $i] :
( ( ( ~ ( ~ ( in @ SV152 @ SV34 )
| ~ ( SV92 @ SV152 ) ) )
= $false )
| ( ( in @ ( sK10_SY694 @ SV92 @ SV34 ) @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(859,plain,
! [SV92: $i > $o,SV34: $i,SV153: $i] :
( ( ( ~ ( ~ ( in @ SV153 @ SV34 )
| ~ ( SV92 @ SV153 ) ) )
= $false )
| ( ( SV92 @ ( sK10_SY694 @ SV92 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(860,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ ( sK36_SY755 @ SV131 @ SV36 ) )
| ( SV131
= ( sK36_SY755 @ SV131 @ SV36 ) ) )
= $false )
| ( ( SV36 @ SV131 )
= $false )
| ( ( ~ ! [SY582: $i] :
~ ~ ( ~ ( SV36 @ SY582 )
| ~ ! [SY583: $i] :
( ~ ( SV36 @ SY583 )
| ( SY582 = SY583 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[807]) ).
thf(861,plain,
! [SV132: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ ( sK37_SY756 @ SV132 @ SV40 ) )
| ( SV132
= ( sK37_SY756 @ SV132 @ SV40 ) ) )
= $false )
| ( ( SV40 @ SV132 )
= $false )
| ( ( ~ ! [SY590: $i] :
~ ! [SY591: $i] :
~ ( ~ ( ~ ( SV40 @ SY591 )
| ( SY591 = SY590 ) )
| ~ ( ( SY591 != SY590 )
| ( SV40 @ SY591 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[808]) ).
thf(862,plain,
! [SV133: $i,SV41: $i > $o] :
( ( ( ~ ( SV41 @ ( sK38_SY757 @ SV133 @ SV41 ) )
| ( SV133
= ( sK38_SY757 @ SV133 @ SV41 ) ) )
= $false )
| ( ( SV41 @ SV133 )
= $false )
| ( ( ~ ! [SY594: $i] :
~ ( SV41 @ SY594 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[809]) ).
thf(863,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ ( sK27_SY597 @ SV134 @ SV43 ) ) )
= $false )
| ( ( ~ ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[810]) ).
thf(864,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ ( sK33_SY773 @ SV134 @ SV43 ) )
| ( ( sK27_SY597 @ SV134 @ SV43 )
= ( sK33_SY773 @ SV134 @ SV43 ) ) )
= $false )
| ( ( ~ ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[810]) ).
thf(865,plain,
! [SV135: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK39_SY758 @ SV135 @ SV49 ) )
| ( SV135
= ( sK39_SY758 @ SV135 @ SV49 ) ) )
= $false )
| ( ( SV49 @ SV135 )
= $false )
| ( ( ! [SY609: $i,SY610: $i] :
( ~ ( SV49 @ SY609 )
| ~ ( SV49 @ SY610 )
| ( SY609 = SY610 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[811]) ).
thf(866,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) ) )
= $false )
| ( ( ~ ( ( ( sK19_SY759 @ SV136 @ SV50 )
!= SV136 )
| ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) ) ) )
= $true )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[812]) ).
thf(867,plain,
! [SV50: $i > $o,SV136: $i] :
( ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( ~ ( ( ( sK19_SY759 @ SV136 @ SV50 )
!= SV136 )
| ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) ) ) )
= $true )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[812]) ).
thf(868,plain,
! [SV52: $i] :
( ( ( ~ ( in @ ( sK24_SY618 @ SV52 ) @ omega )
| ~ ( in @ ( sK24_SY618 @ SV52 ) @ SV52 ) )
= $false )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY619: $i] :
( ~ ( in @ SY619 @ omega )
| ( in @ SY619 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(869,plain,
! [SV52: $i,SV154: $i] :
( ( ( ~ ( in @ SV154 @ omega ) )
= $true )
| ( ( in @ SV154 @ SV52 )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( in @ ( setadjoin @ ( sK24_SY618 @ SV52 ) @ ( sK24_SY618 @ SV52 ) ) @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[814]) ).
thf(870,plain,
! [SV156: $i] :
( ( ~ ( sK1_SX0 @ SV156 )
| ( sK15_SY702 = SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(871,plain,
! [SV106: $i,SV147: $i,SV58: $i,SV137: $i] :
( ( ( ~ ( in @ SV137 @ SV58 )
| ( in @ SV147 @ SV106 ) )
= $true )
| ( ( SV137 = SV147 )
= $false )
| ( ( SV58 = SV106 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[819]) ).
thf(872,plain,
! [SV58: $i,SV137: $i,SV106: $i,SV147: $i] :
( ( ( ~ ( in @ SV147 @ SV106 )
| ( in @ SV137 @ SV58 ) )
= $true )
| ( ( SV137 = SV147 )
= $false )
| ( ( SV58 = SV106 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[820]) ).
thf(873,plain,
! [SV61: $i,SV139: $i] :
( ( ( ~ ( in @ ( sK25_SY635 @ SV139 @ SV61 ) @ SV61 ) )
= $false )
| ( ( in @ SV139 @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[821]) ).
thf(874,plain,
! [SV61: $i,SV139: $i] :
( ( ( ~ ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ ( sK25_SY635 @ SV139 @ SV61 ) )
| ~ ( in @ SY771 @ SV61 ) ) )
= $false )
| ( ( in @ SV139 @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[821]) ).
thf(875,plain,
! [SV107: $i,SV63: $i > $i > $o,SV157: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
| ~ ! [SY780: $i] :
~ ~ ( ~ ( in @ SY780 @ SV107 )
| ~ ( SV63 @ SY780 @ SV157 ) ) )
| ~ ( ~ ~ ! [SY781: $i] :
~ ~ ( ~ ( in @ SY781 @ SV107 )
| ~ ( SV63 @ SY781 @ SV157 ) )
| ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) ) ) ) )
= $true )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(876,plain,
! [SV150: $i,SV107: $i,SV63: $i > $i > $o] :
( ( ( ~ ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 ) )
= $true )
| ( ( ~ ! [SY772: $i] :
( ~ ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SY772 )
| ( SV150 = SY772 ) ) )
= $true )
| ( ( ~ ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(877,plain,
! [SV64: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ ( sK29_SY721 @ SV64 @ SV108 ) )
| ~ ( in @ ( sK29_SY721 @ SV64 @ SV108 ) @ SV64 ) )
= $false )
| ( ( in @ SV108 @ ( setunion @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[824]) ).
thf(878,plain,
! [SV64: $i,SV151: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ SV151 )
| ~ ( in @ SV151 @ SV64 ) )
= $true )
| ( ( in @ SV108 @ ( setunion @ SV64 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(879,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(880,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[827]) ).
thf(881,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
| ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[828]) ).
thf(882,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
| ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[829]) ).
thf(883,plain,
! [SV12: $i,SV75: $i] :
( ( ( ~ ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 ) )
= $false )
| ( ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 )
= $true )
| ( ( SV12 = SV75 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[830]) ).
thf(884,plain,
! [SV12: $i,SV75: $i] :
( ( ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 )
= $false )
| ( ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 )
= $true )
| ( ( SV12 = SV75 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[830]) ).
thf(885,plain,
! [SV12: $i,SV75: $i] :
( ( ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 )
= $true )
| ( ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 )
= $false )
| ( ( SV12 = SV75 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(886,plain,
! [SV76: $i > $o,SV13: $i,SV158: $i] :
( ( ( ~ ( in @ SV158 @ SV13 )
| ~ ( SV76 @ SV158 ) )
= $true )
| ( ( in @ ( sK17_SY668 @ SV76 @ SV13 ) @ SV13 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(887,plain,
! [SV76: $i > $o,SV13: $i,SV159: $i] :
( ( ( ~ ( in @ SV159 @ SV13 )
| ~ ( SV76 @ SV159 ) )
= $true )
| ( ( SV76 @ ( sK17_SY668 @ SV76 @ SV13 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(888,plain,
! [SV141: $i,SV77: $i > $o,SV14: $i] :
( ( ( ( dsetconstr @ SV14
@ ^ [SY671: $i] : ( SV77 @ SY671 ) )
!= emptyset )
= $true )
| ( $false = $true )
| ( ( in @ SV141 @ SV14 )
= $false )
| ( ( SV77 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(889,plain,
! [SV15: $i,SV78: $i > $o,SV142: $i] :
( ( ( ~ ( in @ ( sK30_SY673 @ SV142 @ SV78 @ SV15 ) @ SV15 )
| ~ ~ ( SV78 @ ( sK30_SY673 @ SV142 @ SV78 @ SV15 ) ) )
= $false )
| ( ( SV78 @ SV142 )
= $true )
| ( ( in @ SV142 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(890,plain,
! [SV79: $i > $o,SV16: $i,SV160: $i] :
( ( ( ~ ( in @ SV160 @ SV16 )
| ~ ( SV79 @ SV160 ) )
= $true )
| ( ( in @ ( sK18_SY674 @ SV79 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(891,plain,
! [SV79: $i > $o,SV16: $i,SV161: $i] :
( ( ( ~ ( in @ SV161 @ SV16 )
| ~ ( SV79 @ SV161 ) )
= $true )
| ( ( SV79 @ ( sK18_SY674 @ SV79 @ SV16 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(892,plain,
! [SV18: $i] :
( ( ~ ! [SY724: $i] :
( ~ ( in @ SY724 @ ( sK2_SY521 @ SV18 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY724 )
| ( in @ SY523 @ SV18 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[839]) ).
thf(893,plain,
! [SV18: $i] :
( ( ~ ! [SY726: $i,SY727: $i] :
( ~ ~ ( ~ ( in @ SY726 @ SV18 )
| ~ ( in @ SY727 @ SV18 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SY726 @ SY728 )
| ( in @ SY727 @ SY728 ) )
| ~ ( ~ ( in @ SY727 @ SY728 )
| ( in @ SY726 @ SY728 ) ) ) )
| ( SY726 = SY727 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[839]) ).
thf(894,plain,
! [SV162: $i,SV18: $i,SV155: $i] :
( ( ~ ~ ( ~ ( in @ SV155 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SV162 @ ( sK2_SY521 @ SV18 ) ) )
| ! [SY782: $i] :
( ~ ( in @ SY782 @ SV155 )
| ( in @ SY782 @ SV162 ) )
| ! [SY783: $i] :
( ~ ( in @ SY783 @ SV162 )
| ( in @ SY783 @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(895,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ! [SY764: $i] :
( ~ ( in @ SY764 @ SV148 )
| ( in @ SY764 @ SV18 ) ) )
= $true )
| ( ( ~ ~ ! [SY765: $i] :
~ ( in @ SY765 @ SV148 ) )
= $true )
| ( ( ~ ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[841]) ).
thf(896,plain,
! [SV127: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ ( sK34_SY751 @ SV127 @ SV21 ) ) )
= $false )
| ( ( SV21 @ SV127 )
= $false )
| ( ( SV21
@ ( descr
@ ^ [SY546: $i] : ( SV21 @ SY546 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[842]) ).
thf(897,plain,
! [SV21: $i > $o,SV127: $i] :
( ( ( SV127
= ( sK34_SY751 @ SV127 @ SV21 ) )
= $false )
| ( ( SV21 @ SV127 )
= $false )
| ( ( SV21
@ ( descr
@ ^ [SY546: $i] : ( SV21 @ SY546 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[842]) ).
thf(898,plain,
! [SV24: $i,SV84: $i > $o,SV143: $i] :
( ( ( ~ ( in @ ( sK31_SY683 @ SV143 @ SV84 @ SV24 ) @ SV24 )
| ~ ~ ( SV84 @ ( sK31_SY683 @ SV143 @ SV84 @ SV24 ) ) )
= $false )
| ( ( SV84 @ SV143 )
= $true )
| ( ( in @ SV143 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(899,plain,
! [SV29: $i,SV144: $i,SV88: $i > $o] :
( ( ( SV88 @ SV144 )
= $true )
| ( ( in @ SV144 @ SV29 )
= $false )
| ( ( ~ ! [SY687: $i] :
( ~ ( in @ SY687 @ SV29 )
| ( SV88 @ SY687 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[847]) ).
thf(900,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ~ ( SV30 @ ( sK35_SY753 @ SV129 @ SV30 ) ) )
= $false )
| ( ( SV30 @ SV129 )
= $false )
| ( ( ~ ! [SY565: $i] :
~ ~ ( ~ ( SV30 @ SY565 )
| ~ ! [SY566: $i] :
( ~ ( SV30 @ SY566 )
| ( SY565 = SY566 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[848]) ).
thf(901,plain,
! [SV30: $i > $o,SV129: $i] :
( ( ( SV129
= ( sK35_SY753 @ SV129 @ SV30 ) )
= $false )
| ( ( SV30 @ SV129 )
= $false )
| ( ( ~ ! [SY565: $i] :
~ ~ ( ~ ( SV30 @ SY565 )
| ~ ! [SY566: $i] :
( ~ ( SV30 @ SY566 )
| ( SY565 = SY566 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[848]) ).
thf(902,plain,
! [SV89: $i,SV31: $i] :
( ( ( in @ ( sK32_SY689 @ SV31 @ SV89 ) @ SV89 )
= $true )
| ( ( SV31 = SV89 )
= $true )
| ( ( in @ ( sK9_SY688 @ SV89 @ SV31 ) @ SV31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[849]) ).
thf(903,plain,
! [SV33: $i,SV146: $o,SV91: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV91 )
| SV146 )
= $false )
| ( SV146 = $true )
| ( ( SV116 = SV33 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(904,plain,
! [SV33: $i,SV146: $o,SV91: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV91 ) )
= $false )
| ( SV146 = $true )
| ( SV146 = $false )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(905,plain,
! [SV91: $i,SV33: $i,SV116: $i,SV146: $o] :
( ( SV146 = $false )
| ( SV146 = $true )
| ( SV146 = $false )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(906,plain,
! [SV33: $i,SV91: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV91 )
| $true )
= $false )
| ( $true = $true )
| ( ( SV116 = SV33 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(907,plain,
! [SV33: $i,SV91: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV91 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(908,plain,
! [SV91: $i,SV33: $i,SV116: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(909,plain,
! [SV33: $i,SV91: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV91 )
| $false )
= $false )
| ( $false = $true )
| ( ( SV116 = SV33 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(910,plain,
! [SV33: $i,SV91: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV91 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(911,plain,
! [SV91: $i,SV33: $i,SV116: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(912,plain,
! [SV92: $i > $o,SV34: $i,SV152: $i] :
( ( ( ~ ( in @ SV152 @ SV34 )
| ~ ( SV92 @ SV152 ) )
= $true )
| ( ( in @ ( sK10_SY694 @ SV92 @ SV34 ) @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[858]) ).
thf(913,plain,
! [SV92: $i > $o,SV34: $i,SV153: $i] :
( ( ( ~ ( in @ SV153 @ SV34 )
| ~ ( SV92 @ SV153 ) )
= $true )
| ( ( SV92 @ ( sK10_SY694 @ SV92 @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[859]) ).
thf(914,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ ( sK36_SY755 @ SV131 @ SV36 ) ) )
= $false )
| ( ( SV36 @ SV131 )
= $false )
| ( ( ~ ! [SY582: $i] :
~ ~ ( ~ ( SV36 @ SY582 )
| ~ ! [SY583: $i] :
( ~ ( SV36 @ SY583 )
| ( SY582 = SY583 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[860]) ).
thf(915,plain,
! [SV36: $i > $o,SV131: $i] :
( ( ( SV131
= ( sK36_SY755 @ SV131 @ SV36 ) )
= $false )
| ( ( SV36 @ SV131 )
= $false )
| ( ( ~ ! [SY582: $i] :
~ ~ ( ~ ( SV36 @ SY582 )
| ~ ! [SY583: $i] :
( ~ ( SV36 @ SY583 )
| ( SY582 = SY583 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[860]) ).
thf(916,plain,
! [SV132: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ ( sK37_SY756 @ SV132 @ SV40 ) ) )
= $false )
| ( ( SV40 @ SV132 )
= $false )
| ( ( ~ ! [SY590: $i] :
~ ! [SY591: $i] :
~ ( ~ ( ~ ( SV40 @ SY591 )
| ( SY591 = SY590 ) )
| ~ ( ( SY591 != SY590 )
| ( SV40 @ SY591 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[861]) ).
thf(917,plain,
! [SV40: $i > $o,SV132: $i] :
( ( ( SV132
= ( sK37_SY756 @ SV132 @ SV40 ) )
= $false )
| ( ( SV40 @ SV132 )
= $false )
| ( ( ~ ! [SY590: $i] :
~ ! [SY591: $i] :
~ ( ~ ( ~ ( SV40 @ SY591 )
| ( SY591 = SY590 ) )
| ~ ( ( SY591 != SY590 )
| ( SV40 @ SY591 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[861]) ).
thf(918,plain,
! [SV133: $i,SV41: $i > $o] :
( ( ( ~ ( SV41 @ ( sK38_SY757 @ SV133 @ SV41 ) ) )
= $false )
| ( ( SV41 @ SV133 )
= $false )
| ( ( ~ ! [SY594: $i] :
~ ( SV41 @ SY594 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[862]) ).
thf(919,plain,
! [SV41: $i > $o,SV133: $i] :
( ( ( SV133
= ( sK38_SY757 @ SV133 @ SV41 ) )
= $false )
| ( ( SV41 @ SV133 )
= $false )
| ( ( ~ ! [SY594: $i] :
~ ( SV41 @ SY594 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[862]) ).
thf(920,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( SV43 @ ( sK27_SY597 @ SV134 @ SV43 ) )
= $true )
| ( ( ~ ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[863]) ).
thf(921,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ ( sK33_SY773 @ SV134 @ SV43 ) ) )
= $false )
| ( ( ~ ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[864]) ).
thf(922,plain,
! [SV43: $i > $o,SV134: $i] :
( ( ( ( sK27_SY597 @ SV134 @ SV43 )
= ( sK33_SY773 @ SV134 @ SV43 ) )
= $false )
| ( ( ~ ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[864]) ).
thf(923,plain,
! [SV135: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK39_SY758 @ SV135 @ SV49 ) ) )
= $false )
| ( ( SV49 @ SV135 )
= $false )
| ( ( ! [SY609: $i,SY610: $i] :
( ~ ( SV49 @ SY609 )
| ~ ( SV49 @ SY610 )
| ( SY609 = SY610 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[865]) ).
thf(924,plain,
! [SV49: $i > $o,SV135: $i] :
( ( ( SV135
= ( sK39_SY758 @ SV135 @ SV49 ) )
= $false )
| ( ( SV49 @ SV135 )
= $false )
| ( ( ! [SY609: $i,SY610: $i] :
( ~ ( SV49 @ SY609 )
| ~ ( SV49 @ SY610 )
| ( SY609 = SY610 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[865]) ).
thf(925,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( ~ ( ( ( sK19_SY759 @ SV136 @ SV50 )
!= SV136 )
| ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) ) ) )
= $true )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[866]) ).
thf(926,plain,
! [SV50: $i > $o,SV136: $i] :
( ( ( ( ( sK19_SY759 @ SV136 @ SV50 )
!= SV136 )
| ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) ) )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(927,plain,
! [SV52: $i] :
( ( ( ~ ( in @ ( sK24_SY618 @ SV52 ) @ omega ) )
= $false )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY619: $i] :
( ~ ( in @ SY619 @ omega )
| ( in @ SY619 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[868]) ).
thf(928,plain,
! [SV52: $i] :
( ( ( ~ ( in @ ( sK24_SY618 @ SV52 ) @ SV52 ) )
= $false )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY619: $i] :
( ~ ( in @ SY619 @ omega )
| ( in @ SY619 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[868]) ).
thf(929,plain,
! [SV52: $i,SV154: $i] :
( ( ( in @ SV154 @ omega )
= $false )
| ( ( in @ SV154 @ SV52 )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( in @ ( setadjoin @ ( sK24_SY618 @ SV52 ) @ ( sK24_SY618 @ SV52 ) ) @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(930,plain,
! [SV156: $i] :
( ( ( ~ ( sK1_SX0 @ SV156 ) )
= $true )
| ( ( sK15_SY702 = SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(931,plain,
! [SV106: $i,SV147: $i,SV58: $i,SV137: $i] :
( ( ( ~ ( in @ SV137 @ SV58 ) )
= $true )
| ( ( in @ SV147 @ SV106 )
= $true )
| ( ( SV137 = SV147 )
= $false )
| ( ( SV58 = SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(932,plain,
! [SV58: $i,SV137: $i,SV106: $i,SV147: $i] :
( ( ( ~ ( in @ SV147 @ SV106 ) )
= $true )
| ( ( in @ SV137 @ SV58 )
= $true )
| ( ( SV137 = SV147 )
= $false )
| ( ( SV58 = SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(933,plain,
! [SV61: $i,SV139: $i] :
( ( ( in @ ( sK25_SY635 @ SV139 @ SV61 ) @ SV61 )
= $true )
| ( ( in @ SV139 @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[873]) ).
thf(934,plain,
! [SV61: $i,SV139: $i] :
( ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ ( sK25_SY635 @ SV139 @ SV61 ) )
| ~ ( in @ SY771 @ SV61 ) ) )
= $true )
| ( ( in @ SV139 @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[874]) ).
thf(935,plain,
! [SV107: $i,SV63: $i > $i > $o,SV157: $i] :
( ( ( ~ ( ~ ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
| ~ ! [SY780: $i] :
~ ~ ( ~ ( in @ SY780 @ SV107 )
| ~ ( SV63 @ SY780 @ SV157 ) ) )
| ~ ( ~ ~ ! [SY781: $i] :
~ ~ ( ~ ( in @ SY781 @ SV107 )
| ~ ( SV63 @ SY781 @ SV157 ) )
| ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) ) ) )
= $false )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[875]) ).
thf(936,plain,
! [SV150: $i,SV107: $i,SV63: $i > $i > $o] :
( ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( ~ ! [SY772: $i] :
( ~ ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SY772 )
| ( SV150 = SY772 ) ) )
= $true )
| ( ( ~ ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(937,plain,
! [SV64: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ ( sK29_SY721 @ SV64 @ SV108 ) ) )
= $false )
| ( ( in @ SV108 @ ( setunion @ SV64 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[877]) ).
thf(938,plain,
! [SV108: $i,SV64: $i] :
( ( ( ~ ( in @ ( sK29_SY721 @ SV64 @ SV108 ) @ SV64 ) )
= $false )
| ( ( in @ SV108 @ ( setunion @ SV64 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[877]) ).
thf(939,plain,
! [SV64: $i,SV151: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ SV151 ) )
= $true )
| ( ( ~ ( in @ SV151 @ SV64 ) )
= $true )
| ( ( in @ SV108 @ ( setunion @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(940,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) ) )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(941,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) ) )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[880]) ).
thf(942,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
| ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(943,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[882]) ).
thf(944,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[882]) ).
thf(945,plain,
! [SV12: $i,SV75: $i] :
( ( ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV75 )
= $true )
| ( ( in @ ( sK8_SY667 @ SV75 @ SV12 ) @ SV12 )
= $true )
| ( ( SV12 = SV75 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[883]) ).
thf(946,plain,
! [SV76: $i > $o,SV13: $i,SV158: $i] :
( ( ( ~ ( in @ SV158 @ SV13 ) )
= $true )
| ( ( ~ ( SV76 @ SV158 ) )
= $true )
| ( ( in @ ( sK17_SY668 @ SV76 @ SV13 ) @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(947,plain,
! [SV76: $i > $o,SV13: $i,SV159: $i] :
( ( ( ~ ( in @ SV159 @ SV13 ) )
= $true )
| ( ( ~ ( SV76 @ SV159 ) )
= $true )
| ( ( SV76 @ ( sK17_SY668 @ SV76 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(948,plain,
! [SV141: $i,SV77: $i > $o,SV14: $i] :
( ( ( ( dsetconstr @ SV14
@ ^ [SY671: $i] : ( SV77 @ SY671 ) )
= emptyset )
= $false )
| ( $false = $true )
| ( ( in @ SV141 @ SV14 )
= $false )
| ( ( SV77 @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(949,plain,
! [SV15: $i,SV78: $i > $o,SV142: $i] :
( ( ( ~ ( in @ ( sK30_SY673 @ SV142 @ SV78 @ SV15 ) @ SV15 ) )
= $false )
| ( ( SV78 @ SV142 )
= $true )
| ( ( in @ SV142 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[889]) ).
thf(950,plain,
! [SV15: $i,SV142: $i,SV78: $i > $o] :
( ( ( ~ ~ ( SV78 @ ( sK30_SY673 @ SV142 @ SV78 @ SV15 ) ) )
= $false )
| ( ( SV78 @ SV142 )
= $true )
| ( ( in @ SV142 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[889]) ).
thf(951,plain,
! [SV79: $i > $o,SV16: $i,SV160: $i] :
( ( ( ~ ( in @ SV160 @ SV16 ) )
= $true )
| ( ( ~ ( SV79 @ SV160 ) )
= $true )
| ( ( in @ ( sK18_SY674 @ SV79 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(952,plain,
! [SV79: $i > $o,SV16: $i,SV161: $i] :
( ( ( ~ ( in @ SV161 @ SV16 ) )
= $true )
| ( ( ~ ( SV79 @ SV161 ) )
= $true )
| ( ( SV79 @ ( sK18_SY674 @ SV79 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(953,plain,
! [SV18: $i] :
( ( ! [SY724: $i] :
( ~ ( in @ SY724 @ ( sK2_SY521 @ SV18 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ SY724 )
| ( in @ SY523 @ SV18 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[892]) ).
thf(954,plain,
! [SV18: $i] :
( ( ! [SY726: $i,SY727: $i] :
( ~ ~ ( ~ ( in @ SY726 @ SV18 )
| ~ ( in @ SY727 @ SV18 ) )
| ~ ! [SY728: $i] :
( ~ ( in @ SY728 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SY726 @ SY728 )
| ( in @ SY727 @ SY728 ) )
| ~ ( ~ ( in @ SY727 @ SY728 )
| ( in @ SY726 @ SY728 ) ) ) )
| ( SY726 = SY727 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[893]) ).
thf(955,plain,
! [SV162: $i,SV18: $i,SV155: $i] :
( ( ( ~ ~ ( ~ ( in @ SV155 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SV162 @ ( sK2_SY521 @ SV18 ) ) ) )
= $true )
| ( ( ! [SY782: $i] :
( ~ ( in @ SY782 @ SV155 )
| ( in @ SY782 @ SV162 ) )
| ! [SY783: $i] :
( ~ ( in @ SY783 @ SV162 )
| ( in @ SY783 @ SV155 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[894]) ).
thf(956,plain,
! [SV18: $i,SV148: $i] :
( ( ( ! [SY764: $i] :
( ~ ( in @ SY764 @ SV148 )
| ( in @ SY764 @ SV18 ) ) )
= $false )
| ( ( ~ ~ ! [SY765: $i] :
~ ( in @ SY765 @ SV148 ) )
= $true )
| ( ( ~ ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(957,plain,
! [SV127: $i,SV21: $i > $o] :
( ( ( SV21 @ ( sK34_SY751 @ SV127 @ SV21 ) )
= $true )
| ( ( SV21 @ SV127 )
= $false )
| ( ( SV21
@ ( descr
@ ^ [SY546: $i] : ( SV21 @ SY546 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[896]) ).
thf(958,plain,
! [SV24: $i,SV84: $i > $o,SV143: $i] :
( ( ( ~ ( in @ ( sK31_SY683 @ SV143 @ SV84 @ SV24 ) @ SV24 ) )
= $false )
| ( ( SV84 @ SV143 )
= $true )
| ( ( in @ SV143 @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[898]) ).
thf(959,plain,
! [SV24: $i,SV143: $i,SV84: $i > $o] :
( ( ( ~ ~ ( SV84 @ ( sK31_SY683 @ SV143 @ SV84 @ SV24 ) ) )
= $false )
| ( ( SV84 @ SV143 )
= $true )
| ( ( in @ SV143 @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[898]) ).
thf(960,plain,
! [SV144: $i,SV88: $i > $o,SV29: $i] :
( ( ( ! [SY687: $i] :
( ~ ( in @ SY687 @ SV29 )
| ( SV88 @ SY687 ) ) )
= $false )
| ( ( in @ SV144 @ SV29 )
= $false )
| ( ( SV88 @ SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(961,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( SV30 @ ( sK35_SY753 @ SV129 @ SV30 ) )
= $true )
| ( ( SV30 @ SV129 )
= $false )
| ( ( ~ ! [SY565: $i] :
~ ~ ( ~ ( SV30 @ SY565 )
| ~ ! [SY566: $i] :
( ~ ( SV30 @ SY566 )
| ( SY565 = SY566 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[900]) ).
thf(962,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ! [SY565: $i] :
~ ~ ( ~ ( SV30 @ SY565 )
| ~ ! [SY566: $i] :
( ~ ( SV30 @ SY566 )
| ( SY565 = SY566 ) ) ) )
= $false )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV129
= ( sK35_SY753 @ SV129 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(963,plain,
! [SV33: $i,SV146: $o,SV91: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV91 ) )
= $false )
| ( SV146 = $true )
| ( ( SV116 = SV33 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[903]) ).
thf(964,plain,
! [SV91: $i,SV33: $i,SV116: $i,SV146: $o] :
( ( SV146 = $false )
| ( SV146 = $true )
| ( ( SV116 = SV33 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[903]) ).
thf(965,plain,
! [SV33: $i,SV146: $o,SV91: $i,SV116: $i] :
( ( ( in @ SV116 @ SV91 )
= $true )
| ( SV146 = $true )
| ( SV146 = $false )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[904]) ).
thf(966,plain,
! [SV33: $i,SV91: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV91 ) )
= $false )
| ( $true = $true )
| ( ( SV116 = SV33 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(967,plain,
! [SV91: $i,SV33: $i,SV116: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( SV116 = SV33 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(968,plain,
! [SV33: $i,SV91: $i,SV116: $i] :
( ( ( in @ SV116 @ SV91 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[907]) ).
thf(969,plain,
! [SV33: $i,SV91: $i,SV116: $i] :
( ( ( ~ ( in @ SV116 @ SV91 ) )
= $false )
| ( $false = $true )
| ( ( SV116 = SV33 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[909]) ).
thf(970,plain,
! [SV91: $i,SV33: $i,SV116: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( SV116 = SV33 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[909]) ).
thf(971,plain,
! [SV33: $i,SV91: $i,SV116: $i] :
( ( ( in @ SV116 @ SV91 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[910]) ).
thf(972,plain,
! [SV92: $i > $o,SV34: $i,SV152: $i] :
( ( ( ~ ( in @ SV152 @ SV34 ) )
= $true )
| ( ( ~ ( SV92 @ SV152 ) )
= $true )
| ( ( in @ ( sK10_SY694 @ SV92 @ SV34 ) @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(973,plain,
! [SV92: $i > $o,SV34: $i,SV153: $i] :
( ( ( ~ ( in @ SV153 @ SV34 ) )
= $true )
| ( ( ~ ( SV92 @ SV153 ) )
= $true )
| ( ( SV92 @ ( sK10_SY694 @ SV92 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(974,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( SV36 @ ( sK36_SY755 @ SV131 @ SV36 ) )
= $true )
| ( ( SV36 @ SV131 )
= $false )
| ( ( ~ ! [SY582: $i] :
~ ~ ( ~ ( SV36 @ SY582 )
| ~ ! [SY583: $i] :
( ~ ( SV36 @ SY583 )
| ( SY582 = SY583 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[914]) ).
thf(975,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ! [SY582: $i] :
~ ~ ( ~ ( SV36 @ SY582 )
| ~ ! [SY583: $i] :
( ~ ( SV36 @ SY583 )
| ( SY582 = SY583 ) ) ) )
= $false )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV131
= ( sK36_SY755 @ SV131 @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(976,plain,
! [SV132: $i,SV40: $i > $o] :
( ( ( SV40 @ ( sK37_SY756 @ SV132 @ SV40 ) )
= $true )
| ( ( SV40 @ SV132 )
= $false )
| ( ( ~ ! [SY590: $i] :
~ ! [SY591: $i] :
~ ( ~ ( ~ ( SV40 @ SY591 )
| ( SY591 = SY590 ) )
| ~ ( ( SY591 != SY590 )
| ( SV40 @ SY591 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[916]) ).
thf(977,plain,
! [SV132: $i,SV40: $i > $o] :
( ( ( ! [SY590: $i] :
~ ! [SY591: $i] :
~ ( ~ ( ~ ( SV40 @ SY591 )
| ( SY591 = SY590 ) )
| ~ ( ( SY591 != SY590 )
| ( SV40 @ SY591 ) ) ) )
= $false )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV132
= ( sK37_SY756 @ SV132 @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(978,plain,
! [SV133: $i,SV41: $i > $o] :
( ( ( SV41 @ ( sK38_SY757 @ SV133 @ SV41 ) )
= $true )
| ( ( SV41 @ SV133 )
= $false )
| ( ( ~ ! [SY594: $i] :
~ ( SV41 @ SY594 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[918]) ).
thf(979,plain,
! [SV133: $i,SV41: $i > $o] :
( ( ( ! [SY594: $i] :
~ ( SV41 @ SY594 ) )
= $false )
| ( ( SV41 @ SV133 )
= $false )
| ( ( SV133
= ( sK38_SY757 @ SV133 @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(980,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $false )
| ( ( SV43 @ ( sK27_SY597 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(981,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( SV43 @ ( sK33_SY773 @ SV134 @ SV43 ) )
= $true )
| ( ( ~ ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[921]) ).
thf(982,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $false )
| ( ( ( sK27_SY597 @ SV134 @ SV43 )
= ( sK33_SY773 @ SV134 @ SV43 ) )
= $false )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(983,plain,
! [SV135: $i,SV49: $i > $o] :
( ( ( SV49 @ ( sK39_SY758 @ SV135 @ SV49 ) )
= $true )
| ( ( SV49 @ SV135 )
= $false )
| ( ( ! [SY609: $i,SY610: $i] :
( ~ ( SV49 @ SY609 )
| ~ ( SV49 @ SY610 )
| ( SY609 = SY610 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[923]) ).
thf(984,plain,
! [SV135: $i,SV163: $i,SV49: $i > $o] :
( ( ( ! [SY784: $i] :
( ~ ( SV49 @ SV163 )
| ~ ( SV49 @ SY784 )
| ( SV163 = SY784 ) ) )
= $true )
| ( ( SV49 @ SV135 )
= $false )
| ( ( SV135
= ( sK39_SY758 @ SV135 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(985,plain,
! [SV50: $i > $o,SV136: $i] :
( ( ( ( ( sK19_SY759 @ SV136 @ SV50 )
!= SV136 )
| ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) ) )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(986,plain,
! [SV50: $i > $o,SV136: $i] :
( ( ( ( sK19_SY759 @ SV136 @ SV50 )
!= SV136 )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[926]) ).
thf(987,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[926]) ).
thf(988,plain,
! [SV52: $i] :
( ( ( in @ ( sK24_SY618 @ SV52 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY619: $i] :
( ~ ( in @ SY619 @ omega )
| ( in @ SY619 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[927]) ).
thf(989,plain,
! [SV52: $i] :
( ( ( in @ ( sK24_SY618 @ SV52 ) @ SV52 )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY619: $i] :
( ~ ( in @ SY619 @ omega )
| ( in @ SY619 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[928]) ).
thf(990,plain,
! [SV156: $i] :
( ( ( sK1_SX0 @ SV156 )
= $false )
| ( ( sK15_SY702 = SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(991,plain,
! [SV106: $i,SV147: $i,SV58: $i,SV137: $i] :
( ( ( in @ SV137 @ SV58 )
= $false )
| ( ( in @ SV147 @ SV106 )
= $true )
| ( ( SV137 = SV147 )
= $false )
| ( ( SV58 = SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(992,plain,
! [SV58: $i,SV137: $i,SV106: $i,SV147: $i] :
( ( ( in @ SV147 @ SV106 )
= $false )
| ( ( in @ SV137 @ SV58 )
= $true )
| ( ( SV137 = SV147 )
= $false )
| ( ( SV58 = SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(993,plain,
! [SV61: $i,SV139: $i] :
( ( ( ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ ( sK25_SY635 @ SV139 @ SV61 ) )
| ~ ( in @ SY771 @ SV61 ) ) )
= $false )
| ( ( in @ SV139 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(994,plain,
! [SV107: $i,SV63: $i > $i > $o,SV157: $i] :
( ( ( ~ ( ~ ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
| ~ ! [SY780: $i] :
~ ~ ( ~ ( in @ SY780 @ SV107 )
| ~ ( SV63 @ SY780 @ SV157 ) ) ) )
= $false )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[935]) ).
thf(995,plain,
! [SV157: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ~ ( ~ ~ ! [SY781: $i] :
~ ~ ( ~ ( in @ SY781 @ SV107 )
| ~ ( SV63 @ SY781 @ SV157 ) )
| ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) ) ) )
= $false )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[935]) ).
thf(996,plain,
! [SV150: $i,SV107: $i,SV63: $i > $i > $o] :
( ( ( ! [SY772: $i] :
( ~ ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SY772 )
| ( SV150 = SY772 ) ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( ~ ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(997,plain,
! [SV64: $i,SV108: $i] :
( ( ( in @ SV108 @ ( sK29_SY721 @ SV64 @ SV108 ) )
= $true )
| ( ( in @ SV108 @ ( setunion @ SV64 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[937]) ).
thf(998,plain,
! [SV108: $i,SV64: $i] :
( ( ( in @ ( sK29_SY721 @ SV64 @ SV108 ) @ SV64 )
= $true )
| ( ( in @ SV108 @ ( setunion @ SV64 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[938]) ).
thf(999,plain,
! [SV64: $i,SV151: $i,SV108: $i] :
( ( ( in @ SV108 @ SV151 )
= $false )
| ( ( ~ ( in @ SV151 @ SV64 ) )
= $true )
| ( ( in @ SV108 @ ( setunion @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(1000,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[940]) ).
thf(1001,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[941]) ).
thf(1002,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(1003,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(1004,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[943]) ).
thf(1005,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(1006,plain,
! [SV76: $i > $o,SV13: $i,SV158: $i] :
( ( ( in @ SV158 @ SV13 )
= $false )
| ( ( ~ ( SV76 @ SV158 ) )
= $true )
| ( ( in @ ( sK17_SY668 @ SV76 @ SV13 ) @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[946]) ).
thf(1007,plain,
! [SV76: $i > $o,SV13: $i,SV159: $i] :
( ( ( in @ SV159 @ SV13 )
= $false )
| ( ( ~ ( SV76 @ SV159 ) )
= $true )
| ( ( SV76 @ ( sK17_SY668 @ SV76 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(1008,plain,
! [SV15: $i,SV78: $i > $o,SV142: $i] :
( ( ( in @ ( sK30_SY673 @ SV142 @ SV78 @ SV15 ) @ SV15 )
= $true )
| ( ( SV78 @ SV142 )
= $true )
| ( ( in @ SV142 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[949]) ).
thf(1009,plain,
! [SV15: $i,SV142: $i,SV78: $i > $o] :
( ( ( ~ ( SV78 @ ( sK30_SY673 @ SV142 @ SV78 @ SV15 ) ) )
= $true )
| ( ( SV78 @ SV142 )
= $true )
| ( ( in @ SV142 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(1010,plain,
! [SV79: $i > $o,SV16: $i,SV160: $i] :
( ( ( in @ SV160 @ SV16 )
= $false )
| ( ( ~ ( SV79 @ SV160 ) )
= $true )
| ( ( in @ ( sK18_SY674 @ SV79 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(1011,plain,
! [SV79: $i > $o,SV16: $i,SV161: $i] :
( ( ( in @ SV161 @ SV16 )
= $false )
| ( ( ~ ( SV79 @ SV161 ) )
= $true )
| ( ( SV79 @ ( sK18_SY674 @ SV79 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(1012,plain,
! [SV18: $i,SV164: $i] :
( ( ~ ( in @ SV164 @ ( sK2_SY521 @ SV18 ) )
| ! [SY785: $i] :
( ~ ( in @ SY785 @ SV164 )
| ( in @ SY785 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1013,plain,
! [SV18: $i,SV165: $i] :
( ( ! [SY786: $i] :
( ~ ~ ( ~ ( in @ SV165 @ SV18 )
| ~ ( in @ SY786 @ SV18 ) )
| ~ ! [SY787: $i] :
( ~ ( in @ SY787 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SV165 @ SY787 )
| ( in @ SY786 @ SY787 ) )
| ~ ( ~ ( in @ SY786 @ SY787 )
| ( in @ SV165 @ SY787 ) ) ) )
| ( SV165 = SY786 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1014,plain,
! [SV162: $i,SV18: $i,SV155: $i] :
( ( ( ~ ( ~ ( in @ SV155 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SV162 @ ( sK2_SY521 @ SV18 ) ) ) )
= $false )
| ( ( ! [SY782: $i] :
( ~ ( in @ SY782 @ SV155 )
| ( in @ SY782 @ SV162 ) )
| ! [SY783: $i] :
( ~ ( in @ SY783 @ SV162 )
| ( in @ SY783 @ SV155 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1015,plain,
! [SV148: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
| ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 ) )
= $false )
| ( ( ~ ~ ! [SY765: $i] :
~ ( in @ SY765 @ SV148 ) )
= $true )
| ( ( ~ ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[956]) ).
thf(1016,plain,
! [SV24: $i,SV84: $i > $o,SV143: $i] :
( ( ( in @ ( sK31_SY683 @ SV143 @ SV84 @ SV24 ) @ SV24 )
= $true )
| ( ( SV84 @ SV143 )
= $true )
| ( ( in @ SV143 @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[958]) ).
thf(1017,plain,
! [SV24: $i,SV143: $i,SV84: $i > $o] :
( ( ( ~ ( SV84 @ ( sK31_SY683 @ SV143 @ SV84 @ SV24 ) ) )
= $true )
| ( ( SV84 @ SV143 )
= $true )
| ( ( in @ SV143 @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[959]) ).
thf(1018,plain,
! [SV29: $i,SV88: $i > $o,SV144: $i] :
( ( ( ~ ( in @ ( sK41_SY687 @ SV144 @ SV88 @ SV29 ) @ SV29 )
| ( SV88 @ ( sK41_SY687 @ SV144 @ SV88 @ SV29 ) ) )
= $false )
| ( ( in @ SV144 @ SV29 )
= $false )
| ( ( SV88 @ SV144 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[960]) ).
thf(1019,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ! [SY565: $i] :
~ ~ ( ~ ( SV30 @ SY565 )
| ~ ! [SY566: $i] :
( ~ ( SV30 @ SY566 )
| ( SY565 = SY566 ) ) ) )
= $false )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV30 @ ( sK35_SY753 @ SV129 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(1020,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ~ ~ ( ~ ( SV30 @ ( sK42_SY565 @ SV129 @ SV30 ) )
| ~ ! [SY788: $i] :
( ~ ( SV30 @ SY788 )
| ( ( sK42_SY565 @ SV129 @ SV30 )
= SY788 ) ) ) )
= $false )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV129
= ( sK35_SY753 @ SV129 @ SV30 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[962]) ).
thf(1021,plain,
! [SV33: $i,SV146: $o,SV91: $i,SV116: $i] :
( ( ( in @ SV116 @ SV91 )
= $true )
| ( SV146 = $true )
| ( ( SV116 = SV33 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[963]) ).
thf(1022,plain,
! [SV33: $i,SV91: $i,SV116: $i] :
( ( ( in @ SV116 @ SV91 )
= $true )
| ( $true = $true )
| ( ( SV116 = SV33 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[966]) ).
thf(1023,plain,
! [SV33: $i,SV91: $i,SV116: $i] :
( ( ( in @ SV116 @ SV91 )
= $true )
| ( $false = $true )
| ( ( SV116 = SV33 )
= $true )
| ( ( in @ SV116 @ ( setadjoin @ SV33 @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[969]) ).
thf(1024,plain,
! [SV92: $i > $o,SV34: $i,SV152: $i] :
( ( ( in @ SV152 @ SV34 )
= $false )
| ( ( ~ ( SV92 @ SV152 ) )
= $true )
| ( ( in @ ( sK10_SY694 @ SV92 @ SV34 ) @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1025,plain,
! [SV92: $i > $o,SV34: $i,SV153: $i] :
( ( ( in @ SV153 @ SV34 )
= $false )
| ( ( ~ ( SV92 @ SV153 ) )
= $true )
| ( ( SV92 @ ( sK10_SY694 @ SV92 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(1026,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ! [SY582: $i] :
~ ~ ( ~ ( SV36 @ SY582 )
| ~ ! [SY583: $i] :
( ~ ( SV36 @ SY583 )
| ( SY582 = SY583 ) ) ) )
= $false )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV36 @ ( sK36_SY755 @ SV131 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1027,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ~ ~ ( ~ ( SV36 @ ( sK43_SY582 @ SV131 @ SV36 ) )
| ~ ! [SY789: $i] :
( ~ ( SV36 @ SY789 )
| ( ( sK43_SY582 @ SV131 @ SV36 )
= SY789 ) ) ) )
= $false )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV131
= ( sK36_SY755 @ SV131 @ SV36 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[975]) ).
thf(1028,plain,
! [SV132: $i,SV40: $i > $o] :
( ( ( ! [SY590: $i] :
~ ! [SY591: $i] :
~ ( ~ ( ~ ( SV40 @ SY591 )
| ( SY591 = SY590 ) )
| ~ ( ( SY591 != SY590 )
| ( SV40 @ SY591 ) ) ) )
= $false )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV40 @ ( sK37_SY756 @ SV132 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1029,plain,
! [SV132: $i,SV40: $i > $o] :
( ( ( ~ ! [SY790: $i] :
~ ( ~ ( ~ ( SV40 @ SY790 )
| ( SY790
= ( sK44_SY590 @ SV132 @ SV40 ) ) )
| ~ ( ( SY790
!= ( sK44_SY590 @ SV132 @ SV40 ) )
| ( SV40 @ SY790 ) ) ) )
= $false )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV132
= ( sK37_SY756 @ SV132 @ SV40 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[977]) ).
thf(1030,plain,
! [SV133: $i,SV41: $i > $o] :
( ( ( ! [SY594: $i] :
~ ( SV41 @ SY594 ) )
= $false )
| ( ( SV41 @ SV133 )
= $false )
| ( ( SV41 @ ( sK38_SY757 @ SV133 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1031,plain,
! [SV133: $i,SV41: $i > $o] :
( ( ( ~ ( SV41 @ ( sK45_SY594 @ SV133 @ SV41 ) ) )
= $false )
| ( ( SV41 @ SV133 )
= $false )
| ( ( SV133
= ( sK38_SY757 @ SV133 @ SV41 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[979]) ).
thf(1032,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ~ ( ~ ( SV43 @ ( sK46_SY599 @ SV134 @ SV43 ) )
| ~ ! [SY791: $i] :
( ~ ( SV43 @ SY791 )
| ( ( sK46_SY599 @ SV134 @ SV43 )
= SY791 ) ) ) )
= $false )
| ( ( SV43 @ ( sK27_SY597 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[980]) ).
thf(1033,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ! [SY599: $i] :
~ ~ ( ~ ( SV43 @ SY599 )
| ~ ! [SY600: $i] :
( ~ ( SV43 @ SY600 )
| ( SY599 = SY600 ) ) ) )
= $false )
| ( ( SV43 @ ( sK33_SY773 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1034,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ~ ( ~ ( SV43 @ ( sK47_SY599 @ SV134 @ SV43 ) )
| ~ ! [SY792: $i] :
( ~ ( SV43 @ SY792 )
| ( ( sK47_SY599 @ SV134 @ SV43 )
= SY792 ) ) ) )
= $false )
| ( ( ( sK27_SY597 @ SV134 @ SV43 )
= ( sK33_SY773 @ SV134 @ SV43 ) )
= $false )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[982]) ).
thf(1035,plain,
! [SV135: $i,SV166: $i,SV49: $i > $o] :
( ( ( ! [SY793: $i] :
( ~ ( SV49 @ SV166 )
| ~ ( SV49 @ SY793 )
| ( SV166 = SY793 ) ) )
= $true )
| ( ( SV49 @ SV135 )
= $false )
| ( ( SV49 @ ( sK39_SY758 @ SV135 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1036,plain,
! [SV135: $i,SV167: $i,SV163: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV163 )
| ~ ( SV49 @ SV167 )
| ( SV163 = SV167 ) )
= $true )
| ( ( SV49 @ SV135 )
= $false )
| ( ( SV135
= ( sK39_SY758 @ SV135 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1037,plain,
! [SV50: $i > $o,SV136: $i] :
( ( ( ( sK19_SY759 @ SV136 @ SV50 )
!= SV136 )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[985]) ).
thf(1038,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[985]) ).
thf(1039,plain,
! [SV50: $i > $o,SV136: $i] :
( ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[986]) ).
thf(1040,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1041,plain,
! [SV52: $i,SV168: $i] :
( ( ( ~ ( in @ SV168 @ omega )
| ( in @ SV168 @ SV52 ) )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( in @ ( sK24_SY618 @ SV52 ) @ omega )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1042,plain,
! [SV52: $i,SV169: $i] :
( ( ( ~ ( in @ SV169 @ omega )
| ( in @ SV169 @ SV52 ) )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( in @ ( sK24_SY618 @ SV52 ) @ SV52 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1043,plain,
! [SV61: $i,SV139: $i] :
( ( ( ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ ( sK25_SY635 @ SV139 @ SV61 ) )
| ~ ( in @ SY771 @ SV61 ) ) )
= $true )
| ( ( in @ SV139 @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[993]) ).
thf(1044,plain,
! [SV107: $i,SV63: $i > $i > $o,SV157: $i] :
( ( ( ~ ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
| ~ ! [SY780: $i] :
~ ~ ( ~ ( in @ SY780 @ SV107 )
| ~ ( SV63 @ SY780 @ SV157 ) ) )
= $true )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[994]) ).
thf(1045,plain,
! [SV157: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ~ ~ ! [SY781: $i] :
~ ~ ( ~ ( in @ SY781 @ SV107 )
| ~ ( SV63 @ SY781 @ SV157 ) )
| ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) ) )
= $true )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[995]) ).
thf(1046,plain,
! [SV150: $i,SV107: $i,SV63: $i > $i > $o] :
( ( ( ~ ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
| ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( ~ ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[996]) ).
thf(1047,plain,
! [SV108: $i,SV64: $i,SV151: $i] :
( ( ( in @ SV151 @ SV64 )
= $false )
| ( ( in @ SV108 @ SV151 )
= $false )
| ( ( in @ SV108 @ ( setunion @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1048,plain,
! [SV73: $i > $o,SV170: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ SV170 )
| ~ ! [SY794: $i] :
( ~ ( SV10 @ SY794 )
| ( SV170 = SY794 ) ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1049,plain,
! [SV10: $i > $o,SV171: $i,SV73: $i > $o] :
( ( ( ~ ~ ( ~ ( SV73 @ SV171 )
| ~ ! [SY795: $i] :
( ~ ( SV73 @ SY795 )
| ( SV171 = SY795 ) ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1050,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1002]) ).
thf(1051,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1052,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1053,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1005]) ).
thf(1054,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1005]) ).
thf(1055,plain,
! [SV13: $i,SV158: $i,SV76: $i > $o] :
( ( ( SV76 @ SV158 )
= $false )
| ( ( in @ SV158 @ SV13 )
= $false )
| ( ( in @ ( sK17_SY668 @ SV76 @ SV13 ) @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1056,plain,
! [SV13: $i,SV159: $i,SV76: $i > $o] :
( ( ( SV76 @ SV159 )
= $false )
| ( ( in @ SV159 @ SV13 )
= $false )
| ( ( SV76 @ ( sK17_SY668 @ SV76 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1057,plain,
! [SV15: $i,SV142: $i,SV78: $i > $o] :
( ( ( SV78 @ ( sK30_SY673 @ SV142 @ SV78 @ SV15 ) )
= $false )
| ( ( SV78 @ SV142 )
= $true )
| ( ( in @ SV142 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1058,plain,
! [SV16: $i,SV160: $i,SV79: $i > $o] :
( ( ( SV79 @ SV160 )
= $false )
| ( ( in @ SV160 @ SV16 )
= $false )
| ( ( in @ ( sK18_SY674 @ SV79 @ SV16 ) @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1059,plain,
! [SV16: $i,SV161: $i,SV79: $i > $o] :
( ( ( SV79 @ SV161 )
= $false )
| ( ( in @ SV161 @ SV16 )
= $false )
| ( ( SV79 @ ( sK18_SY674 @ SV79 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1060,plain,
! [SV18: $i,SV164: $i] :
( ( ( ~ ( in @ SV164 @ ( sK2_SY521 @ SV18 ) ) )
= $true )
| ( ( ! [SY785: $i] :
( ~ ( in @ SY785 @ SV164 )
| ( in @ SY785 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1061,plain,
! [SV172: $i,SV18: $i,SV165: $i] :
( ( ~ ~ ( ~ ( in @ SV165 @ SV18 )
| ~ ( in @ SV172 @ SV18 ) )
| ~ ! [SY796: $i] :
( ~ ( in @ SY796 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SV165 @ SY796 )
| ( in @ SV172 @ SY796 ) )
| ~ ( ~ ( in @ SV172 @ SY796 )
| ( in @ SV165 @ SY796 ) ) ) )
| ( SV165 = SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1062,plain,
! [SV162: $i,SV18: $i,SV155: $i] :
( ( ( ~ ( in @ SV155 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SV162 @ ( sK2_SY521 @ SV18 ) ) )
= $true )
| ( ( ! [SY782: $i] :
( ~ ( in @ SY782 @ SV155 )
| ( in @ SY782 @ SV162 ) )
| ! [SY783: $i] :
( ~ ( in @ SY783 @ SV162 )
| ( in @ SY783 @ SV155 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1014]) ).
thf(1063,plain,
! [SV148: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 ) )
= $false )
| ( ( ~ ~ ! [SY765: $i] :
~ ( in @ SY765 @ SV148 ) )
= $true )
| ( ( ~ ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1015]) ).
thf(1064,plain,
! [SV148: $i,SV18: $i] :
( ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( ~ ~ ! [SY765: $i] :
~ ( in @ SY765 @ SV148 ) )
= $true )
| ( ( ~ ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1015]) ).
thf(1065,plain,
! [SV24: $i,SV143: $i,SV84: $i > $o] :
( ( ( SV84 @ ( sK31_SY683 @ SV143 @ SV84 @ SV24 ) )
= $false )
| ( ( SV84 @ SV143 )
= $true )
| ( ( in @ SV143 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1066,plain,
! [SV29: $i,SV88: $i > $o,SV144: $i] :
( ( ( ~ ( in @ ( sK41_SY687 @ SV144 @ SV88 @ SV29 ) @ SV29 ) )
= $false )
| ( ( in @ SV144 @ SV29 )
= $false )
| ( ( SV88 @ SV144 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1018]) ).
thf(1067,plain,
! [SV29: $i,SV144: $i,SV88: $i > $o] :
( ( ( SV88 @ ( sK41_SY687 @ SV144 @ SV88 @ SV29 ) )
= $false )
| ( ( in @ SV144 @ SV29 )
= $false )
| ( ( SV88 @ SV144 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1018]) ).
thf(1068,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ~ ~ ( ~ ( SV30 @ ( sK49_SY565 @ SV129 @ SV30 ) )
| ~ ! [SY797: $i] :
( ~ ( SV30 @ SY797 )
| ( ( sK49_SY565 @ SV129 @ SV30 )
= SY797 ) ) ) )
= $false )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV30 @ ( sK35_SY753 @ SV129 @ SV30 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1019]) ).
thf(1069,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ~ ( ~ ( SV30 @ ( sK42_SY565 @ SV129 @ SV30 ) )
| ~ ! [SY788: $i] :
( ~ ( SV30 @ SY788 )
| ( ( sK42_SY565 @ SV129 @ SV30 )
= SY788 ) ) ) )
= $true )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV129
= ( sK35_SY753 @ SV129 @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1020]) ).
thf(1070,plain,
! [SV34: $i,SV152: $i,SV92: $i > $o] :
( ( ( SV92 @ SV152 )
= $false )
| ( ( in @ SV152 @ SV34 )
= $false )
| ( ( in @ ( sK10_SY694 @ SV92 @ SV34 ) @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1071,plain,
! [SV34: $i,SV153: $i,SV92: $i > $o] :
( ( ( SV92 @ SV153 )
= $false )
| ( ( in @ SV153 @ SV34 )
= $false )
| ( ( SV92 @ ( sK10_SY694 @ SV92 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1072,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ~ ~ ( ~ ( SV36 @ ( sK50_SY582 @ SV131 @ SV36 ) )
| ~ ! [SY798: $i] :
( ~ ( SV36 @ SY798 )
| ( ( sK50_SY582 @ SV131 @ SV36 )
= SY798 ) ) ) )
= $false )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV36 @ ( sK36_SY755 @ SV131 @ SV36 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1026]) ).
thf(1073,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ~ ( ~ ( SV36 @ ( sK43_SY582 @ SV131 @ SV36 ) )
| ~ ! [SY789: $i] :
( ~ ( SV36 @ SY789 )
| ( ( sK43_SY582 @ SV131 @ SV36 )
= SY789 ) ) ) )
= $true )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV131
= ( sK36_SY755 @ SV131 @ SV36 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1027]) ).
thf(1074,plain,
! [SV132: $i,SV40: $i > $o] :
( ( ( ~ ! [SY799: $i] :
~ ( ~ ( ~ ( SV40 @ SY799 )
| ( SY799
= ( sK51_SY590 @ SV132 @ SV40 ) ) )
| ~ ( ( SY799
!= ( sK51_SY590 @ SV132 @ SV40 ) )
| ( SV40 @ SY799 ) ) ) )
= $false )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV40 @ ( sK37_SY756 @ SV132 @ SV40 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1028]) ).
thf(1075,plain,
! [SV132: $i,SV40: $i > $o] :
( ( ( ! [SY790: $i] :
~ ( ~ ( ~ ( SV40 @ SY790 )
| ( SY790
= ( sK44_SY590 @ SV132 @ SV40 ) ) )
| ~ ( ( SY790
!= ( sK44_SY590 @ SV132 @ SV40 ) )
| ( SV40 @ SY790 ) ) ) )
= $true )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV132
= ( sK37_SY756 @ SV132 @ SV40 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1029]) ).
thf(1076,plain,
! [SV133: $i,SV41: $i > $o] :
( ( ( ~ ( SV41 @ ( sK52_SY594 @ SV133 @ SV41 ) ) )
= $false )
| ( ( SV41 @ SV133 )
= $false )
| ( ( SV41 @ ( sK38_SY757 @ SV133 @ SV41 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1030]) ).
thf(1077,plain,
! [SV133: $i,SV41: $i > $o] :
( ( ( SV41 @ ( sK45_SY594 @ SV133 @ SV41 ) )
= $true )
| ( ( SV41 @ SV133 )
= $false )
| ( ( SV133
= ( sK38_SY757 @ SV133 @ SV41 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1031]) ).
thf(1078,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ( ~ ( SV43 @ ( sK46_SY599 @ SV134 @ SV43 ) )
| ~ ! [SY791: $i] :
( ~ ( SV43 @ SY791 )
| ( ( sK46_SY599 @ SV134 @ SV43 )
= SY791 ) ) ) )
= $true )
| ( ( SV43 @ ( sK27_SY597 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1032]) ).
thf(1079,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ~ ( ~ ( SV43 @ ( sK53_SY599 @ SV134 @ SV43 ) )
| ~ ! [SY800: $i] :
( ~ ( SV43 @ SY800 )
| ( ( sK53_SY599 @ SV134 @ SV43 )
= SY800 ) ) ) )
= $false )
| ( ( SV43 @ ( sK33_SY773 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1033]) ).
thf(1080,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ( ~ ( SV43 @ ( sK47_SY599 @ SV134 @ SV43 ) )
| ~ ! [SY792: $i] :
( ~ ( SV43 @ SY792 )
| ( ( sK47_SY599 @ SV134 @ SV43 )
= SY792 ) ) ) )
= $true )
| ( ( ( sK27_SY597 @ SV134 @ SV43 )
= ( sK33_SY773 @ SV134 @ SV43 ) )
= $false )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1034]) ).
thf(1081,plain,
! [SV135: $i,SV173: $i,SV166: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV166 )
| ~ ( SV49 @ SV173 )
| ( SV166 = SV173 ) )
= $true )
| ( ( SV49 @ SV135 )
= $false )
| ( ( SV49 @ ( sK39_SY758 @ SV135 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1082,plain,
! [SV135: $i,SV167: $i,SV163: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV163 ) )
= $true )
| ( ( ~ ( SV49 @ SV167 )
| ( SV163 = SV167 ) )
= $true )
| ( ( SV49 @ SV135 )
= $false )
| ( ( SV135
= ( sK39_SY758 @ SV135 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1083,plain,
! [SV50: $i > $o,SV136: $i] :
( ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( ~ ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1037]) ).
thf(1084,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1085,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1086,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ~ ( ~ ( SV50 @ ( sK54_SY613 @ SV136 @ SV50 ) )
| ~ ! [SY801: $i] :
( ~ ( SV50 @ SY801 )
| ( ( sK54_SY613 @ SV136 @ SV50 )
= SY801 ) ) ) )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1040]) ).
thf(1087,plain,
! [SV52: $i,SV168: $i] :
( ( ( ~ ( in @ SV168 @ omega ) )
= $true )
| ( ( in @ SV168 @ SV52 )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( in @ ( sK24_SY618 @ SV52 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1041]) ).
thf(1088,plain,
! [SV52: $i,SV169: $i] :
( ( ( ~ ( in @ SV169 @ omega ) )
= $true )
| ( ( in @ SV169 @ SV52 )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( in @ ( sK24_SY618 @ SV52 ) @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1042]) ).
thf(1089,plain,
! [SV61: $i,SV139: $i,SV174: $i] :
( ( ( ~ ~ ( ~ ( in @ SV174 @ ( sK25_SY635 @ SV139 @ SV61 ) )
| ~ ( in @ SV174 @ SV61 ) ) )
= $true )
| ( ( in @ SV139 @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1090,plain,
! [SV107: $i,SV63: $i > $i > $o,SV157: $i] :
( ( ( ~ ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) ) )
= $true )
| ( ( ~ ! [SY780: $i] :
~ ~ ( ~ ( in @ SY780 @ SV107 )
| ~ ( SV63 @ SY780 @ SV157 ) ) )
= $true )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1044]) ).
thf(1091,plain,
! [SV157: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ~ ~ ! [SY781: $i] :
~ ~ ( ~ ( in @ SY781 @ SV107 )
| ~ ( SV63 @ SY781 @ SV157 ) ) )
= $true )
| ( ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
= $true )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1092,plain,
! [SV150: $i,SV107: $i,SV63: $i > $i > $o] :
( ( ( ~ ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( ~ ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1093,plain,
! [SV63: $i > $i > $o,SV107: $i,SV150: $i] :
( ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( ~ ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1094,plain,
! [SV73: $i > $o,SV170: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ SV170 )
| ~ ! [SY794: $i] :
( ~ ( SV10 @ SY794 )
| ( SV170 = SY794 ) ) ) )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1095,plain,
! [SV10: $i > $o,SV171: $i,SV73: $i > $o] :
( ( ( ~ ( ~ ( SV73 @ SV171 )
| ~ ! [SY795: $i] :
( ~ ( SV73 @ SY795 )
| ( SV171 = SY795 ) ) ) )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1096,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
| ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1097,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1051]) ).
thf(1098,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1051]) ).
thf(1099,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1100,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1101,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1053]) ).
thf(1102,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1054]) ).
thf(1103,plain,
! [SV18: $i,SV164: $i] :
( ( ( in @ SV164 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( ! [SY785: $i] :
( ~ ( in @ SY785 @ SV164 )
| ( in @ SY785 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1104,plain,
! [SV172: $i,SV18: $i,SV165: $i] :
( ( ( ~ ~ ( ~ ( in @ SV165 @ SV18 )
| ~ ( in @ SV172 @ SV18 ) ) )
= $true )
| ( ( ~ ! [SY796: $i] :
( ~ ( in @ SY796 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SV165 @ SY796 )
| ( in @ SV172 @ SY796 ) )
| ~ ( ~ ( in @ SV172 @ SY796 )
| ( in @ SV165 @ SY796 ) ) ) )
| ( SV165 = SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1105,plain,
! [SV162: $i,SV18: $i,SV155: $i] :
( ( ( ~ ( in @ SV155 @ ( sK2_SY521 @ SV18 ) ) )
= $true )
| ( ( ~ ( in @ SV162 @ ( sK2_SY521 @ SV18 ) ) )
= $true )
| ( ( ! [SY782: $i] :
( ~ ( in @ SY782 @ SV155 )
| ( in @ SY782 @ SV162 ) )
| ! [SY783: $i] :
( ~ ( in @ SY783 @ SV162 )
| ( in @ SY783 @ SV155 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1106,plain,
! [SV148: $i,SV18: $i] :
( ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( ~ ~ ! [SY765: $i] :
~ ( in @ SY765 @ SV148 ) )
= $true )
| ( ( ~ ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1063]) ).
thf(1107,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ! [SY765: $i] :
~ ( in @ SY765 @ SV148 ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( ~ ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1064]) ).
thf(1108,plain,
! [SV29: $i,SV88: $i > $o,SV144: $i] :
( ( ( in @ ( sK41_SY687 @ SV144 @ SV88 @ SV29 ) @ SV29 )
= $true )
| ( ( in @ SV144 @ SV29 )
= $false )
| ( ( SV88 @ SV144 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1066]) ).
thf(1109,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ~ ( ~ ( SV30 @ ( sK49_SY565 @ SV129 @ SV30 ) )
| ~ ! [SY797: $i] :
( ~ ( SV30 @ SY797 )
| ( ( sK49_SY565 @ SV129 @ SV30 )
= SY797 ) ) ) )
= $true )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV30 @ ( sK35_SY753 @ SV129 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1068]) ).
thf(1110,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ~ ( SV30 @ ( sK42_SY565 @ SV129 @ SV30 ) )
| ~ ! [SY788: $i] :
( ~ ( SV30 @ SY788 )
| ( ( sK42_SY565 @ SV129 @ SV30 )
= SY788 ) ) )
= $false )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV129
= ( sK35_SY753 @ SV129 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1111,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ~ ( ~ ( SV36 @ ( sK50_SY582 @ SV131 @ SV36 ) )
| ~ ! [SY798: $i] :
( ~ ( SV36 @ SY798 )
| ( ( sK50_SY582 @ SV131 @ SV36 )
= SY798 ) ) ) )
= $true )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV36 @ ( sK36_SY755 @ SV131 @ SV36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1072]) ).
thf(1112,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ ( sK43_SY582 @ SV131 @ SV36 ) )
| ~ ! [SY789: $i] :
( ~ ( SV36 @ SY789 )
| ( ( sK43_SY582 @ SV131 @ SV36 )
= SY789 ) ) )
= $false )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV131
= ( sK36_SY755 @ SV131 @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1073]) ).
thf(1113,plain,
! [SV132: $i,SV40: $i > $o] :
( ( ( ! [SY799: $i] :
~ ( ~ ( ~ ( SV40 @ SY799 )
| ( SY799
= ( sK51_SY590 @ SV132 @ SV40 ) ) )
| ~ ( ( SY799
!= ( sK51_SY590 @ SV132 @ SV40 ) )
| ( SV40 @ SY799 ) ) ) )
= $true )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV40 @ ( sK37_SY756 @ SV132 @ SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1114,plain,
! [SV132: $i,SV175: $i,SV40: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV40 @ SV175 )
| ( SV175
= ( sK44_SY590 @ SV132 @ SV40 ) ) )
| ~ ( ( SV175
!= ( sK44_SY590 @ SV132 @ SV40 ) )
| ( SV40 @ SV175 ) ) ) )
= $true )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV132
= ( sK37_SY756 @ SV132 @ SV40 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1115,plain,
! [SV133: $i,SV41: $i > $o] :
( ( ( SV41 @ ( sK52_SY594 @ SV133 @ SV41 ) )
= $true )
| ( ( SV41 @ SV133 )
= $false )
| ( ( SV41 @ ( sK38_SY757 @ SV133 @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1076]) ).
thf(1116,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ ( sK46_SY599 @ SV134 @ SV43 ) )
| ~ ! [SY791: $i] :
( ~ ( SV43 @ SY791 )
| ( ( sK46_SY599 @ SV134 @ SV43 )
= SY791 ) ) )
= $false )
| ( ( SV43 @ ( sK27_SY597 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1117,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ( ~ ( SV43 @ ( sK53_SY599 @ SV134 @ SV43 ) )
| ~ ! [SY800: $i] :
( ~ ( SV43 @ SY800 )
| ( ( sK53_SY599 @ SV134 @ SV43 )
= SY800 ) ) ) )
= $true )
| ( ( SV43 @ ( sK33_SY773 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1079]) ).
thf(1118,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ ( sK47_SY599 @ SV134 @ SV43 ) )
| ~ ! [SY792: $i] :
( ~ ( SV43 @ SY792 )
| ( ( sK47_SY599 @ SV134 @ SV43 )
= SY792 ) ) )
= $false )
| ( ( ( sK27_SY597 @ SV134 @ SV43 )
= ( sK33_SY773 @ SV134 @ SV43 ) )
= $false )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1119,plain,
! [SV135: $i,SV173: $i,SV166: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV166 ) )
= $true )
| ( ( ~ ( SV49 @ SV173 )
| ( SV166 = SV173 ) )
= $true )
| ( ( SV49 @ SV135 )
= $false )
| ( ( SV49 @ ( sK39_SY758 @ SV135 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1081]) ).
thf(1120,plain,
! [SV135: $i,SV167: $i,SV163: $i,SV49: $i > $o] :
( ( ( SV49 @ SV163 )
= $false )
| ( ( ~ ( SV49 @ SV167 )
| ( SV163 = SV167 ) )
= $true )
| ( ( SV49 @ SV135 )
= $false )
| ( ( SV135
= ( sK39_SY758 @ SV135 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1121,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ! [SY613: $i] :
~ ~ ( ~ ( SV50 @ SY613 )
| ~ ! [SY614: $i] :
( ~ ( SV50 @ SY614 )
| ( SY613 = SY614 ) ) ) )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1122,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ~ ( ~ ( SV50 @ ( sK55_SY613 @ SV136 @ SV50 ) )
| ~ ! [SY802: $i] :
( ~ ( SV50 @ SY802 )
| ( ( sK55_SY613 @ SV136 @ SV50 )
= SY802 ) ) ) )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1084]) ).
thf(1123,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ~ ( ~ ( SV50 @ ( sK56_SY613 @ SV136 @ SV50 ) )
| ~ ! [SY803: $i] :
( ~ ( SV50 @ SY803 )
| ( ( sK56_SY613 @ SV136 @ SV50 )
= SY803 ) ) ) )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1085]) ).
thf(1124,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ( ~ ( SV50 @ ( sK54_SY613 @ SV136 @ SV50 ) )
| ~ ! [SY801: $i] :
( ~ ( SV50 @ SY801 )
| ( ( sK54_SY613 @ SV136 @ SV50 )
= SY801 ) ) ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1086]) ).
thf(1125,plain,
! [SV52: $i,SV168: $i] :
( ( ( in @ SV168 @ omega )
= $false )
| ( ( in @ SV168 @ SV52 )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( in @ ( sK24_SY618 @ SV52 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1087]) ).
thf(1126,plain,
! [SV52: $i,SV169: $i] :
( ( ( in @ SV169 @ omega )
= $false )
| ( ( in @ SV169 @ SV52 )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( in @ ( sK24_SY618 @ SV52 ) @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1127,plain,
! [SV61: $i,SV139: $i,SV174: $i] :
( ( ( ~ ( ~ ( in @ SV174 @ ( sK25_SY635 @ SV139 @ SV61 ) )
| ~ ( in @ SV174 @ SV61 ) ) )
= $false )
| ( ( in @ SV139 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1128,plain,
! [SV107: $i,SV63: $i > $i > $o,SV157: $i] :
( ( ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
= $false )
| ( ( ~ ! [SY780: $i] :
~ ~ ( ~ ( in @ SY780 @ SV107 )
| ~ ( SV63 @ SY780 @ SV157 ) ) )
= $true )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1129,plain,
! [SV157: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ~ ! [SY781: $i] :
~ ~ ( ~ ( in @ SY781 @ SV107 )
| ~ ( SV63 @ SY781 @ SV157 ) ) )
= $false )
| ( ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
= $true )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1130,plain,
! [SV150: $i,SV107: $i,SV63: $i > $i > $o] :
( ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( ~ ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1092]) ).
thf(1131,plain,
! [SV150: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1132,plain,
! [SV73: $i > $o,SV170: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV170 )
| ~ ! [SY794: $i] :
( ~ ( SV10 @ SY794 )
| ( SV170 = SY794 ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1094]) ).
thf(1133,plain,
! [SV10: $i > $o,SV171: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV171 )
| ~ ! [SY795: $i] :
( ~ ( SV73 @ SY795 )
| ( SV171 = SY795 ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1095]) ).
thf(1134,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1096]) ).
thf(1135,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1096]) ).
thf(1136,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1097]) ).
thf(1137,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1098]) ).
thf(1138,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1099]) ).
thf(1139,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1100]) ).
thf(1140,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1101]) ).
thf(1141,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1102]) ).
thf(1142,plain,
! [SV18: $i,SV164: $i,SV176: $i] :
( ( ( ~ ( in @ SV176 @ SV164 )
| ( in @ SV176 @ SV18 ) )
= $true )
| ( ( in @ SV164 @ ( sK2_SY521 @ SV18 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1143,plain,
! [SV172: $i,SV18: $i,SV165: $i] :
( ( ( ~ ( ~ ( in @ SV165 @ SV18 )
| ~ ( in @ SV172 @ SV18 ) ) )
= $false )
| ( ( ~ ! [SY796: $i] :
( ~ ( in @ SY796 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SV165 @ SY796 )
| ( in @ SV172 @ SY796 ) )
| ~ ( ~ ( in @ SV172 @ SY796 )
| ( in @ SV165 @ SY796 ) ) ) )
| ( SV165 = SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1144,plain,
! [SV162: $i,SV18: $i,SV155: $i] :
( ( ( in @ SV155 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( ~ ( in @ SV162 @ ( sK2_SY521 @ SV18 ) ) )
= $true )
| ( ( ! [SY782: $i] :
( ~ ( in @ SY782 @ SV155 )
| ( in @ SY782 @ SV162 ) )
| ! [SY783: $i] :
( ~ ( in @ SY783 @ SV162 )
| ( in @ SY783 @ SV155 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1145,plain,
! [SV18: $i,SV148: $i] :
( ( ( ~ ! [SY765: $i] :
~ ( in @ SY765 @ SV148 ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( ~ ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1146,plain,
! [SV18: $i,SV148: $i] :
( ( ( ! [SY765: $i] :
~ ( in @ SY765 @ SV148 ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( ~ ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1107]) ).
thf(1147,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ~ ( SV30 @ ( sK49_SY565 @ SV129 @ SV30 ) )
| ~ ! [SY797: $i] :
( ~ ( SV30 @ SY797 )
| ( ( sK49_SY565 @ SV129 @ SV30 )
= SY797 ) ) )
= $false )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV30 @ ( sK35_SY753 @ SV129 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1148,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ~ ( SV30 @ ( sK42_SY565 @ SV129 @ SV30 ) ) )
= $false )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV129
= ( sK35_SY753 @ SV129 @ SV30 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1110]) ).
thf(1149,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ~ ! [SY788: $i] :
( ~ ( SV30 @ SY788 )
| ( ( sK42_SY565 @ SV129 @ SV30 )
= SY788 ) ) )
= $false )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV129
= ( sK35_SY753 @ SV129 @ SV30 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1110]) ).
thf(1150,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ ( sK50_SY582 @ SV131 @ SV36 ) )
| ~ ! [SY798: $i] :
( ~ ( SV36 @ SY798 )
| ( ( sK50_SY582 @ SV131 @ SV36 )
= SY798 ) ) )
= $false )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV36 @ ( sK36_SY755 @ SV131 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1151,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ ( sK43_SY582 @ SV131 @ SV36 ) ) )
= $false )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV131
= ( sK36_SY755 @ SV131 @ SV36 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1112]) ).
thf(1152,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ~ ! [SY789: $i] :
( ~ ( SV36 @ SY789 )
| ( ( sK43_SY582 @ SV131 @ SV36 )
= SY789 ) ) )
= $false )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV131
= ( sK36_SY755 @ SV131 @ SV36 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1112]) ).
thf(1153,plain,
! [SV132: $i,SV177: $i,SV40: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV40 @ SV177 )
| ( SV177
= ( sK51_SY590 @ SV132 @ SV40 ) ) )
| ~ ( ( SV177
!= ( sK51_SY590 @ SV132 @ SV40 ) )
| ( SV40 @ SV177 ) ) ) )
= $true )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV40 @ ( sK37_SY756 @ SV132 @ SV40 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1154,plain,
! [SV132: $i,SV175: $i,SV40: $i > $o] :
( ( ( ~ ( ~ ( SV40 @ SV175 )
| ( SV175
= ( sK44_SY590 @ SV132 @ SV40 ) ) )
| ~ ( ( SV175
!= ( sK44_SY590 @ SV132 @ SV40 ) )
| ( SV40 @ SV175 ) ) )
= $false )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV132
= ( sK37_SY756 @ SV132 @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1155,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ ( sK46_SY599 @ SV134 @ SV43 ) ) )
= $false )
| ( ( SV43 @ ( sK27_SY597 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1116]) ).
thf(1156,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ! [SY791: $i] :
( ~ ( SV43 @ SY791 )
| ( ( sK46_SY599 @ SV134 @ SV43 )
= SY791 ) ) )
= $false )
| ( ( SV43 @ ( sK27_SY597 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1116]) ).
thf(1157,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ ( sK53_SY599 @ SV134 @ SV43 ) )
| ~ ! [SY800: $i] :
( ~ ( SV43 @ SY800 )
| ( ( sK53_SY599 @ SV134 @ SV43 )
= SY800 ) ) )
= $false )
| ( ( SV43 @ ( sK33_SY773 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1158,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ ( sK47_SY599 @ SV134 @ SV43 ) ) )
= $false )
| ( ( ( sK27_SY597 @ SV134 @ SV43 )
= ( sK33_SY773 @ SV134 @ SV43 ) )
= $false )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1159,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ! [SY792: $i] :
( ~ ( SV43 @ SY792 )
| ( ( sK47_SY599 @ SV134 @ SV43 )
= SY792 ) ) )
= $false )
| ( ( ( sK27_SY597 @ SV134 @ SV43 )
= ( sK33_SY773 @ SV134 @ SV43 ) )
= $false )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1160,plain,
! [SV135: $i,SV173: $i,SV166: $i,SV49: $i > $o] :
( ( ( SV49 @ SV166 )
= $false )
| ( ( ~ ( SV49 @ SV173 )
| ( SV166 = SV173 ) )
= $true )
| ( ( SV49 @ SV135 )
= $false )
| ( ( SV49 @ ( sK39_SY758 @ SV135 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1161,plain,
! [SV135: $i,SV163: $i,SV167: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV167 ) )
= $true )
| ( ( SV163 = SV167 )
= $true )
| ( ( SV49 @ SV163 )
= $false )
| ( ( SV49 @ SV135 )
= $false )
| ( ( SV135
= ( sK39_SY758 @ SV135 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1120]) ).
thf(1162,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ~ ( ~ ( SV50 @ ( sK57_SY613 @ SV136 @ SV50 ) )
| ~ ! [SY804: $i] :
( ~ ( SV50 @ SY804 )
| ( ( sK57_SY613 @ SV136 @ SV50 )
= SY804 ) ) ) )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1121]) ).
thf(1163,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ( ~ ( SV50 @ ( sK55_SY613 @ SV136 @ SV50 ) )
| ~ ! [SY802: $i] :
( ~ ( SV50 @ SY802 )
| ( ( sK55_SY613 @ SV136 @ SV50 )
= SY802 ) ) ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1122]) ).
thf(1164,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ( ~ ( SV50 @ ( sK56_SY613 @ SV136 @ SV50 ) )
| ~ ! [SY803: $i] :
( ~ ( SV50 @ SY803 )
| ( ( sK56_SY613 @ SV136 @ SV50 )
= SY803 ) ) ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1123]) ).
thf(1165,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ ( sK54_SY613 @ SV136 @ SV50 ) )
| ~ ! [SY801: $i] :
( ~ ( SV50 @ SY801 )
| ( ( sK54_SY613 @ SV136 @ SV50 )
= SY801 ) ) )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1166,plain,
! [SV61: $i,SV139: $i,SV174: $i] :
( ( ( ~ ( in @ SV174 @ ( sK25_SY635 @ SV139 @ SV61 ) )
| ~ ( in @ SV174 @ SV61 ) )
= $true )
| ( ( in @ SV139 @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1127]) ).
thf(1167,plain,
! [SV157: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ! [SY780: $i] :
~ ~ ( ~ ( in @ SY780 @ SV107 )
| ~ ( SV63 @ SY780 @ SV157 ) ) )
= $false )
| ( ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
= $false )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1168,plain,
! [SV157: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ! [SY781: $i] :
~ ~ ( ~ ( in @ SY781 @ SV107 )
| ~ ( SV63 @ SY781 @ SV157 ) ) )
= $true )
| ( ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
= $true )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1129]) ).
thf(1169,plain,
! [SV150: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ! [SY717: $i] :
~ ! [SY718: $i] :
~ ( ~ ( ~ ( in @ SY718 @ SY717 )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY718 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY718 ) )
| ( in @ SY718 @ SY717 ) ) ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1170,plain,
! [SV107: $i,SV63: $i > $i > $o,SV150: $i] :
( ( ( ~ ! [SY805: $i] :
~ ( ~ ( ~ ( in @ SY805 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY805 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY805 ) )
| ( in @ SY805 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) ) ) ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1131]) ).
thf(1171,plain,
! [SV73: $i > $o,SV170: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV170 ) )
= $true )
| ( ( ~ ! [SY794: $i] :
( ~ ( SV10 @ SY794 )
| ( SV170 = SY794 ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1172,plain,
! [SV10: $i > $o,SV171: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV171 ) )
= $true )
| ( ( ~ ! [SY795: $i] :
( ~ ( SV73 @ SY795 )
| ( SV171 = SY795 ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1173,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) )
| ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1134]) ).
thf(1174,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) )
| ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1135]) ).
thf(1175,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1176,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1137]) ).
thf(1177,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1178,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1179,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) ) )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1180,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) ) )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1181,plain,
! [SV18: $i,SV164: $i,SV176: $i] :
( ( ( ~ ( in @ SV176 @ SV164 ) )
= $true )
| ( ( in @ SV176 @ SV18 )
= $true )
| ( ( in @ SV164 @ ( sK2_SY521 @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1182,plain,
! [SV172: $i,SV18: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ SV18 )
| ~ ( in @ SV172 @ SV18 ) )
= $true )
| ( ( ~ ! [SY796: $i] :
( ~ ( in @ SY796 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SV165 @ SY796 )
| ( in @ SV172 @ SY796 ) )
| ~ ( ~ ( in @ SV172 @ SY796 )
| ( in @ SV165 @ SY796 ) ) ) )
| ( SV165 = SV172 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1143]) ).
thf(1183,plain,
! [SV155: $i,SV18: $i,SV162: $i] :
( ( ( in @ SV162 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( in @ SV155 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( ! [SY782: $i] :
( ~ ( in @ SY782 @ SV155 )
| ( in @ SY782 @ SV162 ) )
| ! [SY783: $i] :
( ~ ( in @ SY783 @ SV162 )
| ( in @ SY783 @ SV155 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1184,plain,
! [SV18: $i,SV148: $i] :
( ( ( ! [SY765: $i] :
~ ( in @ SY765 @ SV148 ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( ~ ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1145]) ).
thf(1185,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( ~ ( in @ SV178 @ SV148 ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( ~ ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1186,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ~ ( SV30 @ ( sK49_SY565 @ SV129 @ SV30 ) ) )
= $false )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV30 @ ( sK35_SY753 @ SV129 @ SV30 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1147]) ).
thf(1187,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ~ ! [SY797: $i] :
( ~ ( SV30 @ SY797 )
| ( ( sK49_SY565 @ SV129 @ SV30 )
= SY797 ) ) )
= $false )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV30 @ ( sK35_SY753 @ SV129 @ SV30 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1147]) ).
thf(1188,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( SV30 @ ( sK42_SY565 @ SV129 @ SV30 ) )
= $true )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV129
= ( sK35_SY753 @ SV129 @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1148]) ).
thf(1189,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ! [SY788: $i] :
( ~ ( SV30 @ SY788 )
| ( ( sK42_SY565 @ SV129 @ SV30 )
= SY788 ) ) )
= $true )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV129
= ( sK35_SY753 @ SV129 @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1149]) ).
thf(1190,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ ( sK50_SY582 @ SV131 @ SV36 ) ) )
= $false )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV36 @ ( sK36_SY755 @ SV131 @ SV36 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1150]) ).
thf(1191,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ~ ! [SY798: $i] :
( ~ ( SV36 @ SY798 )
| ( ( sK50_SY582 @ SV131 @ SV36 )
= SY798 ) ) )
= $false )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV36 @ ( sK36_SY755 @ SV131 @ SV36 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1150]) ).
thf(1192,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( SV36 @ ( sK43_SY582 @ SV131 @ SV36 ) )
= $true )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV131
= ( sK36_SY755 @ SV131 @ SV36 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1151]) ).
thf(1193,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ! [SY789: $i] :
( ~ ( SV36 @ SY789 )
| ( ( sK43_SY582 @ SV131 @ SV36 )
= SY789 ) ) )
= $true )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV131
= ( sK36_SY755 @ SV131 @ SV36 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1152]) ).
thf(1194,plain,
! [SV132: $i,SV177: $i,SV40: $i > $o] :
( ( ( ~ ( ~ ( SV40 @ SV177 )
| ( SV177
= ( sK51_SY590 @ SV132 @ SV40 ) ) )
| ~ ( ( SV177
!= ( sK51_SY590 @ SV132 @ SV40 ) )
| ( SV40 @ SV177 ) ) )
= $false )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV40 @ ( sK37_SY756 @ SV132 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1195,plain,
! [SV132: $i,SV175: $i,SV40: $i > $o] :
( ( ( ~ ( ~ ( SV40 @ SV175 )
| ( SV175
= ( sK44_SY590 @ SV132 @ SV40 ) ) ) )
= $false )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV132
= ( sK37_SY756 @ SV132 @ SV40 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1154]) ).
thf(1196,plain,
! [SV40: $i > $o,SV132: $i,SV175: $i] :
( ( ( ~ ( ( SV175
!= ( sK44_SY590 @ SV132 @ SV40 ) )
| ( SV40 @ SV175 ) ) )
= $false )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV132
= ( sK37_SY756 @ SV132 @ SV40 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1154]) ).
thf(1197,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( SV43 @ ( sK46_SY599 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ ( sK27_SY597 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1155]) ).
thf(1198,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ! [SY791: $i] :
( ~ ( SV43 @ SY791 )
| ( ( sK46_SY599 @ SV134 @ SV43 )
= SY791 ) ) )
= $true )
| ( ( SV43 @ ( sK27_SY597 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1156]) ).
thf(1199,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ ( sK53_SY599 @ SV134 @ SV43 ) ) )
= $false )
| ( ( SV43 @ ( sK33_SY773 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1157]) ).
thf(1200,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ~ ! [SY800: $i] :
( ~ ( SV43 @ SY800 )
| ( ( sK53_SY599 @ SV134 @ SV43 )
= SY800 ) ) )
= $false )
| ( ( SV43 @ ( sK33_SY773 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1157]) ).
thf(1201,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( SV43 @ ( sK47_SY599 @ SV134 @ SV43 ) )
= $true )
| ( ( ( sK27_SY597 @ SV134 @ SV43 )
= ( sK33_SY773 @ SV134 @ SV43 ) )
= $false )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1158]) ).
thf(1202,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ! [SY792: $i] :
( ~ ( SV43 @ SY792 )
| ( ( sK47_SY599 @ SV134 @ SV43 )
= SY792 ) ) )
= $true )
| ( ( ( sK27_SY597 @ SV134 @ SV43 )
= ( sK33_SY773 @ SV134 @ SV43 ) )
= $false )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1203,plain,
! [SV135: $i,SV166: $i,SV173: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV173 ) )
= $true )
| ( ( SV166 = SV173 )
= $true )
| ( ( SV49 @ SV166 )
= $false )
| ( ( SV49 @ SV135 )
= $false )
| ( ( SV49 @ ( sK39_SY758 @ SV135 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1204,plain,
! [SV135: $i,SV163: $i,SV167: $i,SV49: $i > $o] :
( ( ( SV49 @ SV167 )
= $false )
| ( ( SV163 = SV167 )
= $true )
| ( ( SV49 @ SV163 )
= $false )
| ( ( SV49 @ SV135 )
= $false )
| ( ( SV135
= ( sK39_SY758 @ SV135 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1205,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ( ~ ( SV50 @ ( sK57_SY613 @ SV136 @ SV50 ) )
| ~ ! [SY804: $i] :
( ~ ( SV50 @ SY804 )
| ( ( sK57_SY613 @ SV136 @ SV50 )
= SY804 ) ) ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1162]) ).
thf(1206,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ ( sK55_SY613 @ SV136 @ SV50 ) )
| ~ ! [SY802: $i] :
( ~ ( SV50 @ SY802 )
| ( ( sK55_SY613 @ SV136 @ SV50 )
= SY802 ) ) )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1207,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ ( sK56_SY613 @ SV136 @ SV50 ) )
| ~ ! [SY803: $i] :
( ~ ( SV50 @ SY803 )
| ( ( sK56_SY613 @ SV136 @ SV50 )
= SY803 ) ) )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1208,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ ( sK54_SY613 @ SV136 @ SV50 ) ) )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1165]) ).
thf(1209,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ! [SY801: $i] :
( ~ ( SV50 @ SY801 )
| ( ( sK54_SY613 @ SV136 @ SV50 )
= SY801 ) ) )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1165]) ).
thf(1210,plain,
! [SV61: $i,SV139: $i,SV174: $i] :
( ( ( ~ ( in @ SV174 @ ( sK25_SY635 @ SV139 @ SV61 ) ) )
= $true )
| ( ( ~ ( in @ SV174 @ SV61 ) )
= $true )
| ( ( in @ SV139 @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1166]) ).
thf(1211,plain,
! [SV107: $i,SV63: $i > $i > $o,SV157: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK59_SY780 @ SV157 @ SV63 @ SV107 ) @ SV107 )
| ~ ( SV63 @ ( sK59_SY780 @ SV157 @ SV63 @ SV107 ) @ SV157 ) ) )
= $false )
| ( ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
= $false )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1167]) ).
thf(1212,plain,
! [SV157: $i,SV63: $i > $i > $o,SV107: $i,SV179: $i] :
( ( ( ~ ~ ( ~ ( in @ SV179 @ SV107 )
| ~ ( SV63 @ SV179 @ SV157 ) ) )
= $true )
| ( ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
= $true )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1213,plain,
! [SV107: $i,SV63: $i > $i > $o,SV150: $i] :
( ( ( ~ ! [SY808: $i] :
~ ( ~ ( ~ ( in @ SY808 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY808 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY808 ) )
| ( in @ SY808 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) ) ) ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1169]) ).
thf(1214,plain,
! [SV107: $i,SV63: $i > $i > $o,SV150: $i] :
( ( ( ! [SY805: $i] :
~ ( ~ ( ~ ( in @ SY805 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY805 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY805 ) )
| ( in @ SY805 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) ) ) ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1170]) ).
thf(1215,plain,
! [SV73: $i > $o,SV170: $i,SV10: $i > $o] :
( ( ( SV10 @ SV170 )
= $false )
| ( ( ~ ! [SY794: $i] :
( ~ ( SV10 @ SY794 )
| ( SV170 = SY794 ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1216,plain,
! [SV10: $i > $o,SV171: $i,SV73: $i > $o] :
( ( ( SV73 @ SV171 )
= $false )
| ( ( ~ ! [SY795: $i] :
( ~ ( SV73 @ SY795 )
| ( SV171 = SY795 ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1217,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1218,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1219,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) ) )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1220,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) ) )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1221,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) ) )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1222,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) ) )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1178]) ).
thf(1223,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1179]) ).
thf(1224,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1180]) ).
thf(1225,plain,
! [SV18: $i,SV164: $i,SV176: $i] :
( ( ( in @ SV176 @ SV164 )
= $false )
| ( ( in @ SV176 @ SV18 )
= $true )
| ( ( in @ SV164 @ ( sK2_SY521 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1226,plain,
! [SV172: $i,SV18: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ SV18 ) )
= $true )
| ( ( ~ ( in @ SV172 @ SV18 ) )
= $true )
| ( ( ~ ! [SY796: $i] :
( ~ ( in @ SY796 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SV165 @ SY796 )
| ( in @ SV172 @ SY796 ) )
| ~ ( ~ ( in @ SV172 @ SY796 )
| ( in @ SV165 @ SY796 ) ) ) )
| ( SV165 = SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1182]) ).
thf(1227,plain,
! [SV18: $i,SV162: $i,SV155: $i] :
( ( ( ! [SY782: $i] :
( ~ ( in @ SY782 @ SV155 )
| ( in @ SY782 @ SV162 ) ) )
= $true )
| ( ( ! [SY783: $i] :
( ~ ( in @ SY783 @ SV162 )
| ( in @ SY783 @ SV155 ) ) )
= $true )
| ( ( in @ SV155 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( in @ SV162 @ ( sK2_SY521 @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1183]) ).
thf(1228,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( ~ ( in @ SV180 @ SV148 ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( ~ ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1229,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( in @ SV178 @ SV148 )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( ~ ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1230,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( SV30 @ ( sK49_SY565 @ SV129 @ SV30 ) )
= $true )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV30 @ ( sK35_SY753 @ SV129 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1186]) ).
thf(1231,plain,
! [SV129: $i,SV30: $i > $o] :
( ( ( ! [SY797: $i] :
( ~ ( SV30 @ SY797 )
| ( ( sK49_SY565 @ SV129 @ SV30 )
= SY797 ) ) )
= $true )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV30 @ ( sK35_SY753 @ SV129 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1187]) ).
thf(1232,plain,
! [SV129: $i,SV181: $i,SV30: $i > $o] :
( ( ( ~ ( SV30 @ SV181 )
| ( ( sK42_SY565 @ SV129 @ SV30 )
= SV181 ) )
= $true )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV129
= ( sK35_SY753 @ SV129 @ SV30 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1233,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( SV36 @ ( sK50_SY582 @ SV131 @ SV36 ) )
= $true )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV36 @ ( sK36_SY755 @ SV131 @ SV36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1234,plain,
! [SV131: $i,SV36: $i > $o] :
( ( ( ! [SY798: $i] :
( ~ ( SV36 @ SY798 )
| ( ( sK50_SY582 @ SV131 @ SV36 )
= SY798 ) ) )
= $true )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV36 @ ( sK36_SY755 @ SV131 @ SV36 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1191]) ).
thf(1235,plain,
! [SV131: $i,SV182: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ SV182 )
| ( ( sK43_SY582 @ SV131 @ SV36 )
= SV182 ) )
= $true )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV131
= ( sK36_SY755 @ SV131 @ SV36 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1236,plain,
! [SV132: $i,SV177: $i,SV40: $i > $o] :
( ( ( ~ ( ~ ( SV40 @ SV177 )
| ( SV177
= ( sK51_SY590 @ SV132 @ SV40 ) ) ) )
= $false )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV40 @ ( sK37_SY756 @ SV132 @ SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1194]) ).
thf(1237,plain,
! [SV40: $i > $o,SV132: $i,SV177: $i] :
( ( ( ~ ( ( SV177
!= ( sK51_SY590 @ SV132 @ SV40 ) )
| ( SV40 @ SV177 ) ) )
= $false )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV40 @ ( sK37_SY756 @ SV132 @ SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1194]) ).
thf(1238,plain,
! [SV132: $i,SV175: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ SV175 )
| ( SV175
= ( sK44_SY590 @ SV132 @ SV40 ) ) )
= $true )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV132
= ( sK37_SY756 @ SV132 @ SV40 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1195]) ).
thf(1239,plain,
! [SV40: $i > $o,SV132: $i,SV175: $i] :
( ( ( ( SV175
!= ( sK44_SY590 @ SV132 @ SV40 ) )
| ( SV40 @ SV175 ) )
= $true )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV132
= ( sK37_SY756 @ SV132 @ SV40 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1196]) ).
thf(1240,plain,
! [SV134: $i,SV183: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ SV183 )
| ( ( sK46_SY599 @ SV134 @ SV43 )
= SV183 ) )
= $true )
| ( ( SV43 @ ( sK27_SY597 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1241,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( SV43 @ ( sK53_SY599 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ ( sK33_SY773 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1199]) ).
thf(1242,plain,
! [SV134: $i,SV43: $i > $o] :
( ( ( ! [SY800: $i] :
( ~ ( SV43 @ SY800 )
| ( ( sK53_SY599 @ SV134 @ SV43 )
= SY800 ) ) )
= $true )
| ( ( SV43 @ ( sK33_SY773 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1200]) ).
thf(1243,plain,
! [SV134: $i,SV184: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ SV184 )
| ( ( sK47_SY599 @ SV134 @ SV43 )
= SV184 ) )
= $true )
| ( ( ( sK27_SY597 @ SV134 @ SV43 )
= ( sK33_SY773 @ SV134 @ SV43 ) )
= $false )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1244,plain,
! [SV135: $i,SV166: $i,SV173: $i,SV49: $i > $o] :
( ( ( SV49 @ SV173 )
= $false )
| ( ( SV166 = SV173 )
= $true )
| ( ( SV49 @ SV166 )
= $false )
| ( ( SV49 @ SV135 )
= $false )
| ( ( SV49 @ ( sK39_SY758 @ SV135 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1245,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ ( sK57_SY613 @ SV136 @ SV50 ) )
| ~ ! [SY804: $i] :
( ~ ( SV50 @ SY804 )
| ( ( sK57_SY613 @ SV136 @ SV50 )
= SY804 ) ) )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1246,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ ( sK55_SY613 @ SV136 @ SV50 ) ) )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1206]) ).
thf(1247,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ! [SY802: $i] :
( ~ ( SV50 @ SY802 )
| ( ( sK55_SY613 @ SV136 @ SV50 )
= SY802 ) ) )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1206]) ).
thf(1248,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ ( sK56_SY613 @ SV136 @ SV50 ) ) )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1207]) ).
thf(1249,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ! [SY803: $i] :
( ~ ( SV50 @ SY803 )
| ( ( sK56_SY613 @ SV136 @ SV50 )
= SY803 ) ) )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1207]) ).
thf(1250,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( SV50 @ ( sK54_SY613 @ SV136 @ SV50 ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1208]) ).
thf(1251,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ! [SY801: $i] :
( ~ ( SV50 @ SY801 )
| ( ( sK54_SY613 @ SV136 @ SV50 )
= SY801 ) ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1209]) ).
thf(1252,plain,
! [SV61: $i,SV139: $i,SV174: $i] :
( ( ( in @ SV174 @ ( sK25_SY635 @ SV139 @ SV61 ) )
= $false )
| ( ( ~ ( in @ SV174 @ SV61 ) )
= $true )
| ( ( in @ SV139 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1253,plain,
! [SV107: $i,SV63: $i > $i > $o,SV157: $i] :
( ( ( ~ ( ~ ( in @ ( sK59_SY780 @ SV157 @ SV63 @ SV107 ) @ SV107 )
| ~ ( SV63 @ ( sK59_SY780 @ SV157 @ SV63 @ SV107 ) @ SV157 ) ) )
= $true )
| ( ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
= $false )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1211]) ).
thf(1254,plain,
! [SV157: $i,SV63: $i > $i > $o,SV107: $i,SV179: $i] :
( ( ( ~ ( ~ ( in @ SV179 @ SV107 )
| ~ ( SV63 @ SV179 @ SV157 ) ) )
= $false )
| ( ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
= $true )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1255,plain,
! [SV107: $i,SV63: $i > $i > $o,SV150: $i] :
( ( ( ! [SY808: $i] :
~ ( ~ ( ~ ( in @ SY808 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
| ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719 @ SV107 )
| ~ ( SV63 @ SY719 @ SY808 ) ) )
| ~ ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( in @ SY720 @ SV107 )
| ~ ( SV63 @ SY720 @ SY808 ) )
| ( in @ SY808 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) ) ) ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1213]) ).
thf(1256,plain,
! [SV107: $i,SV63: $i > $i > $o,SV150: $i,SV185: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
| ~ ! [SY811: $i] :
~ ~ ( ~ ( in @ SY811 @ SV107 )
| ~ ( SV63 @ SY811 @ SV185 ) ) )
| ~ ( ~ ~ ! [SY812: $i] :
~ ~ ( ~ ( in @ SY812 @ SV107 )
| ~ ( SV63 @ SY812 @ SV185 ) )
| ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) ) ) ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1257,plain,
! [SV73: $i > $o,SV170: $i,SV10: $i > $o] :
( ( ( ! [SY794: $i] :
( ~ ( SV10 @ SY794 )
| ( SV170 = SY794 ) ) )
= $false )
| ( ( SV10 @ SV170 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1258,plain,
! [SV10: $i > $o,SV171: $i,SV73: $i > $o] :
( ( ( ! [SY795: $i] :
( ~ ( SV73 @ SY795 )
| ( SV171 = SY795 ) ) )
= $false )
| ( ( SV73 @ SV171 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1259,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) ) )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1260,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) ) )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1261,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1219]) ).
thf(1262,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1220]) ).
thf(1263,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1221]) ).
thf(1264,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1222]) ).
thf(1265,plain,
! [SV73: $i > $o,SV186: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ SV186 )
| ~ ! [SY813: $i] :
( ~ ( SV10 @ SY813 )
| ( SV186 = SY813 ) ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1266,plain,
! [SV10: $i > $o,SV187: $i,SV73: $i > $o] :
( ( ( ~ ~ ( ~ ( SV73 @ SV187 )
| ~ ! [SY814: $i] :
( ~ ( SV73 @ SY814 )
| ( SV187 = SY814 ) ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1267,plain,
! [SV172: $i,SV18: $i,SV165: $i] :
( ( ( in @ SV165 @ SV18 )
= $false )
| ( ( ~ ( in @ SV172 @ SV18 ) )
= $true )
| ( ( ~ ! [SY796: $i] :
( ~ ( in @ SY796 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SV165 @ SY796 )
| ( in @ SV172 @ SY796 ) )
| ~ ( ~ ( in @ SV172 @ SY796 )
| ( in @ SV165 @ SY796 ) ) ) )
| ( SV165 = SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1268,plain,
! [SV18: $i,SV162: $i,SV155: $i,SV188: $i] :
( ( ( ~ ( in @ SV188 @ SV155 )
| ( in @ SV188 @ SV162 ) )
= $true )
| ( ( ! [SY783: $i] :
( ~ ( in @ SY783 @ SV162 )
| ( in @ SY783 @ SV155 ) ) )
= $true )
| ( ( in @ SV155 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( in @ SV162 @ ( sK2_SY521 @ SV18 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1269,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( in @ SV180 @ SV148 )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( ~ ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1270,plain,
! [SV178: $i,SV148: $i,SV18: $i] :
( ( ( ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1271,plain,
! [SV129: $i,SV189: $i,SV30: $i > $o] :
( ( ( ~ ( SV30 @ SV189 )
| ( ( sK49_SY565 @ SV129 @ SV30 )
= SV189 ) )
= $true )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV30 @ ( sK35_SY753 @ SV129 @ SV30 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1272,plain,
! [SV129: $i,SV181: $i,SV30: $i > $o] :
( ( ( ~ ( SV30 @ SV181 ) )
= $true )
| ( ( ( sK42_SY565 @ SV129 @ SV30 )
= SV181 )
= $true )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV129
= ( sK35_SY753 @ SV129 @ SV30 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1232]) ).
thf(1273,plain,
! [SV131: $i,SV190: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ SV190 )
| ( ( sK50_SY582 @ SV131 @ SV36 )
= SV190 ) )
= $true )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV36 @ ( sK36_SY755 @ SV131 @ SV36 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1274,plain,
! [SV131: $i,SV182: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ SV182 ) )
= $true )
| ( ( ( sK43_SY582 @ SV131 @ SV36 )
= SV182 )
= $true )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV131
= ( sK36_SY755 @ SV131 @ SV36 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1235]) ).
thf(1275,plain,
! [SV132: $i,SV177: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ SV177 )
| ( SV177
= ( sK51_SY590 @ SV132 @ SV40 ) ) )
= $true )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV40 @ ( sK37_SY756 @ SV132 @ SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1236]) ).
thf(1276,plain,
! [SV40: $i > $o,SV132: $i,SV177: $i] :
( ( ( ( SV177
!= ( sK51_SY590 @ SV132 @ SV40 ) )
| ( SV40 @ SV177 ) )
= $true )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV40 @ ( sK37_SY756 @ SV132 @ SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1237]) ).
thf(1277,plain,
! [SV132: $i,SV175: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ SV175 ) )
= $true )
| ( ( SV175
= ( sK44_SY590 @ SV132 @ SV40 ) )
= $true )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV132
= ( sK37_SY756 @ SV132 @ SV40 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1278,plain,
! [SV40: $i > $o,SV132: $i,SV175: $i] :
( ( ( SV175
!= ( sK44_SY590 @ SV132 @ SV40 ) )
= $true )
| ( ( SV40 @ SV175 )
= $true )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV132
= ( sK37_SY756 @ SV132 @ SV40 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1279,plain,
! [SV134: $i,SV183: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ SV183 ) )
= $true )
| ( ( ( sK46_SY599 @ SV134 @ SV43 )
= SV183 )
= $true )
| ( ( SV43 @ ( sK27_SY597 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1280,plain,
! [SV134: $i,SV191: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ SV191 )
| ( ( sK53_SY599 @ SV134 @ SV43 )
= SV191 ) )
= $true )
| ( ( SV43 @ ( sK33_SY773 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1281,plain,
! [SV134: $i,SV184: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ SV184 ) )
= $true )
| ( ( ( sK47_SY599 @ SV134 @ SV43 )
= SV184 )
= $true )
| ( ( ( sK27_SY597 @ SV134 @ SV43 )
= ( sK33_SY773 @ SV134 @ SV43 ) )
= $false )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1243]) ).
thf(1282,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ ( sK57_SY613 @ SV136 @ SV50 ) ) )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1245]) ).
thf(1283,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ~ ! [SY804: $i] :
( ~ ( SV50 @ SY804 )
| ( ( sK57_SY613 @ SV136 @ SV50 )
= SY804 ) ) )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1245]) ).
thf(1284,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( SV50 @ ( sK55_SY613 @ SV136 @ SV50 ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1246]) ).
thf(1285,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ! [SY802: $i] :
( ~ ( SV50 @ SY802 )
| ( ( sK55_SY613 @ SV136 @ SV50 )
= SY802 ) ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1247]) ).
thf(1286,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( SV50 @ ( sK56_SY613 @ SV136 @ SV50 ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1248]) ).
thf(1287,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ! [SY803: $i] :
( ~ ( SV50 @ SY803 )
| ( ( sK56_SY613 @ SV136 @ SV50 )
= SY803 ) ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1249]) ).
thf(1288,plain,
! [SV136: $i,SV192: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ SV192 )
| ( ( sK54_SY613 @ SV136 @ SV50 )
= SV192 ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1289,plain,
! [SV139: $i,SV61: $i,SV174: $i] :
( ( ( in @ SV174 @ SV61 )
= $false )
| ( ( in @ SV174 @ ( sK25_SY635 @ SV139 @ SV61 ) )
= $false )
| ( ( in @ SV139 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1290,plain,
! [SV107: $i,SV63: $i > $i > $o,SV157: $i] :
( ( ( ~ ( in @ ( sK59_SY780 @ SV157 @ SV63 @ SV107 ) @ SV107 )
| ~ ( SV63 @ ( sK59_SY780 @ SV157 @ SV63 @ SV107 ) @ SV157 ) )
= $false )
| ( ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
= $false )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1291,plain,
! [SV157: $i,SV63: $i > $i > $o,SV107: $i,SV179: $i] :
( ( ( ~ ( in @ SV179 @ SV107 )
| ~ ( SV63 @ SV179 @ SV157 ) )
= $true )
| ( ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
= $true )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1254]) ).
thf(1292,plain,
! [SV107: $i,SV63: $i > $i > $o,SV150: $i,SV193: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
| ~ ! [SY815: $i] :
~ ~ ( ~ ( in @ SY815 @ SV107 )
| ~ ( SV63 @ SY815 @ SV193 ) ) )
| ~ ( ~ ~ ! [SY816: $i] :
~ ~ ( ~ ( in @ SY816 @ SV107 )
| ~ ( SV63 @ SY816 @ SV193 ) )
| ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) ) ) ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1293,plain,
! [SV107: $i,SV63: $i > $i > $o,SV150: $i,SV185: $i] :
( ( ( ~ ( ~ ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
| ~ ! [SY811: $i] :
~ ~ ( ~ ( in @ SY811 @ SV107 )
| ~ ( SV63 @ SY811 @ SV185 ) ) )
| ~ ( ~ ~ ! [SY812: $i] :
~ ~ ( ~ ( in @ SY812 @ SV107 )
| ~ ( SV63 @ SY812 @ SV185 ) )
| ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) ) ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1256]) ).
thf(1294,plain,
! [SV170: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
| ( SV170
= ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) ) )
= $false )
| ( ( SV10 @ SV170 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1257]) ).
thf(1295,plain,
! [SV171: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
| ( SV171
= ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) ) )
= $false )
| ( ( SV73 @ SV171 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1258]) ).
thf(1296,plain,
! [SV73: $i > $o,SV10: $i > $o] :
( ( ( ! [SY495: $i] :
~ ~ ( ~ ( SV10 @ SY495 )
| ~ ! [SY496: $i] :
( ~ ( SV10 @ SY496 )
| ( SY495 = SY496 ) ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1259]) ).
thf(1297,plain,
! [SV10: $i > $o,SV73: $i > $o] :
( ( ( ! [SY662: $i] :
~ ~ ( ~ ( SV73 @ SY662 )
| ~ ! [SY663: $i] :
( ~ ( SV73 @ SY663 )
| ( SY662 = SY663 ) ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1260]) ).
thf(1298,plain,
! [SV73: $i > $o,SV194: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ SV194 )
| ~ ! [SY817: $i] :
( ~ ( SV10 @ SY817 )
| ( SV194 = SY817 ) ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1299,plain,
! [SV10: $i > $o,SV195: $i,SV73: $i > $o] :
( ( ( ~ ~ ( ~ ( SV73 @ SV195 )
| ~ ! [SY818: $i] :
( ~ ( SV73 @ SY818 )
| ( SV195 = SY818 ) ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1300,plain,
! [SV73: $i > $o,SV196: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ SV196 )
| ~ ! [SY819: $i] :
( ~ ( SV10 @ SY819 )
| ( SV196 = SY819 ) ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1301,plain,
! [SV10: $i > $o,SV197: $i,SV73: $i > $o] :
( ( ( ~ ~ ( ~ ( SV73 @ SV197 )
| ~ ! [SY820: $i] :
( ~ ( SV73 @ SY820 )
| ( SV197 = SY820 ) ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1302,plain,
! [SV73: $i > $o,SV186: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ SV186 )
| ~ ! [SY813: $i] :
( ~ ( SV10 @ SY813 )
| ( SV186 = SY813 ) ) ) )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1303,plain,
! [SV10: $i > $o,SV187: $i,SV73: $i > $o] :
( ( ( ~ ( ~ ( SV73 @ SV187 )
| ~ ! [SY814: $i] :
( ~ ( SV73 @ SY814 )
| ( SV187 = SY814 ) ) ) )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1304,plain,
! [SV165: $i,SV18: $i,SV172: $i] :
( ( ( in @ SV172 @ SV18 )
= $false )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( ~ ! [SY796: $i] :
( ~ ( in @ SY796 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SV165 @ SY796 )
| ( in @ SV172 @ SY796 ) )
| ~ ( ~ ( in @ SV172 @ SY796 )
| ( in @ SV165 @ SY796 ) ) ) )
| ( SV165 = SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1267]) ).
thf(1305,plain,
! [SV18: $i,SV162: $i,SV155: $i,SV188: $i] :
( ( ( ~ ( in @ SV188 @ SV155 ) )
= $true )
| ( ( in @ SV188 @ SV162 )
= $true )
| ( ( ! [SY783: $i] :
( ~ ( in @ SY783 @ SV162 )
| ( in @ SY783 @ SV155 ) ) )
= $true )
| ( ( in @ SV155 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( in @ SV162 @ ( sK2_SY521 @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1268]) ).
thf(1306,plain,
! [SV180: $i,SV148: $i,SV18: $i] :
( ( ( ! [SY766: $i] :
~ ~ ! [SY767: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY766 @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY767 @ SV148 ) )
| ~ ~ ~ ! [SY768: $i] :
~ ~ ( ~ ( in @ SY768 @ SY766 )
| ~ ( in @ SY768 @ SV148 ) ) )
| ~ ! [SY739: $i] :
( ~ ( in @ SY739 @ ( sK2_SY521 @ SV18 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY739 )
| ( in @ SX6 @ SY766 ) )
| ( in @ SY767 @ SY739 ) ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1307,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( ~ ~ ! [SY821: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY821 @ SV148 ) )
| ~ ~ ~ ! [SY822: $i] :
~ ~ ( ~ ( in @ SY822 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
| ~ ( in @ SY822 @ SV148 ) ) )
| ~ ! [SY823: $i] :
( ~ ( in @ SY823 @ ( sK2_SY521 @ SV18 ) )
| ! [SY824: $i] :
( ~ ( in @ SY824 @ SY823 )
| ( in @ SY824 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) ) )
| ( in @ SY821 @ SY823 ) ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1270]) ).
thf(1308,plain,
! [SV129: $i,SV189: $i,SV30: $i > $o] :
( ( ( ~ ( SV30 @ SV189 ) )
= $true )
| ( ( ( sK49_SY565 @ SV129 @ SV30 )
= SV189 )
= $true )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV30 @ ( sK35_SY753 @ SV129 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1271]) ).
thf(1309,plain,
! [SV129: $i,SV181: $i,SV30: $i > $o] :
( ( ( SV30 @ SV181 )
= $false )
| ( ( ( sK42_SY565 @ SV129 @ SV30 )
= SV181 )
= $true )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV129
= ( sK35_SY753 @ SV129 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1272]) ).
thf(1310,plain,
! [SV131: $i,SV190: $i,SV36: $i > $o] :
( ( ( ~ ( SV36 @ SV190 ) )
= $true )
| ( ( ( sK50_SY582 @ SV131 @ SV36 )
= SV190 )
= $true )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV36 @ ( sK36_SY755 @ SV131 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1273]) ).
thf(1311,plain,
! [SV131: $i,SV182: $i,SV36: $i > $o] :
( ( ( SV36 @ SV182 )
= $false )
| ( ( ( sK43_SY582 @ SV131 @ SV36 )
= SV182 )
= $true )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV131
= ( sK36_SY755 @ SV131 @ SV36 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1312,plain,
! [SV132: $i,SV177: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ SV177 ) )
= $true )
| ( ( SV177
= ( sK51_SY590 @ SV132 @ SV40 ) )
= $true )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV40 @ ( sK37_SY756 @ SV132 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1313,plain,
! [SV40: $i > $o,SV132: $i,SV177: $i] :
( ( ( SV177
!= ( sK51_SY590 @ SV132 @ SV40 ) )
= $true )
| ( ( SV40 @ SV177 )
= $true )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV40 @ ( sK37_SY756 @ SV132 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1276]) ).
thf(1314,plain,
! [SV132: $i,SV175: $i,SV40: $i > $o] :
( ( ( SV40 @ SV175 )
= $false )
| ( ( SV175
= ( sK44_SY590 @ SV132 @ SV40 ) )
= $true )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV132
= ( sK37_SY756 @ SV132 @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1315,plain,
! [SV40: $i > $o,SV132: $i,SV175: $i] :
( ( ( SV175
= ( sK44_SY590 @ SV132 @ SV40 ) )
= $false )
| ( ( SV40 @ SV175 )
= $true )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV132
= ( sK37_SY756 @ SV132 @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1316,plain,
! [SV134: $i,SV183: $i,SV43: $i > $o] :
( ( ( SV43 @ SV183 )
= $false )
| ( ( ( sK46_SY599 @ SV134 @ SV43 )
= SV183 )
= $true )
| ( ( SV43 @ ( sK27_SY597 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1317,plain,
! [SV134: $i,SV191: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ SV191 ) )
= $true )
| ( ( ( sK53_SY599 @ SV134 @ SV43 )
= SV191 )
= $true )
| ( ( SV43 @ ( sK33_SY773 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1280]) ).
thf(1318,plain,
! [SV134: $i,SV184: $i,SV43: $i > $o] :
( ( ( SV43 @ SV184 )
= $false )
| ( ( ( sK47_SY599 @ SV134 @ SV43 )
= SV184 )
= $true )
| ( ( ( sK27_SY597 @ SV134 @ SV43 )
= ( sK33_SY773 @ SV134 @ SV43 ) )
= $false )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1319,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( SV50 @ ( sK57_SY613 @ SV136 @ SV50 ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1282]) ).
thf(1320,plain,
! [SV136: $i,SV50: $i > $o] :
( ( ( ! [SY804: $i] :
( ~ ( SV50 @ SY804 )
| ( ( sK57_SY613 @ SV136 @ SV50 )
= SY804 ) ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1283]) ).
thf(1321,plain,
! [SV136: $i,SV198: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ SV198 )
| ( ( sK55_SY613 @ SV136 @ SV50 )
= SV198 ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1322,plain,
! [SV136: $i,SV199: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ SV199 )
| ( ( sK56_SY613 @ SV136 @ SV50 )
= SV199 ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1323,plain,
! [SV136: $i,SV192: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ SV192 ) )
= $true )
| ( ( ( sK54_SY613 @ SV136 @ SV50 )
= SV192 )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1288]) ).
thf(1324,plain,
! [SV107: $i,SV63: $i > $i > $o,SV157: $i] :
( ( ( ~ ( in @ ( sK59_SY780 @ SV157 @ SV63 @ SV107 ) @ SV107 ) )
= $false )
| ( ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
= $false )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1325,plain,
! [SV107: $i,SV157: $i,SV63: $i > $i > $o] :
( ( ( ~ ( SV63 @ ( sK59_SY780 @ SV157 @ SV63 @ SV107 ) @ SV157 ) )
= $false )
| ( ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
= $false )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1326,plain,
! [SV157: $i,SV63: $i > $i > $o,SV107: $i,SV179: $i] :
( ( ( ~ ( in @ SV179 @ SV107 ) )
= $true )
| ( ( ~ ( SV63 @ SV179 @ SV157 ) )
= $true )
| ( ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
= $true )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1291]) ).
thf(1327,plain,
! [SV107: $i,SV63: $i > $i > $o,SV150: $i,SV193: $i] :
( ( ( ~ ( ~ ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
| ~ ! [SY815: $i] :
~ ~ ( ~ ( in @ SY815 @ SV107 )
| ~ ( SV63 @ SY815 @ SV193 ) ) )
| ~ ( ~ ~ ! [SY816: $i] :
~ ~ ( ~ ( in @ SY816 @ SV107 )
| ~ ( SV63 @ SY816 @ SV193 ) )
| ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) ) ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1328,plain,
! [SV107: $i,SV63: $i > $i > $o,SV150: $i,SV185: $i] :
( ( ( ~ ( ~ ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
| ~ ! [SY811: $i] :
~ ~ ( ~ ( in @ SY811 @ SV107 )
| ~ ( SV63 @ SY811 @ SV185 ) ) ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1293]) ).
thf(1329,plain,
! [SV150: $i,SV185: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ~ ( ~ ~ ! [SY812: $i] :
~ ~ ( ~ ( in @ SY812 @ SV107 )
| ~ ( SV63 @ SY812 @ SV185 ) )
| ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) ) ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1293]) ).
thf(1330,plain,
! [SV170: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) ) )
= $false )
| ( ( SV10 @ SV170 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1294]) ).
thf(1331,plain,
! [SV10: $i > $o,SV73: $i > $o,SV170: $i] :
( ( ( SV170
= ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $false )
| ( ( SV10 @ SV170 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1294]) ).
thf(1332,plain,
! [SV171: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) ) )
= $false )
| ( ( SV73 @ SV171 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1295]) ).
thf(1333,plain,
! [SV73: $i > $o,SV10: $i > $o,SV171: $i] :
( ( ( SV171
= ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $false )
| ( ( SV73 @ SV171 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1295]) ).
thf(1334,plain,
! [SV73: $i > $o,SV200: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ SV200 )
| ~ ! [SY825: $i] :
( ~ ( SV10 @ SY825 )
| ( SV200 = SY825 ) ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1335,plain,
! [SV10: $i > $o,SV201: $i,SV73: $i > $o] :
( ( ( ~ ~ ( ~ ( SV73 @ SV201 )
| ~ ! [SY826: $i] :
( ~ ( SV73 @ SY826 )
| ( SV201 = SY826 ) ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1336,plain,
! [SV73: $i > $o,SV194: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ SV194 )
| ~ ! [SY817: $i] :
( ~ ( SV10 @ SY817 )
| ( SV194 = SY817 ) ) ) )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1337,plain,
! [SV10: $i > $o,SV195: $i,SV73: $i > $o] :
( ( ( ~ ( ~ ( SV73 @ SV195 )
| ~ ! [SY818: $i] :
( ~ ( SV73 @ SY818 )
| ( SV195 = SY818 ) ) ) )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1338,plain,
! [SV73: $i > $o,SV196: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ SV196 )
| ~ ! [SY819: $i] :
( ~ ( SV10 @ SY819 )
| ( SV196 = SY819 ) ) ) )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1339,plain,
! [SV10: $i > $o,SV197: $i,SV73: $i > $o] :
( ( ( ~ ( ~ ( SV73 @ SV197 )
| ~ ! [SY820: $i] :
( ~ ( SV73 @ SY820 )
| ( SV197 = SY820 ) ) ) )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1340,plain,
! [SV73: $i > $o,SV186: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV186 )
| ~ ! [SY813: $i] :
( ~ ( SV10 @ SY813 )
| ( SV186 = SY813 ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1302]) ).
thf(1341,plain,
! [SV10: $i > $o,SV187: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV187 )
| ~ ! [SY814: $i] :
( ~ ( SV73 @ SY814 )
| ( SV187 = SY814 ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1303]) ).
thf(1342,plain,
! [SV172: $i,SV165: $i,SV18: $i] :
( ( ( ~ ! [SY796: $i] :
( ~ ( in @ SY796 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SV165 @ SY796 )
| ( in @ SV172 @ SY796 ) )
| ~ ( ~ ( in @ SV172 @ SY796 )
| ( in @ SV165 @ SY796 ) ) ) ) )
= $true )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1304]) ).
thf(1343,plain,
! [SV18: $i,SV162: $i,SV155: $i,SV188: $i] :
( ( ( in @ SV188 @ SV155 )
= $false )
| ( ( in @ SV188 @ SV162 )
= $true )
| ( ( ! [SY783: $i] :
( ~ ( in @ SY783 @ SV162 )
| ( in @ SY783 @ SV155 ) ) )
= $true )
| ( ( in @ SV155 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( in @ SV162 @ ( sK2_SY521 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1344,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( ~ ~ ! [SY827: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY827 @ SV148 ) )
| ~ ~ ~ ! [SY828: $i] :
~ ~ ( ~ ( in @ SY828 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
| ~ ( in @ SY828 @ SV148 ) ) )
| ~ ! [SY829: $i] :
( ~ ( in @ SY829 @ ( sK2_SY521 @ SV18 ) )
| ! [SY830: $i] :
( ~ ( in @ SY830 @ SY829 )
| ( in @ SY830 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) ) )
| ( in @ SY827 @ SY829 ) ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1306]) ).
thf(1345,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( ~ ! [SY821: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY821 @ SV148 ) )
| ~ ~ ~ ! [SY822: $i] :
~ ~ ( ~ ( in @ SY822 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
| ~ ( in @ SY822 @ SV148 ) ) )
| ~ ! [SY823: $i] :
( ~ ( in @ SY823 @ ( sK2_SY521 @ SV18 ) )
| ! [SY824: $i] :
( ~ ( in @ SY824 @ SY823 )
| ( in @ SY824 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) ) )
| ( in @ SY821 @ SY823 ) ) ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1307]) ).
thf(1346,plain,
! [SV129: $i,SV189: $i,SV30: $i > $o] :
( ( ( SV30 @ SV189 )
= $false )
| ( ( ( sK49_SY565 @ SV129 @ SV30 )
= SV189 )
= $true )
| ( ( SV30 @ SV129 )
= $false )
| ( ( SV30 @ ( sK35_SY753 @ SV129 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1347,plain,
! [SV131: $i,SV190: $i,SV36: $i > $o] :
( ( ( SV36 @ SV190 )
= $false )
| ( ( ( sK50_SY582 @ SV131 @ SV36 )
= SV190 )
= $true )
| ( ( SV36 @ SV131 )
= $false )
| ( ( SV36 @ ( sK36_SY755 @ SV131 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1348,plain,
! [SV132: $i,SV177: $i,SV40: $i > $o] :
( ( ( SV40 @ SV177 )
= $false )
| ( ( SV177
= ( sK51_SY590 @ SV132 @ SV40 ) )
= $true )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV40 @ ( sK37_SY756 @ SV132 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1349,plain,
! [SV40: $i > $o,SV132: $i,SV177: $i] :
( ( ( SV177
= ( sK51_SY590 @ SV132 @ SV40 ) )
= $false )
| ( ( SV40 @ SV177 )
= $true )
| ( ( SV40 @ SV132 )
= $false )
| ( ( SV40 @ ( sK37_SY756 @ SV132 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1350,plain,
! [SV134: $i,SV191: $i,SV43: $i > $o] :
( ( ( SV43 @ SV191 )
= $false )
| ( ( ( sK53_SY599 @ SV134 @ SV43 )
= SV191 )
= $true )
| ( ( SV43 @ ( sK33_SY773 @ SV134 @ SV43 ) )
= $true )
| ( ( SV43 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1317]) ).
thf(1351,plain,
! [SV136: $i,SV202: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ SV202 )
| ( ( sK57_SY613 @ SV136 @ SV50 )
= SV202 ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1352,plain,
! [SV136: $i,SV198: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ SV198 ) )
= $true )
| ( ( ( sK55_SY613 @ SV136 @ SV50 )
= SV198 )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1321]) ).
thf(1353,plain,
! [SV136: $i,SV199: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ SV199 ) )
= $true )
| ( ( ( sK56_SY613 @ SV136 @ SV50 )
= SV199 )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1354,plain,
! [SV136: $i,SV192: $i,SV50: $i > $o] :
( ( ( SV50 @ SV192 )
= $false )
| ( ( ( sK54_SY613 @ SV136 @ SV50 )
= SV192 )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1355,plain,
! [SV107: $i,SV63: $i > $i > $o,SV157: $i] :
( ( ( in @ ( sK59_SY780 @ SV157 @ SV63 @ SV107 ) @ SV107 )
= $true )
| ( ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
= $false )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1324]) ).
thf(1356,plain,
! [SV107: $i,SV157: $i,SV63: $i > $i > $o] :
( ( ( SV63 @ ( sK59_SY780 @ SV157 @ SV63 @ SV107 ) @ SV157 )
= $true )
| ( ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
= $false )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1325]) ).
thf(1357,plain,
! [SV157: $i,SV63: $i > $i > $o,SV107: $i,SV179: $i] :
( ( ( in @ SV179 @ SV107 )
= $false )
| ( ( ~ ( SV63 @ SV179 @ SV157 ) )
= $true )
| ( ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
= $true )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1358,plain,
! [SV107: $i,SV63: $i > $i > $o,SV150: $i,SV193: $i] :
( ( ( ~ ( ~ ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
| ~ ! [SY815: $i] :
~ ~ ( ~ ( in @ SY815 @ SV107 )
| ~ ( SV63 @ SY815 @ SV193 ) ) ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1327]) ).
thf(1359,plain,
! [SV150: $i,SV193: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ~ ( ~ ~ ! [SY816: $i] :
~ ~ ( ~ ( in @ SY816 @ SV107 )
| ~ ( SV63 @ SY816 @ SV193 ) )
| ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) ) ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1327]) ).
thf(1360,plain,
! [SV107: $i,SV63: $i > $i > $o,SV150: $i,SV185: $i] :
( ( ( ~ ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
| ~ ! [SY811: $i] :
~ ~ ( ~ ( in @ SY811 @ SV107 )
| ~ ( SV63 @ SY811 @ SV185 ) ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1328]) ).
thf(1361,plain,
! [SV150: $i,SV185: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ~ ~ ! [SY812: $i] :
~ ~ ( ~ ( in @ SY812 @ SV107 )
| ~ ( SV63 @ SY812 @ SV185 ) )
| ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1329]) ).
thf(1362,plain,
! [SV170: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( SV10 @ ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $true )
| ( ( SV10 @ SV170 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1330]) ).
thf(1363,plain,
! [SV170: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $false )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV170
= ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1364,plain,
! [SV171: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( SV73 @ ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $true )
| ( ( SV73 @ SV171 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1332]) ).
thf(1365,plain,
! [SV171: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $false )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV171
= ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1333]) ).
thf(1366,plain,
! [SV73: $i > $o,SV200: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ SV200 )
| ~ ! [SY825: $i] :
( ~ ( SV10 @ SY825 )
| ( SV200 = SY825 ) ) ) )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1334]) ).
thf(1367,plain,
! [SV10: $i > $o,SV201: $i,SV73: $i > $o] :
( ( ( ~ ( ~ ( SV73 @ SV201 )
| ~ ! [SY826: $i] :
( ~ ( SV73 @ SY826 )
| ( SV201 = SY826 ) ) ) )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1368,plain,
! [SV73: $i > $o,SV194: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV194 )
| ~ ! [SY817: $i] :
( ~ ( SV10 @ SY817 )
| ( SV194 = SY817 ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1336]) ).
thf(1369,plain,
! [SV10: $i > $o,SV195: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV195 )
| ~ ! [SY818: $i] :
( ~ ( SV73 @ SY818 )
| ( SV195 = SY818 ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1337]) ).
thf(1370,plain,
! [SV73: $i > $o,SV196: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV196 )
| ~ ! [SY819: $i] :
( ~ ( SV10 @ SY819 )
| ( SV196 = SY819 ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1338]) ).
thf(1371,plain,
! [SV10: $i > $o,SV197: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV197 )
| ~ ! [SY820: $i] :
( ~ ( SV73 @ SY820 )
| ( SV197 = SY820 ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1339]) ).
thf(1372,plain,
! [SV73: $i > $o,SV186: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV186 ) )
= $true )
| ( ( ~ ! [SY813: $i] :
( ~ ( SV10 @ SY813 )
| ( SV186 = SY813 ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1373,plain,
! [SV10: $i > $o,SV187: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV187 ) )
= $true )
| ( ( ~ ! [SY814: $i] :
( ~ ( SV73 @ SY814 )
| ( SV187 = SY814 ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1374,plain,
! [SV172: $i,SV165: $i,SV18: $i] :
( ( ( ! [SY796: $i] :
( ~ ( in @ SY796 @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SV165 @ SY796 )
| ( in @ SV172 @ SY796 ) )
| ~ ( ~ ( in @ SV172 @ SY796 )
| ( in @ SV165 @ SY796 ) ) ) ) )
= $false )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1375,plain,
! [SV18: $i,SV188: $i,SV155: $i,SV162: $i,SV203: $i] :
( ( ( ~ ( in @ SV203 @ SV162 )
| ( in @ SV203 @ SV155 ) )
= $true )
| ( ( in @ SV188 @ SV162 )
= $true )
| ( ( in @ SV188 @ SV155 )
= $false )
| ( ( in @ SV155 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( in @ SV162 @ ( sK2_SY521 @ SV18 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1376,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( ~ ! [SY827: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY827 @ SV148 ) )
| ~ ~ ~ ! [SY828: $i] :
~ ~ ( ~ ( in @ SY828 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
| ~ ( in @ SY828 @ SV148 ) ) )
| ~ ! [SY829: $i] :
( ~ ( in @ SY829 @ ( sK2_SY521 @ SV18 ) )
| ! [SY830: $i] :
( ~ ( in @ SY830 @ SY829 )
| ( in @ SY830 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) ) )
| ( in @ SY827 @ SY829 ) ) ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1344]) ).
thf(1377,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( ! [SY821: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY821 @ SV148 ) )
| ~ ~ ~ ! [SY822: $i] :
~ ~ ( ~ ( in @ SY822 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
| ~ ( in @ SY822 @ SV148 ) ) )
| ~ ! [SY823: $i] :
( ~ ( in @ SY823 @ ( sK2_SY521 @ SV18 ) )
| ! [SY824: $i] :
( ~ ( in @ SY824 @ SY823 )
| ( in @ SY824 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) ) )
| ( in @ SY821 @ SY823 ) ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1345]) ).
thf(1378,plain,
! [SV136: $i,SV202: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ SV202 ) )
= $true )
| ( ( ( sK57_SY613 @ SV136 @ SV50 )
= SV202 )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1351]) ).
thf(1379,plain,
! [SV136: $i,SV198: $i,SV50: $i > $o] :
( ( ( SV50 @ SV198 )
= $false )
| ( ( ( sK55_SY613 @ SV136 @ SV50 )
= SV198 )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1352]) ).
thf(1380,plain,
! [SV136: $i,SV199: $i,SV50: $i > $o] :
( ( ( SV50 @ SV199 )
= $false )
| ( ( ( sK56_SY613 @ SV136 @ SV50 )
= SV199 )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $false )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1381,plain,
! [SV107: $i,SV157: $i,SV179: $i,SV63: $i > $i > $o] :
( ( ( SV63 @ SV179 @ SV157 )
= $false )
| ( ( in @ SV179 @ SV107 )
= $false )
| ( ( in @ SV157 @ ( sK28_SY717 @ SV63 @ SV107 ) )
= $true )
| ( ( in @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1357]) ).
thf(1382,plain,
! [SV107: $i,SV63: $i > $i > $o,SV150: $i,SV193: $i] :
( ( ( ~ ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
| ~ ! [SY815: $i] :
~ ~ ( ~ ( in @ SY815 @ SV107 )
| ~ ( SV63 @ SY815 @ SV193 ) ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1358]) ).
thf(1383,plain,
! [SV150: $i,SV193: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ~ ~ ! [SY816: $i] :
~ ~ ( ~ ( in @ SY816 @ SV107 )
| ~ ( SV63 @ SY816 @ SV193 ) )
| ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1359]) ).
thf(1384,plain,
! [SV107: $i,SV63: $i > $i > $o,SV150: $i,SV185: $i] :
( ( ( ~ ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) ) )
= $true )
| ( ( ~ ! [SY811: $i] :
~ ~ ( ~ ( in @ SY811 @ SV107 )
| ~ ( SV63 @ SY811 @ SV185 ) ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1360]) ).
thf(1385,plain,
! [SV150: $i,SV185: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ~ ~ ! [SY812: $i] :
~ ~ ( ~ ( in @ SY812 @ SV107 )
| ~ ( SV63 @ SY812 @ SV185 ) ) )
= $true )
| ( ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1361]) ).
thf(1386,plain,
! [SV170: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $false )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV10 @ ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1387,plain,
! [SV10: $i > $o,SV170: $i,SV73: $i > $o] :
( ( ( ~ ~ ( ~ ( SV73 @ ( sK65_SY660 @ SV170 @ SV10 @ SV73 ) )
| ~ ! [SY831: $i] :
( ~ ( SV73 @ SY831 )
| ( ( sK65_SY660 @ SV170 @ SV10 @ SV73 )
= SY831 ) ) ) )
= $false )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV170
= ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1363]) ).
thf(1388,plain,
! [SV171: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $false )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV73 @ ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1389,plain,
! [SV73: $i > $o,SV171: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ ( sK66_SY501 @ SV171 @ SV73 @ SV10 ) )
| ~ ! [SY832: $i] :
( ~ ( SV10 @ SY832 )
| ( ( sK66_SY501 @ SV171 @ SV73 @ SV10 )
= SY832 ) ) ) )
= $false )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV171
= ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1365]) ).
thf(1390,plain,
! [SV73: $i > $o,SV200: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV200 )
| ~ ! [SY825: $i] :
( ~ ( SV10 @ SY825 )
| ( SV200 = SY825 ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1366]) ).
thf(1391,plain,
! [SV10: $i > $o,SV201: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV201 )
| ~ ! [SY826: $i] :
( ~ ( SV73 @ SY826 )
| ( SV201 = SY826 ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1367]) ).
thf(1392,plain,
! [SV73: $i > $o,SV194: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV194 ) )
= $true )
| ( ( ~ ! [SY817: $i] :
( ~ ( SV10 @ SY817 )
| ( SV194 = SY817 ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1393,plain,
! [SV10: $i > $o,SV195: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV195 ) )
= $true )
| ( ( ~ ! [SY818: $i] :
( ~ ( SV73 @ SY818 )
| ( SV195 = SY818 ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1369]) ).
thf(1394,plain,
! [SV73: $i > $o,SV196: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV196 ) )
= $true )
| ( ( ~ ! [SY819: $i] :
( ~ ( SV10 @ SY819 )
| ( SV196 = SY819 ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1370]) ).
thf(1395,plain,
! [SV10: $i > $o,SV197: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV197 ) )
= $true )
| ( ( ~ ! [SY820: $i] :
( ~ ( SV73 @ SY820 )
| ( SV197 = SY820 ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1371]) ).
thf(1396,plain,
! [SV73: $i > $o,SV186: $i,SV10: $i > $o] :
( ( ( SV10 @ SV186 )
= $false )
| ( ( ~ ! [SY813: $i] :
( ~ ( SV10 @ SY813 )
| ( SV186 = SY813 ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1397,plain,
! [SV10: $i > $o,SV187: $i,SV73: $i > $o] :
( ( ( SV73 @ SV187 )
= $false )
| ( ( ~ ! [SY814: $i] :
( ~ ( SV73 @ SY814 )
| ( SV187 = SY814 ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1398,plain,
! [SV18: $i,SV165: $i,SV172: $i] :
( ( ( ~ ( in @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( ~ ( ~ ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
| ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) ) )
| ~ ( ~ ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
| ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) ) ) ) )
= $false )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1374]) ).
thf(1399,plain,
! [SV18: $i,SV188: $i,SV155: $i,SV162: $i,SV203: $i] :
( ( ( ~ ( in @ SV203 @ SV162 ) )
= $true )
| ( ( in @ SV203 @ SV155 )
= $true )
| ( ( in @ SV188 @ SV162 )
= $true )
| ( ( in @ SV188 @ SV155 )
= $false )
| ( ( in @ SV155 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( in @ SV162 @ ( sK2_SY521 @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1375]) ).
thf(1400,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( ! [SY827: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ SY827 @ SV148 ) )
| ~ ~ ~ ! [SY828: $i] :
~ ~ ( ~ ( in @ SY828 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
| ~ ( in @ SY828 @ SV148 ) ) )
| ~ ! [SY829: $i] :
( ~ ( in @ SY829 @ ( sK2_SY521 @ SV18 ) )
| ! [SY830: $i] :
( ~ ( in @ SY830 @ SY829 )
| ( in @ SY830 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) ) )
| ( in @ SY827 @ SY829 ) ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1401,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SV148 ) )
| ~ ~ ~ ! [SY822: $i] :
~ ~ ( ~ ( in @ SY822 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
| ~ ( in @ SY822 @ SV148 ) ) )
| ~ ! [SY834: $i] :
( ~ ( in @ SY834 @ ( sK2_SY521 @ SV18 ) )
| ! [SY824: $i] :
( ~ ( in @ SY824 @ SY834 )
| ( in @ SY824 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) ) )
| ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SY834 ) ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1377]) ).
thf(1402,plain,
! [SV136: $i,SV202: $i,SV50: $i > $o] :
( ( ( SV50 @ SV202 )
= $false )
| ( ( ( sK57_SY613 @ SV136 @ SV50 )
= SV202 )
= $true )
| ( ( SV50 @ ( sK19_SY759 @ SV136 @ SV50 ) )
= $true )
| ( ( ( sK19_SY759 @ SV136 @ SV50 )
= SV136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1403,plain,
! [SV107: $i,SV63: $i > $i > $o,SV150: $i,SV193: $i] :
( ( ( ~ ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) ) )
= $true )
| ( ( ~ ! [SY815: $i] :
~ ~ ( ~ ( in @ SY815 @ SV107 )
| ~ ( SV63 @ SY815 @ SV193 ) ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1404,plain,
! [SV150: $i,SV193: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ~ ~ ! [SY816: $i] :
~ ~ ( ~ ( in @ SY816 @ SV107 )
| ~ ( SV63 @ SY816 @ SV193 ) ) )
= $true )
| ( ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1383]) ).
thf(1405,plain,
! [SV107: $i,SV63: $i > $i > $o,SV150: $i,SV185: $i] :
( ( ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
= $false )
| ( ( ~ ! [SY811: $i] :
~ ~ ( ~ ( in @ SY811 @ SV107 )
| ~ ( SV63 @ SY811 @ SV185 ) ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1406,plain,
! [SV150: $i,SV185: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ~ ! [SY812: $i] :
~ ~ ( ~ ( in @ SY812 @ SV107 )
| ~ ( SV63 @ SY812 @ SV185 ) ) )
= $false )
| ( ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1407,plain,
! [SV10: $i > $o,SV170: $i,SV73: $i > $o] :
( ( ( ~ ~ ( ~ ( SV73 @ ( sK69_SY660 @ SV170 @ SV10 @ SV73 ) )
| ~ ! [SY836: $i] :
( ~ ( SV73 @ SY836 )
| ( ( sK69_SY660 @ SV170 @ SV10 @ SV73 )
= SY836 ) ) ) )
= $false )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV10 @ ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1386]) ).
thf(1408,plain,
! [SV10: $i > $o,SV170: $i,SV73: $i > $o] :
( ( ( ~ ( ~ ( SV73 @ ( sK65_SY660 @ SV170 @ SV10 @ SV73 ) )
| ~ ! [SY831: $i] :
( ~ ( SV73 @ SY831 )
| ( ( sK65_SY660 @ SV170 @ SV10 @ SV73 )
= SY831 ) ) ) )
= $true )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV170
= ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1387]) ).
thf(1409,plain,
! [SV73: $i > $o,SV171: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ ( sK70_SY501 @ SV171 @ SV73 @ SV10 ) )
| ~ ! [SY837: $i] :
( ~ ( SV10 @ SY837 )
| ( ( sK70_SY501 @ SV171 @ SV73 @ SV10 )
= SY837 ) ) ) )
= $false )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV73 @ ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1388]) ).
thf(1410,plain,
! [SV73: $i > $o,SV171: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ ( sK66_SY501 @ SV171 @ SV73 @ SV10 ) )
| ~ ! [SY832: $i] :
( ~ ( SV10 @ SY832 )
| ( ( sK66_SY501 @ SV171 @ SV73 @ SV10 )
= SY832 ) ) ) )
= $true )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV171
= ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1389]) ).
thf(1411,plain,
! [SV73: $i > $o,SV200: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV200 ) )
= $true )
| ( ( ~ ! [SY825: $i] :
( ~ ( SV10 @ SY825 )
| ( SV200 = SY825 ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1412,plain,
! [SV10: $i > $o,SV201: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV201 ) )
= $true )
| ( ( ~ ! [SY826: $i] :
( ~ ( SV73 @ SY826 )
| ( SV201 = SY826 ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1413,plain,
! [SV73: $i > $o,SV194: $i,SV10: $i > $o] :
( ( ( SV10 @ SV194 )
= $false )
| ( ( ~ ! [SY817: $i] :
( ~ ( SV10 @ SY817 )
| ( SV194 = SY817 ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1414,plain,
! [SV10: $i > $o,SV195: $i,SV73: $i > $o] :
( ( ( SV73 @ SV195 )
= $false )
| ( ( ~ ! [SY818: $i] :
( ~ ( SV73 @ SY818 )
| ( SV195 = SY818 ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1415,plain,
! [SV73: $i > $o,SV196: $i,SV10: $i > $o] :
( ( ( SV10 @ SV196 )
= $false )
| ( ( ~ ! [SY819: $i] :
( ~ ( SV10 @ SY819 )
| ( SV196 = SY819 ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1416,plain,
! [SV10: $i > $o,SV197: $i,SV73: $i > $o] :
( ( ( SV73 @ SV197 )
= $false )
| ( ( ~ ! [SY820: $i] :
( ~ ( SV73 @ SY820 )
| ( SV197 = SY820 ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1395]) ).
thf(1417,plain,
! [SV73: $i > $o,SV186: $i,SV10: $i > $o] :
( ( ( ! [SY813: $i] :
( ~ ( SV10 @ SY813 )
| ( SV186 = SY813 ) ) )
= $false )
| ( ( SV10 @ SV186 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1418,plain,
! [SV10: $i > $o,SV187: $i,SV73: $i > $o] :
( ( ( ! [SY814: $i] :
( ~ ( SV73 @ SY814 )
| ( SV187 = SY814 ) ) )
= $false )
| ( ( SV73 @ SV187 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1397]) ).
thf(1419,plain,
! [SV18: $i,SV165: $i,SV172: $i] :
( ( ( ~ ( in @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) @ ( sK2_SY521 @ SV18 ) ) )
= $false )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1398]) ).
thf(1420,plain,
! [SV18: $i,SV172: $i,SV165: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
| ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) ) )
| ~ ( ~ ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
| ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) ) ) ) )
= $false )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1398]) ).
thf(1421,plain,
! [SV18: $i,SV188: $i,SV155: $i,SV162: $i,SV203: $i] :
( ( ( in @ SV203 @ SV162 )
= $false )
| ( ( in @ SV203 @ SV155 )
= $true )
| ( ( in @ SV188 @ SV162 )
= $true )
| ( ( in @ SV188 @ SV155 )
= $false )
| ( ( in @ SV155 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( in @ SV162 @ ( sK2_SY521 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1422,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SV148 ) )
| ~ ~ ~ ! [SY828: $i] :
~ ~ ( ~ ( in @ SY828 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
| ~ ( in @ SY828 @ SV148 ) ) )
| ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ ( sK2_SY521 @ SV18 ) )
| ! [SY830: $i] :
( ~ ( in @ SY830 @ SY839 )
| ( in @ SY830 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) ) )
| ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SY839 ) ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1400]) ).
thf(1423,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SV148 ) )
| ~ ~ ~ ! [SY822: $i] :
~ ~ ( ~ ( in @ SY822 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
| ~ ( in @ SY822 @ SV148 ) ) )
| ~ ! [SY834: $i] :
( ~ ( in @ SY834 @ ( sK2_SY521 @ SV18 ) )
| ! [SY824: $i] :
( ~ ( in @ SY824 @ SY834 )
| ( in @ SY824 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) ) )
| ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SY834 ) ) ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1401]) ).
thf(1424,plain,
! [SV107: $i,SV63: $i > $i > $o,SV150: $i,SV193: $i] :
( ( ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
= $false )
| ( ( ~ ! [SY815: $i] :
~ ~ ( ~ ( in @ SY815 @ SV107 )
| ~ ( SV63 @ SY815 @ SV193 ) ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1425,plain,
! [SV150: $i,SV193: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ~ ! [SY816: $i] :
~ ~ ( ~ ( in @ SY816 @ SV107 )
| ~ ( SV63 @ SY816 @ SV193 ) ) )
= $false )
| ( ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1426,plain,
! [SV150: $i,SV185: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ! [SY811: $i] :
~ ~ ( ~ ( in @ SY811 @ SV107 )
| ~ ( SV63 @ SY811 @ SV185 ) ) )
= $false )
| ( ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1427,plain,
! [SV150: $i,SV185: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ! [SY812: $i] :
~ ~ ( ~ ( in @ SY812 @ SV107 )
| ~ ( SV63 @ SY812 @ SV185 ) ) )
= $true )
| ( ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1406]) ).
thf(1428,plain,
! [SV10: $i > $o,SV170: $i,SV73: $i > $o] :
( ( ( ~ ( ~ ( SV73 @ ( sK69_SY660 @ SV170 @ SV10 @ SV73 ) )
| ~ ! [SY836: $i] :
( ~ ( SV73 @ SY836 )
| ( ( sK69_SY660 @ SV170 @ SV10 @ SV73 )
= SY836 ) ) ) )
= $true )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV10 @ ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1407]) ).
thf(1429,plain,
! [SV10: $i > $o,SV170: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK65_SY660 @ SV170 @ SV10 @ SV73 ) )
| ~ ! [SY831: $i] :
( ~ ( SV73 @ SY831 )
| ( ( sK65_SY660 @ SV170 @ SV10 @ SV73 )
= SY831 ) ) )
= $false )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV170
= ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1430,plain,
! [SV73: $i > $o,SV171: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ ( sK70_SY501 @ SV171 @ SV73 @ SV10 ) )
| ~ ! [SY837: $i] :
( ~ ( SV10 @ SY837 )
| ( ( sK70_SY501 @ SV171 @ SV73 @ SV10 )
= SY837 ) ) ) )
= $true )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV73 @ ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1409]) ).
thf(1431,plain,
! [SV73: $i > $o,SV171: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK66_SY501 @ SV171 @ SV73 @ SV10 ) )
| ~ ! [SY832: $i] :
( ~ ( SV10 @ SY832 )
| ( ( sK66_SY501 @ SV171 @ SV73 @ SV10 )
= SY832 ) ) )
= $false )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV171
= ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1432,plain,
! [SV73: $i > $o,SV200: $i,SV10: $i > $o] :
( ( ( SV10 @ SV200 )
= $false )
| ( ( ~ ! [SY825: $i] :
( ~ ( SV10 @ SY825 )
| ( SV200 = SY825 ) ) )
= $true )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1411]) ).
thf(1433,plain,
! [SV10: $i > $o,SV201: $i,SV73: $i > $o] :
( ( ( SV73 @ SV201 )
= $false )
| ( ( ~ ! [SY826: $i] :
( ~ ( SV73 @ SY826 )
| ( SV201 = SY826 ) ) )
= $true )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1412]) ).
thf(1434,plain,
! [SV73: $i > $o,SV194: $i,SV10: $i > $o] :
( ( ( ! [SY817: $i] :
( ~ ( SV10 @ SY817 )
| ( SV194 = SY817 ) ) )
= $false )
| ( ( SV10 @ SV194 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1413]) ).
thf(1435,plain,
! [SV10: $i > $o,SV195: $i,SV73: $i > $o] :
( ( ( ! [SY818: $i] :
( ~ ( SV73 @ SY818 )
| ( SV195 = SY818 ) ) )
= $false )
| ( ( SV73 @ SV195 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1436,plain,
! [SV73: $i > $o,SV196: $i,SV10: $i > $o] :
( ( ( ! [SY819: $i] :
( ~ ( SV10 @ SY819 )
| ( SV196 = SY819 ) ) )
= $false )
| ( ( SV10 @ SV196 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1437,plain,
! [SV10: $i > $o,SV197: $i,SV73: $i > $o] :
( ( ( ! [SY820: $i] :
( ~ ( SV73 @ SY820 )
| ( SV197 = SY820 ) ) )
= $false )
| ( ( SV73 @ SV197 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1438,plain,
! [SV186: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
| ( SV186
= ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) ) )
= $false )
| ( ( SV10 @ SV186 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1417]) ).
thf(1439,plain,
! [SV187: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
| ( SV187
= ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) ) )
= $false )
| ( ( SV73 @ SV187 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1418]) ).
thf(1440,plain,
! [SV18: $i,SV165: $i,SV172: $i] :
( ( ( in @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
= $true )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1419]) ).
thf(1441,plain,
! [SV18: $i,SV172: $i,SV165: $i] :
( ( ( ~ ( ~ ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
| ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) ) )
| ~ ( ~ ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
| ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) ) ) )
= $true )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1420]) ).
thf(1442,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SV148 ) )
| ~ ~ ~ ! [SY828: $i] :
~ ~ ( ~ ( in @ SY828 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
| ~ ( in @ SY828 @ SV148 ) ) )
| ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ ( sK2_SY521 @ SV18 ) )
| ! [SY830: $i] :
( ~ ( in @ SY830 @ SY839 )
| ( in @ SY830 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) ) )
| ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SY839 ) ) ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1422]) ).
thf(1443,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SV148 ) )
| ~ ~ ~ ! [SY822: $i] :
~ ~ ( ~ ( in @ SY822 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
| ~ ( in @ SY822 @ SV148 ) ) )
| ~ ! [SY834: $i] :
( ~ ( in @ SY834 @ ( sK2_SY521 @ SV18 ) )
| ! [SY824: $i] :
( ~ ( in @ SY824 @ SY834 )
| ( in @ SY824 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) ) )
| ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SY834 ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1444,plain,
! [SV150: $i,SV193: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ! [SY815: $i] :
~ ~ ( ~ ( in @ SY815 @ SV107 )
| ~ ( SV63 @ SY815 @ SV193 ) ) )
= $false )
| ( ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1445,plain,
! [SV150: $i,SV193: $i,SV63: $i > $i > $o,SV107: $i] :
( ( ( ! [SY816: $i] :
~ ~ ( ~ ( in @ SY816 @ SV107 )
| ~ ( SV63 @ SY816 @ SV193 ) ) )
= $true )
| ( ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1425]) ).
thf(1446,plain,
! [SV107: $i,SV63: $i > $i > $o,SV185: $i,SV150: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK74_SY811 @ SV150 @ SV185 @ SV63 @ SV107 ) @ SV107 )
| ~ ( SV63 @ ( sK74_SY811 @ SV150 @ SV185 @ SV63 @ SV107 ) @ SV185 ) ) )
= $false )
| ( ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1426]) ).
thf(1447,plain,
! [SV150: $i,SV185: $i,SV63: $i > $i > $o,SV107: $i,SV204: $i] :
( ( ( ~ ~ ( ~ ( in @ SV204 @ SV107 )
| ~ ( SV63 @ SV204 @ SV185 ) ) )
= $true )
| ( ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1448,plain,
! [SV10: $i > $o,SV170: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK69_SY660 @ SV170 @ SV10 @ SV73 ) )
| ~ ! [SY836: $i] :
( ~ ( SV73 @ SY836 )
| ( ( sK69_SY660 @ SV170 @ SV10 @ SV73 )
= SY836 ) ) )
= $false )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV10 @ ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1428]) ).
thf(1449,plain,
! [SV10: $i > $o,SV170: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK65_SY660 @ SV170 @ SV10 @ SV73 ) ) )
= $false )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV170
= ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1450,plain,
! [SV10: $i > $o,SV170: $i,SV73: $i > $o] :
( ( ( ~ ! [SY831: $i] :
( ~ ( SV73 @ SY831 )
| ( ( sK65_SY660 @ SV170 @ SV10 @ SV73 )
= SY831 ) ) )
= $false )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV170
= ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1451,plain,
! [SV73: $i > $o,SV171: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK70_SY501 @ SV171 @ SV73 @ SV10 ) )
| ~ ! [SY837: $i] :
( ~ ( SV10 @ SY837 )
| ( ( sK70_SY501 @ SV171 @ SV73 @ SV10 )
= SY837 ) ) )
= $false )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV73 @ ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1430]) ).
thf(1452,plain,
! [SV73: $i > $o,SV171: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK66_SY501 @ SV171 @ SV73 @ SV10 ) ) )
= $false )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV171
= ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1431]) ).
thf(1453,plain,
! [SV73: $i > $o,SV171: $i,SV10: $i > $o] :
( ( ( ~ ! [SY832: $i] :
( ~ ( SV10 @ SY832 )
| ( ( sK66_SY501 @ SV171 @ SV73 @ SV10 )
= SY832 ) ) )
= $false )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV171
= ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1431]) ).
thf(1454,plain,
! [SV73: $i > $o,SV200: $i,SV10: $i > $o] :
( ( ( ! [SY825: $i] :
( ~ ( SV10 @ SY825 )
| ( SV200 = SY825 ) ) )
= $false )
| ( ( SV10 @ SV200 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1455,plain,
! [SV10: $i > $o,SV201: $i,SV73: $i > $o] :
( ( ( ! [SY826: $i] :
( ~ ( SV73 @ SY826 )
| ( SV201 = SY826 ) ) )
= $false )
| ( ( SV73 @ SV201 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1456,plain,
! [SV194: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
| ( SV194
= ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) ) )
= $false )
| ( ( SV10 @ SV194 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1434]) ).
thf(1457,plain,
! [SV195: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
| ( SV195
= ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) ) )
= $false )
| ( ( SV73 @ SV195 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1435]) ).
thf(1458,plain,
! [SV196: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
| ( SV196
= ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) ) )
= $false )
| ( ( SV10 @ SV196 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1436]) ).
thf(1459,plain,
! [SV197: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
| ( SV197
= ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) ) )
= $false )
| ( ( SV73 @ SV197 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1437]) ).
thf(1460,plain,
! [SV186: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) ) )
= $false )
| ( ( SV10 @ SV186 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1438]) ).
thf(1461,plain,
! [SV10: $i > $o,SV73: $i > $o,SV186: $i] :
( ( ( SV186
= ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $false )
| ( ( SV10 @ SV186 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1438]) ).
thf(1462,plain,
! [SV187: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) ) )
= $false )
| ( ( SV73 @ SV187 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1463,plain,
! [SV73: $i > $o,SV10: $i > $o,SV187: $i] :
( ( ( SV187
= ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $false )
| ( ( SV73 @ SV187 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1464,plain,
! [SV18: $i,SV172: $i,SV165: $i] :
( ( ( ~ ( ~ ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
| ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
| ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) ) ) )
= $true )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1441]) ).
thf(1465,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SV148 ) )
| ~ ~ ~ ! [SY828: $i] :
~ ~ ( ~ ( in @ SY828 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
| ~ ( in @ SY828 @ SV148 ) ) )
| ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ ( sK2_SY521 @ SV18 ) )
| ! [SY830: $i] :
( ~ ( in @ SY830 @ SY839 )
| ( in @ SY830 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) ) )
| ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SY839 ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1442]) ).
thf(1466,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SV148 ) )
| ~ ~ ~ ! [SY822: $i] :
~ ~ ( ~ ( in @ SY822 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
| ~ ( in @ SY822 @ SV148 ) ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1467,plain,
! [SV148: $i,SV178: $i,SV18: $i] :
( ( ( ~ ! [SY834: $i] :
( ~ ( in @ SY834 @ ( sK2_SY521 @ SV18 ) )
| ! [SY824: $i] :
( ~ ( in @ SY824 @ SY834 )
| ( in @ SY824 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) ) )
| ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SY834 ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1468,plain,
! [SV107: $i,SV63: $i > $i > $o,SV193: $i,SV150: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK79_SY815 @ SV150 @ SV193 @ SV63 @ SV107 ) @ SV107 )
| ~ ( SV63 @ ( sK79_SY815 @ SV150 @ SV193 @ SV63 @ SV107 ) @ SV193 ) ) )
= $false )
| ( ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1444]) ).
thf(1469,plain,
! [SV150: $i,SV193: $i,SV63: $i > $i > $o,SV107: $i,SV205: $i] :
( ( ( ~ ~ ( ~ ( in @ SV205 @ SV107 )
| ~ ( SV63 @ SV205 @ SV193 ) ) )
= $true )
| ( ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1470,plain,
! [SV107: $i,SV63: $i > $i > $o,SV185: $i,SV150: $i] :
( ( ( ~ ( ~ ( in @ ( sK74_SY811 @ SV150 @ SV185 @ SV63 @ SV107 ) @ SV107 )
| ~ ( SV63 @ ( sK74_SY811 @ SV150 @ SV185 @ SV63 @ SV107 ) @ SV185 ) ) )
= $true )
| ( ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1446]) ).
thf(1471,plain,
! [SV150: $i,SV185: $i,SV63: $i > $i > $o,SV107: $i,SV204: $i] :
( ( ( ~ ( ~ ( in @ SV204 @ SV107 )
| ~ ( SV63 @ SV204 @ SV185 ) ) )
= $false )
| ( ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1447]) ).
thf(1472,plain,
! [SV10: $i > $o,SV170: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK69_SY660 @ SV170 @ SV10 @ SV73 ) ) )
= $false )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV10 @ ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1448]) ).
thf(1473,plain,
! [SV10: $i > $o,SV170: $i,SV73: $i > $o] :
( ( ( ~ ! [SY836: $i] :
( ~ ( SV73 @ SY836 )
| ( ( sK69_SY660 @ SV170 @ SV10 @ SV73 )
= SY836 ) ) )
= $false )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV10 @ ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1448]) ).
thf(1474,plain,
! [SV10: $i > $o,SV170: $i,SV73: $i > $o] :
( ( ( SV73 @ ( sK65_SY660 @ SV170 @ SV10 @ SV73 ) )
= $true )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV170
= ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1449]) ).
thf(1475,plain,
! [SV10: $i > $o,SV170: $i,SV73: $i > $o] :
( ( ( ! [SY831: $i] :
( ~ ( SV73 @ SY831 )
| ( ( sK65_SY660 @ SV170 @ SV10 @ SV73 )
= SY831 ) ) )
= $true )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV170
= ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1450]) ).
thf(1476,plain,
! [SV73: $i > $o,SV171: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK70_SY501 @ SV171 @ SV73 @ SV10 ) ) )
= $false )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV73 @ ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1451]) ).
thf(1477,plain,
! [SV73: $i > $o,SV171: $i,SV10: $i > $o] :
( ( ( ~ ! [SY837: $i] :
( ~ ( SV10 @ SY837 )
| ( ( sK70_SY501 @ SV171 @ SV73 @ SV10 )
= SY837 ) ) )
= $false )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV73 @ ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1451]) ).
thf(1478,plain,
! [SV73: $i > $o,SV171: $i,SV10: $i > $o] :
( ( ( SV10 @ ( sK66_SY501 @ SV171 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV171
= ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1452]) ).
thf(1479,plain,
! [SV73: $i > $o,SV171: $i,SV10: $i > $o] :
( ( ( ! [SY832: $i] :
( ~ ( SV10 @ SY832 )
| ( ( sK66_SY501 @ SV171 @ SV73 @ SV10 )
= SY832 ) ) )
= $true )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV171
= ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1453]) ).
thf(1480,plain,
! [SV200: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
| ( SV200
= ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) ) )
= $false )
| ( ( SV10 @ SV200 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1454]) ).
thf(1481,plain,
! [SV201: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
| ( SV201
= ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) ) )
= $false )
| ( ( SV73 @ SV201 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1455]) ).
thf(1482,plain,
! [SV194: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) ) )
= $false )
| ( ( SV10 @ SV194 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1456]) ).
thf(1483,plain,
! [SV10: $i > $o,SV73: $i > $o,SV194: $i] :
( ( ( SV194
= ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $false )
| ( ( SV10 @ SV194 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1456]) ).
thf(1484,plain,
! [SV195: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) ) )
= $false )
| ( ( SV73 @ SV195 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1457]) ).
thf(1485,plain,
! [SV73: $i > $o,SV10: $i > $o,SV195: $i] :
( ( ( SV195
= ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $false )
| ( ( SV73 @ SV195 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1457]) ).
thf(1486,plain,
! [SV196: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) ) )
= $false )
| ( ( SV10 @ SV196 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1487,plain,
! [SV10: $i > $o,SV73: $i > $o,SV196: $i] :
( ( ( SV196
= ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $false )
| ( ( SV10 @ SV196 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1488,plain,
! [SV197: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) ) )
= $false )
| ( ( SV73 @ SV197 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1459]) ).
thf(1489,plain,
! [SV73: $i > $o,SV10: $i > $o,SV197: $i] :
( ( ( SV197
= ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $false )
| ( ( SV73 @ SV197 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1459]) ).
thf(1490,plain,
! [SV186: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( SV10 @ ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $true )
| ( ( SV10 @ SV186 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1460]) ).
thf(1491,plain,
! [SV186: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $false )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV186
= ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1492,plain,
! [SV187: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( SV73 @ ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $true )
| ( ( SV73 @ SV187 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1462]) ).
thf(1493,plain,
! [SV187: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $false )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV187
= ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1463]) ).
thf(1494,plain,
! [SV18: $i,SV172: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
| ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
| ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) ) ) )
= $true )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1464]) ).
thf(1495,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SV148 ) )
| ~ ~ ~ ! [SY828: $i] :
~ ~ ( ~ ( in @ SY828 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
| ~ ( in @ SY828 @ SV148 ) ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1496,plain,
! [SV148: $i,SV180: $i,SV18: $i] :
( ( ( ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ ( sK2_SY521 @ SV18 ) )
| ! [SY830: $i] :
( ~ ( in @ SY830 @ SY839 )
| ( in @ SY830 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) ) )
| ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SY839 ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1497,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SV148 ) )
| ~ ~ ~ ! [SY822: $i] :
~ ~ ( ~ ( in @ SY822 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
| ~ ( in @ SY822 @ SV148 ) ) ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1466]) ).
thf(1498,plain,
! [SV148: $i,SV178: $i,SV18: $i] :
( ( ( ! [SY834: $i] :
( ~ ( in @ SY834 @ ( sK2_SY521 @ SV18 ) )
| ! [SY824: $i] :
( ~ ( in @ SY824 @ SY834 )
| ( in @ SY824 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) ) )
| ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SY834 ) ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1467]) ).
thf(1499,plain,
! [SV107: $i,SV63: $i > $i > $o,SV193: $i,SV150: $i] :
( ( ( ~ ( ~ ( in @ ( sK79_SY815 @ SV150 @ SV193 @ SV63 @ SV107 ) @ SV107 )
| ~ ( SV63 @ ( sK79_SY815 @ SV150 @ SV193 @ SV63 @ SV107 ) @ SV193 ) ) )
= $true )
| ( ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1468]) ).
thf(1500,plain,
! [SV150: $i,SV193: $i,SV63: $i > $i > $o,SV107: $i,SV205: $i] :
( ( ( ~ ( ~ ( in @ SV205 @ SV107 )
| ~ ( SV63 @ SV205 @ SV193 ) ) )
= $false )
| ( ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1469]) ).
thf(1501,plain,
! [SV107: $i,SV63: $i > $i > $o,SV185: $i,SV150: $i] :
( ( ( ~ ( in @ ( sK74_SY811 @ SV150 @ SV185 @ SV63 @ SV107 ) @ SV107 )
| ~ ( SV63 @ ( sK74_SY811 @ SV150 @ SV185 @ SV63 @ SV107 ) @ SV185 ) )
= $false )
| ( ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1502,plain,
! [SV150: $i,SV185: $i,SV63: $i > $i > $o,SV107: $i,SV204: $i] :
( ( ( ~ ( in @ SV204 @ SV107 )
| ~ ( SV63 @ SV204 @ SV185 ) )
= $true )
| ( ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1471]) ).
thf(1503,plain,
! [SV10: $i > $o,SV170: $i,SV73: $i > $o] :
( ( ( SV73 @ ( sK69_SY660 @ SV170 @ SV10 @ SV73 ) )
= $true )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV10 @ ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1472]) ).
thf(1504,plain,
! [SV10: $i > $o,SV170: $i,SV73: $i > $o] :
( ( ( ! [SY836: $i] :
( ~ ( SV73 @ SY836 )
| ( ( sK69_SY660 @ SV170 @ SV10 @ SV73 )
= SY836 ) ) )
= $true )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV10 @ ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1473]) ).
thf(1505,plain,
! [SV10: $i > $o,SV170: $i,SV206: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV206 )
| ( ( sK65_SY660 @ SV170 @ SV10 @ SV73 )
= SV206 ) )
= $true )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV170
= ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1506,plain,
! [SV73: $i > $o,SV171: $i,SV10: $i > $o] :
( ( ( SV10 @ ( sK70_SY501 @ SV171 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV73 @ ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1476]) ).
thf(1507,plain,
! [SV73: $i > $o,SV171: $i,SV10: $i > $o] :
( ( ( ! [SY837: $i] :
( ~ ( SV10 @ SY837 )
| ( ( sK70_SY501 @ SV171 @ SV73 @ SV10 )
= SY837 ) ) )
= $true )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV73 @ ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1477]) ).
thf(1508,plain,
! [SV73: $i > $o,SV171: $i,SV207: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV207 )
| ( ( sK66_SY501 @ SV171 @ SV73 @ SV10 )
= SV207 ) )
= $true )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV171
= ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1509,plain,
! [SV200: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) ) )
= $false )
| ( ( SV10 @ SV200 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1480]) ).
thf(1510,plain,
! [SV10: $i > $o,SV73: $i > $o,SV200: $i] :
( ( ( SV200
= ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $false )
| ( ( SV10 @ SV200 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1480]) ).
thf(1511,plain,
! [SV201: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) ) )
= $false )
| ( ( SV73 @ SV201 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1481]) ).
thf(1512,plain,
! [SV73: $i > $o,SV10: $i > $o,SV201: $i] :
( ( ( SV201
= ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $false )
| ( ( SV73 @ SV201 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1481]) ).
thf(1513,plain,
! [SV194: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( SV10 @ ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $true )
| ( ( SV10 @ SV194 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1482]) ).
thf(1514,plain,
! [SV194: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $false )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV194
= ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1515,plain,
! [SV195: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( SV73 @ ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $true )
| ( ( SV73 @ SV195 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1484]) ).
thf(1516,plain,
! [SV195: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $false )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV195
= ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1485]) ).
thf(1517,plain,
! [SV196: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( SV10 @ ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $true )
| ( ( SV10 @ SV196 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1486]) ).
thf(1518,plain,
! [SV196: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $false )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV196
= ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1519,plain,
! [SV197: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( SV73 @ ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $true )
| ( ( SV73 @ SV197 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1488]) ).
thf(1520,plain,
! [SV197: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $false )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV197
= ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1521,plain,
! [SV186: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $false )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV10 @ ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1490]) ).
thf(1522,plain,
! [SV10: $i > $o,SV186: $i,SV73: $i > $o] :
( ( ( ~ ~ ( ~ ( SV73 @ ( sK82_SY660 @ SV186 @ SV10 @ SV73 ) )
| ~ ! [SY841: $i] :
( ~ ( SV73 @ SY841 )
| ( ( sK82_SY660 @ SV186 @ SV10 @ SV73 )
= SY841 ) ) ) )
= $false )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV186
= ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1491]) ).
thf(1523,plain,
! [SV187: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $false )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV73 @ ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1524,plain,
! [SV73: $i > $o,SV187: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ ( sK83_SY501 @ SV187 @ SV73 @ SV10 ) )
| ~ ! [SY842: $i] :
( ~ ( SV10 @ SY842 )
| ( ( sK83_SY501 @ SV187 @ SV73 @ SV10 )
= SY842 ) ) ) )
= $false )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV187
= ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1493]) ).
thf(1525,plain,
! [SV18: $i,SV172: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
| ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) ) ) )
= $true )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1494]) ).
thf(1526,plain,
! [SV18: $i,SV165: $i,SV172: $i] :
( ( ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
| ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) ) ) )
= $true )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1494]) ).
thf(1527,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SV148 ) )
| ~ ~ ~ ! [SY828: $i] :
~ ~ ( ~ ( in @ SY828 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
| ~ ( in @ SY828 @ SV148 ) ) ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1495]) ).
thf(1528,plain,
! [SV148: $i,SV180: $i,SV18: $i] :
( ( ( ! [SY839: $i] :
( ~ ( in @ SY839 @ ( sK2_SY521 @ SV18 ) )
| ! [SY830: $i] :
( ~ ( in @ SY830 @ SY839 )
| ( in @ SY830 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) ) )
| ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SY839 ) ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1496]) ).
thf(1529,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SV148 ) )
| ~ ~ ~ ! [SY822: $i] :
~ ~ ( ~ ( in @ SY822 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
| ~ ( in @ SY822 @ SV148 ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1530,plain,
! [SV148: $i,SV178: $i,SV18: $i,SV208: $i] :
( ( ( ~ ( in @ SV208 @ ( sK2_SY521 @ SV18 ) )
| ! [SY843: $i] :
( ~ ( in @ SY843 @ SV208 )
| ( in @ SY843 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) ) )
| ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SV208 ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1531,plain,
! [SV107: $i,SV63: $i > $i > $o,SV193: $i,SV150: $i] :
( ( ( ~ ( in @ ( sK79_SY815 @ SV150 @ SV193 @ SV63 @ SV107 ) @ SV107 )
| ~ ( SV63 @ ( sK79_SY815 @ SV150 @ SV193 @ SV63 @ SV107 ) @ SV193 ) )
= $false )
| ( ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1532,plain,
! [SV150: $i,SV193: $i,SV63: $i > $i > $o,SV107: $i,SV205: $i] :
( ( ( ~ ( in @ SV205 @ SV107 )
| ~ ( SV63 @ SV205 @ SV193 ) )
= $true )
| ( ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1500]) ).
thf(1533,plain,
! [SV107: $i,SV63: $i > $i > $o,SV185: $i,SV150: $i] :
( ( ( ~ ( in @ ( sK74_SY811 @ SV150 @ SV185 @ SV63 @ SV107 ) @ SV107 ) )
= $false )
| ( ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1501]) ).
thf(1534,plain,
! [SV107: $i,SV185: $i,SV150: $i,SV63: $i > $i > $o] :
( ( ( ~ ( SV63 @ ( sK74_SY811 @ SV150 @ SV185 @ SV63 @ SV107 ) @ SV185 ) )
= $false )
| ( ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1501]) ).
thf(1535,plain,
! [SV150: $i,SV185: $i,SV63: $i > $i > $o,SV107: $i,SV204: $i] :
( ( ( ~ ( in @ SV204 @ SV107 ) )
= $true )
| ( ( ~ ( SV63 @ SV204 @ SV185 ) )
= $true )
| ( ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1502]) ).
thf(1536,plain,
! [SV10: $i > $o,SV170: $i,SV209: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV209 )
| ( ( sK69_SY660 @ SV170 @ SV10 @ SV73 )
= SV209 ) )
= $true )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV10 @ ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1537,plain,
! [SV10: $i > $o,SV170: $i,SV206: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV206 ) )
= $true )
| ( ( ( sK65_SY660 @ SV170 @ SV10 @ SV73 )
= SV206 )
= $true )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV170
= ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1505]) ).
thf(1538,plain,
! [SV73: $i > $o,SV171: $i,SV210: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV210 )
| ( ( sK70_SY501 @ SV171 @ SV73 @ SV10 )
= SV210 ) )
= $true )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV73 @ ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1539,plain,
! [SV73: $i > $o,SV171: $i,SV207: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV207 ) )
= $true )
| ( ( ( sK66_SY501 @ SV171 @ SV73 @ SV10 )
= SV207 )
= $true )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV171
= ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1508]) ).
thf(1540,plain,
! [SV200: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( SV10 @ ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $true )
| ( ( SV10 @ SV200 )
= $false )
| ( ( ~ ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1509]) ).
thf(1541,plain,
! [SV200: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $false )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV200
= ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1542,plain,
! [SV201: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( SV73 @ ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $true )
| ( ( SV73 @ SV201 )
= $false )
| ( ( ~ ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1511]) ).
thf(1543,plain,
! [SV201: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $false )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV201
= ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1544,plain,
! [SV194: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $false )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV10 @ ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1513]) ).
thf(1545,plain,
! [SV10: $i > $o,SV194: $i,SV73: $i > $o] :
( ( ( ~ ~ ( ~ ( SV73 @ ( sK84_SY660 @ SV194 @ SV10 @ SV73 ) )
| ~ ! [SY844: $i] :
( ~ ( SV73 @ SY844 )
| ( ( sK84_SY660 @ SV194 @ SV10 @ SV73 )
= SY844 ) ) ) )
= $false )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV194
= ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1514]) ).
thf(1546,plain,
! [SV195: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $false )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV73 @ ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1547,plain,
! [SV73: $i > $o,SV195: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ ( sK85_SY501 @ SV195 @ SV73 @ SV10 ) )
| ~ ! [SY845: $i] :
( ~ ( SV10 @ SY845 )
| ( ( sK85_SY501 @ SV195 @ SV73 @ SV10 )
= SY845 ) ) ) )
= $false )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV195
= ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1516]) ).
thf(1548,plain,
! [SV196: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $false )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV10 @ ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1549,plain,
! [SV10: $i > $o,SV196: $i,SV73: $i > $o] :
( ( ( ~ ~ ( ~ ( SV73 @ ( sK86_SY660 @ SV196 @ SV10 @ SV73 ) )
| ~ ! [SY846: $i] :
( ~ ( SV73 @ SY846 )
| ( ( sK86_SY660 @ SV196 @ SV10 @ SV73 )
= SY846 ) ) ) )
= $false )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV196
= ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1518]) ).
thf(1550,plain,
! [SV197: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $false )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV73 @ ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1551,plain,
! [SV73: $i > $o,SV197: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ ( sK87_SY501 @ SV197 @ SV73 @ SV10 ) )
| ~ ! [SY847: $i] :
( ~ ( SV10 @ SY847 )
| ( ( sK87_SY501 @ SV197 @ SV73 @ SV10 )
= SY847 ) ) ) )
= $false )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV197
= ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1520]) ).
thf(1552,plain,
! [SV10: $i > $o,SV186: $i,SV73: $i > $o] :
( ( ( ~ ~ ( ~ ( SV73 @ ( sK88_SY660 @ SV186 @ SV10 @ SV73 ) )
| ~ ! [SY848: $i] :
( ~ ( SV73 @ SY848 )
| ( ( sK88_SY660 @ SV186 @ SV10 @ SV73 )
= SY848 ) ) ) )
= $false )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV10 @ ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1521]) ).
thf(1553,plain,
! [SV10: $i > $o,SV186: $i,SV73: $i > $o] :
( ( ( ~ ( ~ ( SV73 @ ( sK82_SY660 @ SV186 @ SV10 @ SV73 ) )
| ~ ! [SY841: $i] :
( ~ ( SV73 @ SY841 )
| ( ( sK82_SY660 @ SV186 @ SV10 @ SV73 )
= SY841 ) ) ) )
= $true )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV186
= ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1522]) ).
thf(1554,plain,
! [SV73: $i > $o,SV187: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ ( sK89_SY501 @ SV187 @ SV73 @ SV10 ) )
| ~ ! [SY849: $i] :
( ~ ( SV10 @ SY849 )
| ( ( sK89_SY501 @ SV187 @ SV73 @ SV10 )
= SY849 ) ) ) )
= $false )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV73 @ ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1523]) ).
thf(1555,plain,
! [SV73: $i > $o,SV187: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ ( sK83_SY501 @ SV187 @ SV73 @ SV10 ) )
| ~ ! [SY842: $i] :
( ~ ( SV10 @ SY842 )
| ( ( sK83_SY501 @ SV187 @ SV73 @ SV10 )
= SY842 ) ) ) )
= $true )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV187
= ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1524]) ).
thf(1556,plain,
! [SV18: $i,SV172: $i,SV165: $i] :
( ( ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
| ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) ) ) )
= $true )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1525]) ).
thf(1557,plain,
! [SV18: $i,SV165: $i,SV172: $i] :
( ( ( ~ ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
| ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) ) )
= $false )
| ( ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
= $false )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1558,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SV148 ) )
| ~ ~ ~ ! [SY828: $i] :
~ ~ ( ~ ( in @ SY828 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
| ~ ( in @ SY828 @ SV148 ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1559,plain,
! [SV148: $i,SV180: $i,SV18: $i,SV211: $i] :
( ( ( ~ ( in @ SV211 @ ( sK2_SY521 @ SV18 ) )
| ! [SY850: $i] :
( ~ ( in @ SY850 @ SV211 )
| ( in @ SY850 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) ) )
| ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SV211 ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1560,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SV148 ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1561,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( ~ ~ ~ ! [SY822: $i] :
~ ~ ( ~ ( in @ SY822 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
| ~ ( in @ SY822 @ SV148 ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1529]) ).
thf(1562,plain,
! [SV148: $i,SV178: $i,SV18: $i,SV208: $i] :
( ( ( ~ ( in @ SV208 @ ( sK2_SY521 @ SV18 ) ) )
= $true )
| ( ( ! [SY843: $i] :
( ~ ( in @ SY843 @ SV208 )
| ( in @ SY843 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) ) )
| ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SV208 ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1530]) ).
thf(1563,plain,
! [SV107: $i,SV63: $i > $i > $o,SV193: $i,SV150: $i] :
( ( ( ~ ( in @ ( sK79_SY815 @ SV150 @ SV193 @ SV63 @ SV107 ) @ SV107 ) )
= $false )
| ( ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1531]) ).
thf(1564,plain,
! [SV107: $i,SV193: $i,SV150: $i,SV63: $i > $i > $o] :
( ( ( ~ ( SV63 @ ( sK79_SY815 @ SV150 @ SV193 @ SV63 @ SV107 ) @ SV193 ) )
= $false )
| ( ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1531]) ).
thf(1565,plain,
! [SV150: $i,SV193: $i,SV63: $i > $i > $o,SV107: $i,SV205: $i] :
( ( ( ~ ( in @ SV205 @ SV107 ) )
= $true )
| ( ( ~ ( SV63 @ SV205 @ SV193 ) )
= $true )
| ( ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1566,plain,
! [SV107: $i,SV63: $i > $i > $o,SV185: $i,SV150: $i] :
( ( ( in @ ( sK74_SY811 @ SV150 @ SV185 @ SV63 @ SV107 ) @ SV107 )
= $true )
| ( ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1533]) ).
thf(1567,plain,
! [SV107: $i,SV185: $i,SV150: $i,SV63: $i > $i > $o] :
( ( ( SV63 @ ( sK74_SY811 @ SV150 @ SV185 @ SV63 @ SV107 ) @ SV185 )
= $true )
| ( ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1534]) ).
thf(1568,plain,
! [SV150: $i,SV185: $i,SV63: $i > $i > $o,SV107: $i,SV204: $i] :
( ( ( in @ SV204 @ SV107 )
= $false )
| ( ( ~ ( SV63 @ SV204 @ SV185 ) )
= $true )
| ( ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1535]) ).
thf(1569,plain,
! [SV10: $i > $o,SV170: $i,SV209: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV209 ) )
= $true )
| ( ( ( sK69_SY660 @ SV170 @ SV10 @ SV73 )
= SV209 )
= $true )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV10 @ ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1536]) ).
thf(1570,plain,
! [SV10: $i > $o,SV170: $i,SV206: $i,SV73: $i > $o] :
( ( ( SV73 @ SV206 )
= $false )
| ( ( ( sK65_SY660 @ SV170 @ SV10 @ SV73 )
= SV206 )
= $true )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV170
= ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1571,plain,
! [SV73: $i > $o,SV171: $i,SV210: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV210 ) )
= $true )
| ( ( ( sK70_SY501 @ SV171 @ SV73 @ SV10 )
= SV210 )
= $true )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV73 @ ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1538]) ).
thf(1572,plain,
! [SV73: $i > $o,SV171: $i,SV207: $i,SV10: $i > $o] :
( ( ( SV10 @ SV207 )
= $false )
| ( ( ( sK66_SY501 @ SV171 @ SV73 @ SV10 )
= SV207 )
= $true )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV171
= ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $false )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1573,plain,
! [SV200: $i,SV10: $i > $o,SV73: $i > $o] :
( ( ( ! [SY660: $i] :
~ ~ ( ~ ( SV73 @ SY660 )
| ~ ! [SY661: $i] :
( ~ ( SV73 @ SY661 )
| ( SY660 = SY661 ) ) ) )
= $false )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV10 @ ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1574,plain,
! [SV10: $i > $o,SV200: $i,SV73: $i > $o] :
( ( ( ~ ~ ( ~ ( SV73 @ ( sK90_SY660 @ SV200 @ SV10 @ SV73 ) )
| ~ ! [SY851: $i] :
( ~ ( SV73 @ SY851 )
| ( ( sK90_SY660 @ SV200 @ SV10 @ SV73 )
= SY851 ) ) ) )
= $false )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV200
= ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1541]) ).
thf(1575,plain,
! [SV201: $i,SV73: $i > $o,SV10: $i > $o] :
( ( ( ! [SY501: $i] :
~ ~ ( ~ ( SV10 @ SY501 )
| ~ ! [SY502: $i] :
( ~ ( SV10 @ SY502 )
| ( SY501 = SY502 ) ) ) )
= $false )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV73 @ ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1576,plain,
! [SV73: $i > $o,SV201: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ ( sK91_SY501 @ SV201 @ SV73 @ SV10 ) )
| ~ ! [SY852: $i] :
( ~ ( SV10 @ SY852 )
| ( ( sK91_SY501 @ SV201 @ SV73 @ SV10 )
= SY852 ) ) ) )
= $false )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV201
= ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1543]) ).
thf(1577,plain,
! [SV10: $i > $o,SV194: $i,SV73: $i > $o] :
( ( ( ~ ~ ( ~ ( SV73 @ ( sK92_SY660 @ SV194 @ SV10 @ SV73 ) )
| ~ ! [SY853: $i] :
( ~ ( SV73 @ SY853 )
| ( ( sK92_SY660 @ SV194 @ SV10 @ SV73 )
= SY853 ) ) ) )
= $false )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV10 @ ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1544]) ).
thf(1578,plain,
! [SV10: $i > $o,SV194: $i,SV73: $i > $o] :
( ( ( ~ ( ~ ( SV73 @ ( sK84_SY660 @ SV194 @ SV10 @ SV73 ) )
| ~ ! [SY844: $i] :
( ~ ( SV73 @ SY844 )
| ( ( sK84_SY660 @ SV194 @ SV10 @ SV73 )
= SY844 ) ) ) )
= $true )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV194
= ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1545]) ).
thf(1579,plain,
! [SV73: $i > $o,SV195: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ ( sK93_SY501 @ SV195 @ SV73 @ SV10 ) )
| ~ ! [SY854: $i] :
( ~ ( SV10 @ SY854 )
| ( ( sK93_SY501 @ SV195 @ SV73 @ SV10 )
= SY854 ) ) ) )
= $false )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV73 @ ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1546]) ).
thf(1580,plain,
! [SV73: $i > $o,SV195: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ ( sK85_SY501 @ SV195 @ SV73 @ SV10 ) )
| ~ ! [SY845: $i] :
( ~ ( SV10 @ SY845 )
| ( ( sK85_SY501 @ SV195 @ SV73 @ SV10 )
= SY845 ) ) ) )
= $true )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV195
= ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1547]) ).
thf(1581,plain,
! [SV10: $i > $o,SV196: $i,SV73: $i > $o] :
( ( ( ~ ~ ( ~ ( SV73 @ ( sK94_SY660 @ SV196 @ SV10 @ SV73 ) )
| ~ ! [SY855: $i] :
( ~ ( SV73 @ SY855 )
| ( ( sK94_SY660 @ SV196 @ SV10 @ SV73 )
= SY855 ) ) ) )
= $false )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV10 @ ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1548]) ).
thf(1582,plain,
! [SV10: $i > $o,SV196: $i,SV73: $i > $o] :
( ( ( ~ ( ~ ( SV73 @ ( sK86_SY660 @ SV196 @ SV10 @ SV73 ) )
| ~ ! [SY846: $i] :
( ~ ( SV73 @ SY846 )
| ( ( sK86_SY660 @ SV196 @ SV10 @ SV73 )
= SY846 ) ) ) )
= $true )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV196
= ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1549]) ).
thf(1583,plain,
! [SV73: $i > $o,SV197: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ ( sK95_SY501 @ SV197 @ SV73 @ SV10 ) )
| ~ ! [SY856: $i] :
( ~ ( SV10 @ SY856 )
| ( ( sK95_SY501 @ SV197 @ SV73 @ SV10 )
= SY856 ) ) ) )
= $false )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV73 @ ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1550]) ).
thf(1584,plain,
! [SV73: $i > $o,SV197: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ ( sK87_SY501 @ SV197 @ SV73 @ SV10 ) )
| ~ ! [SY847: $i] :
( ~ ( SV10 @ SY847 )
| ( ( sK87_SY501 @ SV197 @ SV73 @ SV10 )
= SY847 ) ) ) )
= $true )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV197
= ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1551]) ).
thf(1585,plain,
! [SV10: $i > $o,SV186: $i,SV73: $i > $o] :
( ( ( ~ ( ~ ( SV73 @ ( sK88_SY660 @ SV186 @ SV10 @ SV73 ) )
| ~ ! [SY848: $i] :
( ~ ( SV73 @ SY848 )
| ( ( sK88_SY660 @ SV186 @ SV10 @ SV73 )
= SY848 ) ) ) )
= $true )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV10 @ ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1552]) ).
thf(1586,plain,
! [SV10: $i > $o,SV186: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK82_SY660 @ SV186 @ SV10 @ SV73 ) )
| ~ ! [SY841: $i] :
( ~ ( SV73 @ SY841 )
| ( ( sK82_SY660 @ SV186 @ SV10 @ SV73 )
= SY841 ) ) )
= $false )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV186
= ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1587,plain,
! [SV73: $i > $o,SV187: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ ( sK89_SY501 @ SV187 @ SV73 @ SV10 ) )
| ~ ! [SY849: $i] :
( ~ ( SV10 @ SY849 )
| ( ( sK89_SY501 @ SV187 @ SV73 @ SV10 )
= SY849 ) ) ) )
= $true )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV73 @ ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1554]) ).
thf(1588,plain,
! [SV73: $i > $o,SV187: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK83_SY501 @ SV187 @ SV73 @ SV10 ) )
| ~ ! [SY842: $i] :
( ~ ( SV10 @ SY842 )
| ( ( sK83_SY501 @ SV187 @ SV73 @ SV10 )
= SY842 ) ) )
= $false )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV187
= ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1589,plain,
! [SV18: $i,SV165: $i,SV172: $i] :
( ( ( ~ ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
| ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) ) )
= $false )
| ( ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
= $true )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1556]) ).
thf(1590,plain,
! [SV18: $i,SV165: $i,SV172: $i] :
( ( ( ~ ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) ) )
= $false )
| ( ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
= $false )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1591,plain,
! [SV18: $i,SV172: $i,SV165: $i] :
( ( ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
= $false )
| ( ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
= $false )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1592,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SV148 ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1593,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( ~ ~ ~ ! [SY828: $i] :
~ ~ ( ~ ( in @ SY828 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
| ~ ( in @ SY828 @ SV148 ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1594,plain,
! [SV148: $i,SV180: $i,SV18: $i,SV211: $i] :
( ( ( ~ ( in @ SV211 @ ( sK2_SY521 @ SV18 ) ) )
= $true )
| ( ( ! [SY850: $i] :
( ~ ( in @ SY850 @ SV211 )
| ( in @ SY850 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) ) )
| ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SV211 ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1559]) ).
thf(1595,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( ~ ( ~ ( in @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SV148 ) ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1560]) ).
thf(1596,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( ~ ~ ! [SY822: $i] :
~ ~ ( ~ ( in @ SY822 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
| ~ ( in @ SY822 @ SV148 ) ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1561]) ).
thf(1597,plain,
! [SV148: $i,SV178: $i,SV18: $i,SV208: $i] :
( ( ( in @ SV208 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( ! [SY843: $i] :
( ~ ( in @ SY843 @ SV208 )
| ( in @ SY843 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) ) )
| ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SV208 ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1598,plain,
! [SV107: $i,SV63: $i > $i > $o,SV193: $i,SV150: $i] :
( ( ( in @ ( sK79_SY815 @ SV150 @ SV193 @ SV63 @ SV107 ) @ SV107 )
= $true )
| ( ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1563]) ).
thf(1599,plain,
! [SV107: $i,SV193: $i,SV150: $i,SV63: $i > $i > $o] :
( ( ( SV63 @ ( sK79_SY815 @ SV150 @ SV193 @ SV63 @ SV107 ) @ SV193 )
= $true )
| ( ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1564]) ).
thf(1600,plain,
! [SV150: $i,SV193: $i,SV63: $i > $i > $o,SV107: $i,SV205: $i] :
( ( ( in @ SV205 @ SV107 )
= $false )
| ( ( ~ ( SV63 @ SV205 @ SV193 ) )
= $true )
| ( ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1565]) ).
thf(1601,plain,
! [SV150: $i,SV107: $i,SV185: $i,SV204: $i,SV63: $i > $i > $o] :
( ( ( SV63 @ SV204 @ SV185 )
= $false )
| ( ( in @ SV204 @ SV107 )
= $false )
| ( ( in @ SV185 @ ( sK58_SY717 @ SV150 @ SV63 @ SV107 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV150
= ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1568]) ).
thf(1602,plain,
! [SV10: $i > $o,SV170: $i,SV209: $i,SV73: $i > $o] :
( ( ( SV73 @ SV209 )
= $false )
| ( ( ( sK69_SY660 @ SV170 @ SV10 @ SV73 )
= SV209 )
= $true )
| ( ( SV10 @ SV170 )
= $false )
| ( ( SV10 @ ( sK61_SY794 @ SV73 @ SV170 @ SV10 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1603,plain,
! [SV73: $i > $o,SV171: $i,SV210: $i,SV10: $i > $o] :
( ( ( SV10 @ SV210 )
= $false )
| ( ( ( sK70_SY501 @ SV171 @ SV73 @ SV10 )
= SV210 )
= $true )
| ( ( SV73 @ SV171 )
= $false )
| ( ( SV73 @ ( sK62_SY795 @ SV10 @ SV171 @ SV73 ) )
= $true )
| ( ( ( sK6_SY656 @ SV73 @ SV10 )
= ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1604,plain,
! [SV10: $i > $o,SV200: $i,SV73: $i > $o] :
( ( ( ~ ~ ( ~ ( SV73 @ ( sK96_SY660 @ SV200 @ SV10 @ SV73 ) )
| ~ ! [SY857: $i] :
( ~ ( SV73 @ SY857 )
| ( ( sK96_SY660 @ SV200 @ SV10 @ SV73 )
= SY857 ) ) ) )
= $false )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV10 @ ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1573]) ).
thf(1605,plain,
! [SV10: $i > $o,SV200: $i,SV73: $i > $o] :
( ( ( ~ ( ~ ( SV73 @ ( sK90_SY660 @ SV200 @ SV10 @ SV73 ) )
| ~ ! [SY851: $i] :
( ~ ( SV73 @ SY851 )
| ( ( sK90_SY660 @ SV200 @ SV10 @ SV73 )
= SY851 ) ) ) )
= $true )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV200
= ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1574]) ).
thf(1606,plain,
! [SV73: $i > $o,SV201: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ ( sK97_SY501 @ SV201 @ SV73 @ SV10 ) )
| ~ ! [SY858: $i] :
( ~ ( SV10 @ SY858 )
| ( ( sK97_SY501 @ SV201 @ SV73 @ SV10 )
= SY858 ) ) ) )
= $false )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV73 @ ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1575]) ).
thf(1607,plain,
! [SV73: $i > $o,SV201: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ ( sK91_SY501 @ SV201 @ SV73 @ SV10 ) )
| ~ ! [SY852: $i] :
( ~ ( SV10 @ SY852 )
| ( ( sK91_SY501 @ SV201 @ SV73 @ SV10 )
= SY852 ) ) ) )
= $true )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV201
= ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1576]) ).
thf(1608,plain,
! [SV10: $i > $o,SV194: $i,SV73: $i > $o] :
( ( ( ~ ( ~ ( SV73 @ ( sK92_SY660 @ SV194 @ SV10 @ SV73 ) )
| ~ ! [SY853: $i] :
( ~ ( SV73 @ SY853 )
| ( ( sK92_SY660 @ SV194 @ SV10 @ SV73 )
= SY853 ) ) ) )
= $true )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV10 @ ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1577]) ).
thf(1609,plain,
! [SV10: $i > $o,SV194: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK84_SY660 @ SV194 @ SV10 @ SV73 ) )
| ~ ! [SY844: $i] :
( ~ ( SV73 @ SY844 )
| ( ( sK84_SY660 @ SV194 @ SV10 @ SV73 )
= SY844 ) ) )
= $false )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV194
= ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1610,plain,
! [SV73: $i > $o,SV195: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ ( sK93_SY501 @ SV195 @ SV73 @ SV10 ) )
| ~ ! [SY854: $i] :
( ~ ( SV10 @ SY854 )
| ( ( sK93_SY501 @ SV195 @ SV73 @ SV10 )
= SY854 ) ) ) )
= $true )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV73 @ ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1579]) ).
thf(1611,plain,
! [SV73: $i > $o,SV195: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK85_SY501 @ SV195 @ SV73 @ SV10 ) )
| ~ ! [SY845: $i] :
( ~ ( SV10 @ SY845 )
| ( ( sK85_SY501 @ SV195 @ SV73 @ SV10 )
= SY845 ) ) )
= $false )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV195
= ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1612,plain,
! [SV10: $i > $o,SV196: $i,SV73: $i > $o] :
( ( ( ~ ( ~ ( SV73 @ ( sK94_SY660 @ SV196 @ SV10 @ SV73 ) )
| ~ ! [SY855: $i] :
( ~ ( SV73 @ SY855 )
| ( ( sK94_SY660 @ SV196 @ SV10 @ SV73 )
= SY855 ) ) ) )
= $true )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV10 @ ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1581]) ).
thf(1613,plain,
! [SV10: $i > $o,SV196: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK86_SY660 @ SV196 @ SV10 @ SV73 ) )
| ~ ! [SY846: $i] :
( ~ ( SV73 @ SY846 )
| ( ( sK86_SY660 @ SV196 @ SV10 @ SV73 )
= SY846 ) ) )
= $false )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV196
= ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1582]) ).
thf(1614,plain,
! [SV73: $i > $o,SV197: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ ( sK95_SY501 @ SV197 @ SV73 @ SV10 ) )
| ~ ! [SY856: $i] :
( ~ ( SV10 @ SY856 )
| ( ( sK95_SY501 @ SV197 @ SV73 @ SV10 )
= SY856 ) ) ) )
= $true )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV73 @ ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1583]) ).
thf(1615,plain,
! [SV73: $i > $o,SV197: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK87_SY501 @ SV197 @ SV73 @ SV10 ) )
| ~ ! [SY847: $i] :
( ~ ( SV10 @ SY847 )
| ( ( sK87_SY501 @ SV197 @ SV73 @ SV10 )
= SY847 ) ) )
= $false )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV197
= ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1584]) ).
thf(1616,plain,
! [SV10: $i > $o,SV186: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK88_SY660 @ SV186 @ SV10 @ SV73 ) )
| ~ ! [SY848: $i] :
( ~ ( SV73 @ SY848 )
| ( ( sK88_SY660 @ SV186 @ SV10 @ SV73 )
= SY848 ) ) )
= $false )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV10 @ ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1617,plain,
! [SV10: $i > $o,SV186: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK82_SY660 @ SV186 @ SV10 @ SV73 ) ) )
= $false )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV186
= ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1586]) ).
thf(1618,plain,
! [SV10: $i > $o,SV186: $i,SV73: $i > $o] :
( ( ( ~ ! [SY841: $i] :
( ~ ( SV73 @ SY841 )
| ( ( sK82_SY660 @ SV186 @ SV10 @ SV73 )
= SY841 ) ) )
= $false )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV186
= ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1586]) ).
thf(1619,plain,
! [SV73: $i > $o,SV187: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK89_SY501 @ SV187 @ SV73 @ SV10 ) )
| ~ ! [SY849: $i] :
( ~ ( SV10 @ SY849 )
| ( ( sK89_SY501 @ SV187 @ SV73 @ SV10 )
= SY849 ) ) )
= $false )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV73 @ ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1587]) ).
thf(1620,plain,
! [SV73: $i > $o,SV187: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK83_SY501 @ SV187 @ SV73 @ SV10 ) ) )
= $false )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV187
= ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1621,plain,
! [SV73: $i > $o,SV187: $i,SV10: $i > $o] :
( ( ( ~ ! [SY842: $i] :
( ~ ( SV10 @ SY842 )
| ( ( sK83_SY501 @ SV187 @ SV73 @ SV10 )
= SY842 ) ) )
= $false )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV187
= ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1622,plain,
! [SV18: $i,SV165: $i,SV172: $i] :
( ( ( ~ ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) ) )
= $false )
| ( ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
= $true )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1589]) ).
thf(1623,plain,
! [SV18: $i,SV172: $i,SV165: $i] :
( ( ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
= $false )
| ( ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
= $true )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1589]) ).
thf(1624,plain,
! [SV18: $i,SV165: $i,SV172: $i] :
( ( ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
= $true )
| ( ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
= $false )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1590]) ).
thf(1625,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( ~ ( ~ ( in @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SV148 ) ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1592]) ).
thf(1626,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( ~ ~ ! [SY828: $i] :
~ ~ ( ~ ( in @ SY828 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
| ~ ( in @ SY828 @ SV148 ) ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1593]) ).
thf(1627,plain,
! [SV148: $i,SV180: $i,SV18: $i,SV211: $i] :
( ( ( in @ SV211 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( ! [SY850: $i] :
( ~ ( in @ SY850 @ SV211 )
| ( in @ SY850 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) ) )
| ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SV211 ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1628,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( ~ ( in @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SV148 ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1629,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( ~ ! [SY822: $i] :
~ ~ ( ~ ( in @ SY822 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
| ~ ( in @ SY822 @ SV148 ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1596]) ).
thf(1630,plain,
! [SV18: $i,SV148: $i,SV178: $i,SV208: $i] :
( ( ( ! [SY843: $i] :
( ~ ( in @ SY843 @ SV208 )
| ( in @ SY843 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) ) ) )
= $true )
| ( ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SV208 )
= $true )
| ( ( in @ SV208 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1597]) ).
thf(1631,plain,
! [SV150: $i,SV107: $i,SV193: $i,SV205: $i,SV63: $i > $i > $o] :
( ( ( SV63 @ SV205 @ SV193 )
= $false )
| ( ( in @ SV205 @ SV107 )
= $false )
| ( ( in @ SV193 @ ( sK60_SY717 @ SV150 @ SV63 @ SV107 ) )
= $true )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ SV150 )
= $false )
| ( ( SV63 @ ( sK12_SY714 @ SV63 @ SV107 ) @ ( sK48_SY772 @ SV150 @ SV107 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1632,plain,
! [SV10: $i > $o,SV200: $i,SV73: $i > $o] :
( ( ( ~ ( ~ ( SV73 @ ( sK96_SY660 @ SV200 @ SV10 @ SV73 ) )
| ~ ! [SY857: $i] :
( ~ ( SV73 @ SY857 )
| ( ( sK96_SY660 @ SV200 @ SV10 @ SV73 )
= SY857 ) ) ) )
= $true )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV10 @ ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1604]) ).
thf(1633,plain,
! [SV10: $i > $o,SV200: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK90_SY660 @ SV200 @ SV10 @ SV73 ) )
| ~ ! [SY851: $i] :
( ~ ( SV73 @ SY851 )
| ( ( sK90_SY660 @ SV200 @ SV10 @ SV73 )
= SY851 ) ) )
= $false )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV200
= ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1605]) ).
thf(1634,plain,
! [SV73: $i > $o,SV201: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ ( sK97_SY501 @ SV201 @ SV73 @ SV10 ) )
| ~ ! [SY858: $i] :
( ~ ( SV10 @ SY858 )
| ( ( sK97_SY501 @ SV201 @ SV73 @ SV10 )
= SY858 ) ) ) )
= $true )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV73 @ ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1606]) ).
thf(1635,plain,
! [SV73: $i > $o,SV201: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK91_SY501 @ SV201 @ SV73 @ SV10 ) )
| ~ ! [SY852: $i] :
( ~ ( SV10 @ SY852 )
| ( ( sK91_SY501 @ SV201 @ SV73 @ SV10 )
= SY852 ) ) )
= $false )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV201
= ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1636,plain,
! [SV10: $i > $o,SV194: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK92_SY660 @ SV194 @ SV10 @ SV73 ) )
| ~ ! [SY853: $i] :
( ~ ( SV73 @ SY853 )
| ( ( sK92_SY660 @ SV194 @ SV10 @ SV73 )
= SY853 ) ) )
= $false )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV10 @ ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1637,plain,
! [SV10: $i > $o,SV194: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK84_SY660 @ SV194 @ SV10 @ SV73 ) ) )
= $false )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV194
= ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1638,plain,
! [SV10: $i > $o,SV194: $i,SV73: $i > $o] :
( ( ( ~ ! [SY844: $i] :
( ~ ( SV73 @ SY844 )
| ( ( sK84_SY660 @ SV194 @ SV10 @ SV73 )
= SY844 ) ) )
= $false )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV194
= ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1639,plain,
! [SV73: $i > $o,SV195: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK93_SY501 @ SV195 @ SV73 @ SV10 ) )
| ~ ! [SY854: $i] :
( ~ ( SV10 @ SY854 )
| ( ( sK93_SY501 @ SV195 @ SV73 @ SV10 )
= SY854 ) ) )
= $false )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV73 @ ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1640,plain,
! [SV73: $i > $o,SV195: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK85_SY501 @ SV195 @ SV73 @ SV10 ) ) )
= $false )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV195
= ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1611]) ).
thf(1641,plain,
! [SV73: $i > $o,SV195: $i,SV10: $i > $o] :
( ( ( ~ ! [SY845: $i] :
( ~ ( SV10 @ SY845 )
| ( ( sK85_SY501 @ SV195 @ SV73 @ SV10 )
= SY845 ) ) )
= $false )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV195
= ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1611]) ).
thf(1642,plain,
! [SV10: $i > $o,SV196: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK94_SY660 @ SV196 @ SV10 @ SV73 ) )
| ~ ! [SY855: $i] :
( ~ ( SV73 @ SY855 )
| ( ( sK94_SY660 @ SV196 @ SV10 @ SV73 )
= SY855 ) ) )
= $false )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV10 @ ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1612]) ).
thf(1643,plain,
! [SV10: $i > $o,SV196: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK86_SY660 @ SV196 @ SV10 @ SV73 ) ) )
= $false )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV196
= ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1613]) ).
thf(1644,plain,
! [SV10: $i > $o,SV196: $i,SV73: $i > $o] :
( ( ( ~ ! [SY846: $i] :
( ~ ( SV73 @ SY846 )
| ( ( sK86_SY660 @ SV196 @ SV10 @ SV73 )
= SY846 ) ) )
= $false )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV196
= ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1613]) ).
thf(1645,plain,
! [SV73: $i > $o,SV197: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK95_SY501 @ SV197 @ SV73 @ SV10 ) )
| ~ ! [SY856: $i] :
( ~ ( SV10 @ SY856 )
| ( ( sK95_SY501 @ SV197 @ SV73 @ SV10 )
= SY856 ) ) )
= $false )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV73 @ ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1646,plain,
! [SV73: $i > $o,SV197: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK87_SY501 @ SV197 @ SV73 @ SV10 ) ) )
= $false )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV197
= ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1615]) ).
thf(1647,plain,
! [SV73: $i > $o,SV197: $i,SV10: $i > $o] :
( ( ( ~ ! [SY847: $i] :
( ~ ( SV10 @ SY847 )
| ( ( sK87_SY501 @ SV197 @ SV73 @ SV10 )
= SY847 ) ) )
= $false )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV197
= ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1615]) ).
thf(1648,plain,
! [SV10: $i > $o,SV186: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK88_SY660 @ SV186 @ SV10 @ SV73 ) ) )
= $false )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV10 @ ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1616]) ).
thf(1649,plain,
! [SV10: $i > $o,SV186: $i,SV73: $i > $o] :
( ( ( ~ ! [SY848: $i] :
( ~ ( SV73 @ SY848 )
| ( ( sK88_SY660 @ SV186 @ SV10 @ SV73 )
= SY848 ) ) )
= $false )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV10 @ ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1616]) ).
thf(1650,plain,
! [SV10: $i > $o,SV186: $i,SV73: $i > $o] :
( ( ( SV73 @ ( sK82_SY660 @ SV186 @ SV10 @ SV73 ) )
= $true )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV186
= ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1617]) ).
thf(1651,plain,
! [SV10: $i > $o,SV186: $i,SV73: $i > $o] :
( ( ( ! [SY841: $i] :
( ~ ( SV73 @ SY841 )
| ( ( sK82_SY660 @ SV186 @ SV10 @ SV73 )
= SY841 ) ) )
= $true )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV186
= ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1618]) ).
thf(1652,plain,
! [SV73: $i > $o,SV187: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK89_SY501 @ SV187 @ SV73 @ SV10 ) ) )
= $false )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV73 @ ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1619]) ).
thf(1653,plain,
! [SV73: $i > $o,SV187: $i,SV10: $i > $o] :
( ( ( ~ ! [SY849: $i] :
( ~ ( SV10 @ SY849 )
| ( ( sK89_SY501 @ SV187 @ SV73 @ SV10 )
= SY849 ) ) )
= $false )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV73 @ ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1619]) ).
thf(1654,plain,
! [SV73: $i > $o,SV187: $i,SV10: $i > $o] :
( ( ( SV10 @ ( sK83_SY501 @ SV187 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV187
= ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1620]) ).
thf(1655,plain,
! [SV73: $i > $o,SV187: $i,SV10: $i > $o] :
( ( ( ! [SY842: $i] :
( ~ ( SV10 @ SY842 )
| ( ( sK83_SY501 @ SV187 @ SV73 @ SV10 )
= SY842 ) ) )
= $true )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV187
= ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1621]) ).
thf(1656,plain,
! [SV18: $i,SV165: $i,SV172: $i] :
( ( ( in @ SV172 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
= $true )
| ( ( in @ SV165 @ ( sK67_SY796 @ SV172 @ SV165 @ SV18 ) )
= $true )
| ( ( SV165 = SV172 )
= $true )
| ( ( in @ SV165 @ SV18 )
= $false )
| ( ( in @ SV172 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1622]) ).
thf(1657,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( ~ ( in @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
| ~ ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SV148 ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1658,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( ~ ! [SY828: $i] :
~ ~ ( ~ ( in @ SY828 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
| ~ ( in @ SY828 @ SV148 ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1626]) ).
thf(1659,plain,
! [SV18: $i,SV148: $i,SV180: $i,SV211: $i] :
( ( ( ! [SY850: $i] :
( ~ ( in @ SY850 @ SV211 )
| ( in @ SY850 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) ) ) )
= $true )
| ( ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SV211 )
= $true )
| ( ( in @ SV211 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1660,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( ~ ( in @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1628]) ).
thf(1661,plain,
! [SV178: $i,SV148: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SV148 ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1628]) ).
thf(1662,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( ! [SY822: $i] :
~ ~ ( ~ ( in @ SY822 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
| ~ ( in @ SY822 @ SV148 ) ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1629]) ).
thf(1663,plain,
! [SV18: $i,SV148: $i,SV178: $i,SV208: $i,SV212: $i] :
( ( ( ~ ( in @ SV212 @ SV208 )
| ( in @ SV212 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) ) )
= $true )
| ( ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SV208 )
= $true )
| ( ( in @ SV208 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(1664,plain,
! [SV10: $i > $o,SV200: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK96_SY660 @ SV200 @ SV10 @ SV73 ) )
| ~ ! [SY857: $i] :
( ~ ( SV73 @ SY857 )
| ( ( sK96_SY660 @ SV200 @ SV10 @ SV73 )
= SY857 ) ) )
= $false )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV10 @ ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1632]) ).
thf(1665,plain,
! [SV10: $i > $o,SV200: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK90_SY660 @ SV200 @ SV10 @ SV73 ) ) )
= $false )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV200
= ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1633]) ).
thf(1666,plain,
! [SV10: $i > $o,SV200: $i,SV73: $i > $o] :
( ( ( ~ ! [SY851: $i] :
( ~ ( SV73 @ SY851 )
| ( ( sK90_SY660 @ SV200 @ SV10 @ SV73 )
= SY851 ) ) )
= $false )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV200
= ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1633]) ).
thf(1667,plain,
! [SV73: $i > $o,SV201: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK97_SY501 @ SV201 @ SV73 @ SV10 ) )
| ~ ! [SY858: $i] :
( ~ ( SV10 @ SY858 )
| ( ( sK97_SY501 @ SV201 @ SV73 @ SV10 )
= SY858 ) ) )
= $false )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV73 @ ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1634]) ).
thf(1668,plain,
! [SV73: $i > $o,SV201: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK91_SY501 @ SV201 @ SV73 @ SV10 ) ) )
= $false )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV201
= ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1635]) ).
thf(1669,plain,
! [SV73: $i > $o,SV201: $i,SV10: $i > $o] :
( ( ( ~ ! [SY852: $i] :
( ~ ( SV10 @ SY852 )
| ( ( sK91_SY501 @ SV201 @ SV73 @ SV10 )
= SY852 ) ) )
= $false )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV201
= ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1635]) ).
thf(1670,plain,
! [SV10: $i > $o,SV194: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK92_SY660 @ SV194 @ SV10 @ SV73 ) ) )
= $false )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV10 @ ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1636]) ).
thf(1671,plain,
! [SV10: $i > $o,SV194: $i,SV73: $i > $o] :
( ( ( ~ ! [SY853: $i] :
( ~ ( SV73 @ SY853 )
| ( ( sK92_SY660 @ SV194 @ SV10 @ SV73 )
= SY853 ) ) )
= $false )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV10 @ ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1636]) ).
thf(1672,plain,
! [SV10: $i > $o,SV194: $i,SV73: $i > $o] :
( ( ( SV73 @ ( sK84_SY660 @ SV194 @ SV10 @ SV73 ) )
= $true )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV194
= ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1637]) ).
thf(1673,plain,
! [SV10: $i > $o,SV194: $i,SV73: $i > $o] :
( ( ( ! [SY844: $i] :
( ~ ( SV73 @ SY844 )
| ( ( sK84_SY660 @ SV194 @ SV10 @ SV73 )
= SY844 ) ) )
= $true )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV194
= ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1638]) ).
thf(1674,plain,
! [SV73: $i > $o,SV195: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK93_SY501 @ SV195 @ SV73 @ SV10 ) ) )
= $false )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV73 @ ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1639]) ).
thf(1675,plain,
! [SV73: $i > $o,SV195: $i,SV10: $i > $o] :
( ( ( ~ ! [SY854: $i] :
( ~ ( SV10 @ SY854 )
| ( ( sK93_SY501 @ SV195 @ SV73 @ SV10 )
= SY854 ) ) )
= $false )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV73 @ ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1639]) ).
thf(1676,plain,
! [SV73: $i > $o,SV195: $i,SV10: $i > $o] :
( ( ( SV10 @ ( sK85_SY501 @ SV195 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV195
= ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1640]) ).
thf(1677,plain,
! [SV73: $i > $o,SV195: $i,SV10: $i > $o] :
( ( ( ! [SY845: $i] :
( ~ ( SV10 @ SY845 )
| ( ( sK85_SY501 @ SV195 @ SV73 @ SV10 )
= SY845 ) ) )
= $true )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV195
= ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1641]) ).
thf(1678,plain,
! [SV10: $i > $o,SV196: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK94_SY660 @ SV196 @ SV10 @ SV73 ) ) )
= $false )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV10 @ ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1642]) ).
thf(1679,plain,
! [SV10: $i > $o,SV196: $i,SV73: $i > $o] :
( ( ( ~ ! [SY855: $i] :
( ~ ( SV73 @ SY855 )
| ( ( sK94_SY660 @ SV196 @ SV10 @ SV73 )
= SY855 ) ) )
= $false )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV10 @ ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1642]) ).
thf(1680,plain,
! [SV10: $i > $o,SV196: $i,SV73: $i > $o] :
( ( ( SV73 @ ( sK86_SY660 @ SV196 @ SV10 @ SV73 ) )
= $true )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV196
= ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1643]) ).
thf(1681,plain,
! [SV10: $i > $o,SV196: $i,SV73: $i > $o] :
( ( ( ! [SY846: $i] :
( ~ ( SV73 @ SY846 )
| ( ( sK86_SY660 @ SV196 @ SV10 @ SV73 )
= SY846 ) ) )
= $true )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV196
= ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1644]) ).
thf(1682,plain,
! [SV73: $i > $o,SV197: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK95_SY501 @ SV197 @ SV73 @ SV10 ) ) )
= $false )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV73 @ ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1645]) ).
thf(1683,plain,
! [SV73: $i > $o,SV197: $i,SV10: $i > $o] :
( ( ( ~ ! [SY856: $i] :
( ~ ( SV10 @ SY856 )
| ( ( sK95_SY501 @ SV197 @ SV73 @ SV10 )
= SY856 ) ) )
= $false )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV73 @ ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1645]) ).
thf(1684,plain,
! [SV73: $i > $o,SV197: $i,SV10: $i > $o] :
( ( ( SV10 @ ( sK87_SY501 @ SV197 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV197
= ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1646]) ).
thf(1685,plain,
! [SV73: $i > $o,SV197: $i,SV10: $i > $o] :
( ( ( ! [SY847: $i] :
( ~ ( SV10 @ SY847 )
| ( ( sK87_SY501 @ SV197 @ SV73 @ SV10 )
= SY847 ) ) )
= $true )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV197
= ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1647]) ).
thf(1686,plain,
! [SV10: $i > $o,SV186: $i,SV73: $i > $o] :
( ( ( SV73 @ ( sK88_SY660 @ SV186 @ SV10 @ SV73 ) )
= $true )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV10 @ ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1648]) ).
thf(1687,plain,
! [SV10: $i > $o,SV186: $i,SV73: $i > $o] :
( ( ( ! [SY848: $i] :
( ~ ( SV73 @ SY848 )
| ( ( sK88_SY660 @ SV186 @ SV10 @ SV73 )
= SY848 ) ) )
= $true )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV10 @ ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1649]) ).
thf(1688,plain,
! [SV10: $i > $o,SV186: $i,SV213: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV213 )
| ( ( sK82_SY660 @ SV186 @ SV10 @ SV73 )
= SV213 ) )
= $true )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV186
= ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(1689,plain,
! [SV73: $i > $o,SV187: $i,SV10: $i > $o] :
( ( ( SV10 @ ( sK89_SY501 @ SV187 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV73 @ ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1652]) ).
thf(1690,plain,
! [SV73: $i > $o,SV187: $i,SV10: $i > $o] :
( ( ( ! [SY849: $i] :
( ~ ( SV10 @ SY849 )
| ( ( sK89_SY501 @ SV187 @ SV73 @ SV10 )
= SY849 ) ) )
= $true )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV73 @ ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1653]) ).
thf(1691,plain,
! [SV73: $i > $o,SV187: $i,SV214: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV214 )
| ( ( sK83_SY501 @ SV187 @ SV73 @ SV10 )
= SV214 ) )
= $true )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV187
= ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(1692,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( ~ ( in @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1657]) ).
thf(1693,plain,
! [SV180: $i,SV148: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SV148 ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1657]) ).
thf(1694,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( ! [SY828: $i] :
~ ~ ( ~ ( in @ SY828 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
| ~ ( in @ SY828 @ SV148 ) ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1658]) ).
thf(1695,plain,
! [SV18: $i,SV148: $i,SV180: $i,SV211: $i,SV215: $i] :
( ( ( ~ ( in @ SV215 @ SV211 )
| ( in @ SV215 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) ) )
= $true )
| ( ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SV211 )
= $true )
| ( ( in @ SV211 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(1696,plain,
! [SV18: $i,SV148: $i,SV178: $i] :
( ( ( in @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1660]) ).
thf(1697,plain,
! [SV178: $i,SV148: $i,SV18: $i] :
( ( ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SV148 )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1661]) ).
thf(1698,plain,
! [SV18: $i,SV148: $i,SV178: $i,SV216: $i] :
( ( ( ~ ~ ( ~ ( in @ SV216 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
| ~ ( in @ SV216 @ SV148 ) ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(1699,plain,
! [SV18: $i,SV148: $i,SV178: $i,SV208: $i,SV212: $i] :
( ( ( ~ ( in @ SV212 @ SV208 ) )
= $true )
| ( ( in @ SV212 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
= $true )
| ( ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SV208 )
= $true )
| ( ( in @ SV208 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1663]) ).
thf(1700,plain,
! [SV10: $i > $o,SV200: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ ( sK96_SY660 @ SV200 @ SV10 @ SV73 ) ) )
= $false )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV10 @ ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1664]) ).
thf(1701,plain,
! [SV10: $i > $o,SV200: $i,SV73: $i > $o] :
( ( ( ~ ! [SY857: $i] :
( ~ ( SV73 @ SY857 )
| ( ( sK96_SY660 @ SV200 @ SV10 @ SV73 )
= SY857 ) ) )
= $false )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV10 @ ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1664]) ).
thf(1702,plain,
! [SV10: $i > $o,SV200: $i,SV73: $i > $o] :
( ( ( SV73 @ ( sK90_SY660 @ SV200 @ SV10 @ SV73 ) )
= $true )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV200
= ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1665]) ).
thf(1703,plain,
! [SV10: $i > $o,SV200: $i,SV73: $i > $o] :
( ( ( ! [SY851: $i] :
( ~ ( SV73 @ SY851 )
| ( ( sK90_SY660 @ SV200 @ SV10 @ SV73 )
= SY851 ) ) )
= $true )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV200
= ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1666]) ).
thf(1704,plain,
! [SV73: $i > $o,SV201: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK97_SY501 @ SV201 @ SV73 @ SV10 ) ) )
= $false )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV73 @ ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1667]) ).
thf(1705,plain,
! [SV73: $i > $o,SV201: $i,SV10: $i > $o] :
( ( ( ~ ! [SY858: $i] :
( ~ ( SV10 @ SY858 )
| ( ( sK97_SY501 @ SV201 @ SV73 @ SV10 )
= SY858 ) ) )
= $false )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV73 @ ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1667]) ).
thf(1706,plain,
! [SV73: $i > $o,SV201: $i,SV10: $i > $o] :
( ( ( SV10 @ ( sK91_SY501 @ SV201 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV201
= ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1668]) ).
thf(1707,plain,
! [SV73: $i > $o,SV201: $i,SV10: $i > $o] :
( ( ( ! [SY852: $i] :
( ~ ( SV10 @ SY852 )
| ( ( sK91_SY501 @ SV201 @ SV73 @ SV10 )
= SY852 ) ) )
= $true )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV201
= ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1669]) ).
thf(1708,plain,
! [SV10: $i > $o,SV194: $i,SV73: $i > $o] :
( ( ( SV73 @ ( sK92_SY660 @ SV194 @ SV10 @ SV73 ) )
= $true )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV10 @ ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1670]) ).
thf(1709,plain,
! [SV10: $i > $o,SV194: $i,SV73: $i > $o] :
( ( ( ! [SY853: $i] :
( ~ ( SV73 @ SY853 )
| ( ( sK92_SY660 @ SV194 @ SV10 @ SV73 )
= SY853 ) ) )
= $true )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV10 @ ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1671]) ).
thf(1710,plain,
! [SV10: $i > $o,SV194: $i,SV217: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV217 )
| ( ( sK84_SY660 @ SV194 @ SV10 @ SV73 )
= SV217 ) )
= $true )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV194
= ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(1711,plain,
! [SV73: $i > $o,SV195: $i,SV10: $i > $o] :
( ( ( SV10 @ ( sK93_SY501 @ SV195 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV73 @ ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1712,plain,
! [SV73: $i > $o,SV195: $i,SV10: $i > $o] :
( ( ( ! [SY854: $i] :
( ~ ( SV10 @ SY854 )
| ( ( sK93_SY501 @ SV195 @ SV73 @ SV10 )
= SY854 ) ) )
= $true )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV73 @ ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1675]) ).
thf(1713,plain,
! [SV73: $i > $o,SV195: $i,SV218: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV218 )
| ( ( sK85_SY501 @ SV195 @ SV73 @ SV10 )
= SV218 ) )
= $true )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV195
= ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(1714,plain,
! [SV10: $i > $o,SV196: $i,SV73: $i > $o] :
( ( ( SV73 @ ( sK94_SY660 @ SV196 @ SV10 @ SV73 ) )
= $true )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV10 @ ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1678]) ).
thf(1715,plain,
! [SV10: $i > $o,SV196: $i,SV73: $i > $o] :
( ( ( ! [SY855: $i] :
( ~ ( SV73 @ SY855 )
| ( ( sK94_SY660 @ SV196 @ SV10 @ SV73 )
= SY855 ) ) )
= $true )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV10 @ ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1679]) ).
thf(1716,plain,
! [SV10: $i > $o,SV196: $i,SV219: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV219 )
| ( ( sK86_SY660 @ SV196 @ SV10 @ SV73 )
= SV219 ) )
= $true )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV196
= ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(1717,plain,
! [SV73: $i > $o,SV197: $i,SV10: $i > $o] :
( ( ( SV10 @ ( sK95_SY501 @ SV197 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV73 @ ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1682]) ).
thf(1718,plain,
! [SV73: $i > $o,SV197: $i,SV10: $i > $o] :
( ( ( ! [SY856: $i] :
( ~ ( SV10 @ SY856 )
| ( ( sK95_SY501 @ SV197 @ SV73 @ SV10 )
= SY856 ) ) )
= $true )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV73 @ ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1683]) ).
thf(1719,plain,
! [SV73: $i > $o,SV197: $i,SV220: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV220 )
| ( ( sK87_SY501 @ SV197 @ SV73 @ SV10 )
= SV220 ) )
= $true )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV197
= ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(1720,plain,
! [SV10: $i > $o,SV186: $i,SV221: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV221 )
| ( ( sK88_SY660 @ SV186 @ SV10 @ SV73 )
= SV221 ) )
= $true )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV10 @ ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(1721,plain,
! [SV10: $i > $o,SV186: $i,SV213: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV213 ) )
= $true )
| ( ( ( sK82_SY660 @ SV186 @ SV10 @ SV73 )
= SV213 )
= $true )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV186
= ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1688]) ).
thf(1722,plain,
! [SV73: $i > $o,SV187: $i,SV222: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV222 )
| ( ( sK89_SY501 @ SV187 @ SV73 @ SV10 )
= SV222 ) )
= $true )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV73 @ ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(1723,plain,
! [SV73: $i > $o,SV187: $i,SV214: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV214 ) )
= $true )
| ( ( ( sK83_SY501 @ SV187 @ SV73 @ SV10 )
= SV214 )
= $true )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV187
= ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1691]) ).
thf(1724,plain,
! [SV18: $i,SV148: $i,SV180: $i] :
( ( ( in @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) @ ( sK2_SY521 @ SV18 ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1692]) ).
thf(1725,plain,
! [SV180: $i,SV148: $i,SV18: $i] :
( ( ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SV148 )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1693]) ).
thf(1726,plain,
! [SV18: $i,SV148: $i,SV180: $i,SV223: $i] :
( ( ( ~ ~ ( ~ ( in @ SV223 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
| ~ ( in @ SV223 @ SV148 ) ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(1727,plain,
! [SV18: $i,SV148: $i,SV180: $i,SV211: $i,SV215: $i] :
( ( ( ~ ( in @ SV215 @ SV211 ) )
= $true )
| ( ( in @ SV215 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
= $true )
| ( ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SV211 )
= $true )
| ( ( in @ SV211 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1695]) ).
thf(1728,plain,
! [SV18: $i,SV148: $i,SV178: $i,SV216: $i] :
( ( ( ~ ( ~ ( in @ SV216 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
| ~ ( in @ SV216 @ SV148 ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1698]) ).
thf(1729,plain,
! [SV18: $i,SV148: $i,SV178: $i,SV208: $i,SV212: $i] :
( ( ( in @ SV212 @ SV208 )
= $false )
| ( ( in @ SV212 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
= $true )
| ( ( in @ ( sK68_SY821 @ SV18 @ SV148 @ SV178 ) @ SV208 )
= $true )
| ( ( in @ SV208 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1730,plain,
! [SV10: $i > $o,SV200: $i,SV73: $i > $o] :
( ( ( SV73 @ ( sK96_SY660 @ SV200 @ SV10 @ SV73 ) )
= $true )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV10 @ ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1700]) ).
thf(1731,plain,
! [SV10: $i > $o,SV200: $i,SV73: $i > $o] :
( ( ( ! [SY857: $i] :
( ~ ( SV73 @ SY857 )
| ( ( sK96_SY660 @ SV200 @ SV10 @ SV73 )
= SY857 ) ) )
= $true )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV10 @ ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1701]) ).
thf(1732,plain,
! [SV10: $i > $o,SV200: $i,SV224: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV224 )
| ( ( sK90_SY660 @ SV200 @ SV10 @ SV73 )
= SV224 ) )
= $true )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV200
= ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(1733,plain,
! [SV73: $i > $o,SV201: $i,SV10: $i > $o] :
( ( ( SV10 @ ( sK97_SY501 @ SV201 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV73 @ ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1704]) ).
thf(1734,plain,
! [SV73: $i > $o,SV201: $i,SV10: $i > $o] :
( ( ( ! [SY858: $i] :
( ~ ( SV10 @ SY858 )
| ( ( sK97_SY501 @ SV201 @ SV73 @ SV10 )
= SY858 ) ) )
= $true )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV73 @ ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1705]) ).
thf(1735,plain,
! [SV73: $i > $o,SV201: $i,SV225: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV225 )
| ( ( sK91_SY501 @ SV201 @ SV73 @ SV10 )
= SV225 ) )
= $true )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV201
= ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(1736,plain,
! [SV10: $i > $o,SV194: $i,SV226: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV226 )
| ( ( sK92_SY660 @ SV194 @ SV10 @ SV73 )
= SV226 ) )
= $true )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV10 @ ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(1737,plain,
! [SV10: $i > $o,SV194: $i,SV217: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV217 ) )
= $true )
| ( ( ( sK84_SY660 @ SV194 @ SV10 @ SV73 )
= SV217 )
= $true )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV194
= ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1710]) ).
thf(1738,plain,
! [SV73: $i > $o,SV195: $i,SV227: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV227 )
| ( ( sK93_SY501 @ SV195 @ SV73 @ SV10 )
= SV227 ) )
= $true )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV73 @ ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(1739,plain,
! [SV73: $i > $o,SV195: $i,SV218: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV218 ) )
= $true )
| ( ( ( sK85_SY501 @ SV195 @ SV73 @ SV10 )
= SV218 )
= $true )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV195
= ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1713]) ).
thf(1740,plain,
! [SV10: $i > $o,SV196: $i,SV228: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV228 )
| ( ( sK94_SY660 @ SV196 @ SV10 @ SV73 )
= SV228 ) )
= $true )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV10 @ ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(1741,plain,
! [SV10: $i > $o,SV196: $i,SV219: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV219 ) )
= $true )
| ( ( ( sK86_SY660 @ SV196 @ SV10 @ SV73 )
= SV219 )
= $true )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV196
= ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1716]) ).
thf(1742,plain,
! [SV73: $i > $o,SV197: $i,SV229: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV229 )
| ( ( sK95_SY501 @ SV197 @ SV73 @ SV10 )
= SV229 ) )
= $true )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV73 @ ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(1743,plain,
! [SV73: $i > $o,SV197: $i,SV220: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV220 ) )
= $true )
| ( ( ( sK87_SY501 @ SV197 @ SV73 @ SV10 )
= SV220 )
= $true )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV197
= ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1719]) ).
thf(1744,plain,
! [SV10: $i > $o,SV186: $i,SV221: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV221 ) )
= $true )
| ( ( ( sK88_SY660 @ SV186 @ SV10 @ SV73 )
= SV221 )
= $true )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV10 @ ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1720]) ).
thf(1745,plain,
! [SV10: $i > $o,SV186: $i,SV213: $i,SV73: $i > $o] :
( ( ( SV73 @ SV213 )
= $false )
| ( ( ( sK82_SY660 @ SV186 @ SV10 @ SV73 )
= SV213 )
= $true )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV186
= ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1746,plain,
! [SV73: $i > $o,SV187: $i,SV222: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV222 ) )
= $true )
| ( ( ( sK89_SY501 @ SV187 @ SV73 @ SV10 )
= SV222 )
= $true )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV73 @ ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1722]) ).
thf(1747,plain,
! [SV73: $i > $o,SV187: $i,SV214: $i,SV10: $i > $o] :
( ( ( SV10 @ SV214 )
= $false )
| ( ( ( sK83_SY501 @ SV187 @ SV73 @ SV10 )
= SV214 )
= $true )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV187
= ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1723]) ).
thf(1748,plain,
! [SV18: $i,SV148: $i,SV180: $i,SV223: $i] :
( ( ( ~ ( ~ ( in @ SV223 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
| ~ ( in @ SV223 @ SV148 ) ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1726]) ).
thf(1749,plain,
! [SV18: $i,SV148: $i,SV180: $i,SV211: $i,SV215: $i] :
( ( ( in @ SV215 @ SV211 )
= $false )
| ( ( in @ SV215 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
= $true )
| ( ( in @ ( sK71_SY827 @ SV18 @ SV148 @ SV180 ) @ SV211 )
= $true )
| ( ( in @ SV211 @ ( sK2_SY521 @ SV18 ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1727]) ).
thf(1750,plain,
! [SV18: $i,SV148: $i,SV178: $i,SV216: $i] :
( ( ( ~ ( in @ SV216 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
| ~ ( in @ SV216 @ SV148 ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1728]) ).
thf(1751,plain,
! [SV10: $i > $o,SV200: $i,SV230: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV230 )
| ( ( sK96_SY660 @ SV200 @ SV10 @ SV73 )
= SV230 ) )
= $true )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV10 @ ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(1752,plain,
! [SV10: $i > $o,SV200: $i,SV224: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV224 ) )
= $true )
| ( ( ( sK90_SY660 @ SV200 @ SV10 @ SV73 )
= SV224 )
= $true )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV200
= ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1732]) ).
thf(1753,plain,
! [SV73: $i > $o,SV201: $i,SV231: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV231 )
| ( ( sK97_SY501 @ SV201 @ SV73 @ SV10 )
= SV231 ) )
= $true )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV73 @ ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(1754,plain,
! [SV73: $i > $o,SV201: $i,SV225: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV225 ) )
= $true )
| ( ( ( sK91_SY501 @ SV201 @ SV73 @ SV10 )
= SV225 )
= $true )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV201
= ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1735]) ).
thf(1755,plain,
! [SV10: $i > $o,SV194: $i,SV226: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV226 ) )
= $true )
| ( ( ( sK92_SY660 @ SV194 @ SV10 @ SV73 )
= SV226 )
= $true )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV10 @ ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1736]) ).
thf(1756,plain,
! [SV10: $i > $o,SV194: $i,SV217: $i,SV73: $i > $o] :
( ( ( SV73 @ SV217 )
= $false )
| ( ( ( sK84_SY660 @ SV194 @ SV10 @ SV73 )
= SV217 )
= $true )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV194
= ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1757,plain,
! [SV73: $i > $o,SV195: $i,SV227: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV227 ) )
= $true )
| ( ( ( sK93_SY501 @ SV195 @ SV73 @ SV10 )
= SV227 )
= $true )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV73 @ ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1738]) ).
thf(1758,plain,
! [SV73: $i > $o,SV195: $i,SV218: $i,SV10: $i > $o] :
( ( ( SV10 @ SV218 )
= $false )
| ( ( ( sK85_SY501 @ SV195 @ SV73 @ SV10 )
= SV218 )
= $true )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV195
= ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1739]) ).
thf(1759,plain,
! [SV10: $i > $o,SV196: $i,SV228: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV228 ) )
= $true )
| ( ( ( sK94_SY660 @ SV196 @ SV10 @ SV73 )
= SV228 )
= $true )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV10 @ ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1740]) ).
thf(1760,plain,
! [SV10: $i > $o,SV196: $i,SV219: $i,SV73: $i > $o] :
( ( ( SV73 @ SV219 )
= $false )
| ( ( ( sK86_SY660 @ SV196 @ SV10 @ SV73 )
= SV219 )
= $true )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV196
= ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1761,plain,
! [SV73: $i > $o,SV197: $i,SV229: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV229 ) )
= $true )
| ( ( ( sK95_SY501 @ SV197 @ SV73 @ SV10 )
= SV229 )
= $true )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV73 @ ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1742]) ).
thf(1762,plain,
! [SV73: $i > $o,SV197: $i,SV220: $i,SV10: $i > $o] :
( ( ( SV10 @ SV220 )
= $false )
| ( ( ( sK87_SY501 @ SV197 @ SV73 @ SV10 )
= SV220 )
= $true )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV197
= ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(1763,plain,
! [SV10: $i > $o,SV186: $i,SV221: $i,SV73: $i > $o] :
( ( ( SV73 @ SV221 )
= $false )
| ( ( ( sK88_SY660 @ SV186 @ SV10 @ SV73 )
= SV221 )
= $true )
| ( ( SV10 @ SV186 )
= $false )
| ( ( SV10 @ ( sK72_SY813 @ SV73 @ SV186 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1764,plain,
! [SV73: $i > $o,SV187: $i,SV222: $i,SV10: $i > $o] :
( ( ( SV10 @ SV222 )
= $false )
| ( ( ( sK89_SY501 @ SV187 @ SV73 @ SV10 )
= SV222 )
= $true )
| ( ( SV73 @ SV187 )
= $false )
| ( ( SV73 @ ( sK73_SY814 @ SV10 @ SV187 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(1765,plain,
! [SV18: $i,SV148: $i,SV180: $i,SV223: $i] :
( ( ( ~ ( in @ SV223 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
| ~ ( in @ SV223 @ SV148 ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1748]) ).
thf(1766,plain,
! [SV18: $i,SV148: $i,SV178: $i,SV216: $i] :
( ( ( ~ ( in @ SV216 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) ) )
= $true )
| ( ( ~ ( in @ SV216 @ SV148 ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1750]) ).
thf(1767,plain,
! [SV10: $i > $o,SV200: $i,SV230: $i,SV73: $i > $o] :
( ( ( ~ ( SV73 @ SV230 ) )
= $true )
| ( ( ( sK96_SY660 @ SV200 @ SV10 @ SV73 )
= SV230 )
= $true )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV10 @ ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1751]) ).
thf(1768,plain,
! [SV10: $i > $o,SV200: $i,SV224: $i,SV73: $i > $o] :
( ( ( SV73 @ SV224 )
= $false )
| ( ( ( sK90_SY660 @ SV200 @ SV10 @ SV73 )
= SV224 )
= $true )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV200
= ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1752]) ).
thf(1769,plain,
! [SV73: $i > $o,SV201: $i,SV231: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV231 ) )
= $true )
| ( ( ( sK97_SY501 @ SV201 @ SV73 @ SV10 )
= SV231 )
= $true )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV73 @ ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1753]) ).
thf(1770,plain,
! [SV73: $i > $o,SV201: $i,SV225: $i,SV10: $i > $o] :
( ( ( SV10 @ SV225 )
= $false )
| ( ( ( sK91_SY501 @ SV201 @ SV73 @ SV10 )
= SV225 )
= $true )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV201
= ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $false )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1754]) ).
thf(1771,plain,
! [SV10: $i > $o,SV194: $i,SV226: $i,SV73: $i > $o] :
( ( ( SV73 @ SV226 )
= $false )
| ( ( ( sK92_SY660 @ SV194 @ SV10 @ SV73 )
= SV226 )
= $true )
| ( ( SV10 @ SV194 )
= $false )
| ( ( SV10 @ ( sK75_SY817 @ SV73 @ SV194 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(1772,plain,
! [SV73: $i > $o,SV195: $i,SV227: $i,SV10: $i > $o] :
( ( ( SV10 @ SV227 )
= $false )
| ( ( ( sK93_SY501 @ SV195 @ SV73 @ SV10 )
= SV227 )
= $true )
| ( ( SV73 @ SV195 )
= $false )
| ( ( SV73 @ ( sK76_SY818 @ SV10 @ SV195 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1773,plain,
! [SV10: $i > $o,SV196: $i,SV228: $i,SV73: $i > $o] :
( ( ( SV73 @ SV228 )
= $false )
| ( ( ( sK94_SY660 @ SV196 @ SV10 @ SV73 )
= SV228 )
= $true )
| ( ( SV10 @ SV196 )
= $false )
| ( ( SV10 @ ( sK77_SY819 @ SV73 @ SV196 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1759]) ).
thf(1774,plain,
! [SV73: $i > $o,SV197: $i,SV229: $i,SV10: $i > $o] :
( ( ( SV10 @ SV229 )
= $false )
| ( ( ( sK95_SY501 @ SV197 @ SV73 @ SV10 )
= SV229 )
= $true )
| ( ( SV73 @ SV197 )
= $false )
| ( ( SV73 @ ( sK78_SY820 @ SV10 @ SV197 @ SV73 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $false )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1761]) ).
thf(1775,plain,
! [SV18: $i,SV148: $i,SV180: $i,SV223: $i] :
( ( ( ~ ( in @ SV223 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) ) )
= $true )
| ( ( ~ ( in @ SV223 @ SV148 ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1765]) ).
thf(1776,plain,
! [SV18: $i,SV148: $i,SV178: $i,SV216: $i] :
( ( ( in @ SV216 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
= $false )
| ( ( ~ ( in @ SV216 @ SV148 ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1766]) ).
thf(1777,plain,
! [SV10: $i > $o,SV200: $i,SV230: $i,SV73: $i > $o] :
( ( ( SV73 @ SV230 )
= $false )
| ( ( ( sK96_SY660 @ SV200 @ SV10 @ SV73 )
= SV230 )
= $true )
| ( ( SV10 @ SV200 )
= $false )
| ( ( SV10 @ ( sK80_SY825 @ SV73 @ SV200 @ SV10 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1767]) ).
thf(1778,plain,
! [SV73: $i > $o,SV201: $i,SV231: $i,SV10: $i > $o] :
( ( ( SV10 @ SV231 )
= $false )
| ( ( ( sK97_SY501 @ SV201 @ SV73 @ SV10 )
= SV231 )
= $true )
| ( ( SV73 @ SV201 )
= $false )
| ( ( SV73 @ ( sK81_SY826 @ SV10 @ SV201 @ SV73 ) )
= $true )
| ( ( SV10 @ ( sK6_SY656 @ SV73 @ SV10 ) )
= $true )
| ( ( SV73 @ ( sK13_SY750 @ SV10 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1779,plain,
! [SV18: $i,SV148: $i,SV180: $i,SV223: $i] :
( ( ( in @ SV223 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
= $false )
| ( ( ~ ( in @ SV223 @ SV148 ) )
= $true )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1775]) ).
thf(1780,plain,
! [SV18: $i,SV178: $i,SV148: $i,SV216: $i] :
( ( ( in @ SV216 @ SV148 )
= $false )
| ( ( in @ SV216 @ ( sK63_SY766 @ SV178 @ SV148 @ SV18 ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV18 )
= $false )
| ( ( in @ SV178 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(1781,plain,
! [SV18: $i,SV180: $i,SV148: $i,SV223: $i] :
( ( ( in @ SV223 @ SV148 )
= $false )
| ( ( in @ SV223 @ ( sK64_SY766 @ SV180 @ SV148 @ SV18 ) )
= $false )
| ( ( in @ ( sK40_SY764 @ SV18 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV180 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1779]) ).
thf(1782,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[78,1781,1780,1778,1777,1774,1773,1772,1771,1770,1768,1764,1763,1762,1760,1758,1756,1749,1747,1745,1733,1730,1729,1725,1724,1717,1714,1711,1708,1706,1702,1697,1696,1689,1686,1684,1680,1676,1672,1656,1654,1650,1631,1624,1623,1603,1602,1601,1599,1598,1591,1572,1570,1567,1566,1506,1503,1478,1474,1440,1421,1402,1381,1380,1379,1356,1355,1354,1350,1349,1348,1347,1346,1319,1318,1316,1315,1314,1311,1309,1289,1286,1284,1250,1244,1241,1233,1230,1225,1204,1201,1197,1192,1188,1126,1125,1115,1108,1077,1071,1070,1067,1065,1059,1058,1057,1056,1055,1047,1023,1022,1021,1016,1008,998,997,992,991,990,971,970,968,967,965,964,957,948,945,933,929,911,908,905,902,897,885,884,851,850,845,844,843,832,818,817,815,798,793,792,791,790,788,786,785,783,782,780,764,731,717,716,715,697,683,670,653,651,647,645,642,636,616,605,601,592,590,548,535,526,525,524,522,490,489,488,462,460,459,458,456,449,448,443,442,441,418,412,403,402,401,399,398,397,291,290,289,288,287,216,215,214,144,120,82]) ).
thf(1783,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1782]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU556^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.18 % Computer : n003.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Oct 6 15:29:54 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.10/1.75
% 9.10/1.75 No.of.Axioms: 0
% 9.10/1.75
% 9.10/1.75 Length.of.Defs: 15056
% 9.10/1.75
% 9.10/1.75 Contains.Choice.Funs: true
% 9.10/1.75 ............................................................
% 9.10/1.75
% 9.10/1.75 ********************************
% 9.10/1.75 * All subproblems solved! *
% 9.10/1.75 ********************************
% 9.10/1.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:72,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:1782,loop_count:0,foatp_calls:1,translation:fof_full)
% 9.10/1.75
% 9.10/1.75 %**** Beginning of derivation protocol ****
% 9.10/1.75 % SZS output start CNFRefutation
% See solution above
% 9.10/1.76
% 9.10/1.76 %**** End of derivation protocol ****
% 9.10/1.76 %**** no. of clauses in derivation: 1783 ****
% 9.10/1.76 %**** clause counter: 1782 ****
% 9.10/1.76
% 9.10/1.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:72,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:1782,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------