%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU578^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 10:45:17 AM UTC 2026
% Result : Theorem 16.05s 2.95s
% Output : CNFRefutation 16.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 97
% Syntax : Number of formulae : 2297 ( 589 unt; 0 typ; 96 def)
% Number of atoms : 20173 (9338 equ; 0 cnn)
% Maximal formula atoms : 95 ( 8 avg)
% Number of connectives : 43924 (10422 ~;8775 |; 147 &;23631 @)
% ( 56 <=>; 893 =>; 0 <=; 0 <~>)
% Maximal formula depth : 98 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2141 (2141 >; 0 *; 0 +; 0 <<)
% Number of symbols : 228 ( 225 usr; 99 con; 0-4 aty)
% Number of variables : 9762 ( 651 ^;8960 !; 151 ?;9762 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_descr,type,
descr: ( $i > $o ) > $i ).
thf(tp_descr__Cong,type,
descr__Cong: $o ).
thf(tp_descrp,type,
descrp: $o ).
thf(tp_disjoint,type,
disjoint: $i > $i > $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_dsetconstr__Cong,type,
dsetconstr__Cong: $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_emptysetsubset,type,
emptysetsubset: $o ).
thf(tp_eqimpsubset1,type,
eqimpsubset1: $o ).
thf(tp_eqimpsubset2,type,
eqimpsubset2: $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_exuEu,type,
exuEu: $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_notequalI1,type,
notequalI1: $o ).
thf(tp_notequalI2,type,
notequalI2: $o ).
thf(tp_notinemptyset,type,
notinemptyset: $o ).
thf(tp_notinsingleton,type,
notinsingleton: $o ).
thf(tp_notsubsetI,type,
notsubsetI: $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_powersetE1,type,
powersetE1: $o ).
thf(tp_powersetI,type,
powersetI: $o ).
thf(tp_powersetI1,type,
powersetI1: $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_sK100_SY736,type,
sK100_SY736: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK101_SY878,type,
sK101_SY878: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK102_SY736,type,
sK102_SY736: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK103_SY878,type,
sK103_SY878: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK104_SY736,type,
sK104_SY736: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK105_SY878,type,
sK105_SY878: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK106_SY736,type,
sK106_SY736: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK107_SY878,type,
sK107_SY878: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK108_SY736,type,
sK108_SY736: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK109_SY1044,type,
sK109_SY1044: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK10_SY874,type,
sK10_SY874: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK110_SY1045,type,
sK110_SY1045: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK111_SY1046,type,
sK111_SY1046: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK112_SY1047,type,
sK112_SY1047: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK113_SY1051,type,
sK113_SY1051: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK114_SY1052,type,
sK114_SY1052: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK115_SY1053,type,
sK115_SY1053: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK116_SY1061,type,
sK116_SY1061: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK11_SY888,type,
sK11_SY888: $i > $i > $i ).
thf(tp_sK12_SY899,type,
sK12_SY899: $i > $i > $i ).
thf(tp_sK13_SY900,type,
sK13_SY900: ( $i > $o ) > $i > $i ).
thf(tp_sK14_SY640,type,
sK14_SY640: $i > $i ).
thf(tp_sK15_SY946,type,
sK15_SY946: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK16_SY947,type,
sK16_SY947: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK17_SY801,type,
sK17_SY801: $i > $i ).
thf(tp_sK18_SY823,type,
sK18_SY823: ( $i > $o ) > $i > $i ).
thf(tp_sK19_SY894,type,
sK19_SY894: ( $i > $o ) > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY949,type,
sK20_SY949: $i > ( $i > $o ) > $i ).
thf(tp_sK21_SY934,type,
sK21_SY934: $o > $i > $i > $i ).
thf(tp_sK22_SX0,type,
sK22_SX0: $i > $i > $i ).
thf(tp_sK23_SX0,type,
sK23_SX0: $i > $i > $i ).
thf(tp_sK24_SY839,type,
sK24_SY839: $i > $i > $i ).
thf(tp_sK25_SY715,type,
sK25_SY715: $i > $i > $i ).
thf(tp_sK26_SY775,type,
sK26_SY775: $i > $i ).
thf(tp_sK27_SY651,type,
sK27_SY651: $i > ( $i > $o ) > $i ).
thf(tp_sK28_SY848,type,
sK28_SY848: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK29_SY953,type,
sK29_SY953: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(tp_sK2_SY743,type,
sK2_SY743: $i > $i ).
thf(tp_sK30_SY889,type,
sK30_SY889: $i > $i > $i ).
thf(tp_sK31_SY906,type,
sK31_SY906: $i > $i > $i ).
thf(tp_sK32_SY966,type,
sK32_SY966: $i > ( $i > $o ) > $i ).
thf(tp_sK33_SY842,type,
sK33_SY842: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK34_SY889,type,
sK34_SY889: $i > $i > $i ).
thf(tp_sK35_SY903,type,
sK35_SY903: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK36_SY932,type,
sK36_SY932: $i > ( $i > $o ) > $i ).
thf(tp_sK37_SY933,type,
sK37_SY933: $i > ( $i > $o ) > $i ).
thf(tp_sK38_SY935,type,
sK38_SY935: $i > ( $i > $o ) > $i ).
thf(tp_sK39_SY936,type,
sK39_SY936: $i > ( $i > $o ) > $i ).
thf(tp_sK3_SY634,type,
sK3_SY634: $i > $i ).
thf(tp_sK40_SY970,type,
sK40_SY970: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(tp_sK41_SY950,type,
sK41_SY950: $i > ( $i > $o ) > $i ).
thf(tp_sK42_SY951,type,
sK42_SY951: $i > ( $i > $o ) > $i ).
thf(tp_sK43_SY952,type,
sK43_SY952: $i > ( $i > $o ) > $i ).
thf(tp_sK44_SY622,type,
sK44_SY622: $i > ( $i > $o ) > $i ).
thf(tp_sK45_SY630,type,
sK45_SY630: $i > ( $i > $o ) > $i ).
thf(tp_sK46_SY827,type,
sK46_SY827: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK47_SY653,type,
sK47_SY653: $i > ( $i > $o ) > $i ).
thf(tp_sK48_SY653,type,
sK48_SY653: $i > ( $i > $o ) > $i ).
thf(tp_sK49_SY681,type,
sK49_SY681: $i > ( $i > $o ) > $i ).
thf(tp_sK4_SY742,type,
sK4_SY742: $i > $i ).
thf(tp_sK50_SY957,type,
sK50_SY957: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK51_SY959,type,
sK51_SY959: $i > $i > $i ).
thf(tp_sK52_SY799,type,
sK52_SY799: $i > ( $i > $o ) > $i ).
thf(tp_sK53_SY622,type,
sK53_SY622: $i > ( $i > $o ) > $i ).
thf(tp_sK54_SY630,type,
sK54_SY630: $i > ( $i > $o ) > $i ).
thf(tp_sK55_SY653,type,
sK55_SY653: $i > ( $i > $o ) > $i ).
thf(tp_sK56_SY681,type,
sK56_SY681: $i > ( $i > $o ) > $i ).
thf(tp_sK57_SY789,type,
sK57_SY789: $i > ( $i > $o ) > $i ).
thf(tp_sK58_SY799,type,
sK58_SY799: $i > ( $i > $o ) > $i ).
thf(tp_sK59_SY789,type,
sK59_SY789: $i > ( $i > $o ) > $i ).
thf(tp_sK5_SY820,type,
sK5_SY820: $i > $i > $i ).
thf(tp_sK60_SY789,type,
sK60_SY789: $i > ( $i > $o ) > $i ).
thf(tp_sK61_SY848,type,
sK61_SY848: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK62_SY789,type,
sK62_SY789: $i > ( $i > $o ) > $i ).
thf(tp_sK63_SY971,type,
sK63_SY971: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK64_SY848,type,
sK64_SY848: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK65_SY976,type,
sK65_SY976: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK66_SY994,type,
sK66_SY994: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK67_SY995,type,
sK67_SY995: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK68_SY961,type,
sK68_SY961: $i > $i > $i > $i ).
thf(tp_sK69_SY961,type,
sK69_SY961: $i > $i > $i > $i ).
thf(tp_sK6_SY832,type,
sK6_SY832: $i > $i > $i ).
thf(tp_sK70_SY1004,type,
sK70_SY1004: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK71_SY1009,type,
sK71_SY1009: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK72_SY1010,type,
sK72_SY1010: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK73_SY878,type,
sK73_SY878: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK74_SY736,type,
sK74_SY736: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK75_SY996,type,
sK75_SY996: $i > $i > $i > $i ).
thf(tp_sK76_SY1022,type,
sK76_SY1022: $i > $i > $i > $i ).
thf(tp_sK77_SY1013,type,
sK77_SY1013: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK78_SY878,type,
sK78_SY878: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK79_SY736,type,
sK79_SY736: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK7_SY843,type,
sK7_SY843: $i > $i > $i ).
thf(tp_sK80_SY1028,type,
sK80_SY1028: $i > $i > $i > $i ).
thf(tp_sK81_SY1011,type,
sK81_SY1011: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK82_SY1016,type,
sK82_SY1016: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK83_SY1017,type,
sK83_SY1017: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK84_SY1014,type,
sK84_SY1014: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK85_SY1018,type,
sK85_SY1018: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK86_SY1019,type,
sK86_SY1019: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK87_SY1020,type,
sK87_SY1020: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK88_SY1021,type,
sK88_SY1021: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK89_SY1026,type,
sK89_SY1026: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK8_SY845,type,
sK8_SY845: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK90_SY1027,type,
sK90_SY1027: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK91_SY1032,type,
sK91_SY1032: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK92_SY878,type,
sK92_SY878: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK93_SY736,type,
sK93_SY736: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK94_SY1033,type,
sK94_SY1033: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK95_SY878,type,
sK95_SY878: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK96_SY736,type,
sK96_SY736: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK97_SY878,type,
sK97_SY878: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK98_SY736,type,
sK98_SY736: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK99_SY878,type,
sK99_SY878: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK9_SY866,type,
sK9_SY866: ( $i > $o ) > ( $i > $o ) > $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_setadjoinSub,type,
setadjoinSub: $o ).
thf(tp_setadjoinSub2,type,
setadjoinSub2: $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_setextsub,type,
setextsub: $o ).
thf(tp_setoftrueEq,type,
setoftrueEq: $o ).
thf(tp_setsmeet,type,
setsmeet: $i > $i > $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_subset,type,
subset: $i > $i > $o ).
thf(tp_subset2powerset,type,
subset2powerset: $o ).
thf(tp_subsetE,type,
subsetE: $o ).
thf(tp_subsetE2,type,
subsetE2: $o ).
thf(tp_subsetI1,type,
subsetI1: $o ).
thf(tp_subsetI2,type,
subsetI2: $o ).
thf(tp_subsetRefl,type,
subsetRefl: $o ).
thf(tp_subsetTrans,type,
subsetTrans: $o ).
thf(tp_subsetemptysetimpeq,type,
subsetemptysetimpeq: $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(descr__Cong,definition,
( descr__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 ) )
=> ( ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descr__Cong) ).
thf(descrp,definition,
( descrp
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( Xphi
@ ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(dsetconstr__Cong,definition,
( dsetconstr__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstr__Cong) ).
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/sandbox2/benchmark/theBenchmark.p',emptyE1) ).
thf(emptyI,definition,
( emptyI
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
thf(emptyInPowerset,definition,
( emptyInPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,definition,
( emptyinPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyinunitempty,definition,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(emptyset__Cong,definition,
( emptyset__Cong
= ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetsubset,definition,
( emptysetsubset
= ( ! [A: $i] : ( subset @ emptyset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).
thf(eqimpsubset1,definition,
( eqimpsubset1
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,definition,
( eqimpsubset2
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqinunit,definition,
( eqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',exuE2) ).
thf(exuE3e,definition,
( exuE3e
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] : ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',exuE3u) ).
thf(exuEu,definition,
( exuEu
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuEu) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(noeltsimpempty,definition,
( noeltsimpempty
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyE1,definition,
( nonemptyE1
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] : ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(nonemptyI1,definition,
( nonemptyI1
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ( nonempty @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyImpWitness,definition,
( nonemptyImpWitness
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& $true ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',notdexE) ).
thf(notequalI1,definition,
( notequalI1
= ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,definition,
( notequalI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2) ).
thf(notinemptyset,definition,
( notinemptyset
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(notinsingleton,definition,
( notinsingleton
= ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(notsubsetI,definition,
( notsubsetI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega__Cong,definition,
( omega__Cong
= ( omega = omega ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',powersetE) ).
thf(powersetE1,definition,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).
thf(powersetI,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(powersetI1,definition,
( powersetI1
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).
thf(powerset__Cong,definition,
( powerset__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(prop2set2propI,definition,
( prop2set2propI
= ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set2propI) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(prop2setI,definition,
( prop2setI
= ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinSub,definition,
( setadjoinSub
= ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,definition,
( setadjoinSub2
= ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(setextsub,definition,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
thf(setoftrueEq,definition,
( setoftrueEq
= ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setunionI) ).
thf(setunion__Cong,definition,
( setunion__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',singletonsswitch) ).
thf(subPowSU,definition,
( subPowSU
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).
thf(subset2powerset,definition,
( subset2powerset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset) ).
thf(subsetE,definition,
( subsetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,definition,
( subsetE2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2) ).
thf(subsetI1,definition,
( subsetI1
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(subsetI2,definition,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(subsetRefl,definition,
( subsetRefl
= ( ! [A: $i] : ( subset @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,definition,
( subsetTrans
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).
thf(subsetemptysetimpeq,definition,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,definition,
( upairsetIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,definition,
( upairsetIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(vacuousDall,definition,
( vacuousDall
= ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).
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
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $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 ) ) )
=> ( ! [SY18: $i > $i > $o,SY19: $i] :
( ! [SY20: $i] :
( ( in @ SY20 @ SY19 )
=> ? [SY22: $i] :
( ( SY18 @ SY20 @ SY22 )
& ! [SY23: $i] :
( ( SY18 @ SY20 @ SY23 )
=> ( SY22 = SY23 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY19 )
& ( SY18 @ 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 ) ) ) ) ) )
=> ( ! [SY50: $i > $o] :
( ? [SY52: $i] :
( ( SY50 @ SY52 )
& ! [SY53: $i] :
( ( SY50 @ SY53 )
=> ( SY52 = SY53 ) ) )
=> ( SY50
@ ( descr
@ ^ [Xx: $i] : ( SY50 @ 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 ) )
=> ( ! [SY67: $i > $o] :
( ? [SY69: $i] :
( ( SY67 @ SY69 )
& ! [SY70: $i] :
( ( SY67 @ SY70 )
=> ( SY69 = SY70 ) ) )
=> ? [Xx: $i] :
( ( SY67 @ Xx )
& ! [Xy: $i] :
( ( SY67 @ 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 )
=> ( ! [SY79: $i > $o] :
( ? [SY81: $i] :
( ( SY79 @ SY81 )
& ! [SY82: $i] :
( ( SY79 @ SY82 )
=> ( SY81 = SY82 ) ) )
=> ? [Xx: $i] : ( SY79 @ 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 ) ) )
=> ( ! [SY96: $i] :
( ( SY96 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY96 ) )
=> ( ! [SY98: $i,SY99: $i > $o,SY100: $i] :
( ( in @ SY100 @ SY98 )
=> ( ( SY99 @ SY100 )
=> ( ( dsetconstr @ SY98
@ ^ [Xy: $i] : ( SY99 @ Xy ) )
!= emptyset ) ) )
=> ( ! [SY102: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY102 )
=> ( SY102 != 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 ) ) ) )
=> ( ! [SY135: $i > $o] :
( ? [SY137: $i] :
( ( SY135 @ SY137 )
& ! [SY138: $i] :
( ( SY135 @ SY138 )
=> ( SY137 = SY138 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY135 @ Xy )
<=> ( Xy = Xx ) ) )
=> ( ! [SY141: $i] :
( ( SY141 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY141 )
& $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 ) ) )
=> ( ! [SY190: $i > $o] :
( ? [Xx: $i] :
( ( SY190 @ Xx )
& ! [Xy: $i] :
( ( SY190 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY194: $i] :
( ( SY190 @ SY194 )
& ! [SY195: $i] :
( ( SY190 @ SY195 )
=> ( SY194 = SY195 ) ) ) )
=> ( ! [SY196: $i > $o] :
( ? [Xx: $i] : ( SY196 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY196 @ Xx )
=> ( ( SY196 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY201: $i] :
( ( SY196 @ SY201 )
& ! [SY202: $i] :
( ( SY196 @ SY202 )
=> ( SY201 = SY202 ) ) ) ) )
=> ( ! [SY203: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY203 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY207: $i] :
( ( SY203 @ SY207 )
& ! [SY208: $i] :
( ( SY203 @ SY208 )
=> ( SY207 = SY208 ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [SY217: $i > $o] :
( ? [SY219: $i] :
( ( SY217 @ SY219 )
& ! [SY220: $i] :
( ( SY217 @ SY220 )
=> ( SY219 = SY220 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY217 @ Xx )
=> ( ( SY217 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY223: $i > $o,SY224: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY223 @ Xx )
<=> ( SY224 @ Xy ) ) )
=> ( ? [SY228: $i] :
( ( SY223 @ SY228 )
& ! [SY229: $i] :
( ( SY223 @ SY229 )
=> ( SY228 = SY229 ) ) )
<=> ? [SY231: $i] :
( ( SY224 @ SY231 )
& ! [SY232: $i] :
( ( SY224 @ SY232 )
=> ( SY231 = SY232 ) ) ) ) )
=> ( ( 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 )
=> ( ! [SY241: $i > $o] :
( ? [SY243: $i] :
( ( SY241 @ SY243 )
& ! [SY244: $i] :
( ( SY241 @ SY244 )
=> ( SY243 = SY244 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY241 @ Xx )
=> ( ( SY241 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY247: $i > $o,SY248: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY247 @ Xx )
<=> ( SY248 @ Xy ) ) )
=> ( ? [SY252: $i] :
( ( SY247 @ SY252 )
& ! [SY253: $i] :
( ( SY247 @ SY253 )
=> ( SY252 = SY253 ) ) )
=> ( ? [SY255: $i] :
( ( SY248 @ SY255 )
& ! [SY256: $i] :
( ( SY248 @ SY256 )
=> ( SY255 = SY256 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY247 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY248 @ Xx ) ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i] : ( subset @ emptyset @ A )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) )
=> ( ! [A: $i] : ( subset @ A @ A )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) )
=> ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) )
=> ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) )
=> ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) )
=> ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,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,
( ( ! [SY18: $i > $i > $o,SY19: $i] :
( ! [SY20: $i] :
( ( in @ SY20 @ SY19 )
=> ? [SY22: $i] :
( ( SY18 @ SY20 @ SY22 )
& ! [SY23: $i] :
( ( SY18 @ SY20 @ SY23 )
=> ( SY22 = SY23 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY19 )
& ( SY18 @ 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,
( ( ! [SY50: $i > $o] :
( ? [SY52: $i] :
( ( SY50 @ SY52 )
& ! [SY53: $i] :
( ( SY50 @ SY53 )
=> ( SY52 = SY53 ) ) )
=> ( SY50
@ ( descr
@ ^ [Xx: $i] : ( SY50 @ 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,
( ( ! [SY67: $i > $o] :
( ? [SY69: $i] :
( ( SY67 @ SY69 )
& ! [SY70: $i] :
( ( SY67 @ SY70 )
=> ( SY69 = SY70 ) ) )
=> ? [Xx: $i] :
( ( SY67 @ Xx )
& ! [Xy: $i] :
( ( SY67 @ 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,
( ( ! [SY79: $i > $o] :
( ? [SY81: $i] :
( ( SY79 @ SY81 )
& ! [SY82: $i] :
( ( SY79 @ SY82 )
=> ( SY81 = SY82 ) ) )
=> ? [Xx: $i] : ( SY79 @ 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,
( ( ! [SY96: $i] :
( ( SY96 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY96 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [SY98: $i,SY99: $i > $o,SY100: $i] :
( ( in @ SY100 @ SY98 )
=> ( ( SY99 @ SY100 )
=> ( ( dsetconstr @ SY98
@ ^ [Xy: $i] : ( SY99 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [SY102: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY102 )
=> ( SY102 != 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,
( ( ! [SY135: $i > $o] :
( ? [SY137: $i] :
( ( SY135 @ SY137 )
& ! [SY138: $i] :
( ( SY135 @ SY138 )
=> ( SY137 = SY138 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY135 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(46,plain,
( ( ! [SY141: $i] :
( ( SY141 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY141 )
& $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,
( ( ! [SY190: $i > $o] :
( ? [Xx: $i] :
( ( SY190 @ Xx )
& ! [Xy: $i] :
( ( SY190 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY194: $i] :
( ( SY190 @ SY194 )
& ! [SY195: $i] :
( ( SY190 @ SY195 )
=> ( SY194 = SY195 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(65,plain,
( ( ! [SY196: $i > $o] :
( ? [Xx: $i] : ( SY196 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY196 @ Xx )
=> ( ( SY196 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY201: $i] :
( ( SY196 @ SY201 )
& ! [SY202: $i] :
( ( SY196 @ SY202 )
=> ( SY201 = SY202 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(66,plain,
( ( ! [SY203: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY203 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY207: $i] :
( ( SY203 @ SY207 )
& ! [SY208: $i] :
( ( SY203 @ SY208 )
=> ( SY207 = SY208 ) ) ) ) )
= $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,
( ( ! [SY217: $i > $o] :
( ? [SY219: $i] :
( ( SY217 @ SY219 )
& ! [SY220: $i] :
( ( SY217 @ SY220 )
=> ( SY219 = SY220 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY217 @ Xx )
=> ( ( SY217 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(70,plain,
( ( ! [SY223: $i > $o,SY224: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY223 @ Xx )
<=> ( SY224 @ Xy ) ) )
=> ( ? [SY228: $i] :
( ( SY223 @ SY228 )
& ! [SY229: $i] :
( ( SY223 @ SY229 )
=> ( SY228 = SY229 ) ) )
<=> ? [SY231: $i] :
( ( SY224 @ SY231 )
& ! [SY232: $i] :
( ( SY224 @ SY232 )
=> ( SY231 = SY232 ) ) ) ) ) )
= $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,
( ( ! [SY241: $i > $o] :
( ? [SY243: $i] :
( ( SY241 @ SY243 )
& ! [SY244: $i] :
( ( SY241 @ SY244 )
=> ( SY243 = SY244 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY241 @ Xx )
=> ( ( SY241 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(77,plain,
( ( ! [SY247: $i > $o,SY248: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY247 @ Xx )
<=> ( SY248 @ Xy ) ) )
=> ( ? [SY252: $i] :
( ( SY247 @ SY252 )
& ! [SY253: $i] :
( ( SY247 @ SY253 )
=> ( SY252 = SY253 ) ) )
=> ( ? [SY255: $i] :
( ( SY248 @ SY255 )
& ! [SY256: $i] :
( ( SY248 @ SY256 )
=> ( SY255 = SY256 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY247 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY248 @ Xx ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(82,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(83,plain,
( ( ! [A: $i] : ( subset @ emptyset @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(84,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(85,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(86,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(87,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(88,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(89,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(90,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(91,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(92,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(95,plain,
( ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(98,plain,
( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(99,plain,
( ( ~ ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[98]) ).
thf(100,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(101,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(102,plain,
( ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(103,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(104,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(105,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(106,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(107,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(108,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(109,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(110,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(111,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(112,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(113,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(114,plain,
( ( ! [A: $i] : ( subset @ emptyset @ A ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(115,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(116,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(117,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(118,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(119,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(120,plain,
( ( ! [SY247: $i > $o,SY248: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY247 @ Xx )
<=> ( SY248 @ Xy ) ) )
=> ( ? [SY252: $i] :
( ( SY247 @ SY252 )
& ! [SY253: $i] :
( ( SY247 @ SY253 )
=> ( SY252 = SY253 ) ) )
=> ( ? [SY255: $i] :
( ( SY248 @ SY255 )
& ! [SY256: $i] :
( ( SY248 @ SY256 )
=> ( SY255 = SY256 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY247 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY248 @ Xx ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(121,plain,
( ( ! [SY241: $i > $o] :
( ? [SY243: $i] :
( ( SY241 @ SY243 )
& ! [SY244: $i] :
( ( SY241 @ SY244 )
=> ( SY243 = SY244 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY241 @ Xx )
=> ( ( SY241 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(122,plain,
( ( omega = omega )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(123,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(124,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(125,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(126,plain,
( ( emptyset = emptyset )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(127,plain,
( ( ! [SY223: $i > $o,SY224: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY223 @ Xx )
<=> ( SY224 @ Xy ) ) )
=> ( ? [SY228: $i] :
( ( SY223 @ SY228 )
& ! [SY229: $i] :
( ( SY223 @ SY229 )
=> ( SY228 = SY229 ) ) )
<=> ? [SY231: $i] :
( ( SY224 @ SY231 )
& ! [SY232: $i] :
( ( SY224 @ SY232 )
=> ( SY231 = SY232 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(128,plain,
( ( ! [SY217: $i > $o] :
( ? [SY219: $i] :
( ( SY217 @ SY219 )
& ! [SY220: $i] :
( ( SY217 @ SY220 )
=> ( SY219 = SY220 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY217 @ Xx )
=> ( ( SY217 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(129,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(130,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(131,plain,
( ( ! [SY203: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY203 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY207: $i] :
( ( SY203 @ SY207 )
& ! [SY208: $i] :
( ( SY203 @ SY208 )
=> ( SY207 = SY208 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(132,plain,
( ( ! [SY196: $i > $o] :
( ? [Xx: $i] : ( SY196 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY196 @ Xx )
=> ( ( SY196 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY201: $i] :
( ( SY196 @ SY201 )
& ! [SY202: $i] :
( ( SY196 @ SY202 )
=> ( SY201 = SY202 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(133,plain,
( ( ! [SY190: $i > $o] :
( ? [Xx: $i] :
( ( SY190 @ Xx )
& ! [Xy: $i] :
( ( SY190 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY194: $i] :
( ( SY190 @ SY194 )
& ! [SY195: $i] :
( ( SY190 @ SY195 )
=> ( SY194 = SY195 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(134,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(135,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(136,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(137,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(138,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(139,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(140,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(141,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(142,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(143,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(144,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(145,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(146,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(147,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(148,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(149,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(150,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(151,plain,
( ( ! [SY141: $i] :
( ( SY141 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY141 )
& $true ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(152,plain,
( ( ! [SY135: $i > $o] :
( ? [SY137: $i] :
( ( SY135 @ SY137 )
& ! [SY138: $i] :
( ( SY135 @ SY138 )
=> ( SY137 = SY138 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY135 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(153,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(154,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(155,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(156,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(157,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(158,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(159,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(160,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(161,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(162,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(163,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(164,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(165,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(166,plain,
( ( ! [SY102: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY102 )
=> ( SY102 != emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(167,plain,
( ( ! [SY98: $i,SY99: $i > $o,SY100: $i] :
( ( in @ SY100 @ SY98 )
=> ( ( SY99 @ SY100 )
=> ( ( dsetconstr @ SY98
@ ^ [Xy: $i] : ( SY99 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(168,plain,
( ( ! [SY96: $i] :
( ( SY96 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY96 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(169,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(170,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(171,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(172,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(173,plain,
( ( ! [SY79: $i > $o] :
( ? [SY81: $i] :
( ( SY79 @ SY81 )
& ! [SY82: $i] :
( ( SY79 @ SY82 )
=> ( SY81 = SY82 ) ) )
=> ? [Xx: $i] : ( SY79 @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(174,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(175,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(176,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(177,plain,
( ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(178,plain,
( ( ! [SY67: $i > $o] :
( ? [SY69: $i] :
( ( SY67 @ SY69 )
& ! [SY70: $i] :
( ( SY67 @ SY70 )
=> ( SY69 = SY70 ) ) )
=> ? [Xx: $i] :
( ( SY67 @ Xx )
& ! [Xy: $i] :
( ( SY67 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(179,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(180,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(181,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(182,plain,
( ( ! [SY50: $i > $o] :
( ? [SY52: $i] :
( ( SY50 @ SY52 )
& ! [SY53: $i] :
( ( SY50 @ SY53 )
=> ( SY52 = SY53 ) ) )
=> ( SY50
@ ( descr
@ ^ [Xx: $i] : ( SY50 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(183,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(184,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(185,plain,
( ( ! [SY18: $i > $i > $o,SY19: $i] :
( ! [SY20: $i] :
( ( in @ SY20 @ SY19 )
=> ? [SY22: $i] :
( ( SY18 @ SY20 @ SY22 )
& ! [SY23: $i] :
( ( SY18 @ SY20 @ SY23 )
=> ( SY22 = SY23 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY19 )
& ( SY18 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(186,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(187,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(188,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(189,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(190,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(191,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(192,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(193,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(194,plain,
( ( ~ ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(195,plain,
( ( ! [SX0: $o,SX1: $i] :
( ~ ( in @ SX1 @ ( prop2set @ SX0 ) )
| SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[177,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(196,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(197,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(198,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(199,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)],[191,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(200,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(201,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(202,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)],[139,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(203,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setunion @ SX0 )
= ( setunion @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(204,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)],[178,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(205,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(206,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(207,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)],[138,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(208,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(209,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(210,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)],[154,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(211,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(212,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(213,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)],[193,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(214,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(215,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)],[132,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(216,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(217,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(218,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(219,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)],[167,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(220,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)],[190,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(221,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(222,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)],[134,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(223,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)],[128,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(224,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(225,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(226,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)],[133,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(227,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(228,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)],[185,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(229,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)],[130,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(230,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 != emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(231,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)],[129,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(232,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(233,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(234,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( set2prop @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(235,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[175,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(236,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i > $o,SX3: $i > $o] :
( ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ( SX4 != SX5 )
| ~ ( ~ ( ~ ( SX2 @ SX4 )
| ( SX3 @ SX5 ) )
| ~ ( ~ ( SX3 @ SX5 )
| ( SX2 @ SX4 ) ) ) ) )
| ( ( dsetconstr @ SX0
@ ^ [SX4: $i] : ( SX2 @ SX4 ) )
= ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(237,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)],[162,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(238,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)],[184,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(239,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 ) ) )
| ( ( descr
@ ^ [SX2: $i] : ( SX0 @ SX2 ) )
= ( descr
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(240,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(241,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)],[127,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(242,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)],[169,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(243,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(244,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)],[183,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(245,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( in @ emptyset @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(246,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ( in @ SX1 @ emptyset )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(247,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(248,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(249,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(250,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(251,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)],[172,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(252,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)],[143,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(253,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)],[125,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(254,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)],[186,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(255,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| ! [SX1: $o] : SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[176,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(256,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)],[135,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(257,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX2 )
| ( subset @ SX0 @ ( setadjoin @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(258,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(259,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)],[181,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(260,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)],[131,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(261,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(262,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)],[140,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(263,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( powerset @ SX0 )
= ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(264,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)],[152,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(265,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(266,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)],[141,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(267,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)],[121,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(268,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)],[180,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(269,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ emptyset )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(270,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)],[189,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(271,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(272,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( in @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(273,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)],[182,descr__Cong,descrp,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,in__Cong,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setoftrueEq,setunionAx,setunionE,setunionI,setunion__Cong,singletonsswitch,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,uniqinunit,upairsetE,upairsetIL,upairsetIR,vacuousDall,wellorderingAx]) ).
thf(274,plain,
! [SV1: $i] :
( ( ! [SY607: $i] : ( subset @ SY607 @ ( setadjoin @ SV1 @ SY607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(275,plain,
! [SV2: $i] :
( ( subset @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(276,plain,
! [SV3: $i] :
( ( subset @ emptyset @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(277,plain,
! [SV4: $i] :
( ( ! [SY608: $i] : ( in @ SY608 @ ( setadjoin @ SV4 @ ( setadjoin @ SY608 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(278,plain,
! [SV5: $i] :
( ( ! [SY609: $i] : ( in @ SV5 @ ( setadjoin @ SV5 @ ( setadjoin @ SY609 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(279,plain,
! [SV6: $i] :
( ( in @ emptyset @ ( powerset @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(280,plain,
! [SV7: $i] :
( ( in @ emptyset @ ( powerset @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(281,plain,
! [SV8: $i] :
( ( ( dsetconstr @ SV8
@ ^ [Xx: $i] : $true )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(282,plain,
! [SV9: $i] :
( ( ! [SY611: $i] : ( in @ SV9 @ ( setadjoin @ SV9 @ SY611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(283,plain,
! [SV10: $i] :
( ( ~ ( in @ SV10 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(284,plain,
! [SV11: $i] :
( ( ~ ( in @ SV11 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(285,plain,
( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(286,plain,
! [SV12: $o] :
( ( ! [SY612: $i] :
( ~ ( in @ SY612 @ ( prop2set @ SV12 ) )
| SV12 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[195]) ).
thf(287,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $true ) )
| $true ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[195]) ).
thf(288,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $false ) )
| $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[195]) ).
thf(289,plain,
! [SV13: $i] :
( ( ! [SY613: $i] :
( ~ ! [SY614: $i] :
( ~ ( in @ SY614 @ SV13 )
| ( in @ SY614 @ SY613 ) )
| ( subset @ SV13 @ SY613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(290,plain,
! [SV14: $i] :
( ( ! [SY615: $i] :
( ~ ( ( SV14 != SY615 ) )
| ~ ( in @ SY615 @ ( setadjoin @ SV14 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(291,plain,
! [SV15: $i] :
( ( ! [SY616: $i,SY617: $i] :
( ~ ( in @ SY617 @ SY616 )
| ( in @ SY617 @ ( setadjoin @ SV15 @ SY616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(292,plain,
! [SV16: $i] :
( ( ! [SY618: $i,SY619: $i] :
~ ( ~ ( ~ ( in @ SY619 @ ( setadjoin @ SV16 @ SY618 ) )
| ( SY619 = SV16 )
| ( in @ SY619 @ SY618 ) )
| ~ ( ~ ( ( SY619 = SV16 )
| ( in @ SY619 @ SY618 ) )
| ( in @ SY619 @ ( setadjoin @ SV16 @ SY618 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(293,plain,
! [SV17: $i > $o] :
( ( ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( SV17 @ SY620 )
| ~ ! [SY621: $i] :
( ~ ( SV17 @ SY621 )
| ( SY620 = SY621 ) ) )
| ~ ! [SY622: $i] :
~ ( SV17 @ SY622 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(294,plain,
! [SV18: $i] :
( ( ! [SY623: $i] :
( ~ ( in @ SV18 @ ( setadjoin @ SY623 @ emptyset ) )
| ( in @ SY623 @ ( setadjoin @ SV18 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(295,plain,
! [SV19: $i] :
( ( ! [SY624: $i > $o] :
( ~ ~ ~ ! [SY625: $i] :
~ ~ ( ~ ( in @ SY625 @ SV19 )
| ~ ( SY624 @ SY625 ) )
| ! [SY626: $i] :
( ~ ( in @ SY626 @ SV19 )
| ~ ( SY624 @ SY626 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(296,plain,
! [SV20: $i] :
( ( ! [SY627: $i] :
( ( SV20 != SY627 )
| ( ( setunion @ SV20 )
= ( setunion @ SY627 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(297,plain,
! [SV21: $i > $o] :
( ( ~ ~ ! [SY628: $i] :
~ ~ ( ~ ( SV21 @ SY628 )
| ~ ! [SY629: $i] :
( ~ ( SV21 @ SY629 )
| ( SY628 = SY629 ) ) )
| ~ ! [SY630: $i] :
~ ~ ( ~ ( SV21 @ SY630 )
| ~ ! [SY631: $i] :
( ~ ( SV21 @ SY631 )
| ( SY630 = SY631 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(298,plain,
! [SV22: $i] :
( ( ! [SY632: $i,SY633: $i] :
( ~ ( subset @ SV22 @ SY632 )
| ~ ~ ( in @ SY633 @ SY632 )
| ~ ( in @ SY633 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(299,plain,
! [SV23: $i] :
( ( ~ ! [SY634: $i] :
~ ( in @ SY634 @ SV23 )
| ( SV23 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(300,plain,
! [SV24: $i] :
( ( ! [SY635: $i > $o] :
( ~ ~ ! [SY636: $i] :
~ ~ ( ~ ( in @ SY636 @ SV24 )
| ~ ~ ( SY635 @ SY636 ) )
| ~ ! [SY637: $i] :
( ~ ( in @ SY637 @ SV24 )
| ( SY635 @ SY637 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(301,plain,
! [SV25: $i] :
( ( ! [SY638: $i,SY639: $i] :
( ~ ( subset @ SV25 @ SY638 )
| ~ ( in @ SY639 @ SV25 )
| ( in @ SY639 @ SY638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(302,plain,
! [SV26: $i] :
( ( ~ ( ( SV26 != emptyset ) )
| ~ ! [SY640: $i] :
~ ~ ( ~ ( in @ SY640 @ SV26 )
| ~ $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(303,plain,
! [SV27: $i] :
( ( ! [SY641: $i] :
( ~ ( in @ SY641 @ ( setunion @ SV27 ) )
| ! [SY642: $o] :
( ~ ! [SY643: $i] :
( ~ ( in @ SY641 @ SY643 )
| ~ ( in @ SY643 @ SV27 )
| SY642 )
| SY642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(304,plain,
! [SV28: $i] :
( ( ! [SY644: $i] :
( ( SV28 != SY644 )
| ( subset @ SV28 @ SY644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(305,plain,
! [SV29: $i] :
( ( ! [SY645: $i,SY646: $i] :
( ~ ( in @ SY645 @ SY646 )
| ~ ( in @ SY646 @ SV29 )
| ( in @ SY645 @ ( setunion @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(306,plain,
! [SV30: $i] :
( ( ! [SY647: $i] :
( ~ ! [SY648: $i] :
~ ( ~ ( ~ ( in @ SY648 @ SV30 )
| ( in @ SY648 @ SY647 ) )
| ~ ( ~ ( in @ SY648 @ SY647 )
| ( in @ SY648 @ SV30 ) ) )
| ( SV30 = SY647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(307,plain,
! [SV31: $i] :
( ( ! [SY649: $i] :
( ~ ~ ( subset @ SV31 @ SY649 )
| ( SV31 != SY649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(308,plain,
! [SV32: $i > $o] :
( ( ~ ~ ! [SY650: $i] :
~ ( SV32 @ SY650 )
| ~ ! [SY651: $i,SY652: $i] :
( ~ ( SV32 @ SY651 )
| ~ ( SV32 @ SY652 )
| ( SY651 = SY652 ) )
| ~ ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(309,plain,
! [SV33: $i] :
( ( ! [SY655: $i,SY656: $i] :
( ~ ( in @ SY656 @ ( setadjoin @ SV33 @ ( setadjoin @ SY655 @ emptyset ) ) )
| ( SY656 = SV33 )
| ( SY656 = SY655 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(310,plain,
! [SV34: $i] :
( ( ! [SY657: $i,SY658: $i] :
( ~ ( subset @ SV34 @ SY657 )
| ~ ( subset @ SY657 @ SY658 )
| ( subset @ SV34 @ SY658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(311,plain,
! [SV35: $i] :
( ( ! [SY659: $i,SY660: $i] :
( ~ ( in @ SY659 @ ( powerset @ SV35 ) )
| ~ ( in @ SY660 @ SY659 )
| ( in @ SY660 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(312,plain,
! [SV36: $i] :
( ( ! [SY661: $i > $o,SY662: $i] :
( ~ ( in @ SY662 @ SV36 )
| ~ ( SY661 @ SY662 )
| ( ( dsetconstr @ SV36
@ ^ [SX3: $i] : ( SY661 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(313,plain,
! [SV37: $i] :
( ( ! [SY664: $i] :
~ ( ~ ( ~ ( in @ SY664 @ ( powerset @ SV37 ) )
| ! [SY665: $i] :
( ~ ( in @ SY665 @ SY664 )
| ( in @ SY665 @ SV37 ) ) )
| ~ ( ~ ! [SY666: $i] :
( ~ ( in @ SY666 @ SY664 )
| ( in @ SY666 @ SV37 ) )
| ( in @ SY664 @ ( powerset @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(314,plain,
! [SV38: $i] :
( ( ! [SY667: $i,SY668: $i] :
( ~ ( in @ SY668 @ SV38 )
| ~ ~ ( in @ SY668 @ SY667 )
| ( SV38 != SY667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(315,plain,
! [SV39: $i] :
( ( ! [SY669: $i > $o] :
( ~ ~ ! [SY670: $i] :
( ~ ( in @ SY670 @ SV39 )
| ( SY669 @ SY670 ) )
| ~ ! [SY671: $i] :
~ ~ ( ~ ( in @ SY671 @ SV39 )
| ~ ~ ( SY669 @ SY671 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(316,plain,
! [SV40: $i > $o] :
( ( ~ ~ ! [SY672: $i] :
~ ~ ( ~ ( SV40 @ SY672 )
| ~ ! [SY673: $i] :
( ~ ( SV40 @ SY673 )
| ( SY672 = SY673 ) ) )
| ! [SY674: $i,SY675: $i] :
( ~ ( SV40 @ SY674 )
| ~ ( SV40 @ SY675 )
| ( SY674 = SY675 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(317,plain,
! [SV41: $i] :
( ( ! [SY676: $i] :
( ~ ! [SY677: $i] :
( ~ ( in @ SY677 @ SV41 )
| ( in @ SY677 @ SY676 ) )
| ( subset @ SV41 @ SY676 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(318,plain,
! [SV42: $i] :
( ( ! [SY678: $i] :
( ~ ( subset @ SY678 @ SV42 )
| ( in @ SY678 @ ( powerset @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(319,plain,
! [SV43: $i > $o] :
( ( ~ ~ ! [SY679: $i] :
~ ~ ( ~ ( SV43 @ SY679 )
| ~ ! [SY680: $i] :
( ~ ( SV43 @ SY680 )
| ( SY679 = SY680 ) ) )
| ~ ! [SY681: $i] :
~ ~ ( ~ ( SV43 @ SY681 )
| ~ ! [SY682: $i] :
( ~ ( SV43 @ SY682 )
| ( SY681 = SY682 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(320,plain,
! [SV44: $i] :
( ( ! [SY683: $i,SY684: $i] :
( ~ ( in @ SY684 @ SV44 )
| ~ ~ ( in @ SY684 @ SY683 )
| ~ ( subset @ SV44 @ SY683 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(321,plain,
! [SV45: $i > $i > $o] :
( ( ! [SY685: $i] :
( ~ ! [SY686: $i] :
( ~ ( in @ SY686 @ SY685 )
| ~ ! [SY687: $i] :
~ ~ ( ~ ( SV45 @ SY686 @ SY687 )
| ~ ! [SY688: $i] :
( ~ ( SV45 @ SY686 @ SY688 )
| ( SY687 = SY688 ) ) ) )
| ~ ! [SY689: $i] :
~ ! [SY690: $i] :
~ ( ~ ( ~ ( in @ SY690 @ SY689 )
| ~ ! [SY691: $i] :
~ ~ ( ~ ( in @ SY691 @ SY685 )
| ~ ( SV45 @ SY691 @ SY690 ) ) )
| ~ ( ~ ~ ! [SY692: $i] :
~ ~ ( ~ ( in @ SY692 @ SY685 )
| ~ ( SV45 @ SY692 @ SY690 ) )
| ( in @ SY690 @ SY689 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(322,plain,
! [SV46: $i] :
( ( ! [SY693: $i] :
( ( SV46 != SY693 )
| ! [SY694: $i,SY695: $i] :
( ( SY694 != SY695 )
| ~ ( in @ SY694 @ SV46 )
| ( in @ SY695 @ SY693 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(323,plain,
! [SV47: $i] :
( ( ~ ~ ! [SY696: $i] :
~ ( in @ SY696 @ SV47 )
| ( SV47 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(324,plain,
! [SV48: $i] :
( ( ! [SY697: $i] :
( ( SV48 != SY697 )
| ! [SY698: $i,SY699: $i] :
( ( SY698 != SY699 )
| ~ ( ~ ( ~ ( in @ SY698 @ SV48 )
| ( in @ SY699 @ SY697 ) )
| ~ ( ~ ( in @ SY699 @ SY697 )
| ( in @ SY698 @ SV48 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(325,plain,
! [SV49: $i] :
( ( ! [SY700: $i > $o,SY701: $i] :
( ~ ( in @ SY701
@ ( dsetconstr @ SV49
@ ^ [SX3: $i] : ( SY700 @ SX3 ) ) )
| ( SY700 @ SY701 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(326,plain,
! [SV50: $i] :
( ( ! [SY703: $i] :
( ~ ( in @ SY703 @ SV50 )
| ( in @ SY703 @ ( powerset @ ( setunion @ SV50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(327,plain,
! [SV51: $o] :
( ( ~ SV51
| ( set2prop @ ( prop2set @ SV51 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[234]) ).
thf(328,plain,
( ( ~ $true
| ( set2prop @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[234]) ).
thf(329,plain,
( ( ~ $false
| ( set2prop @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[234]) ).
thf(330,plain,
! [SV52: $i] :
( ( ~ ( in @ SV52 @ emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(331,plain,
! [SV53: $i] :
( ( ! [SY704: $i] :
( ( SV53 != SY704 )
| ! [SY705: $i > $o,SY706: $i > $o] :
( ~ ! [SY707: $i] :
( ~ ( in @ SY707 @ SV53 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY704 )
| ( SY707 != SX5 )
| ~ ( ~ ( ~ ( SY705 @ SY707 )
| ( SY706 @ SX5 ) )
| ~ ( ~ ( SY706 @ SX5 )
| ( SY705 @ SY707 ) ) ) ) )
| ( ( dsetconstr @ SV53
@ ^ [SX4: $i] : ( SY705 @ SX4 ) )
= ( dsetconstr @ SY704
@ ^ [SX4: $i] : ( SY706 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(332,plain,
! [SV54: $i] :
( ( ! [SY711: $i,SY712: $i] :
( ~ ( in @ SY712 @ ( setadjoin @ SV54 @ SY711 ) )
| ! [SY713: $o] :
( ~ ( ( SY712 != SV54 )
| SY713 )
| ~ ( ~ ( in @ SY712 @ SY711 )
| SY713 )
| SY713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(333,plain,
! [SV55: $i] :
( ( ~ ~ ! [SY714: $i] :
~ ( in @ SY714 @ SV55 )
| ~ ! [SY715: $i] :
~ ~ ( ~ ( in @ SY715 @ SV55 )
| ~ ~ ~ ! [SY716: $i] :
~ ~ ( ~ ( in @ SY716 @ SY715 )
| ~ ( in @ SY716 @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(334,plain,
! [SV56: $i > $o] :
( ( ! [SY717: $i > $o] :
( ~ ! [SY718: $i,SY719: $i] :
( ( SY718 != SY719 )
| ~ ( ~ ( ~ ( SV56 @ SY718 )
| ( SY717 @ SY719 ) )
| ~ ( ~ ( SY717 @ SY719 )
| ( SV56 @ SY718 ) ) ) )
| ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY717 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY717 @ SX3 )
| ( SX2 = SX3 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SX2: $i] : ( SY717 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(335,plain,
! [SV57: $i] :
( ( ! [SY726: $i] :
( ( SV57 != SY726 )
| ( in @ SV57 @ ( setadjoin @ SY726 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(336,plain,
! [SV58: $i > $o] :
( ( ! [SY727: $i > $o] :
( ~ ! [SY728: $i,SY729: $i] :
( ( SY728 != SY729 )
| ~ ( ~ ( ~ ( SV58 @ SY728 )
| ( SY727 @ SY729 ) )
| ~ ( ~ ( SY727 @ SY729 )
| ( SV58 @ SY728 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SY727 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY727 @ SX3 )
| ( SX2 = SX3 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY727 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY727 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(337,plain,
! [SV59: $i] :
( ( ! [SY738: $i > $o,SY739: $i] :
( ~ ( in @ SY739 @ SV59 )
| ~ ( ~ ( ~ ( in @ SY739
@ ( dsetconstr @ SV59
@ ^ [SX3: $i] : ( SY738 @ SX3 ) ) )
| ( SY738 @ SY739 ) )
| ~ ( ~ ( SY738 @ SY739 )
| ( in @ SY739
@ ( dsetconstr @ SV59
@ ^ [SX3: $i] : ( SY738 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(338,plain,
! [SV60: $i] :
( ( ~ ! [SY742: $i] :
~ ( in @ SY742 @ SV60 )
| ( SV60 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(339,plain,
! [SV61: $i] :
( ( ~ ! [SY743: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY744: $i] :
( ~ ( in @ SY744 @ SY743 )
| ! [SY745: $i] :
( ~ ( in @ SY745 @ SY744 )
| ( in @ SY745 @ SV61 ) ) )
| ~ ! [SY746: $i,SY747: $i] :
( ~ ~ ( ~ ( in @ SY746 @ SV61 )
| ~ ( in @ SY747 @ SV61 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY743 )
| ~ ( ~ ( ~ ( in @ SY746 @ SX4 )
| ( in @ SY747 @ SX4 ) )
| ~ ( ~ ( in @ SY747 @ SX4 )
| ( in @ SY746 @ SX4 ) ) ) )
| ( SY746 = SY747 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY743 )
| ~ ( in @ SX3 @ SY743 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY753: $i] :
( ~ ~ ( ~ ! [SY754: $i] :
( ~ ( in @ SY754 @ SY753 )
| ( in @ SY754 @ SV61 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY753 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY743 )
| ~ ( in @ SX4 @ SY753 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY753 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY743 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(340,plain,
! [SV62: $o] :
( ( ~ SV62
| ( in @ emptyset @ ( prop2set @ SV62 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[245]) ).
thf(341,plain,
( ( ~ $true
| ( in @ emptyset @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[245]) ).
thf(342,plain,
( ( ~ $false
| ( in @ emptyset @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[245]) ).
thf(343,plain,
! [SV63: $i > $o] :
( ( ! [SY761: $i] :
( ~ ( in @ SY761 @ emptyset )
| ( SV63 @ SY761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(344,plain,
! [SV64: $i] :
( ( ! [SY762: $i,SY763: $i] :
( ~ ( in @ SY763 @ ( setadjoin @ SV64 @ SY762 ) )
| ( SY763 = SV64 )
| ( in @ SY763 @ SY762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(345,plain,
! [SV65: $i] :
( ( ~ ( in @ SV65 @ omega )
| ( in @ ( setadjoin @ SV65 @ SV65 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(346,plain,
! [SV66: $i] :
( ( ! [SY764: $i] :
( ~ ( in @ SV66 @ ( setadjoin @ SY764 @ emptyset ) )
| ( SV66 = SY764 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(347,plain,
! [SV67: $i] :
( ( ! [SY765: $i] :
( ( SV67 != SY765 )
| ( subset @ SY765 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(348,plain,
! [SV68: $i] :
( ( ! [SY766: $i] :
( ~ ! [SY767: $i] :
( ~ ( in @ SY767 @ SV68 )
| ( in @ SY767 @ SY766 ) )
| ~ ! [SY768: $i] :
( ~ ( in @ SY768 @ SY766 )
| ( in @ SY768 @ SV68 ) )
| ( SV68 = SY766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(349,plain,
! [SV69: $i] :
( ( ! [SY769: $i > $o] :
( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( in @ SY770 @ SV69 )
| ~ ( SY769 @ SY770 ) )
| ( ( dsetconstr @ SV69
@ ^ [SX2: $i] : ( SY769 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(350,plain,
! [SV70: $i] :
( ( ! [SY772: $i] :
( ( SV70 != SY772 )
| ! [SY773: $i,SY774: $i] :
( ( SY773 != SY774 )
| ( ( setadjoin @ SV70 @ SY773 )
= ( setadjoin @ SY772 @ SY774 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(351,plain,
! [SV71: $i] :
( ( ~ ~ ( ~ ( in @ emptyset @ SV71 )
| ~ ! [SY775: $i] :
( ~ ~ ( ~ ( in @ SY775 @ omega )
| ~ ( in @ SY775 @ SV71 ) )
| ( in @ ( setadjoin @ SY775 @ SY775 ) @ SV71 ) ) )
| ! [SY776: $i] :
( ~ ( in @ SY776 @ omega )
| ( in @ SY776 @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(352,plain,
! [SV72: $i] :
( ( ~ ( in @ SV72 @ emptyset )
| ! [SX1: $o] : SX1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(353,plain,
! [SV73: $i] :
( ( ! [SY778: $i > $o] :
( ~ ~ ~ ! [SY779: $i] :
~ ~ ( ~ ( in @ SY779 @ SV73 )
| ~ ( SY778 @ SY779 ) )
| ! [SY780: $i] :
( ~ ( in @ SY780 @ SV73 )
| ~ ( SY778 @ SY780 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(354,plain,
! [SV74: $i] :
( ( ! [SY781: $i,SY782: $i] :
( ~ ( subset @ SV74 @ SY782 )
| ( subset @ SV74 @ ( setadjoin @ SY781 @ SY782 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(355,plain,
! [SV75: $i] :
( ( ! [SY783: $i] :
( ~ ( in @ SY783 @ ( powerset @ SV75 ) )
| ( subset @ SY783 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(356,plain,
! [SV76: $i] :
( ( ! [SY784: $i > $o,SY785: $i] :
( ~ ( in @ SY785 @ SV76 )
| ~ ( SY784 @ SY785 )
| ( in @ SY785
@ ( dsetconstr @ SV76
@ ^ [SX3: $i] : ( SY784 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(357,plain,
! [SV77: $i > $o] :
( ( ~ ~ ! [SY787: $i] :
~ ! [SY788: $i] :
~ ( ~ ( ~ ( SV77 @ SY788 )
| ( SY788 = SY787 ) )
| ~ ( ( SY788 != SY787 )
| ( SV77 @ SY788 ) ) )
| ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(358,plain,
! [SV78: $i] :
( ( ! [SY791: $i] :
( ~ ! [SY792: $i] :
( ~ ( in @ SY792 @ SY791 )
| ( in @ SY792 @ SV78 ) )
| ( in @ SY791 @ ( powerset @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(359,plain,
! [SV79: $i] :
( ( ! [SY793: $i > $o] :
( ~ ! [SY794: $i] :
( ~ ( in @ SY794 @ SV79 )
| ~ ( SY793 @ SY794 ) )
| ~ ~ ! [SY795: $i] :
~ ~ ( ~ ( in @ SY795 @ SV79 )
| ~ ( SY793 @ SY795 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(360,plain,
! [SV80: $i] :
( ( ! [SY796: $i] :
( ( SV80 != SY796 )
| ( ( powerset @ SV80 )
= ( powerset @ SY796 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(361,plain,
! [SV81: $i > $o] :
( ( ~ ~ ! [SY797: $i] :
~ ~ ( ~ ( SV81 @ SY797 )
| ~ ! [SY798: $i] :
( ~ ( SV81 @ SY798 )
| ( SY797 = SY798 ) ) )
| ~ ! [SY799: $i] :
~ ! [SY800: $i] :
~ ( ~ ( ~ ( SV81 @ SY800 )
| ( SY800 = SY799 ) )
| ~ ( ( SY800 != SY799 )
| ( SV81 @ SY800 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(362,plain,
! [SV82: $i] :
( ( ~ ( ( SV82 != emptyset ) )
| ~ ! [SY801: $i] :
~ ( in @ SY801 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(363,plain,
! [SV83: $i] :
( ( ! [SY802: $i > $o] :
( ~ ~ ! [SY803: $i] :
( ~ ( in @ SY803 @ SV83 )
| ( SY802 @ SY803 ) )
| ~ ! [SY804: $i] :
~ ~ ( ~ ( in @ SY804 @ SV83 )
| ~ ~ ( SY802 @ SY804 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(364,plain,
! [SV84: $i > $o] :
( ( ~ ~ ! [SY805: $i] :
~ ~ ( ~ ( SV84 @ SY805 )
| ~ ! [SY806: $i] :
( ~ ( SV84 @ SY806 )
| ( SY805 = SY806 ) ) )
| ! [SY807: $i,SY808: $i] :
( ~ ( SV84 @ SY807 )
| ~ ( SV84 @ SY808 )
| ( SY807 = SY808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(365,plain,
! [SV85: $i] :
( ( ! [SY809: $i > $o,SY810: $i] :
( ~ ( in @ SY810
@ ( dsetconstr @ SV85
@ ^ [SX3: $i] : ( SY809 @ SX3 ) ) )
| ( in @ SY810 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(366,plain,
! [SV86: $i] :
( ( ~ ( subset @ SV86 @ emptyset )
| ( SV86 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(367,plain,
! [SV87: $i] :
( ( ! [SY812: $i] :
~ ( ~ ( ~ ( in @ SY812 @ ( setunion @ SV87 ) )
| ~ ! [SY813: $i] :
~ ~ ( ~ ( in @ SY812 @ SY813 )
| ~ ( in @ SY813 @ SV87 ) ) )
| ~ ( ~ ~ ! [SY814: $i] :
~ ~ ( ~ ( in @ SY812 @ SY814 )
| ~ ( in @ SY814 @ SV87 ) )
| ( in @ SY812 @ ( setunion @ SV87 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(368,plain,
! [SV88: $i] :
( ( ! [SY815: $i] :
( ~ ( subset @ SV88 @ SY815 )
| ~ ( subset @ SY815 @ SV88 )
| ( SV88 = SY815 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(369,plain,
! [SV89: $i] :
( ( ! [SY816: $i] :
( ~ ( subset @ SV89 @ SY816 )
| ( in @ SV89 @ ( powerset @ SY816 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(370,plain,
! [SV90: $i > $o] :
( ( ~ ~ ! [SY817: $i] :
~ ~ ( ~ ( SV90 @ SY817 )
| ~ ! [SY818: $i] :
( ~ ( SV90 @ SY818 )
| ( SY817 = SY818 ) ) )
| ( SV90
@ ( descr
@ ^ [SY819: $i] : ( SV90 @ SY819 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(371,plain,
! [SV1: $i,SV91: $i] :
( ( subset @ SV91 @ ( setadjoin @ SV1 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(372,plain,
! [SV4: $i,SV92: $i] :
( ( in @ SV92 @ ( setadjoin @ SV4 @ ( setadjoin @ SV92 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(373,plain,
! [SV93: $i,SV5: $i] :
( ( in @ SV5 @ ( setadjoin @ SV5 @ ( setadjoin @ SV93 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(374,plain,
! [SV94: $i,SV9: $i] :
( ( in @ SV9 @ ( setadjoin @ SV9 @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(375,plain,
! [SV10: $i] :
( ( in @ SV10 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(376,plain,
! [SV11: $i] :
( ( in @ SV11 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(377,plain,
( ( in @ sK1_A @ ( powerset @ sK1_A ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[285]) ).
thf(378,plain,
! [SV12: $o,SV95: $i] :
( ( ~ ( in @ SV95 @ ( prop2set @ SV12 ) )
| SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(379,plain,
! [SV96: $i] :
( ( ~ ( in @ SV96 @ ( prop2set @ $true ) )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(380,plain,
! [SV97: $i] :
( ( ~ ( in @ SV97 @ ( prop2set @ $false ) )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(381,plain,
! [SV98: $i,SV13: $i] :
( ( ~ ! [SY820: $i] :
( ~ ( in @ SY820 @ SV13 )
| ( in @ SY820 @ SV98 ) )
| ( subset @ SV13 @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(382,plain,
! [SV99: $i,SV14: $i] :
( ( ~ ( ( SV14 != SV99 ) )
| ~ ( in @ SV99 @ ( setadjoin @ SV14 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(383,plain,
! [SV15: $i,SV100: $i] :
( ( ! [SY821: $i] :
( ~ ( in @ SY821 @ SV100 )
| ( in @ SY821 @ ( setadjoin @ SV15 @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(384,plain,
! [SV101: $i,SV16: $i] :
( ( ! [SY822: $i] :
~ ( ~ ( ~ ( in @ SY822 @ ( setadjoin @ SV16 @ SV101 ) )
| ( SY822 = SV16 )
| ( in @ SY822 @ SV101 ) )
| ~ ( ~ ( ( SY822 = SV16 )
| ( in @ SY822 @ SV101 ) )
| ( in @ SY822 @ ( setadjoin @ SV16 @ SV101 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(385,plain,
! [SV17: $i > $o] :
( ( ( ~ ~ ! [SY620: $i] :
~ ~ ( ~ ( SV17 @ SY620 )
| ~ ! [SY621: $i] :
( ~ ( SV17 @ SY621 )
| ( SY620 = SY621 ) ) ) )
= $true )
| ( ( ~ ! [SY622: $i] :
~ ( SV17 @ SY622 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(386,plain,
! [SV102: $i,SV18: $i] :
( ( ~ ( in @ SV18 @ ( setadjoin @ SV102 @ emptyset ) )
| ( in @ SV102 @ ( setadjoin @ SV18 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(387,plain,
! [SV103: $i > $o,SV19: $i] :
( ( ~ ~ ~ ! [SY823: $i] :
~ ~ ( ~ ( in @ SY823 @ SV19 )
| ~ ( SV103 @ SY823 ) )
| ! [SY824: $i] :
( ~ ( in @ SY824 @ SV19 )
| ~ ( SV103 @ SY824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(388,plain,
! [SV104: $i,SV20: $i] :
( ( ( SV20 != SV104 )
| ( ( setunion @ SV20 )
= ( setunion @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(389,plain,
! [SV21: $i > $o] :
( ( ( ~ ~ ! [SY628: $i] :
~ ~ ( ~ ( SV21 @ SY628 )
| ~ ! [SY629: $i] :
( ~ ( SV21 @ SY629 )
| ( SY628 = SY629 ) ) ) )
= $true )
| ( ( ~ ! [SY630: $i] :
~ ~ ( ~ ( SV21 @ SY630 )
| ~ ! [SY631: $i] :
( ~ ( SV21 @ SY631 )
| ( SY630 = SY631 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(390,plain,
! [SV105: $i,SV22: $i] :
( ( ! [SY825: $i] :
( ~ ( subset @ SV22 @ SV105 )
| ~ ~ ( in @ SY825 @ SV105 )
| ~ ( in @ SY825 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(391,plain,
! [SV23: $i] :
( ( ( ~ ! [SY634: $i] :
~ ( in @ SY634 @ SV23 ) )
= $true )
| ( ( SV23 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(392,plain,
! [SV106: $i > $o,SV24: $i] :
( ( ~ ~ ! [SY826: $i] :
~ ~ ( ~ ( in @ SY826 @ SV24 )
| ~ ~ ( SV106 @ SY826 ) )
| ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ SV24 )
| ( SV106 @ SY827 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(393,plain,
! [SV107: $i,SV25: $i] :
( ( ! [SY828: $i] :
( ~ ( subset @ SV25 @ SV107 )
| ~ ( in @ SY828 @ SV25 )
| ( in @ SY828 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(394,plain,
! [SV26: $i] :
( ( ( ~ ( ( SV26 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY640: $i] :
~ ~ ( ~ ( in @ SY640 @ SV26 )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(395,plain,
! [SV27: $i,SV108: $i] :
( ( ~ ( in @ SV108 @ ( setunion @ SV27 ) )
| ! [SY829: $o] :
( ~ ! [SY830: $i] :
( ~ ( in @ SV108 @ SY830 )
| ~ ( in @ SY830 @ SV27 )
| SY829 )
| SY829 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(396,plain,
! [SV109: $i,SV28: $i] :
( ( ( SV28 != SV109 )
| ( subset @ SV28 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(397,plain,
! [SV29: $i,SV110: $i] :
( ( ! [SY831: $i] :
( ~ ( in @ SV110 @ SY831 )
| ~ ( in @ SY831 @ SV29 )
| ( in @ SV110 @ ( setunion @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(398,plain,
! [SV111: $i,SV30: $i] :
( ( ~ ! [SY832: $i] :
~ ( ~ ( ~ ( in @ SY832 @ SV30 )
| ( in @ SY832 @ SV111 ) )
| ~ ( ~ ( in @ SY832 @ SV111 )
| ( in @ SY832 @ SV30 ) ) )
| ( SV30 = SV111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(399,plain,
! [SV112: $i,SV31: $i] :
( ( ~ ~ ( subset @ SV31 @ SV112 )
| ( SV31 != SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(400,plain,
! [SV32: $i > $o] :
( ( ( ~ ~ ! [SY650: $i] :
~ ( SV32 @ SY650 ) )
= $true )
| ( ( ~ ! [SY651: $i,SY652: $i] :
( ~ ( SV32 @ SY651 )
| ~ ( SV32 @ SY652 )
| ( SY651 = SY652 ) )
| ~ ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(401,plain,
! [SV113: $i,SV33: $i] :
( ( ! [SY833: $i] :
( ~ ( in @ SY833 @ ( setadjoin @ SV33 @ ( setadjoin @ SV113 @ emptyset ) ) )
| ( SY833 = SV33 )
| ( SY833 = SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(402,plain,
! [SV114: $i,SV34: $i] :
( ( ! [SY834: $i] :
( ~ ( subset @ SV34 @ SV114 )
| ~ ( subset @ SV114 @ SY834 )
| ( subset @ SV34 @ SY834 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(403,plain,
! [SV35: $i,SV115: $i] :
( ( ! [SY835: $i] :
( ~ ( in @ SV115 @ ( powerset @ SV35 ) )
| ~ ( in @ SY835 @ SV115 )
| ( in @ SY835 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(404,plain,
! [SV116: $i > $o,SV36: $i] :
( ( ! [SY836: $i] :
( ~ ( in @ SY836 @ SV36 )
| ~ ( SV116 @ SY836 )
| ( ( dsetconstr @ SV36
@ ^ [SY837: $i] : ( SV116 @ SY837 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(405,plain,
! [SV37: $i,SV117: $i] :
( ( ~ ( ~ ( ~ ( in @ SV117 @ ( powerset @ SV37 ) )
| ! [SY838: $i] :
( ~ ( in @ SY838 @ SV117 )
| ( in @ SY838 @ SV37 ) ) )
| ~ ( ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ SV117 )
| ( in @ SY839 @ SV37 ) )
| ( in @ SV117 @ ( powerset @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(406,plain,
! [SV118: $i,SV38: $i] :
( ( ! [SY840: $i] :
( ~ ( in @ SY840 @ SV38 )
| ~ ~ ( in @ SY840 @ SV118 )
| ( SV38 != SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(407,plain,
! [SV119: $i > $o,SV39: $i] :
( ( ~ ~ ! [SY841: $i] :
( ~ ( in @ SY841 @ SV39 )
| ( SV119 @ SY841 ) )
| ~ ! [SY842: $i] :
~ ~ ( ~ ( in @ SY842 @ SV39 )
| ~ ~ ( SV119 @ SY842 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(408,plain,
! [SV40: $i > $o] :
( ( ( ~ ~ ! [SY672: $i] :
~ ~ ( ~ ( SV40 @ SY672 )
| ~ ! [SY673: $i] :
( ~ ( SV40 @ SY673 )
| ( SY672 = SY673 ) ) ) )
= $true )
| ( ( ! [SY674: $i,SY675: $i] :
( ~ ( SV40 @ SY674 )
| ~ ( SV40 @ SY675 )
| ( SY674 = SY675 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(409,plain,
! [SV120: $i,SV41: $i] :
( ( ~ ! [SY843: $i] :
( ~ ( in @ SY843 @ SV41 )
| ( in @ SY843 @ SV120 ) )
| ( subset @ SV41 @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(410,plain,
! [SV42: $i,SV121: $i] :
( ( ~ ( subset @ SV121 @ SV42 )
| ( in @ SV121 @ ( powerset @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(411,plain,
! [SV43: $i > $o] :
( ( ( ~ ~ ! [SY679: $i] :
~ ~ ( ~ ( SV43 @ SY679 )
| ~ ! [SY680: $i] :
( ~ ( SV43 @ SY680 )
| ( SY679 = SY680 ) ) ) )
= $true )
| ( ( ~ ! [SY681: $i] :
~ ~ ( ~ ( SV43 @ SY681 )
| ~ ! [SY682: $i] :
( ~ ( SV43 @ SY682 )
| ( SY681 = SY682 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(412,plain,
! [SV122: $i,SV44: $i] :
( ( ! [SY844: $i] :
( ~ ( in @ SY844 @ SV44 )
| ~ ~ ( in @ SY844 @ SV122 )
| ~ ( subset @ SV44 @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(413,plain,
! [SV45: $i > $i > $o,SV123: $i] :
( ( ~ ! [SY845: $i] :
( ~ ( in @ SY845 @ SV123 )
| ~ ! [SY687: $i] :
~ ~ ( ~ ( SV45 @ SY845 @ SY687 )
| ~ ! [SY688: $i] :
( ~ ( SV45 @ SY845 @ SY688 )
| ( SY687 = SY688 ) ) ) )
| ~ ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(414,plain,
! [SV124: $i,SV46: $i] :
( ( ( SV46 != SV124 )
| ! [SY852: $i,SY853: $i] :
( ( SY852 != SY853 )
| ~ ( in @ SY852 @ SV46 )
| ( in @ SY853 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(415,plain,
! [SV47: $i] :
( ( ( ~ ~ ! [SY696: $i] :
~ ( in @ SY696 @ SV47 ) )
= $true )
| ( ( SV47 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(416,plain,
! [SV125: $i,SV48: $i] :
( ( ( SV48 != SV125 )
| ! [SY854: $i,SY855: $i] :
( ( SY854 != SY855 )
| ~ ( ~ ( ~ ( in @ SY854 @ SV48 )
| ( in @ SY855 @ SV125 ) )
| ~ ( ~ ( in @ SY855 @ SV125 )
| ( in @ SY854 @ SV48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(417,plain,
! [SV126: $i > $o,SV49: $i] :
( ( ! [SY856: $i] :
( ~ ( in @ SY856
@ ( dsetconstr @ SV49
@ ^ [SY857: $i] : ( SV126 @ SY857 ) ) )
| ( SV126 @ SY856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(418,plain,
! [SV50: $i,SV127: $i] :
( ( ~ ( in @ SV127 @ SV50 )
| ( in @ SV127 @ ( powerset @ ( setunion @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(419,plain,
! [SV51: $o] :
( ( ( ~ SV51 ) = $true )
| ( ( set2prop @ ( prop2set @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(420,plain,
( ( ( ~ $true ) = $true )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(421,plain,
( ( ( ~ $false ) = $true )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(422,plain,
! [SV52: $i] :
( ( ( ~ ( in @ SV52 @ emptyset ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(423,plain,
! [SV128: $i,SV53: $i] :
( ( ( SV53 != SV128 )
| ! [SY858: $i > $o,SY859: $i > $o] :
( ~ ! [SY860: $i] :
( ~ ( in @ SY860 @ SV53 )
| ! [SY861: $i] :
( ~ ( in @ SY861 @ SV128 )
| ( SY860 != SY861 )
| ~ ( ~ ( ~ ( SY858 @ SY860 )
| ( SY859 @ SY861 ) )
| ~ ( ~ ( SY859 @ SY861 )
| ( SY858 @ SY860 ) ) ) ) )
| ( ( dsetconstr @ SV53
@ ^ [SX4: $i] : ( SY858 @ SX4 ) )
= ( dsetconstr @ SV128
@ ^ [SX4: $i] : ( SY859 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(424,plain,
! [SV129: $i,SV54: $i] :
( ( ! [SY864: $i] :
( ~ ( in @ SY864 @ ( setadjoin @ SV54 @ SV129 ) )
| ! [SY865: $o] :
( ~ ( ( SY864 != SV54 )
| SY865 )
| ~ ( ~ ( in @ SY864 @ SV129 )
| SY865 )
| SY865 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(425,plain,
! [SV55: $i] :
( ( ( ~ ~ ! [SY714: $i] :
~ ( in @ SY714 @ SV55 ) )
= $true )
| ( ( ~ ! [SY715: $i] :
~ ~ ( ~ ( in @ SY715 @ SV55 )
| ~ ~ ~ ! [SY716: $i] :
~ ~ ( ~ ( in @ SY716 @ SY715 )
| ~ ( in @ SY716 @ SV55 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(426,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ~ ! [SY866: $i,SY867: $i] :
( ( SY866 != SY867 )
| ~ ( ~ ( ~ ( SV56 @ SY866 )
| ( SV130 @ SY867 ) )
| ~ ( ~ ( SV130 @ SY867 )
| ( SV56 @ SY866 ) ) ) )
| ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(427,plain,
! [SV131: $i,SV57: $i] :
( ( ( SV57 != SV131 )
| ( in @ SV57 @ ( setadjoin @ SV131 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(428,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ~ ! [SY874: $i,SY875: $i] :
( ( SY874 != SY875 )
| ~ ( ~ ( ~ ( SV58 @ SY874 )
| ( SV132 @ SY875 ) )
| ~ ( ~ ( SV132 @ SY875 )
| ( SV58 @ SY874 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(429,plain,
! [SV133: $i > $o,SV59: $i] :
( ( ! [SY884: $i] :
( ~ ( in @ SY884 @ SV59 )
| ~ ( ~ ( ~ ( in @ SY884
@ ( dsetconstr @ SV59
@ ^ [SY885: $i] : ( SV133 @ SY885 ) ) )
| ( SV133 @ SY884 ) )
| ~ ( ~ ( SV133 @ SY884 )
| ( in @ SY884
@ ( dsetconstr @ SV59
@ ^ [SY886: $i] : ( SV133 @ SY886 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(430,plain,
! [SV60: $i] :
( ( ( ~ ! [SY742: $i] :
~ ( in @ SY742 @ SV60 ) )
= $true )
| ( ( SV60 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(431,plain,
! [SV61: $i] :
( ( ! [SY743: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY744: $i] :
( ~ ( in @ SY744 @ SY743 )
| ! [SY745: $i] :
( ~ ( in @ SY745 @ SY744 )
| ( in @ SY745 @ SV61 ) ) )
| ~ ! [SY746: $i,SY747: $i] :
( ~ ~ ( ~ ( in @ SY746 @ SV61 )
| ~ ( in @ SY747 @ SV61 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY743 )
| ~ ( ~ ( ~ ( in @ SY746 @ SX4 )
| ( in @ SY747 @ SX4 ) )
| ~ ( ~ ( in @ SY747 @ SX4 )
| ( in @ SY746 @ SX4 ) ) ) )
| ( SY746 = SY747 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY743 )
| ~ ( in @ SX3 @ SY743 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY753: $i] :
( ~ ~ ( ~ ! [SY754: $i] :
( ~ ( in @ SY754 @ SY753 )
| ( in @ SY754 @ SV61 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY753 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY743 )
| ~ ( in @ SX4 @ SY753 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY753 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY743 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(432,plain,
! [SV62: $o] :
( ( ( ~ SV62 ) = $true )
| ( ( in @ emptyset @ ( prop2set @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(433,plain,
( ( ( ~ $true ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(434,plain,
( ( ( ~ $false ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(435,plain,
! [SV63: $i > $o,SV134: $i] :
( ( ~ ( in @ SV134 @ emptyset )
| ( SV63 @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(436,plain,
! [SV135: $i,SV64: $i] :
( ( ! [SY887: $i] :
( ~ ( in @ SY887 @ ( setadjoin @ SV64 @ SV135 ) )
| ( SY887 = SV64 )
| ( in @ SY887 @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(437,plain,
! [SV65: $i] :
( ( ( ~ ( in @ SV65 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV65 @ SV65 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(438,plain,
! [SV136: $i,SV66: $i] :
( ( ~ ( in @ SV66 @ ( setadjoin @ SV136 @ emptyset ) )
| ( SV66 = SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(439,plain,
! [SV137: $i,SV67: $i] :
( ( ( SV67 != SV137 )
| ( subset @ SV137 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(440,plain,
! [SV138: $i,SV68: $i] :
( ( ~ ! [SY888: $i] :
( ~ ( in @ SY888 @ SV68 )
| ( in @ SY888 @ SV138 ) )
| ~ ! [SY889: $i] :
( ~ ( in @ SY889 @ SV138 )
| ( in @ SY889 @ SV68 ) )
| ( SV68 = SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(441,plain,
! [SV139: $i > $o,SV69: $i] :
( ( ~ ~ ! [SY890: $i] :
~ ~ ( ~ ( in @ SY890 @ SV69 )
| ~ ( SV139 @ SY890 ) )
| ( ( dsetconstr @ SV69
@ ^ [SY891: $i] : ( SV139 @ SY891 ) )
!= emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(442,plain,
! [SV140: $i,SV70: $i] :
( ( ( SV70 != SV140 )
| ! [SY892: $i,SY893: $i] :
( ( SY892 != SY893 )
| ( ( setadjoin @ SV70 @ SY892 )
= ( setadjoin @ SV140 @ SY893 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(443,plain,
! [SV71: $i] :
( ( ( ~ ~ ( ~ ( in @ emptyset @ SV71 )
| ~ ! [SY775: $i] :
( ~ ~ ( ~ ( in @ SY775 @ omega )
| ~ ( in @ SY775 @ SV71 ) )
| ( in @ ( setadjoin @ SY775 @ SY775 ) @ SV71 ) ) ) )
= $true )
| ( ( ! [SY776: $i] :
( ~ ( in @ SY776 @ omega )
| ( in @ SY776 @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(444,plain,
! [SV72: $i] :
( ( ( ~ ( in @ SV72 @ emptyset ) )
= $true )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(445,plain,
! [SV141: $i > $o,SV73: $i] :
( ( ~ ~ ~ ! [SY894: $i] :
~ ~ ( ~ ( in @ SY894 @ SV73 )
| ~ ( SV141 @ SY894 ) )
| ! [SY895: $i] :
( ~ ( in @ SY895 @ SV73 )
| ~ ( SV141 @ SY895 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(446,plain,
! [SV142: $i,SV74: $i] :
( ( ! [SY896: $i] :
( ~ ( subset @ SV74 @ SY896 )
| ( subset @ SV74 @ ( setadjoin @ SV142 @ SY896 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(447,plain,
! [SV75: $i,SV143: $i] :
( ( ~ ( in @ SV143 @ ( powerset @ SV75 ) )
| ( subset @ SV143 @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(448,plain,
! [SV144: $i > $o,SV76: $i] :
( ( ! [SY897: $i] :
( ~ ( in @ SY897 @ SV76 )
| ~ ( SV144 @ SY897 )
| ( in @ SY897
@ ( dsetconstr @ SV76
@ ^ [SY898: $i] : ( SV144 @ SY898 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(449,plain,
! [SV77: $i > $o] :
( ( ( ~ ~ ! [SY787: $i] :
~ ! [SY788: $i] :
~ ( ~ ( ~ ( SV77 @ SY788 )
| ( SY788 = SY787 ) )
| ~ ( ( SY788 != SY787 )
| ( SV77 @ SY788 ) ) ) )
= $true )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(450,plain,
! [SV78: $i,SV145: $i] :
( ( ~ ! [SY899: $i] :
( ~ ( in @ SY899 @ SV145 )
| ( in @ SY899 @ SV78 ) )
| ( in @ SV145 @ ( powerset @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(451,plain,
! [SV146: $i > $o,SV79: $i] :
( ( ~ ! [SY900: $i] :
( ~ ( in @ SY900 @ SV79 )
| ~ ( SV146 @ SY900 ) )
| ~ ~ ! [SY901: $i] :
~ ~ ( ~ ( in @ SY901 @ SV79 )
| ~ ( SV146 @ SY901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(452,plain,
! [SV147: $i,SV80: $i] :
( ( ( SV80 != SV147 )
| ( ( powerset @ SV80 )
= ( powerset @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(453,plain,
! [SV81: $i > $o] :
( ( ( ~ ~ ! [SY797: $i] :
~ ~ ( ~ ( SV81 @ SY797 )
| ~ ! [SY798: $i] :
( ~ ( SV81 @ SY798 )
| ( SY797 = SY798 ) ) ) )
= $true )
| ( ( ~ ! [SY799: $i] :
~ ! [SY800: $i] :
~ ( ~ ( ~ ( SV81 @ SY800 )
| ( SY800 = SY799 ) )
| ~ ( ( SY800 != SY799 )
| ( SV81 @ SY800 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(454,plain,
! [SV82: $i] :
( ( ( ~ ( ( SV82 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY801: $i] :
~ ( in @ SY801 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(455,plain,
! [SV148: $i > $o,SV83: $i] :
( ( ~ ~ ! [SY902: $i] :
( ~ ( in @ SY902 @ SV83 )
| ( SV148 @ SY902 ) )
| ~ ! [SY903: $i] :
~ ~ ( ~ ( in @ SY903 @ SV83 )
| ~ ~ ( SV148 @ SY903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(456,plain,
! [SV84: $i > $o] :
( ( ( ~ ~ ! [SY805: $i] :
~ ~ ( ~ ( SV84 @ SY805 )
| ~ ! [SY806: $i] :
( ~ ( SV84 @ SY806 )
| ( SY805 = SY806 ) ) ) )
= $true )
| ( ( ! [SY807: $i,SY808: $i] :
( ~ ( SV84 @ SY807 )
| ~ ( SV84 @ SY808 )
| ( SY807 = SY808 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(457,plain,
! [SV149: $i > $o,SV85: $i] :
( ( ! [SY904: $i] :
( ~ ( in @ SY904
@ ( dsetconstr @ SV85
@ ^ [SY905: $i] : ( SV149 @ SY905 ) ) )
| ( in @ SY904 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(458,plain,
! [SV86: $i] :
( ( ( ~ ( subset @ SV86 @ emptyset ) )
= $true )
| ( ( SV86 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(459,plain,
! [SV87: $i,SV150: $i] :
( ( ~ ( ~ ( ~ ( in @ SV150 @ ( setunion @ SV87 ) )
| ~ ! [SY906: $i] :
~ ~ ( ~ ( in @ SV150 @ SY906 )
| ~ ( in @ SY906 @ SV87 ) ) )
| ~ ( ~ ~ ! [SY907: $i] :
~ ~ ( ~ ( in @ SV150 @ SY907 )
| ~ ( in @ SY907 @ SV87 ) )
| ( in @ SV150 @ ( setunion @ SV87 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(460,plain,
! [SV151: $i,SV88: $i] :
( ( ~ ( subset @ SV88 @ SV151 )
| ~ ( subset @ SV151 @ SV88 )
| ( SV88 = SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(461,plain,
! [SV152: $i,SV89: $i] :
( ( ~ ( subset @ SV89 @ SV152 )
| ( in @ SV89 @ ( powerset @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(462,plain,
! [SV90: $i > $o] :
( ( ( ~ ~ ! [SY817: $i] :
~ ~ ( ~ ( SV90 @ SY817 )
| ~ ! [SY818: $i] :
( ~ ( SV90 @ SY818 )
| ( SY817 = SY818 ) ) ) )
= $true )
| ( ( SV90
@ ( descr
@ ^ [SY819: $i] : ( SV90 @ SY819 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(463,plain,
! [SV12: $o,SV95: $i] :
( ( ( ~ ( in @ SV95 @ ( prop2set @ SV12 ) ) )
= $true )
| ( SV12 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(464,plain,
! [SV96: $i] :
( ( ( ~ ( in @ SV96 @ ( prop2set @ $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(465,plain,
! [SV97: $i] :
( ( ( ~ ( in @ SV97 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(466,plain,
! [SV98: $i,SV13: $i] :
( ( ( ~ ! [SY820: $i] :
( ~ ( in @ SY820 @ SV13 )
| ( in @ SY820 @ SV98 ) ) )
= $true )
| ( ( subset @ SV13 @ SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(467,plain,
! [SV99: $i,SV14: $i] :
( ( ( ~ ( ( SV14 != SV99 ) ) )
= $true )
| ( ( ~ ( in @ SV99 @ ( setadjoin @ SV14 @ emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(468,plain,
! [SV15: $i,SV100: $i,SV153: $i] :
( ( ~ ( in @ SV153 @ SV100 )
| ( in @ SV153 @ ( setadjoin @ SV15 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(469,plain,
! [SV101: $i,SV16: $i,SV154: $i] :
( ( ~ ( ~ ( ~ ( in @ SV154 @ ( setadjoin @ SV16 @ SV101 ) )
| ( SV154 = SV16 )
| ( in @ SV154 @ SV101 ) )
| ~ ( ~ ( ( SV154 = SV16 )
| ( in @ SV154 @ SV101 ) )
| ( in @ SV154 @ ( setadjoin @ SV16 @ SV101 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(470,plain,
! [SV17: $i > $o] :
( ( ( ~ ! [SY620: $i] :
~ ~ ( ~ ( SV17 @ SY620 )
| ~ ! [SY621: $i] :
( ~ ( SV17 @ SY621 )
| ( SY620 = SY621 ) ) ) )
= $false )
| ( ( ~ ! [SY622: $i] :
~ ( SV17 @ SY622 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(471,plain,
! [SV102: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ ( setadjoin @ SV102 @ emptyset ) ) )
= $true )
| ( ( in @ SV102 @ ( setadjoin @ SV18 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(472,plain,
! [SV103: $i > $o,SV19: $i] :
( ( ( ~ ~ ~ ! [SY823: $i] :
~ ~ ( ~ ( in @ SY823 @ SV19 )
| ~ ( SV103 @ SY823 ) ) )
= $true )
| ( ( ! [SY824: $i] :
( ~ ( in @ SY824 @ SV19 )
| ~ ( SV103 @ SY824 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(473,plain,
! [SV104: $i,SV20: $i] :
( ( ( SV20 != SV104 )
= $true )
| ( ( ( setunion @ SV20 )
= ( setunion @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(474,plain,
! [SV21: $i > $o] :
( ( ( ~ ! [SY628: $i] :
~ ~ ( ~ ( SV21 @ SY628 )
| ~ ! [SY629: $i] :
( ~ ( SV21 @ SY629 )
| ( SY628 = SY629 ) ) ) )
= $false )
| ( ( ~ ! [SY630: $i] :
~ ~ ( ~ ( SV21 @ SY630 )
| ~ ! [SY631: $i] :
( ~ ( SV21 @ SY631 )
| ( SY630 = SY631 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(475,plain,
! [SV155: $i,SV105: $i,SV22: $i] :
( ( ~ ( subset @ SV22 @ SV105 )
| ~ ~ ( in @ SV155 @ SV105 )
| ~ ( in @ SV155 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(476,plain,
! [SV23: $i] :
( ( ( ! [SY634: $i] :
~ ( in @ SY634 @ SV23 ) )
= $false )
| ( ( SV23 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(477,plain,
! [SV106: $i > $o,SV24: $i] :
( ( ( ~ ~ ! [SY826: $i] :
~ ~ ( ~ ( in @ SY826 @ SV24 )
| ~ ~ ( SV106 @ SY826 ) ) )
= $true )
| ( ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ SV24 )
| ( SV106 @ SY827 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(478,plain,
! [SV156: $i,SV107: $i,SV25: $i] :
( ( ~ ( subset @ SV25 @ SV107 )
| ~ ( in @ SV156 @ SV25 )
| ( in @ SV156 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(479,plain,
! [SV26: $i] :
( ( ( SV26 != emptyset )
= $false )
| ( ( ~ ! [SY640: $i] :
~ ~ ( ~ ( in @ SY640 @ SV26 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(480,plain,
! [SV27: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ ( setunion @ SV27 ) ) )
= $true )
| ( ( ! [SY829: $o] :
( ~ ! [SY830: $i] :
( ~ ( in @ SV108 @ SY830 )
| ~ ( in @ SY830 @ SV27 )
| SY829 )
| SY829 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(481,plain,
! [SV109: $i,SV28: $i] :
( ( ( SV28 != SV109 )
= $true )
| ( ( subset @ SV28 @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(482,plain,
! [SV29: $i,SV157: $i,SV110: $i] :
( ( ~ ( in @ SV110 @ SV157 )
| ~ ( in @ SV157 @ SV29 )
| ( in @ SV110 @ ( setunion @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(483,plain,
! [SV111: $i,SV30: $i] :
( ( ( ~ ! [SY832: $i] :
~ ( ~ ( ~ ( in @ SY832 @ SV30 )
| ( in @ SY832 @ SV111 ) )
| ~ ( ~ ( in @ SY832 @ SV111 )
| ( in @ SY832 @ SV30 ) ) ) )
= $true )
| ( ( SV30 = SV111 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(484,plain,
! [SV112: $i,SV31: $i] :
( ( ( ~ ~ ( subset @ SV31 @ SV112 ) )
= $true )
| ( ( SV31 != SV112 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[399]) ).
thf(485,plain,
! [SV32: $i > $o] :
( ( ( ~ ! [SY650: $i] :
~ ( SV32 @ SY650 ) )
= $false )
| ( ( ~ ! [SY651: $i,SY652: $i] :
( ~ ( SV32 @ SY651 )
| ~ ( SV32 @ SY652 )
| ( SY651 = SY652 ) )
| ~ ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(486,plain,
! [SV113: $i,SV33: $i,SV158: $i] :
( ( ~ ( in @ SV158 @ ( setadjoin @ SV33 @ ( setadjoin @ SV113 @ emptyset ) ) )
| ( SV158 = SV33 )
| ( SV158 = SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(487,plain,
! [SV159: $i,SV114: $i,SV34: $i] :
( ( ~ ( subset @ SV34 @ SV114 )
| ~ ( subset @ SV114 @ SV159 )
| ( subset @ SV34 @ SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(488,plain,
! [SV160: $i,SV35: $i,SV115: $i] :
( ( ~ ( in @ SV115 @ ( powerset @ SV35 ) )
| ~ ( in @ SV160 @ SV115 )
| ( in @ SV160 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(489,plain,
! [SV116: $i > $o,SV36: $i,SV161: $i] :
( ( ~ ( in @ SV161 @ SV36 )
| ~ ( SV116 @ SV161 )
| ( ( dsetconstr @ SV36
@ ^ [SY837: $i] : ( SV116 @ SY837 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(490,plain,
! [SV37: $i,SV117: $i] :
( ( ~ ( ~ ( in @ SV117 @ ( powerset @ SV37 ) )
| ! [SY838: $i] :
( ~ ( in @ SY838 @ SV117 )
| ( in @ SY838 @ SV37 ) ) )
| ~ ( ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ SV117 )
| ( in @ SY839 @ SV37 ) )
| ( in @ SV117 @ ( powerset @ SV37 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(491,plain,
! [SV118: $i,SV38: $i,SV162: $i] :
( ( ~ ( in @ SV162 @ SV38 )
| ~ ~ ( in @ SV162 @ SV118 )
| ( SV38 != SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(492,plain,
! [SV119: $i > $o,SV39: $i] :
( ( ( ~ ~ ! [SY841: $i] :
( ~ ( in @ SY841 @ SV39 )
| ( SV119 @ SY841 ) ) )
= $true )
| ( ( ~ ! [SY842: $i] :
~ ~ ( ~ ( in @ SY842 @ SV39 )
| ~ ~ ( SV119 @ SY842 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(493,plain,
! [SV40: $i > $o] :
( ( ( ~ ! [SY672: $i] :
~ ~ ( ~ ( SV40 @ SY672 )
| ~ ! [SY673: $i] :
( ~ ( SV40 @ SY673 )
| ( SY672 = SY673 ) ) ) )
= $false )
| ( ( ! [SY674: $i,SY675: $i] :
( ~ ( SV40 @ SY674 )
| ~ ( SV40 @ SY675 )
| ( SY674 = SY675 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(494,plain,
! [SV120: $i,SV41: $i] :
( ( ( ~ ! [SY843: $i] :
( ~ ( in @ SY843 @ SV41 )
| ( in @ SY843 @ SV120 ) ) )
= $true )
| ( ( subset @ SV41 @ SV120 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(495,plain,
! [SV42: $i,SV121: $i] :
( ( ( ~ ( subset @ SV121 @ SV42 ) )
= $true )
| ( ( in @ SV121 @ ( powerset @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(496,plain,
! [SV43: $i > $o] :
( ( ( ~ ! [SY679: $i] :
~ ~ ( ~ ( SV43 @ SY679 )
| ~ ! [SY680: $i] :
( ~ ( SV43 @ SY680 )
| ( SY679 = SY680 ) ) ) )
= $false )
| ( ( ~ ! [SY681: $i] :
~ ~ ( ~ ( SV43 @ SY681 )
| ~ ! [SY682: $i] :
( ~ ( SV43 @ SY682 )
| ( SY681 = SY682 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(497,plain,
! [SV122: $i,SV44: $i,SV163: $i] :
( ( ~ ( in @ SV163 @ SV44 )
| ~ ~ ( in @ SV163 @ SV122 )
| ~ ( subset @ SV44 @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(498,plain,
! [SV45: $i > $i > $o,SV123: $i] :
( ( ( ~ ! [SY845: $i] :
( ~ ( in @ SY845 @ SV123 )
| ~ ! [SY687: $i] :
~ ~ ( ~ ( SV45 @ SY845 @ SY687 )
| ~ ! [SY688: $i] :
( ~ ( SV45 @ SY845 @ SY688 )
| ( SY687 = SY688 ) ) ) ) )
= $true )
| ( ( ~ ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(499,plain,
! [SV124: $i,SV46: $i] :
( ( ( SV46 != SV124 )
= $true )
| ( ( ! [SY852: $i,SY853: $i] :
( ( SY852 != SY853 )
| ~ ( in @ SY852 @ SV46 )
| ( in @ SY853 @ SV124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(500,plain,
! [SV47: $i] :
( ( ( ~ ! [SY696: $i] :
~ ( in @ SY696 @ SV47 ) )
= $false )
| ( ( SV47 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(501,plain,
! [SV125: $i,SV48: $i] :
( ( ( SV48 != SV125 )
= $true )
| ( ( ! [SY854: $i,SY855: $i] :
( ( SY854 != SY855 )
| ~ ( ~ ( ~ ( in @ SY854 @ SV48 )
| ( in @ SY855 @ SV125 ) )
| ~ ( ~ ( in @ SY855 @ SV125 )
| ( in @ SY854 @ SV48 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(502,plain,
! [SV126: $i > $o,SV49: $i,SV164: $i] :
( ( ~ ( in @ SV164
@ ( dsetconstr @ SV49
@ ^ [SY857: $i] : ( SV126 @ SY857 ) ) )
| ( SV126 @ SV164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(503,plain,
! [SV50: $i,SV127: $i] :
( ( ( ~ ( in @ SV127 @ SV50 ) )
= $true )
| ( ( in @ SV127 @ ( powerset @ ( setunion @ SV50 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(504,plain,
! [SV51: $o] :
( ( SV51 = $false )
| ( ( set2prop @ ( prop2set @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(505,plain,
( ( $true = $false )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(506,plain,
( ( $false = $false )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(507,plain,
! [SV52: $i] :
( ( ( in @ SV52 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(508,plain,
! [SV128: $i,SV53: $i] :
( ( ( SV53 != SV128 )
= $true )
| ( ( ! [SY858: $i > $o,SY859: $i > $o] :
( ~ ! [SY860: $i] :
( ~ ( in @ SY860 @ SV53 )
| ! [SY861: $i] :
( ~ ( in @ SY861 @ SV128 )
| ( SY860 != SY861 )
| ~ ( ~ ( ~ ( SY858 @ SY860 )
| ( SY859 @ SY861 ) )
| ~ ( ~ ( SY859 @ SY861 )
| ( SY858 @ SY860 ) ) ) ) )
| ( ( dsetconstr @ SV53
@ ^ [SX4: $i] : ( SY858 @ SX4 ) )
= ( dsetconstr @ SV128
@ ^ [SX4: $i] : ( SY859 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(509,plain,
! [SV129: $i,SV54: $i,SV165: $i] :
( ( ~ ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
| ! [SY910: $o] :
( ~ ( ( SV165 != SV54 )
| SY910 )
| ~ ( ~ ( in @ SV165 @ SV129 )
| SY910 )
| SY910 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(510,plain,
! [SV55: $i] :
( ( ( ~ ! [SY714: $i] :
~ ( in @ SY714 @ SV55 ) )
= $false )
| ( ( ~ ! [SY715: $i] :
~ ~ ( ~ ( in @ SY715 @ SV55 )
| ~ ~ ~ ! [SY716: $i] :
~ ~ ( ~ ( in @ SY716 @ SY715 )
| ~ ( in @ SY716 @ SV55 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(511,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ! [SY866: $i,SY867: $i] :
( ( SY866 != SY867 )
| ~ ( ~ ( ~ ( SV56 @ SY866 )
| ( SV130 @ SY867 ) )
| ~ ( ~ ( SV130 @ SY867 )
| ( SV56 @ SY866 ) ) ) ) )
= $true )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(512,plain,
! [SV131: $i,SV57: $i] :
( ( ( SV57 != SV131 )
= $true )
| ( ( in @ SV57 @ ( setadjoin @ SV131 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(513,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ! [SY874: $i,SY875: $i] :
( ( SY874 != SY875 )
| ~ ( ~ ( ~ ( SV58 @ SY874 )
| ( SV132 @ SY875 ) )
| ~ ( ~ ( SV132 @ SY875 )
| ( SV58 @ SY874 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(514,plain,
! [SV133: $i > $o,SV59: $i,SV166: $i] :
( ( ~ ( in @ SV166 @ SV59 )
| ~ ( ~ ( ~ ( in @ SV166
@ ( dsetconstr @ SV59
@ ^ [SY885: $i] : ( SV133 @ SY885 ) ) )
| ( SV133 @ SV166 ) )
| ~ ( ~ ( SV133 @ SV166 )
| ( in @ SV166
@ ( dsetconstr @ SV59
@ ^ [SY886: $i] : ( SV133 @ SY886 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(515,plain,
! [SV60: $i] :
( ( ( ! [SY742: $i] :
~ ( in @ SY742 @ SV60 ) )
= $false )
| ( ( SV60 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(516,plain,
! [SV61: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY913: $i] :
( ~ ( in @ SY913 @ ( sK2_SY743 @ SV61 ) )
| ! [SY745: $i] :
( ~ ( in @ SY745 @ SY913 )
| ( in @ SY745 @ SV61 ) ) )
| ~ ! [SY915: $i,SY916: $i] :
( ~ ~ ( ~ ( in @ SY915 @ SV61 )
| ~ ( in @ SY916 @ SV61 ) )
| ~ ! [SY917: $i] :
( ~ ( in @ SY917 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SY915 @ SY917 )
| ( in @ SY916 @ SY917 ) )
| ~ ( ~ ( in @ SY916 @ SY917 )
| ( in @ SY915 @ SY917 ) ) ) )
| ( SY915 = SY916 ) ) )
| ~ ! [SY918: $i,SY919: $i] :
( ~ ~ ( ~ ( in @ SY918 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY919 @ ( sK2_SY743 @ SV61 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY918 )
| ( in @ SX4 @ SY919 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY919 )
| ( in @ SX4 @ SY918 ) ) ) )
| ~ ! [SY922: $i] :
( ~ ~ ( ~ ! [SY754: $i] :
( ~ ( in @ SY754 @ SY922 )
| ( in @ SY754 @ SV61 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY922 ) )
| ~ ! [SY925: $i] :
~ ~ ! [SY926: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY925 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY926 @ SY922 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY925 )
| ~ ( in @ SX5 @ SY922 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY925 ) )
| ( in @ SY926 @ SY928 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[431]) ).
thf(517,plain,
! [SV62: $o] :
( ( SV62 = $false )
| ( ( in @ emptyset @ ( prop2set @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(518,plain,
( ( $true = $false )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(519,plain,
( ( $false = $false )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(520,plain,
! [SV63: $i > $o,SV134: $i] :
( ( ( ~ ( in @ SV134 @ emptyset ) )
= $true )
| ( ( SV63 @ SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(521,plain,
! [SV135: $i,SV64: $i,SV167: $i] :
( ( ~ ( in @ SV167 @ ( setadjoin @ SV64 @ SV135 ) )
| ( SV167 = SV64 )
| ( in @ SV167 @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(522,plain,
! [SV65: $i] :
( ( ( in @ SV65 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV65 @ SV65 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(523,plain,
! [SV136: $i,SV66: $i] :
( ( ( ~ ( in @ SV66 @ ( setadjoin @ SV136 @ emptyset ) ) )
= $true )
| ( ( SV66 = SV136 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[438]) ).
thf(524,plain,
! [SV137: $i,SV67: $i] :
( ( ( SV67 != SV137 )
= $true )
| ( ( subset @ SV137 @ SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(525,plain,
! [SV138: $i,SV68: $i] :
( ( ( ~ ! [SY888: $i] :
( ~ ( in @ SY888 @ SV68 )
| ( in @ SY888 @ SV138 ) ) )
= $true )
| ( ( ~ ! [SY889: $i] :
( ~ ( in @ SY889 @ SV138 )
| ( in @ SY889 @ SV68 ) )
| ( SV68 = SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(526,plain,
! [SV139: $i > $o,SV69: $i] :
( ( ( ~ ~ ! [SY890: $i] :
~ ~ ( ~ ( in @ SY890 @ SV69 )
| ~ ( SV139 @ SY890 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV69
@ ^ [SY891: $i] : ( SV139 @ SY891 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(527,plain,
! [SV140: $i,SV70: $i] :
( ( ( SV70 != SV140 )
= $true )
| ( ( ! [SY892: $i,SY893: $i] :
( ( SY892 != SY893 )
| ( ( setadjoin @ SV70 @ SY892 )
= ( setadjoin @ SV140 @ SY893 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(528,plain,
! [SV71: $i] :
( ( ( ~ ( ~ ( in @ emptyset @ SV71 )
| ~ ! [SY775: $i] :
( ~ ~ ( ~ ( in @ SY775 @ omega )
| ~ ( in @ SY775 @ SV71 ) )
| ( in @ ( setadjoin @ SY775 @ SY775 ) @ SV71 ) ) ) )
= $false )
| ( ( ! [SY776: $i] :
( ~ ( in @ SY776 @ omega )
| ( in @ SY776 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(529,plain,
! [SV72: $i] :
( ( ( in @ SV72 @ emptyset )
= $false )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(530,plain,
! [SV141: $i > $o,SV73: $i] :
( ( ( ~ ~ ~ ! [SY894: $i] :
~ ~ ( ~ ( in @ SY894 @ SV73 )
| ~ ( SV141 @ SY894 ) ) )
= $true )
| ( ( ! [SY895: $i] :
( ~ ( in @ SY895 @ SV73 )
| ~ ( SV141 @ SY895 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(531,plain,
! [SV142: $i,SV168: $i,SV74: $i] :
( ( ~ ( subset @ SV74 @ SV168 )
| ( subset @ SV74 @ ( setadjoin @ SV142 @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(532,plain,
! [SV75: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ ( powerset @ SV75 ) ) )
= $true )
| ( ( subset @ SV143 @ SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(533,plain,
! [SV144: $i > $o,SV76: $i,SV169: $i] :
( ( ~ ( in @ SV169 @ SV76 )
| ~ ( SV144 @ SV169 )
| ( in @ SV169
@ ( dsetconstr @ SV76
@ ^ [SY898: $i] : ( SV144 @ SY898 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(534,plain,
! [SV77: $i > $o] :
( ( ( ~ ! [SY787: $i] :
~ ! [SY788: $i] :
~ ( ~ ( ~ ( SV77 @ SY788 )
| ( SY788 = SY787 ) )
| ~ ( ( SY788 != SY787 )
| ( SV77 @ SY788 ) ) ) )
= $false )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(535,plain,
! [SV78: $i,SV145: $i] :
( ( ( ~ ! [SY899: $i] :
( ~ ( in @ SY899 @ SV145 )
| ( in @ SY899 @ SV78 ) ) )
= $true )
| ( ( in @ SV145 @ ( powerset @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(536,plain,
! [SV146: $i > $o,SV79: $i] :
( ( ( ~ ! [SY900: $i] :
( ~ ( in @ SY900 @ SV79 )
| ~ ( SV146 @ SY900 ) ) )
= $true )
| ( ( ~ ~ ! [SY901: $i] :
~ ~ ( ~ ( in @ SY901 @ SV79 )
| ~ ( SV146 @ SY901 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(537,plain,
! [SV147: $i,SV80: $i] :
( ( ( SV80 != SV147 )
= $true )
| ( ( ( powerset @ SV80 )
= ( powerset @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(538,plain,
! [SV81: $i > $o] :
( ( ( ~ ! [SY797: $i] :
~ ~ ( ~ ( SV81 @ SY797 )
| ~ ! [SY798: $i] :
( ~ ( SV81 @ SY798 )
| ( SY797 = SY798 ) ) ) )
= $false )
| ( ( ~ ! [SY799: $i] :
~ ! [SY800: $i] :
~ ( ~ ( ~ ( SV81 @ SY800 )
| ( SY800 = SY799 ) )
| ~ ( ( SY800 != SY799 )
| ( SV81 @ SY800 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(539,plain,
! [SV82: $i] :
( ( ( SV82 != emptyset )
= $false )
| ( ( ~ ! [SY801: $i] :
~ ( in @ SY801 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(540,plain,
! [SV148: $i > $o,SV83: $i] :
( ( ( ~ ~ ! [SY902: $i] :
( ~ ( in @ SY902 @ SV83 )
| ( SV148 @ SY902 ) ) )
= $true )
| ( ( ~ ! [SY903: $i] :
~ ~ ( ~ ( in @ SY903 @ SV83 )
| ~ ~ ( SV148 @ SY903 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(541,plain,
! [SV84: $i > $o] :
( ( ( ~ ! [SY805: $i] :
~ ~ ( ~ ( SV84 @ SY805 )
| ~ ! [SY806: $i] :
( ~ ( SV84 @ SY806 )
| ( SY805 = SY806 ) ) ) )
= $false )
| ( ( ! [SY807: $i,SY808: $i] :
( ~ ( SV84 @ SY807 )
| ~ ( SV84 @ SY808 )
| ( SY807 = SY808 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(542,plain,
! [SV149: $i > $o,SV85: $i,SV170: $i] :
( ( ~ ( in @ SV170
@ ( dsetconstr @ SV85
@ ^ [SY905: $i] : ( SV149 @ SY905 ) ) )
| ( in @ SV170 @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(543,plain,
! [SV86: $i] :
( ( ( subset @ SV86 @ emptyset )
= $false )
| ( ( SV86 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(544,plain,
! [SV87: $i,SV150: $i] :
( ( ~ ( ~ ( in @ SV150 @ ( setunion @ SV87 ) )
| ~ ! [SY906: $i] :
~ ~ ( ~ ( in @ SV150 @ SY906 )
| ~ ( in @ SY906 @ SV87 ) ) )
| ~ ( ~ ~ ! [SY907: $i] :
~ ~ ( ~ ( in @ SV150 @ SY907 )
| ~ ( in @ SY907 @ SV87 ) )
| ( in @ SV150 @ ( setunion @ SV87 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(545,plain,
! [SV151: $i,SV88: $i] :
( ( ( ~ ( subset @ SV88 @ SV151 ) )
= $true )
| ( ( ~ ( subset @ SV151 @ SV88 )
| ( SV88 = SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(546,plain,
! [SV152: $i,SV89: $i] :
( ( ( ~ ( subset @ SV89 @ SV152 ) )
= $true )
| ( ( in @ SV89 @ ( powerset @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(547,plain,
! [SV90: $i > $o] :
( ( ( ~ ! [SY817: $i] :
~ ~ ( ~ ( SV90 @ SY817 )
| ~ ! [SY818: $i] :
( ~ ( SV90 @ SY818 )
| ( SY817 = SY818 ) ) ) )
= $false )
| ( ( SV90
@ ( descr
@ ^ [SY819: $i] : ( SV90 @ SY819 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(548,plain,
! [SV12: $o,SV95: $i] :
( ( ( in @ SV95 @ ( prop2set @ SV12 ) )
= $false )
| ( SV12 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(549,plain,
! [SV96: $i] :
( ( ( in @ SV96 @ ( prop2set @ $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(550,plain,
! [SV97: $i] :
( ( ( in @ SV97 @ ( prop2set @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(551,plain,
! [SV98: $i,SV13: $i] :
( ( ( ! [SY820: $i] :
( ~ ( in @ SY820 @ SV13 )
| ( in @ SY820 @ SV98 ) ) )
= $false )
| ( ( subset @ SV13 @ SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(552,plain,
! [SV99: $i,SV14: $i] :
( ( ( SV14 != SV99 )
= $false )
| ( ( ~ ( in @ SV99 @ ( setadjoin @ SV14 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(553,plain,
! [SV15: $i,SV100: $i,SV153: $i] :
( ( ( ~ ( in @ SV153 @ SV100 ) )
= $true )
| ( ( in @ SV153 @ ( setadjoin @ SV15 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(554,plain,
! [SV101: $i,SV16: $i,SV154: $i] :
( ( ~ ( ~ ( in @ SV154 @ ( setadjoin @ SV16 @ SV101 ) )
| ( SV154 = SV16 )
| ( in @ SV154 @ SV101 ) )
| ~ ( ~ ( ( SV154 = SV16 )
| ( in @ SV154 @ SV101 ) )
| ( in @ SV154 @ ( setadjoin @ SV16 @ SV101 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(555,plain,
! [SV17: $i > $o] :
( ( ( ! [SY620: $i] :
~ ~ ( ~ ( SV17 @ SY620 )
| ~ ! [SY621: $i] :
( ~ ( SV17 @ SY621 )
| ( SY620 = SY621 ) ) ) )
= $true )
| ( ( ~ ! [SY622: $i] :
~ ( SV17 @ SY622 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(556,plain,
! [SV102: $i,SV18: $i] :
( ( ( in @ SV18 @ ( setadjoin @ SV102 @ emptyset ) )
= $false )
| ( ( in @ SV102 @ ( setadjoin @ SV18 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(557,plain,
! [SV103: $i > $o,SV19: $i] :
( ( ( ~ ~ ! [SY823: $i] :
~ ~ ( ~ ( in @ SY823 @ SV19 )
| ~ ( SV103 @ SY823 ) ) )
= $false )
| ( ( ! [SY824: $i] :
( ~ ( in @ SY824 @ SV19 )
| ~ ( SV103 @ SY824 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(558,plain,
! [SV104: $i,SV20: $i] :
( ( ( SV20 = SV104 )
= $false )
| ( ( ( setunion @ SV20 )
= ( setunion @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(559,plain,
! [SV21: $i > $o] :
( ( ( ! [SY628: $i] :
~ ~ ( ~ ( SV21 @ SY628 )
| ~ ! [SY629: $i] :
( ~ ( SV21 @ SY629 )
| ( SY628 = SY629 ) ) ) )
= $true )
| ( ( ~ ! [SY630: $i] :
~ ~ ( ~ ( SV21 @ SY630 )
| ~ ! [SY631: $i] :
( ~ ( SV21 @ SY631 )
| ( SY630 = SY631 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(560,plain,
! [SV155: $i,SV105: $i,SV22: $i] :
( ( ( ~ ( subset @ SV22 @ SV105 ) )
= $true )
| ( ( ~ ~ ( in @ SV155 @ SV105 )
| ~ ( in @ SV155 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(561,plain,
! [SV23: $i] :
( ( ( ~ ( in @ ( sK3_SY634 @ SV23 ) @ SV23 ) )
= $false )
| ( ( SV23 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[476]) ).
thf(562,plain,
! [SV106: $i > $o,SV24: $i] :
( ( ( ~ ! [SY826: $i] :
~ ~ ( ~ ( in @ SY826 @ SV24 )
| ~ ~ ( SV106 @ SY826 ) ) )
= $false )
| ( ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ SV24 )
| ( SV106 @ SY827 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(563,plain,
! [SV156: $i,SV107: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV107 ) )
= $true )
| ( ( ~ ( in @ SV156 @ SV25 )
| ( in @ SV156 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(564,plain,
! [SV26: $i] :
( ( ( SV26 = emptyset )
= $true )
| ( ( ~ ! [SY640: $i] :
~ ~ ( ~ ( in @ SY640 @ SV26 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(565,plain,
! [SV27: $i,SV108: $i] :
( ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false )
| ( ( ! [SY829: $o] :
( ~ ! [SY830: $i] :
( ~ ( in @ SV108 @ SY830 )
| ~ ( in @ SY830 @ SV27 )
| SY829 )
| SY829 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(566,plain,
! [SV109: $i,SV28: $i] :
( ( ( SV28 = SV109 )
= $false )
| ( ( subset @ SV28 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(567,plain,
! [SV29: $i,SV157: $i,SV110: $i] :
( ( ( ~ ( in @ SV110 @ SV157 ) )
= $true )
| ( ( ~ ( in @ SV157 @ SV29 )
| ( in @ SV110 @ ( setunion @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(568,plain,
! [SV111: $i,SV30: $i] :
( ( ( ! [SY832: $i] :
~ ( ~ ( ~ ( in @ SY832 @ SV30 )
| ( in @ SY832 @ SV111 ) )
| ~ ( ~ ( in @ SY832 @ SV111 )
| ( in @ SY832 @ SV30 ) ) ) )
= $false )
| ( ( SV30 = SV111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(569,plain,
! [SV112: $i,SV31: $i] :
( ( ( ~ ( subset @ SV31 @ SV112 ) )
= $false )
| ( ( SV31 != SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(570,plain,
! [SV32: $i > $o] :
( ( ( ! [SY650: $i] :
~ ( SV32 @ SY650 ) )
= $true )
| ( ( ~ ! [SY651: $i,SY652: $i] :
( ~ ( SV32 @ SY651 )
| ~ ( SV32 @ SY652 )
| ( SY651 = SY652 ) )
| ~ ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[485]) ).
thf(571,plain,
! [SV113: $i,SV33: $i,SV158: $i] :
( ( ( ~ ( in @ SV158 @ ( setadjoin @ SV33 @ ( setadjoin @ SV113 @ emptyset ) ) ) )
= $true )
| ( ( ( SV158 = SV33 )
| ( SV158 = SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(572,plain,
! [SV159: $i,SV114: $i,SV34: $i] :
( ( ( ~ ( subset @ SV34 @ SV114 ) )
= $true )
| ( ( ~ ( subset @ SV114 @ SV159 )
| ( subset @ SV34 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(573,plain,
! [SV160: $i,SV35: $i,SV115: $i] :
( ( ( ~ ( in @ SV115 @ ( powerset @ SV35 ) ) )
= $true )
| ( ( ~ ( in @ SV160 @ SV115 )
| ( in @ SV160 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(574,plain,
! [SV116: $i > $o,SV36: $i,SV161: $i] :
( ( ( ~ ( in @ SV161 @ SV36 ) )
= $true )
| ( ( ~ ( SV116 @ SV161 )
| ( ( dsetconstr @ SV36
@ ^ [SY837: $i] : ( SV116 @ SY837 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(575,plain,
! [SV37: $i,SV117: $i] :
( ( ~ ( ~ ( in @ SV117 @ ( powerset @ SV37 ) )
| ! [SY838: $i] :
( ~ ( in @ SY838 @ SV117 )
| ( in @ SY838 @ SV37 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(576,plain,
! [SV37: $i,SV117: $i] :
( ( ~ ( ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ SV117 )
| ( in @ SY839 @ SV37 ) )
| ( in @ SV117 @ ( powerset @ SV37 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(577,plain,
! [SV118: $i,SV38: $i,SV162: $i] :
( ( ( ~ ( in @ SV162 @ SV38 ) )
= $true )
| ( ( ~ ~ ( in @ SV162 @ SV118 )
| ( SV38 != SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(578,plain,
! [SV119: $i > $o,SV39: $i] :
( ( ( ~ ! [SY841: $i] :
( ~ ( in @ SY841 @ SV39 )
| ( SV119 @ SY841 ) ) )
= $false )
| ( ( ~ ! [SY842: $i] :
~ ~ ( ~ ( in @ SY842 @ SV39 )
| ~ ~ ( SV119 @ SY842 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(579,plain,
! [SV40: $i > $o] :
( ( ( ! [SY672: $i] :
~ ~ ( ~ ( SV40 @ SY672 )
| ~ ! [SY673: $i] :
( ~ ( SV40 @ SY673 )
| ( SY672 = SY673 ) ) ) )
= $true )
| ( ( ! [SY674: $i,SY675: $i] :
( ~ ( SV40 @ SY674 )
| ~ ( SV40 @ SY675 )
| ( SY674 = SY675 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[493]) ).
thf(580,plain,
! [SV120: $i,SV41: $i] :
( ( ( ! [SY843: $i] :
( ~ ( in @ SY843 @ SV41 )
| ( in @ SY843 @ SV120 ) ) )
= $false )
| ( ( subset @ SV41 @ SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(581,plain,
! [SV42: $i,SV121: $i] :
( ( ( subset @ SV121 @ SV42 )
= $false )
| ( ( in @ SV121 @ ( powerset @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(582,plain,
! [SV43: $i > $o] :
( ( ( ! [SY679: $i] :
~ ~ ( ~ ( SV43 @ SY679 )
| ~ ! [SY680: $i] :
( ~ ( SV43 @ SY680 )
| ( SY679 = SY680 ) ) ) )
= $true )
| ( ( ~ ! [SY681: $i] :
~ ~ ( ~ ( SV43 @ SY681 )
| ~ ! [SY682: $i] :
( ~ ( SV43 @ SY682 )
| ( SY681 = SY682 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[496]) ).
thf(583,plain,
! [SV122: $i,SV44: $i,SV163: $i] :
( ( ( ~ ( in @ SV163 @ SV44 ) )
= $true )
| ( ( ~ ~ ( in @ SV163 @ SV122 )
| ~ ( subset @ SV44 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(584,plain,
! [SV45: $i > $i > $o,SV123: $i] :
( ( ( ! [SY845: $i] :
( ~ ( in @ SY845 @ SV123 )
| ~ ! [SY687: $i] :
~ ~ ( ~ ( SV45 @ SY845 @ SY687 )
| ~ ! [SY688: $i] :
( ~ ( SV45 @ SY845 @ SY688 )
| ( SY687 = SY688 ) ) ) ) )
= $false )
| ( ( ~ ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(585,plain,
! [SV124: $i,SV46: $i] :
( ( ( SV46 = SV124 )
= $false )
| ( ( ! [SY852: $i,SY853: $i] :
( ( SY852 != SY853 )
| ~ ( in @ SY852 @ SV46 )
| ( in @ SY853 @ SV124 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(586,plain,
! [SV47: $i] :
( ( ( ! [SY696: $i] :
~ ( in @ SY696 @ SV47 ) )
= $true )
| ( ( SV47 != emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(587,plain,
! [SV125: $i,SV48: $i] :
( ( ( SV48 = SV125 )
= $false )
| ( ( ! [SY854: $i,SY855: $i] :
( ( SY854 != SY855 )
| ~ ( ~ ( ~ ( in @ SY854 @ SV48 )
| ( in @ SY855 @ SV125 ) )
| ~ ( ~ ( in @ SY855 @ SV125 )
| ( in @ SY854 @ SV48 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(588,plain,
! [SV126: $i > $o,SV49: $i,SV164: $i] :
( ( ( ~ ( in @ SV164
@ ( dsetconstr @ SV49
@ ^ [SY857: $i] : ( SV126 @ SY857 ) ) ) )
= $true )
| ( ( SV126 @ SV164 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(589,plain,
! [SV50: $i,SV127: $i] :
( ( ( in @ SV127 @ SV50 )
= $false )
| ( ( in @ SV127 @ ( powerset @ ( setunion @ SV50 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(590,plain,
! [SV128: $i,SV53: $i] :
( ( ( SV53 = SV128 )
= $false )
| ( ( ! [SY858: $i > $o,SY859: $i > $o] :
( ~ ! [SY860: $i] :
( ~ ( in @ SY860 @ SV53 )
| ! [SY861: $i] :
( ~ ( in @ SY861 @ SV128 )
| ( SY860 != SY861 )
| ~ ( ~ ( ~ ( SY858 @ SY860 )
| ( SY859 @ SY861 ) )
| ~ ( ~ ( SY859 @ SY861 )
| ( SY858 @ SY860 ) ) ) ) )
| ( ( dsetconstr @ SV53
@ ^ [SX4: $i] : ( SY858 @ SX4 ) )
= ( dsetconstr @ SV128
@ ^ [SX4: $i] : ( SY859 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(591,plain,
! [SV129: $i,SV54: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) ) )
= $true )
| ( ( ! [SY910: $o] :
( ~ ( ( SV165 != SV54 )
| SY910 )
| ~ ( ~ ( in @ SV165 @ SV129 )
| SY910 )
| SY910 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(592,plain,
! [SV55: $i] :
( ( ( ! [SY714: $i] :
~ ( in @ SY714 @ SV55 ) )
= $true )
| ( ( ~ ! [SY715: $i] :
~ ~ ( ~ ( in @ SY715 @ SV55 )
| ~ ~ ~ ! [SY716: $i] :
~ ~ ( ~ ( in @ SY716 @ SY715 )
| ~ ( in @ SY716 @ SV55 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(593,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ! [SY866: $i,SY867: $i] :
( ( SY866 != SY867 )
| ~ ( ~ ( ~ ( SV56 @ SY866 )
| ( SV130 @ SY867 ) )
| ~ ( ~ ( SV130 @ SY867 )
| ( SV56 @ SY866 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(594,plain,
! [SV131: $i,SV57: $i] :
( ( ( SV57 = SV131 )
= $false )
| ( ( in @ SV57 @ ( setadjoin @ SV131 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(595,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ! [SY874: $i,SY875: $i] :
( ( SY874 != SY875 )
| ~ ( ~ ( ~ ( SV58 @ SY874 )
| ( SV132 @ SY875 ) )
| ~ ( ~ ( SV132 @ SY875 )
| ( SV58 @ SY874 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(596,plain,
! [SV133: $i > $o,SV59: $i,SV166: $i] :
( ( ( ~ ( in @ SV166 @ SV59 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV166
@ ( dsetconstr @ SV59
@ ^ [SY885: $i] : ( SV133 @ SY885 ) ) )
| ( SV133 @ SV166 ) )
| ~ ( ~ ( SV133 @ SV166 )
| ( in @ SV166
@ ( dsetconstr @ SV59
@ ^ [SY886: $i] : ( SV133 @ SY886 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(597,plain,
! [SV60: $i] :
( ( ( ~ ( in @ ( sK4_SY742 @ SV60 ) @ SV60 ) )
= $false )
| ( ( SV60 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[515]) ).
thf(598,plain,
! [SV61: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY913: $i] :
( ~ ( in @ SY913 @ ( sK2_SY743 @ SV61 ) )
| ! [SY745: $i] :
( ~ ( in @ SY745 @ SY913 )
| ( in @ SY745 @ SV61 ) ) )
| ~ ! [SY915: $i,SY916: $i] :
( ~ ~ ( ~ ( in @ SY915 @ SV61 )
| ~ ( in @ SY916 @ SV61 ) )
| ~ ! [SY917: $i] :
( ~ ( in @ SY917 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SY915 @ SY917 )
| ( in @ SY916 @ SY917 ) )
| ~ ( ~ ( in @ SY916 @ SY917 )
| ( in @ SY915 @ SY917 ) ) ) )
| ( SY915 = SY916 ) ) )
| ~ ! [SY918: $i,SY919: $i] :
( ~ ~ ( ~ ( in @ SY918 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY919 @ ( sK2_SY743 @ SV61 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY918 )
| ( in @ SX4 @ SY919 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY919 )
| ( in @ SX4 @ SY918 ) ) ) )
| ~ ! [SY922: $i] :
( ~ ~ ( ~ ! [SY754: $i] :
( ~ ( in @ SY754 @ SY922 )
| ( in @ SY754 @ SV61 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY922 ) )
| ~ ! [SY925: $i] :
~ ~ ! [SY926: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY925 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY926 @ SY922 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY925 )
| ~ ( in @ SX5 @ SY922 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY925 ) )
| ( in @ SY926 @ SY928 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[516]) ).
thf(599,plain,
! [SV63: $i > $o,SV134: $i] :
( ( ( in @ SV134 @ emptyset )
= $false )
| ( ( SV63 @ SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(600,plain,
! [SV135: $i,SV64: $i,SV167: $i] :
( ( ( ~ ( in @ SV167 @ ( setadjoin @ SV64 @ SV135 ) ) )
= $true )
| ( ( ( SV167 = SV64 )
| ( in @ SV167 @ SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(601,plain,
! [SV136: $i,SV66: $i] :
( ( ( in @ SV66 @ ( setadjoin @ SV136 @ emptyset ) )
= $false )
| ( ( SV66 = SV136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(602,plain,
! [SV137: $i,SV67: $i] :
( ( ( SV67 = SV137 )
= $false )
| ( ( subset @ SV137 @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(603,plain,
! [SV138: $i,SV68: $i] :
( ( ( ! [SY888: $i] :
( ~ ( in @ SY888 @ SV68 )
| ( in @ SY888 @ SV138 ) ) )
= $false )
| ( ( ~ ! [SY889: $i] :
( ~ ( in @ SY889 @ SV138 )
| ( in @ SY889 @ SV68 ) )
| ( SV68 = SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(604,plain,
! [SV139: $i > $o,SV69: $i] :
( ( ( ~ ! [SY890: $i] :
~ ~ ( ~ ( in @ SY890 @ SV69 )
| ~ ( SV139 @ SY890 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV69
@ ^ [SY891: $i] : ( SV139 @ SY891 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(605,plain,
! [SV140: $i,SV70: $i] :
( ( ( SV70 = SV140 )
= $false )
| ( ( ! [SY892: $i,SY893: $i] :
( ( SY892 != SY893 )
| ( ( setadjoin @ SV70 @ SY892 )
= ( setadjoin @ SV140 @ SY893 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(606,plain,
! [SV71: $i] :
( ( ( ~ ( in @ emptyset @ SV71 )
| ~ ! [SY775: $i] :
( ~ ~ ( ~ ( in @ SY775 @ omega )
| ~ ( in @ SY775 @ SV71 ) )
| ( in @ ( setadjoin @ SY775 @ SY775 ) @ SV71 ) ) )
= $true )
| ( ( ! [SY776: $i] :
( ~ ( in @ SY776 @ omega )
| ( in @ SY776 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(607,plain,
! [SV72: $i,SV171: $o] :
( ( SV171 = $true )
| ( ( in @ SV72 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[529]) ).
thf(608,plain,
! [SV72: $i] :
( ( $true = $true )
| ( ( in @ SV72 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[529]) ).
thf(609,plain,
! [SV72: $i] :
( ( $false = $true )
| ( ( in @ SV72 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[529]) ).
thf(610,plain,
! [SV141: $i > $o,SV73: $i] :
( ( ( ~ ~ ! [SY894: $i] :
~ ~ ( ~ ( in @ SY894 @ SV73 )
| ~ ( SV141 @ SY894 ) ) )
= $false )
| ( ( ! [SY895: $i] :
( ~ ( in @ SY895 @ SV73 )
| ~ ( SV141 @ SY895 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(611,plain,
! [SV142: $i,SV168: $i,SV74: $i] :
( ( ( ~ ( subset @ SV74 @ SV168 ) )
= $true )
| ( ( subset @ SV74 @ ( setadjoin @ SV142 @ SV168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[531]) ).
thf(612,plain,
! [SV75: $i,SV143: $i] :
( ( ( in @ SV143 @ ( powerset @ SV75 ) )
= $false )
| ( ( subset @ SV143 @ SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(613,plain,
! [SV144: $i > $o,SV76: $i,SV169: $i] :
( ( ( ~ ( in @ SV169 @ SV76 ) )
= $true )
| ( ( ~ ( SV144 @ SV169 )
| ( in @ SV169
@ ( dsetconstr @ SV76
@ ^ [SY898: $i] : ( SV144 @ SY898 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[533]) ).
thf(614,plain,
! [SV77: $i > $o] :
( ( ( ! [SY787: $i] :
~ ! [SY788: $i] :
~ ( ~ ( ~ ( SV77 @ SY788 )
| ( SY788 = SY787 ) )
| ~ ( ( SY788 != SY787 )
| ( SV77 @ SY788 ) ) ) )
= $true )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(615,plain,
! [SV78: $i,SV145: $i] :
( ( ( ! [SY899: $i] :
( ~ ( in @ SY899 @ SV145 )
| ( in @ SY899 @ SV78 ) ) )
= $false )
| ( ( in @ SV145 @ ( powerset @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(616,plain,
! [SV146: $i > $o,SV79: $i] :
( ( ( ! [SY900: $i] :
( ~ ( in @ SY900 @ SV79 )
| ~ ( SV146 @ SY900 ) ) )
= $false )
| ( ( ~ ~ ! [SY901: $i] :
~ ~ ( ~ ( in @ SY901 @ SV79 )
| ~ ( SV146 @ SY901 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(617,plain,
! [SV147: $i,SV80: $i] :
( ( ( SV80 = SV147 )
= $false )
| ( ( ( powerset @ SV80 )
= ( powerset @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(618,plain,
! [SV81: $i > $o] :
( ( ( ! [SY797: $i] :
~ ~ ( ~ ( SV81 @ SY797 )
| ~ ! [SY798: $i] :
( ~ ( SV81 @ SY798 )
| ( SY797 = SY798 ) ) ) )
= $true )
| ( ( ~ ! [SY799: $i] :
~ ! [SY800: $i] :
~ ( ~ ( ~ ( SV81 @ SY800 )
| ( SY800 = SY799 ) )
| ~ ( ( SY800 != SY799 )
| ( SV81 @ SY800 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(619,plain,
! [SV82: $i] :
( ( ( SV82 = emptyset )
= $true )
| ( ( ~ ! [SY801: $i] :
~ ( in @ SY801 @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(620,plain,
! [SV148: $i > $o,SV83: $i] :
( ( ( ~ ! [SY902: $i] :
( ~ ( in @ SY902 @ SV83 )
| ( SV148 @ SY902 ) ) )
= $false )
| ( ( ~ ! [SY903: $i] :
~ ~ ( ~ ( in @ SY903 @ SV83 )
| ~ ~ ( SV148 @ SY903 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(621,plain,
! [SV84: $i > $o] :
( ( ( ! [SY805: $i] :
~ ~ ( ~ ( SV84 @ SY805 )
| ~ ! [SY806: $i] :
( ~ ( SV84 @ SY806 )
| ( SY805 = SY806 ) ) ) )
= $true )
| ( ( ! [SY807: $i,SY808: $i] :
( ~ ( SV84 @ SY807 )
| ~ ( SV84 @ SY808 )
| ( SY807 = SY808 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(622,plain,
! [SV149: $i > $o,SV85: $i,SV170: $i] :
( ( ( ~ ( in @ SV170
@ ( dsetconstr @ SV85
@ ^ [SY905: $i] : ( SV149 @ SY905 ) ) ) )
= $true )
| ( ( in @ SV170 @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(623,plain,
! [SV87: $i,SV150: $i] :
( ( ~ ( ~ ( in @ SV150 @ ( setunion @ SV87 ) )
| ~ ! [SY906: $i] :
~ ~ ( ~ ( in @ SV150 @ SY906 )
| ~ ( in @ SY906 @ SV87 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[544]) ).
thf(624,plain,
! [SV87: $i,SV150: $i] :
( ( ~ ( ~ ~ ! [SY907: $i] :
~ ~ ( ~ ( in @ SV150 @ SY907 )
| ~ ( in @ SY907 @ SV87 ) )
| ( in @ SV150 @ ( setunion @ SV87 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[544]) ).
thf(625,plain,
! [SV151: $i,SV88: $i] :
( ( ( subset @ SV88 @ SV151 )
= $false )
| ( ( ~ ( subset @ SV151 @ SV88 )
| ( SV88 = SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(626,plain,
! [SV152: $i,SV89: $i] :
( ( ( subset @ SV89 @ SV152 )
= $false )
| ( ( in @ SV89 @ ( powerset @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(627,plain,
! [SV90: $i > $o] :
( ( ( ! [SY817: $i] :
~ ~ ( ~ ( SV90 @ SY817 )
| ~ ! [SY818: $i] :
( ~ ( SV90 @ SY818 )
| ( SY817 = SY818 ) ) ) )
= $true )
| ( ( SV90
@ ( descr
@ ^ [SY819: $i] : ( SV90 @ SY819 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(628,plain,
! [SV13: $i,SV98: $i] :
( ( ( ~ ( in @ ( sK5_SY820 @ SV98 @ SV13 ) @ SV13 )
| ( in @ ( sK5_SY820 @ SV98 @ SV13 ) @ SV98 ) )
= $false )
| ( ( subset @ SV13 @ SV98 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[551]) ).
thf(629,plain,
! [SV99: $i,SV14: $i] :
( ( ( SV14 = SV99 )
= $true )
| ( ( ~ ( in @ SV99 @ ( setadjoin @ SV14 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(630,plain,
! [SV15: $i,SV100: $i,SV153: $i] :
( ( ( in @ SV153 @ SV100 )
= $false )
| ( ( in @ SV153 @ ( setadjoin @ SV15 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(631,plain,
! [SV101: $i,SV16: $i,SV154: $i] :
( ( ~ ( ~ ( in @ SV154 @ ( setadjoin @ SV16 @ SV101 ) )
| ( SV154 = SV16 )
| ( in @ SV154 @ SV101 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[554]) ).
thf(632,plain,
! [SV101: $i,SV16: $i,SV154: $i] :
( ( ~ ( ~ ( ( SV154 = SV16 )
| ( in @ SV154 @ SV101 ) )
| ( in @ SV154 @ ( setadjoin @ SV16 @ SV101 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[554]) ).
thf(633,plain,
! [SV172: $i,SV17: $i > $o] :
( ( ( ~ ~ ( ~ ( SV17 @ SV172 )
| ~ ! [SY932: $i] :
( ~ ( SV17 @ SY932 )
| ( SV172 = SY932 ) ) ) )
= $true )
| ( ( ~ ! [SY622: $i] :
~ ( SV17 @ SY622 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(634,plain,
! [SV103: $i > $o,SV19: $i] :
( ( ( ~ ! [SY823: $i] :
~ ~ ( ~ ( in @ SY823 @ SV19 )
| ~ ( SV103 @ SY823 ) ) )
= $true )
| ( ( ! [SY824: $i] :
( ~ ( in @ SY824 @ SV19 )
| ~ ( SV103 @ SY824 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(635,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ~ ~ ( ~ ( SV21 @ SV173 )
| ~ ! [SY933: $i] :
( ~ ( SV21 @ SY933 )
| ( SV173 = SY933 ) ) ) )
= $true )
| ( ( ~ ! [SY630: $i] :
~ ~ ( ~ ( SV21 @ SY630 )
| ~ ! [SY631: $i] :
( ~ ( SV21 @ SY631 )
| ( SY630 = SY631 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(636,plain,
! [SV155: $i,SV105: $i,SV22: $i] :
( ( ( subset @ SV22 @ SV105 )
= $false )
| ( ( ~ ~ ( in @ SV155 @ SV105 )
| ~ ( in @ SV155 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(637,plain,
! [SV23: $i] :
( ( ( in @ ( sK3_SY634 @ SV23 ) @ SV23 )
= $true )
| ( ( SV23 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(638,plain,
! [SV106: $i > $o,SV24: $i] :
( ( ( ! [SY826: $i] :
~ ~ ( ~ ( in @ SY826 @ SV24 )
| ~ ~ ( SV106 @ SY826 ) ) )
= $true )
| ( ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ SV24 )
| ( SV106 @ SY827 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(639,plain,
! [SV156: $i,SV107: $i,SV25: $i] :
( ( ( subset @ SV25 @ SV107 )
= $false )
| ( ( ~ ( in @ SV156 @ SV25 )
| ( in @ SV156 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(640,plain,
! [SV26: $i] :
( ( ( ! [SY640: $i] :
~ ~ ( ~ ( in @ SY640 @ SV26 )
| ~ $true ) )
= $false )
| ( ( SV26 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(641,plain,
! [SV174: $o,SV27: $i,SV108: $i] :
( ( ( ~ ! [SY934: $i] :
( ~ ( in @ SV108 @ SY934 )
| ~ ( in @ SY934 @ SV27 )
| SV174 )
| SV174 )
= $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[565]) ).
thf(642,plain,
! [SV27: $i,SV108: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV108 @ SX0 )
| ~ ( in @ SX0 @ SV27 )
| $true )
| $true )
= $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[565]) ).
thf(643,plain,
! [SV27: $i,SV108: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV108 @ SX0 )
| ~ ( in @ SX0 @ SV27 )
| $false )
| $false )
= $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[565]) ).
thf(644,plain,
! [SV29: $i,SV157: $i,SV110: $i] :
( ( ( in @ SV110 @ SV157 )
= $false )
| ( ( ~ ( in @ SV157 @ SV29 )
| ( in @ SV110 @ ( setunion @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(645,plain,
! [SV30: $i,SV111: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 )
| ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 ) )
| ~ ( ~ ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 )
| ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 ) ) ) )
= $false )
| ( ( SV30 = SV111 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[568]) ).
thf(646,plain,
! [SV112: $i,SV31: $i] :
( ( ( subset @ SV31 @ SV112 )
= $true )
| ( ( SV31 != SV112 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[569]) ).
thf(647,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ( SV32 @ SV175 ) )
= $true )
| ( ( ~ ! [SY651: $i,SY652: $i] :
( ~ ( SV32 @ SY651 )
| ~ ( SV32 @ SY652 )
| ( SY651 = SY652 ) )
| ~ ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(648,plain,
! [SV113: $i,SV33: $i,SV158: $i] :
( ( ( in @ SV158 @ ( setadjoin @ SV33 @ ( setadjoin @ SV113 @ emptyset ) ) )
= $false )
| ( ( ( SV158 = SV33 )
| ( SV158 = SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(649,plain,
! [SV159: $i,SV114: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV114 )
= $false )
| ( ( ~ ( subset @ SV114 @ SV159 )
| ( subset @ SV34 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(650,plain,
! [SV160: $i,SV35: $i,SV115: $i] :
( ( ( in @ SV115 @ ( powerset @ SV35 ) )
= $false )
| ( ( ~ ( in @ SV160 @ SV115 )
| ( in @ SV160 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(651,plain,
! [SV116: $i > $o,SV36: $i,SV161: $i] :
( ( ( in @ SV161 @ SV36 )
= $false )
| ( ( ~ ( SV116 @ SV161 )
| ( ( dsetconstr @ SV36
@ ^ [SY837: $i] : ( SV116 @ SY837 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(652,plain,
! [SV37: $i,SV117: $i] :
( ( ~ ( in @ SV117 @ ( powerset @ SV37 ) )
| ! [SY838: $i] :
( ~ ( in @ SY838 @ SV117 )
| ( in @ SY838 @ SV37 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(653,plain,
! [SV37: $i,SV117: $i] :
( ( ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ SV117 )
| ( in @ SY839 @ SV37 ) )
| ( in @ SV117 @ ( powerset @ SV37 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[576]) ).
thf(654,plain,
! [SV118: $i,SV38: $i,SV162: $i] :
( ( ( in @ SV162 @ SV38 )
= $false )
| ( ( ~ ~ ( in @ SV162 @ SV118 )
| ( SV38 != SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(655,plain,
! [SV119: $i > $o,SV39: $i] :
( ( ( ! [SY841: $i] :
( ~ ( in @ SY841 @ SV39 )
| ( SV119 @ SY841 ) ) )
= $true )
| ( ( ~ ! [SY842: $i] :
~ ~ ( ~ ( in @ SY842 @ SV39 )
| ~ ~ ( SV119 @ SY842 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(656,plain,
! [SV176: $i,SV40: $i > $o] :
( ( ( ~ ~ ( ~ ( SV40 @ SV176 )
| ~ ! [SY935: $i] :
( ~ ( SV40 @ SY935 )
| ( SV176 = SY935 ) ) ) )
= $true )
| ( ( ! [SY674: $i,SY675: $i] :
( ~ ( SV40 @ SY674 )
| ~ ( SV40 @ SY675 )
| ( SY674 = SY675 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(657,plain,
! [SV41: $i,SV120: $i] :
( ( ( ~ ( in @ ( sK7_SY843 @ SV120 @ SV41 ) @ SV41 )
| ( in @ ( sK7_SY843 @ SV120 @ SV41 ) @ SV120 ) )
= $false )
| ( ( subset @ SV41 @ SV120 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[580]) ).
thf(658,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ~ ~ ( ~ ( SV43 @ SV177 )
| ~ ! [SY936: $i] :
( ~ ( SV43 @ SY936 )
| ( SV177 = SY936 ) ) ) )
= $true )
| ( ( ~ ! [SY681: $i] :
~ ~ ( ~ ( SV43 @ SY681 )
| ~ ! [SY682: $i] :
( ~ ( SV43 @ SY682 )
| ( SY681 = SY682 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(659,plain,
! [SV122: $i,SV44: $i,SV163: $i] :
( ( ( in @ SV163 @ SV44 )
= $false )
| ( ( ~ ~ ( in @ SV163 @ SV122 )
| ~ ( subset @ SV44 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(660,plain,
! [SV123: $i,SV45: $i > $i > $o] :
( ( ( ~ ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
| ~ ! [SY937: $i] :
~ ~ ( ~ ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SY937 )
| ~ ! [SY938: $i] :
( ~ ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SY938 )
| ( SY937 = SY938 ) ) ) )
= $false )
| ( ( ~ ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[584]) ).
thf(661,plain,
! [SV124: $i,SV46: $i,SV178: $i] :
( ( ( ! [SY939: $i] :
( ( SV178 != SY939 )
| ~ ( in @ SV178 @ SV46 )
| ( in @ SY939 @ SV124 ) ) )
= $true )
| ( ( SV46 = SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(662,plain,
! [SV47: $i,SV179: $i] :
( ( ( ~ ( in @ SV179 @ SV47 ) )
= $true )
| ( ( SV47 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(663,plain,
! [SV125: $i,SV48: $i,SV180: $i] :
( ( ( ! [SY940: $i] :
( ( SV180 != SY940 )
| ~ ( ~ ( ~ ( in @ SV180 @ SV48 )
| ( in @ SY940 @ SV125 ) )
| ~ ( ~ ( in @ SY940 @ SV125 )
| ( in @ SV180 @ SV48 ) ) ) ) )
= $true )
| ( ( SV48 = SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(664,plain,
! [SV126: $i > $o,SV49: $i,SV164: $i] :
( ( ( in @ SV164
@ ( dsetconstr @ SV49
@ ^ [SY857: $i] : ( SV126 @ SY857 ) ) )
= $false )
| ( ( SV126 @ SV164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(665,plain,
! [SV181: $i > $o,SV128: $i,SV53: $i] :
( ( ( ! [SY941: $i > $o] :
( ~ ! [SY942: $i] :
( ~ ( in @ SY942 @ SV53 )
| ! [SY943: $i] :
( ~ ( in @ SY943 @ SV128 )
| ( SY942 != SY943 )
| ~ ( ~ ( ~ ( SV181 @ SY942 )
| ( SY941 @ SY943 ) )
| ~ ( ~ ( SY941 @ SY943 )
| ( SV181 @ SY942 ) ) ) ) )
| ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SX4: $i] : ( SY941 @ SX4 ) ) ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(666,plain,
! [SV129: $i,SV54: $i,SV165: $i] :
( ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false )
| ( ( ! [SY910: $o] :
( ~ ( ( SV165 != SV54 )
| SY910 )
| ~ ( ~ ( in @ SV165 @ SV129 )
| SY910 )
| SY910 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(667,plain,
! [SV55: $i,SV182: $i] :
( ( ( ~ ( in @ SV182 @ SV55 ) )
= $true )
| ( ( ~ ! [SY715: $i] :
~ ~ ( ~ ( in @ SY715 @ SV55 )
| ~ ~ ~ ! [SY716: $i] :
~ ~ ( ~ ( in @ SY716 @ SY715 )
| ~ ( in @ SY716 @ SV55 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(668,plain,
! [SV56: $i > $o,SV130: $i > $o] :
( ( ( ! [SY946: $i] :
( ( ( sK9_SY866 @ SV130 @ SV56 )
!= SY946 )
| ~ ( ~ ( ~ ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
| ( SV130 @ SY946 ) )
| ~ ( ~ ( SV130 @ SY946 )
| ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[593]) ).
thf(669,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ! [SY947: $i] :
( ( ( sK10_SY874 @ SV132 @ SV58 )
!= SY947 )
| ~ ( ~ ( ~ ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
| ( SV132 @ SY947 ) )
| ~ ( ~ ( SV132 @ SY947 )
| ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[595]) ).
thf(670,plain,
! [SV133: $i > $o,SV59: $i,SV166: $i] :
( ( ( in @ SV166 @ SV59 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV166
@ ( dsetconstr @ SV59
@ ^ [SY885: $i] : ( SV133 @ SY885 ) ) )
| ( SV133 @ SV166 ) )
| ~ ( ~ ( SV133 @ SV166 )
| ( in @ SV166
@ ( dsetconstr @ SV59
@ ^ [SY886: $i] : ( SV133 @ SY886 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(671,plain,
! [SV60: $i] :
( ( ( in @ ( sK4_SY742 @ SV60 ) @ SV60 )
= $true )
| ( ( SV60 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[597]) ).
thf(672,plain,
! [SV61: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY913: $i] :
( ~ ( in @ SY913 @ ( sK2_SY743 @ SV61 ) )
| ! [SY745: $i] :
( ~ ( in @ SY745 @ SY913 )
| ( in @ SY745 @ SV61 ) ) )
| ~ ! [SY915: $i,SY916: $i] :
( ~ ~ ( ~ ( in @ SY915 @ SV61 )
| ~ ( in @ SY916 @ SV61 ) )
| ~ ! [SY917: $i] :
( ~ ( in @ SY917 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SY915 @ SY917 )
| ( in @ SY916 @ SY917 ) )
| ~ ( ~ ( in @ SY916 @ SY917 )
| ( in @ SY915 @ SY917 ) ) ) )
| ( SY915 = SY916 ) ) )
| ~ ! [SY918: $i,SY919: $i] :
( ~ ~ ( ~ ( in @ SY918 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY919 @ ( sK2_SY743 @ SV61 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY918 )
| ( in @ SX4 @ SY919 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY919 )
| ( in @ SX4 @ SY918 ) ) ) )
| ~ ! [SY922: $i] :
( ~ ~ ( ~ ! [SY754: $i] :
( ~ ( in @ SY754 @ SY922 )
| ( in @ SY754 @ SV61 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY922 ) )
| ~ ! [SY925: $i] :
~ ~ ! [SY926: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY925 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY926 @ SY922 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY925 )
| ~ ( in @ SX5 @ SY922 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY925 ) )
| ( in @ SY926 @ SY928 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(673,plain,
! [SV135: $i,SV64: $i,SV167: $i] :
( ( ( in @ SV167 @ ( setadjoin @ SV64 @ SV135 ) )
= $false )
| ( ( ( SV167 = SV64 )
| ( in @ SV167 @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(674,plain,
! [SV68: $i,SV138: $i] :
( ( ( ~ ( in @ ( sK11_SY888 @ SV138 @ SV68 ) @ SV68 )
| ( in @ ( sK11_SY888 @ SV138 @ SV68 ) @ SV138 ) )
= $false )
| ( ( ~ ! [SY889: $i] :
( ~ ( in @ SY889 @ SV138 )
| ( in @ SY889 @ SV68 ) )
| ( SV68 = SV138 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[603]) ).
thf(675,plain,
! [SV139: $i > $o,SV69: $i] :
( ( ( ! [SY890: $i] :
~ ~ ( ~ ( in @ SY890 @ SV69 )
| ~ ( SV139 @ SY890 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV69
@ ^ [SY891: $i] : ( SV139 @ SY891 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[604]) ).
thf(676,plain,
! [SV140: $i,SV70: $i,SV183: $i] :
( ( ( ! [SY948: $i] :
( ( SV183 != SY948 )
| ( ( setadjoin @ SV70 @ SV183 )
= ( setadjoin @ SV140 @ SY948 ) ) ) )
= $true )
| ( ( SV70 = SV140 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(677,plain,
! [SV71: $i] :
( ( ( ~ ( in @ emptyset @ SV71 ) )
= $true )
| ( ( ~ ! [SY775: $i] :
( ~ ~ ( ~ ( in @ SY775 @ omega )
| ~ ( in @ SY775 @ SV71 ) )
| ( in @ ( setadjoin @ SY775 @ SY775 ) @ SV71 ) ) )
= $true )
| ( ( ! [SY776: $i] :
( ~ ( in @ SY776 @ omega )
| ( in @ SY776 @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(678,plain,
! [SV141: $i > $o,SV73: $i] :
( ( ( ~ ! [SY894: $i] :
~ ~ ( ~ ( in @ SY894 @ SV73 )
| ~ ( SV141 @ SY894 ) ) )
= $true )
| ( ( ! [SY895: $i] :
( ~ ( in @ SY895 @ SV73 )
| ~ ( SV141 @ SY895 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[610]) ).
thf(679,plain,
! [SV142: $i,SV168: $i,SV74: $i] :
( ( ( subset @ SV74 @ SV168 )
= $false )
| ( ( subset @ SV74 @ ( setadjoin @ SV142 @ SV168 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(680,plain,
! [SV144: $i > $o,SV76: $i,SV169: $i] :
( ( ( in @ SV169 @ SV76 )
= $false )
| ( ( ~ ( SV144 @ SV169 )
| ( in @ SV169
@ ( dsetconstr @ SV76
@ ^ [SY898: $i] : ( SV144 @ SY898 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(681,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ! [SY949: $i] :
~ ( ~ ( ~ ( SV77 @ SY949 )
| ( SY949 = SV184 ) )
| ~ ( ( SY949 != SV184 )
| ( SV77 @ SY949 ) ) ) )
= $true )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(682,plain,
! [SV145: $i,SV78: $i] :
( ( ( ~ ( in @ ( sK12_SY899 @ SV78 @ SV145 ) @ SV145 )
| ( in @ ( sK12_SY899 @ SV78 @ SV145 ) @ SV78 ) )
= $false )
| ( ( in @ SV145 @ ( powerset @ SV78 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[615]) ).
thf(683,plain,
! [SV79: $i,SV146: $i > $o] :
( ( ( ~ ( in @ ( sK13_SY900 @ SV146 @ SV79 ) @ SV79 )
| ~ ( SV146 @ ( sK13_SY900 @ SV146 @ SV79 ) ) )
= $false )
| ( ( ~ ~ ! [SY901: $i] :
~ ~ ( ~ ( in @ SY901 @ SV79 )
| ~ ( SV146 @ SY901 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[616]) ).
thf(684,plain,
! [SV185: $i,SV81: $i > $o] :
( ( ( ~ ~ ( ~ ( SV81 @ SV185 )
| ~ ! [SY950: $i] :
( ~ ( SV81 @ SY950 )
| ( SV185 = SY950 ) ) ) )
= $true )
| ( ( ~ ! [SY799: $i] :
~ ! [SY800: $i] :
~ ( ~ ( ~ ( SV81 @ SY800 )
| ( SY800 = SY799 ) )
| ~ ( ( SY800 != SY799 )
| ( SV81 @ SY800 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(685,plain,
! [SV82: $i] :
( ( ( ! [SY801: $i] :
~ ( in @ SY801 @ SV82 ) )
= $false )
| ( ( SV82 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(686,plain,
! [SV148: $i > $o,SV83: $i] :
( ( ( ! [SY902: $i] :
( ~ ( in @ SY902 @ SV83 )
| ( SV148 @ SY902 ) ) )
= $true )
| ( ( ~ ! [SY903: $i] :
~ ~ ( ~ ( in @ SY903 @ SV83 )
| ~ ~ ( SV148 @ SY903 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[620]) ).
thf(687,plain,
! [SV186: $i,SV84: $i > $o] :
( ( ( ~ ~ ( ~ ( SV84 @ SV186 )
| ~ ! [SY951: $i] :
( ~ ( SV84 @ SY951 )
| ( SV186 = SY951 ) ) ) )
= $true )
| ( ( ! [SY807: $i,SY808: $i] :
( ~ ( SV84 @ SY807 )
| ~ ( SV84 @ SY808 )
| ( SY807 = SY808 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(688,plain,
! [SV149: $i > $o,SV85: $i,SV170: $i] :
( ( ( in @ SV170
@ ( dsetconstr @ SV85
@ ^ [SY905: $i] : ( SV149 @ SY905 ) ) )
= $false )
| ( ( in @ SV170 @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(689,plain,
! [SV87: $i,SV150: $i] :
( ( ~ ( in @ SV150 @ ( setunion @ SV87 ) )
| ~ ! [SY906: $i] :
~ ~ ( ~ ( in @ SV150 @ SY906 )
| ~ ( in @ SY906 @ SV87 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[623]) ).
thf(690,plain,
! [SV87: $i,SV150: $i] :
( ( ~ ~ ! [SY907: $i] :
~ ~ ( ~ ( in @ SV150 @ SY907 )
| ~ ( in @ SY907 @ SV87 ) )
| ( in @ SV150 @ ( setunion @ SV87 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[624]) ).
thf(691,plain,
! [SV88: $i,SV151: $i] :
( ( ( ~ ( subset @ SV151 @ SV88 ) )
= $true )
| ( ( SV88 = SV151 )
= $true )
| ( ( subset @ SV88 @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(692,plain,
! [SV187: $i,SV90: $i > $o] :
( ( ( ~ ~ ( ~ ( SV90 @ SV187 )
| ~ ! [SY952: $i] :
( ~ ( SV90 @ SY952 )
| ( SV187 = SY952 ) ) ) )
= $true )
| ( ( SV90
@ ( descr
@ ^ [SY819: $i] : ( SV90 @ SY819 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(693,plain,
! [SV13: $i,SV98: $i] :
( ( ( ~ ( in @ ( sK5_SY820 @ SV98 @ SV13 ) @ SV13 ) )
= $false )
| ( ( subset @ SV13 @ SV98 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[628]) ).
thf(694,plain,
! [SV13: $i,SV98: $i] :
( ( ( in @ ( sK5_SY820 @ SV98 @ SV13 ) @ SV98 )
= $false )
| ( ( subset @ SV13 @ SV98 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[628]) ).
thf(695,plain,
! [SV14: $i,SV99: $i] :
( ( ( in @ SV99 @ ( setadjoin @ SV14 @ emptyset ) )
= $false )
| ( ( SV14 = SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(696,plain,
! [SV101: $i,SV16: $i,SV154: $i] :
( ( ~ ( in @ SV154 @ ( setadjoin @ SV16 @ SV101 ) )
| ( SV154 = SV16 )
| ( in @ SV154 @ SV101 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[631]) ).
thf(697,plain,
! [SV101: $i,SV16: $i,SV154: $i] :
( ( ~ ( ( SV154 = SV16 )
| ( in @ SV154 @ SV101 ) )
| ( in @ SV154 @ ( setadjoin @ SV16 @ SV101 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[632]) ).
thf(698,plain,
! [SV172: $i,SV17: $i > $o] :
( ( ( ~ ( ~ ( SV17 @ SV172 )
| ~ ! [SY932: $i] :
( ~ ( SV17 @ SY932 )
| ( SV172 = SY932 ) ) ) )
= $false )
| ( ( ~ ! [SY622: $i] :
~ ( SV17 @ SY622 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(699,plain,
! [SV103: $i > $o,SV19: $i] :
( ( ( ! [SY823: $i] :
~ ~ ( ~ ( in @ SY823 @ SV19 )
| ~ ( SV103 @ SY823 ) ) )
= $false )
| ( ( ! [SY824: $i] :
( ~ ( in @ SY824 @ SV19 )
| ~ ( SV103 @ SY824 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(700,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ~ ( ~ ( SV21 @ SV173 )
| ~ ! [SY933: $i] :
( ~ ( SV21 @ SY933 )
| ( SV173 = SY933 ) ) ) )
= $false )
| ( ( ~ ! [SY630: $i] :
~ ~ ( ~ ( SV21 @ SY630 )
| ~ ! [SY631: $i] :
( ~ ( SV21 @ SY631 )
| ( SY630 = SY631 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(701,plain,
! [SV22: $i,SV105: $i,SV155: $i] :
( ( ( ~ ~ ( in @ SV155 @ SV105 ) )
= $true )
| ( ( ~ ( in @ SV155 @ SV22 ) )
= $true )
| ( ( subset @ SV22 @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(702,plain,
! [SV106: $i > $o,SV24: $i,SV188: $i] :
( ( ( ~ ~ ( ~ ( in @ SV188 @ SV24 )
| ~ ~ ( SV106 @ SV188 ) ) )
= $true )
| ( ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ SV24 )
| ( SV106 @ SY827 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(703,plain,
! [SV107: $i,SV25: $i,SV156: $i] :
( ( ( ~ ( in @ SV156 @ SV25 ) )
= $true )
| ( ( in @ SV156 @ SV107 )
= $true )
| ( ( subset @ SV25 @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(704,plain,
! [SV26: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_SY640 @ SV26 ) @ SV26 )
| ~ $true ) )
= $false )
| ( ( SV26 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[640]) ).
thf(705,plain,
! [SV174: $o,SV27: $i,SV108: $i] :
( ( ( ~ ! [SY934: $i] :
( ~ ( in @ SV108 @ SY934 )
| ~ ( in @ SY934 @ SV27 )
| SV174 ) )
= $true )
| ( SV174 = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(706,plain,
! [SV27: $i,SV108: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV108 @ SX0 )
| ~ ( in @ SX0 @ SV27 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(707,plain,
! [SV27: $i,SV108: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV108 @ SX0 )
| ~ ( in @ SX0 @ SV27 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(708,plain,
! [SV110: $i,SV29: $i,SV157: $i] :
( ( ( ~ ( in @ SV157 @ SV29 ) )
= $true )
| ( ( in @ SV110 @ ( setunion @ SV29 ) )
= $true )
| ( ( in @ SV110 @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(709,plain,
! [SV30: $i,SV111: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 )
| ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 ) )
| ~ ( ~ ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 )
| ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 ) ) )
= $true )
| ( ( SV30 = SV111 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[645]) ).
thf(710,plain,
! [SV112: $i,SV31: $i] :
( ( ( SV31 = SV112 )
= $false )
| ( ( subset @ SV31 @ SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(711,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( SV32 @ SV175 )
= $false )
| ( ( ~ ! [SY651: $i,SY652: $i] :
( ~ ( SV32 @ SY651 )
| ~ ( SV32 @ SY652 )
| ( SY651 = SY652 ) )
| ~ ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(712,plain,
! [SV113: $i,SV33: $i,SV158: $i] :
( ( ( SV158 = SV33 )
= $true )
| ( ( SV158 = SV113 )
= $true )
| ( ( in @ SV158 @ ( setadjoin @ SV33 @ ( setadjoin @ SV113 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(713,plain,
! [SV34: $i,SV159: $i,SV114: $i] :
( ( ( ~ ( subset @ SV114 @ SV159 ) )
= $true )
| ( ( subset @ SV34 @ SV159 )
= $true )
| ( ( subset @ SV34 @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(714,plain,
! [SV35: $i,SV115: $i,SV160: $i] :
( ( ( ~ ( in @ SV160 @ SV115 ) )
= $true )
| ( ( in @ SV160 @ SV35 )
= $true )
| ( ( in @ SV115 @ ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(715,plain,
! [SV36: $i,SV161: $i,SV116: $i > $o] :
( ( ( ~ ( SV116 @ SV161 ) )
= $true )
| ( ( ( dsetconstr @ SV36
@ ^ [SY837: $i] : ( SV116 @ SY837 ) )
!= emptyset )
= $true )
| ( ( in @ SV161 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(716,plain,
! [SV37: $i,SV117: $i] :
( ( ( ~ ( in @ SV117 @ ( powerset @ SV37 ) ) )
= $true )
| ( ( ! [SY838: $i] :
( ~ ( in @ SY838 @ SV117 )
| ( in @ SY838 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(717,plain,
! [SV37: $i,SV117: $i] :
( ( ( ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ SV117 )
| ( in @ SY839 @ SV37 ) ) )
= $true )
| ( ( in @ SV117 @ ( powerset @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[653]) ).
thf(718,plain,
! [SV38: $i,SV118: $i,SV162: $i] :
( ( ( ~ ~ ( in @ SV162 @ SV118 ) )
= $true )
| ( ( SV38 != SV118 )
= $true )
| ( ( in @ SV162 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[654]) ).
thf(719,plain,
! [SV119: $i > $o,SV39: $i,SV189: $i] :
( ( ( ~ ( in @ SV189 @ SV39 )
| ( SV119 @ SV189 ) )
= $true )
| ( ( ~ ! [SY842: $i] :
~ ~ ( ~ ( in @ SY842 @ SV39 )
| ~ ~ ( SV119 @ SY842 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(720,plain,
! [SV176: $i,SV40: $i > $o] :
( ( ( ~ ( ~ ( SV40 @ SV176 )
| ~ ! [SY935: $i] :
( ~ ( SV40 @ SY935 )
| ( SV176 = SY935 ) ) ) )
= $false )
| ( ( ! [SY674: $i,SY675: $i] :
( ~ ( SV40 @ SY674 )
| ~ ( SV40 @ SY675 )
| ( SY674 = SY675 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(721,plain,
! [SV41: $i,SV120: $i] :
( ( ( ~ ( in @ ( sK7_SY843 @ SV120 @ SV41 ) @ SV41 ) )
= $false )
| ( ( subset @ SV41 @ SV120 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[657]) ).
thf(722,plain,
! [SV41: $i,SV120: $i] :
( ( ( in @ ( sK7_SY843 @ SV120 @ SV41 ) @ SV120 )
= $false )
| ( ( subset @ SV41 @ SV120 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[657]) ).
thf(723,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ~ ( ~ ( SV43 @ SV177 )
| ~ ! [SY936: $i] :
( ~ ( SV43 @ SY936 )
| ( SV177 = SY936 ) ) ) )
= $false )
| ( ( ~ ! [SY681: $i] :
~ ~ ( ~ ( SV43 @ SY681 )
| ~ ! [SY682: $i] :
( ~ ( SV43 @ SY682 )
| ( SY681 = SY682 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(724,plain,
! [SV44: $i,SV122: $i,SV163: $i] :
( ( ( ~ ~ ( in @ SV163 @ SV122 ) )
= $true )
| ( ( ~ ( subset @ SV44 @ SV122 ) )
= $true )
| ( ( in @ SV163 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(725,plain,
! [SV123: $i,SV45: $i > $i > $o] :
( ( ( ~ ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 ) )
= $false )
| ( ( ~ ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[660]) ).
thf(726,plain,
! [SV123: $i,SV45: $i > $i > $o] :
( ( ( ~ ! [SY937: $i] :
~ ~ ( ~ ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SY937 )
| ~ ! [SY938: $i] :
( ~ ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SY938 )
| ( SY937 = SY938 ) ) ) )
= $false )
| ( ( ~ ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[660]) ).
thf(727,plain,
! [SV124: $i,SV46: $i,SV190: $i,SV178: $i] :
( ( ( ( SV178 != SV190 )
| ~ ( in @ SV178 @ SV46 )
| ( in @ SV190 @ SV124 ) )
= $true )
| ( ( SV46 = SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(728,plain,
! [SV47: $i,SV179: $i] :
( ( ( in @ SV179 @ SV47 )
= $false )
| ( ( SV47 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(729,plain,
! [SV125: $i,SV48: $i,SV191: $i,SV180: $i] :
( ( ( ( SV180 != SV191 )
| ~ ( ~ ( ~ ( in @ SV180 @ SV48 )
| ( in @ SV191 @ SV125 ) )
| ~ ( ~ ( in @ SV191 @ SV125 )
| ( in @ SV180 @ SV48 ) ) ) )
= $true )
| ( ( SV48 = SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(730,plain,
! [SV192: $i > $o,SV181: $i > $o,SV128: $i,SV53: $i] :
( ( ( ~ ! [SY953: $i] :
( ~ ( in @ SY953 @ SV53 )
| ! [SY954: $i] :
( ~ ( in @ SY954 @ SV128 )
| ( SY953 != SY954 )
| ~ ( ~ ( ~ ( SV181 @ SY953 )
| ( SV192 @ SY954 ) )
| ~ ( ~ ( SV192 @ SY954 )
| ( SV181 @ SY953 ) ) ) ) )
| ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(731,plain,
! [SV129: $i,SV193: $o,SV54: $i,SV165: $i] :
( ( ( ~ ( ( SV165 != SV54 )
| SV193 )
| ~ ( ~ ( in @ SV165 @ SV129 )
| SV193 )
| SV193 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[666]) ).
thf(732,plain,
! [SV129: $i,SV54: $i,SV165: $i] :
( ( ( ~ ( ( SV165 != SV54 )
| $true )
| ~ ( ~ ( in @ SV165 @ SV129 )
| $true )
| $true )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[666]) ).
thf(733,plain,
! [SV129: $i,SV54: $i,SV165: $i] :
( ( ( ~ ( ( SV165 != SV54 )
| $false )
| ~ ( ~ ( in @ SV165 @ SV129 )
| $false )
| $false )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[666]) ).
thf(734,plain,
! [SV55: $i,SV182: $i] :
( ( ( in @ SV182 @ SV55 )
= $false )
| ( ( ~ ! [SY715: $i] :
~ ~ ( ~ ( in @ SY715 @ SV55 )
| ~ ~ ~ ! [SY716: $i] :
~ ~ ( ~ ( in @ SY716 @ SY715 )
| ~ ( in @ SY716 @ SV55 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(735,plain,
! [SV56: $i > $o,SV130: $i > $o] :
( ( ( ( ( sK9_SY866 @ SV130 @ SV56 )
!= ( sK15_SY946 @ SV56 @ SV130 ) )
| ~ ( ~ ( ~ ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
| ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) ) )
| ~ ( ~ ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
| ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[668]) ).
thf(736,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ( ( sK10_SY874 @ SV132 @ SV58 )
!= ( sK16_SY947 @ SV58 @ SV132 ) )
| ~ ( ~ ( ~ ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
| ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) ) )
| ~ ( ~ ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
| ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[669]) ).
thf(737,plain,
! [SV133: $i > $o,SV59: $i,SV166: $i] :
( ( ( ~ ( ~ ( in @ SV166
@ ( dsetconstr @ SV59
@ ^ [SY885: $i] : ( SV133 @ SY885 ) ) )
| ( SV133 @ SV166 ) )
| ~ ( ~ ( SV133 @ SV166 )
| ( in @ SV166
@ ( dsetconstr @ SV59
@ ^ [SY886: $i] : ( SV133 @ SY886 ) ) ) ) )
= $false )
| ( ( in @ SV166 @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(738,plain,
! [SV61: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY913: $i] :
( ~ ( in @ SY913 @ ( sK2_SY743 @ SV61 ) )
| ! [SY745: $i] :
( ~ ( in @ SY745 @ SY913 )
| ( in @ SY745 @ SV61 ) ) )
| ~ ! [SY915: $i,SY916: $i] :
( ~ ~ ( ~ ( in @ SY915 @ SV61 )
| ~ ( in @ SY916 @ SV61 ) )
| ~ ! [SY917: $i] :
( ~ ( in @ SY917 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SY915 @ SY917 )
| ( in @ SY916 @ SY917 ) )
| ~ ( ~ ( in @ SY916 @ SY917 )
| ( in @ SY915 @ SY917 ) ) ) )
| ( SY915 = SY916 ) ) )
| ~ ! [SY918: $i,SY919: $i] :
( ~ ~ ( ~ ( in @ SY918 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY919 @ ( sK2_SY743 @ SV61 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY918 )
| ( in @ SX4 @ SY919 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY919 )
| ( in @ SX4 @ SY918 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[672]) ).
thf(739,plain,
! [SV61: $i] :
( ( ~ ! [SY922: $i] :
( ~ ~ ( ~ ! [SY754: $i] :
( ~ ( in @ SY754 @ SY922 )
| ( in @ SY754 @ SV61 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY922 ) )
| ~ ! [SY925: $i] :
~ ~ ! [SY926: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY925 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY926 @ SY922 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY925 )
| ~ ( in @ SX5 @ SY922 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY925 ) )
| ( in @ SY926 @ SY928 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[672]) ).
thf(740,plain,
! [SV135: $i,SV64: $i,SV167: $i] :
( ( ( SV167 = SV64 )
= $true )
| ( ( in @ SV167 @ SV135 )
= $true )
| ( ( in @ SV167 @ ( setadjoin @ SV64 @ SV135 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(741,plain,
! [SV68: $i,SV138: $i] :
( ( ( ~ ( in @ ( sK11_SY888 @ SV138 @ SV68 ) @ SV68 ) )
= $false )
| ( ( ~ ! [SY889: $i] :
( ~ ( in @ SY889 @ SV138 )
| ( in @ SY889 @ SV68 ) )
| ( SV68 = SV138 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(742,plain,
! [SV68: $i,SV138: $i] :
( ( ( in @ ( sK11_SY888 @ SV138 @ SV68 ) @ SV138 )
= $false )
| ( ( ~ ! [SY889: $i] :
( ~ ( in @ SY889 @ SV138 )
| ( in @ SY889 @ SV68 ) )
| ( SV68 = SV138 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(743,plain,
! [SV139: $i > $o,SV69: $i,SV194: $i] :
( ( ( ~ ~ ( ~ ( in @ SV194 @ SV69 )
| ~ ( SV139 @ SV194 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV69
@ ^ [SY891: $i] : ( SV139 @ SY891 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(744,plain,
! [SV140: $i,SV70: $i,SV195: $i,SV183: $i] :
( ( ( ( SV183 != SV195 )
| ( ( setadjoin @ SV70 @ SV183 )
= ( setadjoin @ SV140 @ SV195 ) ) )
= $true )
| ( ( SV70 = SV140 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(745,plain,
! [SV71: $i] :
( ( ( in @ emptyset @ SV71 )
= $false )
| ( ( ~ ! [SY775: $i] :
( ~ ~ ( ~ ( in @ SY775 @ omega )
| ~ ( in @ SY775 @ SV71 ) )
| ( in @ ( setadjoin @ SY775 @ SY775 ) @ SV71 ) ) )
= $true )
| ( ( ! [SY776: $i] :
( ~ ( in @ SY776 @ omega )
| ( in @ SY776 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(746,plain,
! [SV141: $i > $o,SV73: $i] :
( ( ( ! [SY894: $i] :
~ ~ ( ~ ( in @ SY894 @ SV73 )
| ~ ( SV141 @ SY894 ) ) )
= $false )
| ( ( ! [SY895: $i] :
( ~ ( in @ SY895 @ SV73 )
| ~ ( SV141 @ SY895 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(747,plain,
! [SV76: $i,SV169: $i,SV144: $i > $o] :
( ( ( ~ ( SV144 @ SV169 ) )
= $true )
| ( ( in @ SV169
@ ( dsetconstr @ SV76
@ ^ [SY898: $i] : ( SV144 @ SY898 ) ) )
= $true )
| ( ( in @ SV169 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(748,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ! [SY949: $i] :
~ ( ~ ( ~ ( SV77 @ SY949 )
| ( SY949 = SV184 ) )
| ~ ( ( SY949 != SV184 )
| ( SV77 @ SY949 ) ) ) )
= $false )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(749,plain,
! [SV145: $i,SV78: $i] :
( ( ( ~ ( in @ ( sK12_SY899 @ SV78 @ SV145 ) @ SV145 ) )
= $false )
| ( ( in @ SV145 @ ( powerset @ SV78 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(750,plain,
! [SV145: $i,SV78: $i] :
( ( ( in @ ( sK12_SY899 @ SV78 @ SV145 ) @ SV78 )
= $false )
| ( ( in @ SV145 @ ( powerset @ SV78 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(751,plain,
! [SV79: $i,SV146: $i > $o] :
( ( ( ~ ( in @ ( sK13_SY900 @ SV146 @ SV79 ) @ SV79 ) )
= $false )
| ( ( ~ ~ ! [SY901: $i] :
~ ~ ( ~ ( in @ SY901 @ SV79 )
| ~ ( SV146 @ SY901 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[683]) ).
thf(752,plain,
! [SV79: $i,SV146: $i > $o] :
( ( ( ~ ( SV146 @ ( sK13_SY900 @ SV146 @ SV79 ) ) )
= $false )
| ( ( ~ ~ ! [SY901: $i] :
~ ~ ( ~ ( in @ SY901 @ SV79 )
| ~ ( SV146 @ SY901 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[683]) ).
thf(753,plain,
! [SV185: $i,SV81: $i > $o] :
( ( ( ~ ( ~ ( SV81 @ SV185 )
| ~ ! [SY950: $i] :
( ~ ( SV81 @ SY950 )
| ( SV185 = SY950 ) ) ) )
= $false )
| ( ( ~ ! [SY799: $i] :
~ ! [SY800: $i] :
~ ( ~ ( ~ ( SV81 @ SY800 )
| ( SY800 = SY799 ) )
| ~ ( ( SY800 != SY799 )
| ( SV81 @ SY800 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(754,plain,
! [SV82: $i] :
( ( ( ~ ( in @ ( sK17_SY801 @ SV82 ) @ SV82 ) )
= $false )
| ( ( SV82 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[685]) ).
thf(755,plain,
! [SV148: $i > $o,SV83: $i,SV196: $i] :
( ( ( ~ ( in @ SV196 @ SV83 )
| ( SV148 @ SV196 ) )
= $true )
| ( ( ~ ! [SY903: $i] :
~ ~ ( ~ ( in @ SY903 @ SV83 )
| ~ ~ ( SV148 @ SY903 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(756,plain,
! [SV186: $i,SV84: $i > $o] :
( ( ( ~ ( ~ ( SV84 @ SV186 )
| ~ ! [SY951: $i] :
( ~ ( SV84 @ SY951 )
| ( SV186 = SY951 ) ) ) )
= $false )
| ( ( ! [SY807: $i,SY808: $i] :
( ~ ( SV84 @ SY807 )
| ~ ( SV84 @ SY808 )
| ( SY807 = SY808 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(757,plain,
! [SV87: $i,SV150: $i] :
( ( ( ~ ( in @ SV150 @ ( setunion @ SV87 ) ) )
= $true )
| ( ( ~ ! [SY906: $i] :
~ ~ ( ~ ( in @ SV150 @ SY906 )
| ~ ( in @ SY906 @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(758,plain,
! [SV87: $i,SV150: $i] :
( ( ( ~ ~ ! [SY907: $i] :
~ ~ ( ~ ( in @ SV150 @ SY907 )
| ~ ( in @ SY907 @ SV87 ) ) )
= $true )
| ( ( in @ SV150 @ ( setunion @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[690]) ).
thf(759,plain,
! [SV88: $i,SV151: $i] :
( ( ( subset @ SV151 @ SV88 )
= $false )
| ( ( SV88 = SV151 )
= $true )
| ( ( subset @ SV88 @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(760,plain,
! [SV187: $i,SV90: $i > $o] :
( ( ( ~ ( ~ ( SV90 @ SV187 )
| ~ ! [SY952: $i] :
( ~ ( SV90 @ SY952 )
| ( SV187 = SY952 ) ) ) )
= $false )
| ( ( SV90
@ ( descr
@ ^ [SY819: $i] : ( SV90 @ SY819 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(761,plain,
! [SV13: $i,SV98: $i] :
( ( ( in @ ( sK5_SY820 @ SV98 @ SV13 ) @ SV13 )
= $true )
| ( ( subset @ SV13 @ SV98 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[693]) ).
thf(762,plain,
! [SV101: $i,SV16: $i,SV154: $i] :
( ( ( ~ ( in @ SV154 @ ( setadjoin @ SV16 @ SV101 ) ) )
= $true )
| ( ( ( SV154 = SV16 )
| ( in @ SV154 @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(763,plain,
! [SV101: $i,SV16: $i,SV154: $i] :
( ( ( ~ ( ( SV154 = SV16 )
| ( in @ SV154 @ SV101 ) ) )
= $true )
| ( ( in @ SV154 @ ( setadjoin @ SV16 @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(764,plain,
! [SV172: $i,SV17: $i > $o] :
( ( ( ~ ( SV17 @ SV172 )
| ~ ! [SY932: $i] :
( ~ ( SV17 @ SY932 )
| ( SV172 = SY932 ) ) )
= $true )
| ( ( ~ ! [SY622: $i] :
~ ( SV17 @ SY622 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[698]) ).
thf(765,plain,
! [SV19: $i,SV103: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY823 @ SV103 @ SV19 ) @ SV19 )
| ~ ( SV103 @ ( sK18_SY823 @ SV103 @ SV19 ) ) ) )
= $false )
| ( ( ! [SY824: $i] :
( ~ ( in @ SY824 @ SV19 )
| ~ ( SV103 @ SY824 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[699]) ).
thf(766,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ SV173 )
| ~ ! [SY933: $i] :
( ~ ( SV21 @ SY933 )
| ( SV173 = SY933 ) ) )
= $true )
| ( ( ~ ! [SY630: $i] :
~ ~ ( ~ ( SV21 @ SY630 )
| ~ ! [SY631: $i] :
( ~ ( SV21 @ SY631 )
| ( SY630 = SY631 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[700]) ).
thf(767,plain,
! [SV22: $i,SV105: $i,SV155: $i] :
( ( ( ~ ( in @ SV155 @ SV105 ) )
= $false )
| ( ( ~ ( in @ SV155 @ SV22 ) )
= $true )
| ( ( subset @ SV22 @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(768,plain,
! [SV106: $i > $o,SV24: $i,SV188: $i] :
( ( ( ~ ( ~ ( in @ SV188 @ SV24 )
| ~ ~ ( SV106 @ SV188 ) ) )
= $false )
| ( ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ SV24 )
| ( SV106 @ SY827 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(769,plain,
! [SV107: $i,SV25: $i,SV156: $i] :
( ( ( in @ SV156 @ SV25 )
= $false )
| ( ( in @ SV156 @ SV107 )
= $true )
| ( ( subset @ SV25 @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(770,plain,
! [SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_SY640 @ SV26 ) @ SV26 )
| ~ $true ) )
= $true )
| ( ( SV26 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[704]) ).
thf(771,plain,
! [SV174: $o,SV27: $i,SV108: $i] :
( ( ( ! [SY934: $i] :
( ~ ( in @ SV108 @ SY934 )
| ~ ( in @ SY934 @ SV27 )
| SV174 ) )
= $false )
| ( SV174 = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(772,plain,
! [SV27: $i,SV108: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV108 @ SX0 )
| ~ ( in @ SX0 @ SV27 )
| $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(773,plain,
! [SV27: $i,SV108: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV108 @ SX0 )
| ~ ( in @ SX0 @ SV27 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(774,plain,
! [SV110: $i,SV29: $i,SV157: $i] :
( ( ( in @ SV157 @ SV29 )
= $false )
| ( ( in @ SV110 @ ( setunion @ SV29 ) )
= $true )
| ( ( in @ SV110 @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(775,plain,
! [SV30: $i,SV111: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 )
| ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 )
| ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 ) ) )
= $true )
| ( ( SV30 = SV111 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[709]) ).
thf(776,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ! [SY651: $i,SY652: $i] :
( ~ ( SV32 @ SY651 )
| ~ ( SV32 @ SY652 )
| ( SY651 = SY652 ) ) )
= $true )
| ( ( ~ ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[711]) ).
thf(777,plain,
! [SV34: $i,SV159: $i,SV114: $i] :
( ( ( subset @ SV114 @ SV159 )
= $false )
| ( ( subset @ SV34 @ SV159 )
= $true )
| ( ( subset @ SV34 @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(778,plain,
! [SV35: $i,SV115: $i,SV160: $i] :
( ( ( in @ SV160 @ SV115 )
= $false )
| ( ( in @ SV160 @ SV35 )
= $true )
| ( ( in @ SV115 @ ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(779,plain,
! [SV36: $i,SV161: $i,SV116: $i > $o] :
( ( ( SV116 @ SV161 )
= $false )
| ( ( ( dsetconstr @ SV36
@ ^ [SY837: $i] : ( SV116 @ SY837 ) )
!= emptyset )
= $true )
| ( ( in @ SV161 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(780,plain,
! [SV37: $i,SV117: $i] :
( ( ( in @ SV117 @ ( powerset @ SV37 ) )
= $false )
| ( ( ! [SY838: $i] :
( ~ ( in @ SY838 @ SV117 )
| ( in @ SY838 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(781,plain,
! [SV37: $i,SV117: $i] :
( ( ( ! [SY839: $i] :
( ~ ( in @ SY839 @ SV117 )
| ( in @ SY839 @ SV37 ) ) )
= $false )
| ( ( in @ SV117 @ ( powerset @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(782,plain,
! [SV38: $i,SV118: $i,SV162: $i] :
( ( ( ~ ( in @ SV162 @ SV118 ) )
= $false )
| ( ( SV38 != SV118 )
= $true )
| ( ( in @ SV162 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(783,plain,
! [SV119: $i > $o,SV39: $i,SV189: $i] :
( ( ( ~ ( in @ SV189 @ SV39 ) )
= $true )
| ( ( SV119 @ SV189 )
= $true )
| ( ( ~ ! [SY842: $i] :
~ ~ ( ~ ( in @ SY842 @ SV39 )
| ~ ~ ( SV119 @ SY842 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(784,plain,
! [SV176: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ SV176 )
| ~ ! [SY935: $i] :
( ~ ( SV40 @ SY935 )
| ( SV176 = SY935 ) ) )
= $true )
| ( ( ! [SY674: $i,SY675: $i] :
( ~ ( SV40 @ SY674 )
| ~ ( SV40 @ SY675 )
| ( SY674 = SY675 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[720]) ).
thf(785,plain,
! [SV41: $i,SV120: $i] :
( ( ( in @ ( sK7_SY843 @ SV120 @ SV41 ) @ SV41 )
= $true )
| ( ( subset @ SV41 @ SV120 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[721]) ).
thf(786,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ SV177 )
| ~ ! [SY936: $i] :
( ~ ( SV43 @ SY936 )
| ( SV177 = SY936 ) ) )
= $true )
| ( ( ~ ! [SY681: $i] :
~ ~ ( ~ ( SV43 @ SY681 )
| ~ ! [SY682: $i] :
( ~ ( SV43 @ SY682 )
| ( SY681 = SY682 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[723]) ).
thf(787,plain,
! [SV44: $i,SV122: $i,SV163: $i] :
( ( ( ~ ( in @ SV163 @ SV122 ) )
= $false )
| ( ( ~ ( subset @ SV44 @ SV122 ) )
= $true )
| ( ( in @ SV163 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(788,plain,
! [SV123: $i,SV45: $i > $i > $o] :
( ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true )
| ( ( ~ ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[725]) ).
thf(789,plain,
! [SV123: $i,SV45: $i > $i > $o] :
( ( ( ! [SY937: $i] :
~ ~ ( ~ ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SY937 )
| ~ ! [SY938: $i] :
( ~ ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SY938 )
| ( SY937 = SY938 ) ) ) )
= $true )
| ( ( ~ ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[726]) ).
thf(790,plain,
! [SV124: $i,SV46: $i,SV190: $i,SV178: $i] :
( ( ( SV178 != SV190 )
= $true )
| ( ( ~ ( in @ SV178 @ SV46 )
| ( in @ SV190 @ SV124 ) )
= $true )
| ( ( SV46 = SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(791,plain,
! [SV179: $i,SV47: $i] :
( ( ( SV47 = emptyset )
= $false )
| ( ( in @ SV179 @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(792,plain,
! [SV125: $i,SV48: $i,SV191: $i,SV180: $i] :
( ( ( SV180 != SV191 )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV180 @ SV48 )
| ( in @ SV191 @ SV125 ) )
| ~ ( ~ ( in @ SV191 @ SV125 )
| ( in @ SV180 @ SV48 ) ) ) )
= $true )
| ( ( SV48 = SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[729]) ).
thf(793,plain,
! [SV192: $i > $o,SV181: $i > $o,SV128: $i,SV53: $i] :
( ( ( ~ ! [SY953: $i] :
( ~ ( in @ SY953 @ SV53 )
| ! [SY954: $i] :
( ~ ( in @ SY954 @ SV128 )
| ( SY953 != SY954 )
| ~ ( ~ ( ~ ( SV181 @ SY953 )
| ( SV192 @ SY954 ) )
| ~ ( ~ ( SV192 @ SY954 )
| ( SV181 @ SY953 ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(794,plain,
! [SV129: $i,SV193: $o,SV54: $i,SV165: $i] :
( ( ( ~ ( ( SV165 != SV54 )
| SV193 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| SV193 )
| SV193 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(795,plain,
! [SV129: $i,SV54: $i,SV165: $i] :
( ( ( ~ ( ( SV165 != SV54 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| $true )
| $true )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(796,plain,
! [SV129: $i,SV54: $i,SV165: $i] :
( ( ( ~ ( ( SV165 != SV54 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| $false )
| $false )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(797,plain,
! [SV182: $i,SV55: $i] :
( ( ( ! [SY715: $i] :
~ ~ ( ~ ( in @ SY715 @ SV55 )
| ~ ~ ~ ! [SY716: $i] :
~ ~ ( ~ ( in @ SY716 @ SY715 )
| ~ ( in @ SY716 @ SV55 ) ) ) )
= $false )
| ( ( in @ SV182 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(798,plain,
! [SV56: $i > $o,SV130: $i > $o] :
( ( ( ( sK9_SY866 @ SV130 @ SV56 )
!= ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[735]) ).
thf(799,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
| ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) ) )
| ~ ( ~ ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
| ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[735]) ).
thf(800,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ( sK10_SY874 @ SV132 @ SV58 )
!= ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[736]) ).
thf(801,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
| ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) ) )
| ~ ( ~ ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
| ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[736]) ).
thf(802,plain,
! [SV133: $i > $o,SV59: $i,SV166: $i] :
( ( ( ~ ( ~ ( in @ SV166
@ ( dsetconstr @ SV59
@ ^ [SY885: $i] : ( SV133 @ SY885 ) ) )
| ( SV133 @ SV166 ) ) )
= $false )
| ( ( in @ SV166 @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[737]) ).
thf(803,plain,
! [SV59: $i,SV166: $i,SV133: $i > $o] :
( ( ( ~ ( ~ ( SV133 @ SV166 )
| ( in @ SV166
@ ( dsetconstr @ SV59
@ ^ [SY886: $i] : ( SV133 @ SY886 ) ) ) ) )
= $false )
| ( ( in @ SV166 @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[737]) ).
thf(804,plain,
! [SV61: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY913: $i] :
( ~ ( in @ SY913 @ ( sK2_SY743 @ SV61 ) )
| ! [SY745: $i] :
( ~ ( in @ SY745 @ SY913 )
| ( in @ SY745 @ SV61 ) ) )
| ~ ! [SY915: $i,SY916: $i] :
( ~ ~ ( ~ ( in @ SY915 @ SV61 )
| ~ ( in @ SY916 @ SV61 ) )
| ~ ! [SY917: $i] :
( ~ ( in @ SY917 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SY915 @ SY917 )
| ( in @ SY916 @ SY917 ) )
| ~ ( ~ ( in @ SY916 @ SY917 )
| ( in @ SY915 @ SY917 ) ) ) )
| ( SY915 = SY916 ) ) )
| ~ ! [SY918: $i,SY919: $i] :
( ~ ~ ( ~ ( in @ SY918 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY919 @ ( sK2_SY743 @ SV61 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY918 )
| ( in @ SX4 @ SY919 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY919 )
| ( in @ SX4 @ SY918 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[738]) ).
thf(805,plain,
! [SV61: $i] :
( ( ! [SY922: $i] :
( ~ ~ ( ~ ! [SY754: $i] :
( ~ ( in @ SY754 @ SY922 )
| ( in @ SY754 @ SV61 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY922 ) )
| ~ ! [SY925: $i] :
~ ~ ! [SY926: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY925 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY926 @ SY922 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY925 )
| ~ ( in @ SX5 @ SY922 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY925 ) )
| ( in @ SY926 @ SY928 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[739]) ).
thf(806,plain,
! [SV68: $i,SV138: $i] :
( ( ( in @ ( sK11_SY888 @ SV138 @ SV68 ) @ SV68 )
= $true )
| ( ( ~ ! [SY889: $i] :
( ~ ( in @ SY889 @ SV138 )
| ( in @ SY889 @ SV68 ) )
| ( SV68 = SV138 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[741]) ).
thf(807,plain,
! [SV68: $i,SV138: $i] :
( ( ( ~ ! [SY889: $i] :
( ~ ( in @ SY889 @ SV138 )
| ( in @ SY889 @ SV68 ) ) )
= $true )
| ( ( SV68 = SV138 )
= $true )
| ( ( in @ ( sK11_SY888 @ SV138 @ SV68 ) @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(808,plain,
! [SV139: $i > $o,SV69: $i,SV194: $i] :
( ( ( ~ ( ~ ( in @ SV194 @ SV69 )
| ~ ( SV139 @ SV194 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV69
@ ^ [SY891: $i] : ( SV139 @ SY891 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(809,plain,
! [SV140: $i,SV70: $i,SV195: $i,SV183: $i] :
( ( ( SV183 != SV195 )
= $true )
| ( ( ( setadjoin @ SV70 @ SV183 )
= ( setadjoin @ SV140 @ SV195 ) )
= $true )
| ( ( SV70 = SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(810,plain,
! [SV71: $i] :
( ( ( ! [SY775: $i] :
( ~ ~ ( ~ ( in @ SY775 @ omega )
| ~ ( in @ SY775 @ SV71 ) )
| ( in @ ( setadjoin @ SY775 @ SY775 ) @ SV71 ) ) )
= $false )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( ! [SY776: $i] :
( ~ ( in @ SY776 @ omega )
| ( in @ SY776 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(811,plain,
! [SV73: $i,SV141: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY894 @ SV141 @ SV73 ) @ SV73 )
| ~ ( SV141 @ ( sK19_SY894 @ SV141 @ SV73 ) ) ) )
= $false )
| ( ( ! [SY895: $i] :
( ~ ( in @ SY895 @ SV73 )
| ~ ( SV141 @ SY895 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[746]) ).
thf(812,plain,
! [SV76: $i,SV169: $i,SV144: $i > $o] :
( ( ( SV144 @ SV169 )
= $false )
| ( ( in @ SV169
@ ( dsetconstr @ SV76
@ ^ [SY898: $i] : ( SV144 @ SY898 ) ) )
= $true )
| ( ( in @ SV169 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(813,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
| ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 ) )
| ~ ( ( ( sK20_SY949 @ SV184 @ SV77 )
!= SV184 )
| ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) ) ) ) )
= $false )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[748]) ).
thf(814,plain,
! [SV145: $i,SV78: $i] :
( ( ( in @ ( sK12_SY899 @ SV78 @ SV145 ) @ SV145 )
= $true )
| ( ( in @ SV145 @ ( powerset @ SV78 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[749]) ).
thf(815,plain,
! [SV79: $i,SV146: $i > $o] :
( ( ( in @ ( sK13_SY900 @ SV146 @ SV79 ) @ SV79 )
= $true )
| ( ( ~ ~ ! [SY901: $i] :
~ ~ ( ~ ( in @ SY901 @ SV79 )
| ~ ( SV146 @ SY901 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[751]) ).
thf(816,plain,
! [SV79: $i,SV146: $i > $o] :
( ( ( SV146 @ ( sK13_SY900 @ SV146 @ SV79 ) )
= $true )
| ( ( ~ ~ ! [SY901: $i] :
~ ~ ( ~ ( in @ SY901 @ SV79 )
| ~ ( SV146 @ SY901 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[752]) ).
thf(817,plain,
! [SV185: $i,SV81: $i > $o] :
( ( ( ~ ( SV81 @ SV185 )
| ~ ! [SY950: $i] :
( ~ ( SV81 @ SY950 )
| ( SV185 = SY950 ) ) )
= $true )
| ( ( ~ ! [SY799: $i] :
~ ! [SY800: $i] :
~ ( ~ ( ~ ( SV81 @ SY800 )
| ( SY800 = SY799 ) )
| ~ ( ( SY800 != SY799 )
| ( SV81 @ SY800 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[753]) ).
thf(818,plain,
! [SV82: $i] :
( ( ( in @ ( sK17_SY801 @ SV82 ) @ SV82 )
= $true )
| ( ( SV82 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[754]) ).
thf(819,plain,
! [SV148: $i > $o,SV83: $i,SV196: $i] :
( ( ( ~ ( in @ SV196 @ SV83 ) )
= $true )
| ( ( SV148 @ SV196 )
= $true )
| ( ( ~ ! [SY903: $i] :
~ ~ ( ~ ( in @ SY903 @ SV83 )
| ~ ~ ( SV148 @ SY903 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(820,plain,
! [SV186: $i,SV84: $i > $o] :
( ( ( ~ ( SV84 @ SV186 )
| ~ ! [SY951: $i] :
( ~ ( SV84 @ SY951 )
| ( SV186 = SY951 ) ) )
= $true )
| ( ( ! [SY807: $i,SY808: $i] :
( ~ ( SV84 @ SY807 )
| ~ ( SV84 @ SY808 )
| ( SY807 = SY808 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[756]) ).
thf(821,plain,
! [SV87: $i,SV150: $i] :
( ( ( in @ SV150 @ ( setunion @ SV87 ) )
= $false )
| ( ( ~ ! [SY906: $i] :
~ ~ ( ~ ( in @ SV150 @ SY906 )
| ~ ( in @ SY906 @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(822,plain,
! [SV87: $i,SV150: $i] :
( ( ( ~ ! [SY907: $i] :
~ ~ ( ~ ( in @ SV150 @ SY907 )
| ~ ( in @ SY907 @ SV87 ) ) )
= $false )
| ( ( in @ SV150 @ ( setunion @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(823,plain,
! [SV187: $i,SV90: $i > $o] :
( ( ( ~ ( SV90 @ SV187 )
| ~ ! [SY952: $i] :
( ~ ( SV90 @ SY952 )
| ( SV187 = SY952 ) ) )
= $true )
| ( ( SV90
@ ( descr
@ ^ [SY819: $i] : ( SV90 @ SY819 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[760]) ).
thf(824,plain,
! [SV101: $i,SV16: $i,SV154: $i] :
( ( ( in @ SV154 @ ( setadjoin @ SV16 @ SV101 ) )
= $false )
| ( ( ( SV154 = SV16 )
| ( in @ SV154 @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(825,plain,
! [SV101: $i,SV16: $i,SV154: $i] :
( ( ( ( SV154 = SV16 )
| ( in @ SV154 @ SV101 ) )
= $false )
| ( ( in @ SV154 @ ( setadjoin @ SV16 @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(826,plain,
! [SV172: $i,SV17: $i > $o] :
( ( ( ~ ( SV17 @ SV172 ) )
= $true )
| ( ( ~ ! [SY932: $i] :
( ~ ( SV17 @ SY932 )
| ( SV172 = SY932 ) ) )
= $true )
| ( ( ~ ! [SY622: $i] :
~ ( SV17 @ SY622 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(827,plain,
! [SV19: $i,SV103: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK18_SY823 @ SV103 @ SV19 ) @ SV19 )
| ~ ( SV103 @ ( sK18_SY823 @ SV103 @ SV19 ) ) ) )
= $true )
| ( ( ! [SY824: $i] :
( ~ ( in @ SY824 @ SV19 )
| ~ ( SV103 @ SY824 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[765]) ).
thf(828,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ SV173 ) )
= $true )
| ( ( ~ ! [SY933: $i] :
( ~ ( SV21 @ SY933 )
| ( SV173 = SY933 ) ) )
= $true )
| ( ( ~ ! [SY630: $i] :
~ ~ ( ~ ( SV21 @ SY630 )
| ~ ! [SY631: $i] :
( ~ ( SV21 @ SY631 )
| ( SY630 = SY631 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(829,plain,
! [SV22: $i,SV105: $i,SV155: $i] :
( ( ( in @ SV155 @ SV105 )
= $true )
| ( ( ~ ( in @ SV155 @ SV22 ) )
= $true )
| ( ( subset @ SV22 @ SV105 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[767]) ).
thf(830,plain,
! [SV106: $i > $o,SV24: $i,SV188: $i] :
( ( ( ~ ( in @ SV188 @ SV24 )
| ~ ~ ( SV106 @ SV188 ) )
= $true )
| ( ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ SV24 )
| ( SV106 @ SY827 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[768]) ).
thf(831,plain,
! [SV26: $i] :
( ( ( ~ ( in @ ( sK14_SY640 @ SV26 ) @ SV26 )
| ~ $true )
= $false )
| ( ( SV26 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(832,plain,
! [SV27: $i,SV174: $o,SV108: $i] :
( ( ( ~ ( in @ SV108 @ ( sK21_SY934 @ SV174 @ SV27 @ SV108 ) )
| ~ ( in @ ( sK21_SY934 @ SV174 @ SV27 @ SV108 ) @ SV27 )
| SV174 )
= $false )
| ( SV174 = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[771]) ).
thf(833,plain,
! [SV27: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ ( sK22_SX0 @ SV27 @ SV108 ) )
| ~ ( in @ ( sK22_SX0 @ SV27 @ SV108 ) @ SV27 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[772]) ).
thf(834,plain,
! [SV27: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ ( sK23_SX0 @ SV27 @ SV108 ) )
| ~ ( in @ ( sK23_SX0 @ SV27 @ SV108 ) @ SV27 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[773]) ).
thf(835,plain,
! [SV30: $i,SV111: $i] :
( ( ( ~ ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 )
| ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 )
| ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 ) ) )
= $true )
| ( ( SV30 = SV111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(836,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ! [SY651: $i,SY652: $i] :
( ~ ( SV32 @ SY651 )
| ~ ( SV32 @ SY652 )
| ( SY651 = SY652 ) ) )
= $false )
| ( ( ~ ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(837,plain,
! [SV161: $i,SV116: $i > $o,SV36: $i] :
( ( ( ( dsetconstr @ SV36
@ ^ [SY837: $i] : ( SV116 @ SY837 ) )
= emptyset )
= $false )
| ( ( SV116 @ SV161 )
= $false )
| ( ( in @ SV161 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(838,plain,
! [SV37: $i,SV117: $i,SV197: $i] :
( ( ( ~ ( in @ SV197 @ SV117 )
| ( in @ SV197 @ SV37 ) )
= $true )
| ( ( in @ SV117 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(839,plain,
! [SV117: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK24_SY839 @ SV37 @ SV117 ) @ SV117 )
| ( in @ ( sK24_SY839 @ SV37 @ SV117 ) @ SV37 ) )
= $false )
| ( ( in @ SV117 @ ( powerset @ SV37 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[781]) ).
thf(840,plain,
! [SV38: $i,SV118: $i,SV162: $i] :
( ( ( in @ SV162 @ SV118 )
= $true )
| ( ( SV38 != SV118 )
= $true )
| ( ( in @ SV162 @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[782]) ).
thf(841,plain,
! [SV119: $i > $o,SV39: $i,SV189: $i] :
( ( ( in @ SV189 @ SV39 )
= $false )
| ( ( SV119 @ SV189 )
= $true )
| ( ( ~ ! [SY842: $i] :
~ ~ ( ~ ( in @ SY842 @ SV39 )
| ~ ~ ( SV119 @ SY842 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(842,plain,
! [SV176: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ SV176 ) )
= $true )
| ( ( ~ ! [SY935: $i] :
( ~ ( SV40 @ SY935 )
| ( SV176 = SY935 ) ) )
= $true )
| ( ( ! [SY674: $i,SY675: $i] :
( ~ ( SV40 @ SY674 )
| ~ ( SV40 @ SY675 )
| ( SY674 = SY675 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[784]) ).
thf(843,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ SV177 ) )
= $true )
| ( ( ~ ! [SY936: $i] :
( ~ ( SV43 @ SY936 )
| ( SV177 = SY936 ) ) )
= $true )
| ( ( ~ ! [SY681: $i] :
~ ~ ( ~ ( SV43 @ SY681 )
| ~ ! [SY682: $i] :
( ~ ( SV43 @ SY682 )
| ( SY681 = SY682 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[786]) ).
thf(844,plain,
! [SV44: $i,SV122: $i,SV163: $i] :
( ( ( in @ SV163 @ SV122 )
= $true )
| ( ( ~ ( subset @ SV44 @ SV122 ) )
= $true )
| ( ( in @ SV163 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[787]) ).
thf(845,plain,
! [SV45: $i > $i > $o,SV123: $i] :
( ( ( ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(846,plain,
! [SV198: $i,SV123: $i,SV45: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
| ~ ! [SY957: $i] :
( ~ ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SY957 )
| ( SV198 = SY957 ) ) ) )
= $true )
| ( ( ~ ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(847,plain,
! [SV124: $i,SV46: $i,SV190: $i,SV178: $i] :
( ( ( SV178 = SV190 )
= $false )
| ( ( ~ ( in @ SV178 @ SV46 )
| ( in @ SV190 @ SV124 ) )
= $true )
| ( ( SV46 = SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(848,plain,
! [SV125: $i,SV48: $i,SV191: $i,SV180: $i] :
( ( ( SV180 = SV191 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV180 @ SV48 )
| ( in @ SV191 @ SV125 ) )
| ~ ( ~ ( in @ SV191 @ SV125 )
| ( in @ SV180 @ SV48 ) ) ) )
= $true )
| ( ( SV48 = SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(849,plain,
! [SV192: $i > $o,SV181: $i > $o,SV128: $i,SV53: $i] :
( ( ( ! [SY953: $i] :
( ~ ( in @ SY953 @ SV53 )
| ! [SY954: $i] :
( ~ ( in @ SY954 @ SV128 )
| ( SY953 != SY954 )
| ~ ( ~ ( ~ ( SV181 @ SY953 )
| ( SV192 @ SY954 ) )
| ~ ( ~ ( SV192 @ SY954 )
| ( SV181 @ SY953 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(850,plain,
! [SV129: $i,SV193: $o,SV54: $i,SV165: $i] :
( ( ( ( SV165 != SV54 )
| SV193 )
= $false )
| ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| SV193 )
| SV193 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(851,plain,
! [SV129: $i,SV54: $i,SV165: $i] :
( ( ( ( SV165 != SV54 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| $true )
| $true )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(852,plain,
! [SV129: $i,SV54: $i,SV165: $i] :
( ( ( ( SV165 != SV54 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| $false )
| $false )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(853,plain,
! [SV55: $i,SV182: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK25_SY715 @ SV182 @ SV55 ) @ SV55 )
| ~ ~ ~ ! [SY958: $i] :
~ ~ ( ~ ( in @ SY958 @ ( sK25_SY715 @ SV182 @ SV55 ) )
| ~ ( in @ SY958 @ SV55 ) ) ) )
= $false )
| ( ( in @ SV182 @ SV55 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[797]) ).
thf(854,plain,
! [SV56: $i > $o,SV130: $i > $o] :
( ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(855,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ( ~ ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
| ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) ) )
| ~ ( ~ ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
| ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(856,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(857,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
| ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) ) )
| ~ ( ~ ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
| ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(858,plain,
! [SV133: $i > $o,SV59: $i,SV166: $i] :
( ( ( ~ ( in @ SV166
@ ( dsetconstr @ SV59
@ ^ [SY885: $i] : ( SV133 @ SY885 ) ) )
| ( SV133 @ SV166 ) )
= $true )
| ( ( in @ SV166 @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[802]) ).
thf(859,plain,
! [SV59: $i,SV166: $i,SV133: $i > $o] :
( ( ( ~ ( SV133 @ SV166 )
| ( in @ SV166
@ ( dsetconstr @ SV59
@ ^ [SY886: $i] : ( SV133 @ SY886 ) ) ) )
= $true )
| ( ( in @ SV166 @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(860,plain,
! [SV61: $i] :
( ( ~ ~ ( ~ ! [SY913: $i] :
( ~ ( in @ SY913 @ ( sK2_SY743 @ SV61 ) )
| ! [SY745: $i] :
( ~ ( in @ SY745 @ SY913 )
| ( in @ SY745 @ SV61 ) ) )
| ~ ! [SY915: $i,SY916: $i] :
( ~ ~ ( ~ ( in @ SY915 @ SV61 )
| ~ ( in @ SY916 @ SV61 ) )
| ~ ! [SY917: $i] :
( ~ ( in @ SY917 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SY915 @ SY917 )
| ( in @ SY916 @ SY917 ) )
| ~ ( ~ ( in @ SY916 @ SY917 )
| ( in @ SY915 @ SY917 ) ) ) )
| ( SY915 = SY916 ) ) )
| ~ ! [SY918: $i,SY919: $i] :
( ~ ~ ( ~ ( in @ SY918 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY919 @ ( sK2_SY743 @ SV61 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY918 )
| ( in @ SX4 @ SY919 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY919 )
| ( in @ SX4 @ SY918 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(861,plain,
! [SV61: $i,SV199: $i] :
( ( ~ ~ ( ~ ! [SY959: $i] :
( ~ ( in @ SY959 @ SV199 )
| ( in @ SY959 @ SV61 ) )
| ~ ~ ! [SY960: $i] :
~ ( in @ SY960 @ SV199 ) )
| ~ ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(862,plain,
! [SV68: $i,SV138: $i] :
( ( ( ~ ! [SY889: $i] :
( ~ ( in @ SY889 @ SV138 )
| ( in @ SY889 @ SV68 ) ) )
= $true )
| ( ( SV68 = SV138 )
= $true )
| ( ( in @ ( sK11_SY888 @ SV138 @ SV68 ) @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[806]) ).
thf(863,plain,
! [SV68: $i,SV138: $i] :
( ( ( ! [SY889: $i] :
( ~ ( in @ SY889 @ SV138 )
| ( in @ SY889 @ SV68 ) ) )
= $false )
| ( ( SV68 = SV138 )
= $true )
| ( ( in @ ( sK11_SY888 @ SV138 @ SV68 ) @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(864,plain,
! [SV139: $i > $o,SV69: $i,SV194: $i] :
( ( ( ~ ( in @ SV194 @ SV69 )
| ~ ( SV139 @ SV194 ) )
= $true )
| ( ( ( ( dsetconstr @ SV69
@ ^ [SY891: $i] : ( SV139 @ SY891 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[808]) ).
thf(865,plain,
! [SV140: $i,SV70: $i,SV195: $i,SV183: $i] :
( ( ( SV183 = SV195 )
= $false )
| ( ( ( setadjoin @ SV70 @ SV183 )
= ( setadjoin @ SV140 @ SV195 ) )
= $true )
| ( ( SV70 = SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(866,plain,
! [SV71: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK26_SY775 @ SV71 ) @ omega )
| ~ ( in @ ( sK26_SY775 @ SV71 ) @ SV71 ) )
| ( in @ ( setadjoin @ ( sK26_SY775 @ SV71 ) @ ( sK26_SY775 @ SV71 ) ) @ SV71 ) )
= $false )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( ! [SY776: $i] :
( ~ ( in @ SY776 @ omega )
| ( in @ SY776 @ SV71 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[810]) ).
thf(867,plain,
! [SV73: $i,SV141: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK19_SY894 @ SV141 @ SV73 ) @ SV73 )
| ~ ( SV141 @ ( sK19_SY894 @ SV141 @ SV73 ) ) ) )
= $true )
| ( ( ! [SY895: $i] :
( ~ ( in @ SY895 @ SV73 )
| ~ ( SV141 @ SY895 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[811]) ).
thf(868,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ( ~ ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
| ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 ) )
| ~ ( ( ( sK20_SY949 @ SV184 @ SV77 )
!= SV184 )
| ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) ) ) )
= $true )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[813]) ).
thf(869,plain,
! [SV146: $i > $o,SV79: $i] :
( ( ( ~ ! [SY901: $i] :
~ ~ ( ~ ( in @ SY901 @ SV79 )
| ~ ( SV146 @ SY901 ) ) )
= $false )
| ( ( in @ ( sK13_SY900 @ SV146 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(870,plain,
! [SV146: $i > $o,SV79: $i] :
( ( ( ~ ! [SY901: $i] :
~ ~ ( ~ ( in @ SY901 @ SV79 )
| ~ ( SV146 @ SY901 ) ) )
= $false )
| ( ( SV146 @ ( sK13_SY900 @ SV146 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(871,plain,
! [SV185: $i,SV81: $i > $o] :
( ( ( ~ ( SV81 @ SV185 ) )
= $true )
| ( ( ~ ! [SY950: $i] :
( ~ ( SV81 @ SY950 )
| ( SV185 = SY950 ) ) )
= $true )
| ( ( ~ ! [SY799: $i] :
~ ! [SY800: $i] :
~ ( ~ ( ~ ( SV81 @ SY800 )
| ( SY800 = SY799 ) )
| ~ ( ( SY800 != SY799 )
| ( SV81 @ SY800 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[817]) ).
thf(872,plain,
! [SV148: $i > $o,SV83: $i,SV196: $i] :
( ( ( in @ SV196 @ SV83 )
= $false )
| ( ( SV148 @ SV196 )
= $true )
| ( ( ~ ! [SY903: $i] :
~ ~ ( ~ ( in @ SY903 @ SV83 )
| ~ ~ ( SV148 @ SY903 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[819]) ).
thf(873,plain,
! [SV186: $i,SV84: $i > $o] :
( ( ( ~ ( SV84 @ SV186 ) )
= $true )
| ( ( ~ ! [SY951: $i] :
( ~ ( SV84 @ SY951 )
| ( SV186 = SY951 ) ) )
= $true )
| ( ( ! [SY807: $i,SY808: $i] :
( ~ ( SV84 @ SY807 )
| ~ ( SV84 @ SY808 )
| ( SY807 = SY808 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[820]) ).
thf(874,plain,
! [SV87: $i,SV150: $i] :
( ( ( ! [SY906: $i] :
~ ~ ( ~ ( in @ SV150 @ SY906 )
| ~ ( in @ SY906 @ SV87 ) ) )
= $false )
| ( ( in @ SV150 @ ( setunion @ SV87 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[821]) ).
thf(875,plain,
! [SV87: $i,SV150: $i] :
( ( ( ! [SY907: $i] :
~ ~ ( ~ ( in @ SV150 @ SY907 )
| ~ ( in @ SY907 @ SV87 ) ) )
= $true )
| ( ( in @ SV150 @ ( setunion @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(876,plain,
! [SV187: $i,SV90: $i > $o] :
( ( ( ~ ( SV90 @ SV187 ) )
= $true )
| ( ( ~ ! [SY952: $i] :
( ~ ( SV90 @ SY952 )
| ( SV187 = SY952 ) ) )
= $true )
| ( ( SV90
@ ( descr
@ ^ [SY819: $i] : ( SV90 @ SY819 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(877,plain,
! [SV101: $i,SV16: $i,SV154: $i] :
( ( ( SV154 = SV16 )
= $true )
| ( ( in @ SV154 @ SV101 )
= $true )
| ( ( in @ SV154 @ ( setadjoin @ SV16 @ SV101 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[824]) ).
thf(878,plain,
! [SV101: $i,SV16: $i,SV154: $i] :
( ( ( SV154 = SV16 )
= $false )
| ( ( in @ SV154 @ ( setadjoin @ SV16 @ SV101 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[825]) ).
thf(879,plain,
! [SV16: $i,SV101: $i,SV154: $i] :
( ( ( in @ SV154 @ SV101 )
= $false )
| ( ( in @ SV154 @ ( setadjoin @ SV16 @ SV101 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[825]) ).
thf(880,plain,
! [SV172: $i,SV17: $i > $o] :
( ( ( SV17 @ SV172 )
= $false )
| ( ( ~ ! [SY932: $i] :
( ~ ( SV17 @ SY932 )
| ( SV172 = SY932 ) ) )
= $true )
| ( ( ~ ! [SY622: $i] :
~ ( SV17 @ SY622 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(881,plain,
! [SV19: $i,SV103: $i > $o] :
( ( ( ~ ( in @ ( sK18_SY823 @ SV103 @ SV19 ) @ SV19 )
| ~ ( SV103 @ ( sK18_SY823 @ SV103 @ SV19 ) ) )
= $false )
| ( ( ! [SY824: $i] :
( ~ ( in @ SY824 @ SV19 )
| ~ ( SV103 @ SY824 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(882,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( SV21 @ SV173 )
= $false )
| ( ( ~ ! [SY933: $i] :
( ~ ( SV21 @ SY933 )
| ( SV173 = SY933 ) ) )
= $true )
| ( ( ~ ! [SY630: $i] :
~ ~ ( ~ ( SV21 @ SY630 )
| ~ ! [SY631: $i] :
( ~ ( SV21 @ SY631 )
| ( SY630 = SY631 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(883,plain,
! [SV105: $i,SV22: $i,SV155: $i] :
( ( ( in @ SV155 @ SV22 )
= $false )
| ( ( in @ SV155 @ SV105 )
= $true )
| ( ( subset @ SV22 @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[829]) ).
thf(884,plain,
! [SV106: $i > $o,SV24: $i,SV188: $i] :
( ( ( ~ ( in @ SV188 @ SV24 ) )
= $true )
| ( ( ~ ~ ( SV106 @ SV188 ) )
= $true )
| ( ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ SV24 )
| ( SV106 @ SY827 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[830]) ).
thf(885,plain,
! [SV26: $i] :
( ( ( ~ ( in @ ( sK14_SY640 @ SV26 ) @ SV26 ) )
= $false )
| ( ( SV26 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[831]) ).
thf(886,plain,
! [SV26: $i] :
( ( ( ~ $true ) = $false )
| ( ( SV26 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[831]) ).
thf(887,plain,
! [SV27: $i,SV174: $o,SV108: $i] :
( ( ( ~ ( in @ SV108 @ ( sK21_SY934 @ SV174 @ SV27 @ SV108 ) ) )
= $false )
| ( SV174 = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[832]) ).
thf(888,plain,
! [SV108: $i,SV27: $i,SV174: $o] :
( ( ( ~ ( in @ ( sK21_SY934 @ SV174 @ SV27 @ SV108 ) @ SV27 )
| SV174 )
= $false )
| ( SV174 = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[832]) ).
thf(889,plain,
! [SV27: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ ( sK22_SX0 @ SV27 @ SV108 ) ) )
= $false )
| ( $true = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[833]) ).
thf(890,plain,
! [SV108: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK22_SX0 @ SV27 @ SV108 ) @ SV27 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[833]) ).
thf(891,plain,
! [SV27: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ ( sK23_SX0 @ SV27 @ SV108 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[834]) ).
thf(892,plain,
! [SV108: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK23_SX0 @ SV27 @ SV108 ) @ SV27 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[834]) ).
thf(893,plain,
! [SV30: $i,SV111: $i] :
( ( ( ~ ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 )
| ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 ) ) )
= $true )
| ( ( SV30 = SV111 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[835]) ).
thf(894,plain,
! [SV30: $i,SV111: $i] :
( ( ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 )
| ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 ) ) )
= $true )
| ( ( SV30 = SV111 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[835]) ).
thf(895,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ! [SY966: $i] :
( ~ ( SV32 @ ( sK27_SY651 @ SV175 @ SV32 ) )
| ~ ( SV32 @ SY966 )
| ( ( sK27_SY651 @ SV175 @ SV32 )
= SY966 ) ) )
= $false )
| ( ( ~ ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[836]) ).
thf(896,plain,
! [SV37: $i,SV117: $i,SV197: $i] :
( ( ( ~ ( in @ SV197 @ SV117 ) )
= $true )
| ( ( in @ SV197 @ SV37 )
= $true )
| ( ( in @ SV117 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[838]) ).
thf(897,plain,
! [SV117: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK24_SY839 @ SV37 @ SV117 ) @ SV117 ) )
= $false )
| ( ( in @ SV117 @ ( powerset @ SV37 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[839]) ).
thf(898,plain,
! [SV117: $i,SV37: $i] :
( ( ( in @ ( sK24_SY839 @ SV37 @ SV117 ) @ SV37 )
= $false )
| ( ( in @ SV117 @ ( powerset @ SV37 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[839]) ).
thf(899,plain,
! [SV162: $i,SV118: $i,SV38: $i] :
( ( ( SV38 = SV118 )
= $false )
| ( ( in @ SV162 @ SV118 )
= $true )
| ( ( in @ SV162 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[840]) ).
thf(900,plain,
! [SV189: $i,SV119: $i > $o,SV39: $i] :
( ( ( ! [SY842: $i] :
~ ~ ( ~ ( in @ SY842 @ SV39 )
| ~ ~ ( SV119 @ SY842 ) ) )
= $false )
| ( ( SV119 @ SV189 )
= $true )
| ( ( in @ SV189 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(901,plain,
! [SV176: $i,SV40: $i > $o] :
( ( ( SV40 @ SV176 )
= $false )
| ( ( ~ ! [SY935: $i] :
( ~ ( SV40 @ SY935 )
| ( SV176 = SY935 ) ) )
= $true )
| ( ( ! [SY674: $i,SY675: $i] :
( ~ ( SV40 @ SY674 )
| ~ ( SV40 @ SY675 )
| ( SY674 = SY675 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(902,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( SV43 @ SV177 )
= $false )
| ( ( ~ ! [SY936: $i] :
( ~ ( SV43 @ SY936 )
| ( SV177 = SY936 ) ) )
= $true )
| ( ( ~ ! [SY681: $i] :
~ ~ ( ~ ( SV43 @ SY681 )
| ~ ! [SY682: $i] :
( ~ ( SV43 @ SY682 )
| ( SY681 = SY682 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(903,plain,
! [SV163: $i,SV122: $i,SV44: $i] :
( ( ( subset @ SV44 @ SV122 )
= $false )
| ( ( in @ SV163 @ SV122 )
= $true )
| ( ( in @ SV163 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(904,plain,
! [SV123: $i,SV45: $i > $i > $o] :
( ( ( ~ ! [SY967: $i] :
~ ( ~ ( ~ ( in @ SY967 @ ( sK28_SY848 @ SV45 @ SV123 ) )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY967 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY967 ) )
| ( in @ SY967 @ ( sK28_SY848 @ SV45 @ SV123 ) ) ) ) )
= $false )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[845]) ).
thf(905,plain,
! [SV198: $i,SV123: $i,SV45: $i > $i > $o] :
( ( ( ~ ( ~ ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
| ~ ! [SY957: $i] :
( ~ ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SY957 )
| ( SV198 = SY957 ) ) ) )
= $false )
| ( ( ~ ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(906,plain,
! [SV124: $i,SV190: $i,SV46: $i,SV178: $i] :
( ( ( ~ ( in @ SV178 @ SV46 ) )
= $true )
| ( ( in @ SV190 @ SV124 )
= $true )
| ( ( SV178 = SV190 )
= $false )
| ( ( SV46 = SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(907,plain,
! [SV125: $i,SV191: $i,SV48: $i,SV180: $i] :
( ( ( ~ ( ~ ( in @ SV180 @ SV48 )
| ( in @ SV191 @ SV125 ) )
| ~ ( ~ ( in @ SV191 @ SV125 )
| ( in @ SV180 @ SV48 ) ) )
= $false )
| ( ( SV180 = SV191 )
= $false )
| ( ( SV48 = SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(908,plain,
! [SV53: $i,SV128: $i,SV181: $i > $o,SV192: $i > $o] :
( ( ( ~ ( in @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) @ SV53 )
| ! [SY970: $i] :
( ~ ( in @ SY970 @ SV128 )
| ( ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 )
!= SY970 )
| ~ ( ~ ( ~ ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) )
| ( SV192 @ SY970 ) )
| ~ ( ~ ( SV192 @ SY970 )
| ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[849]) ).
thf(909,plain,
! [SV193: $o,SV129: $i,SV54: $i,SV165: $i] :
( ( ( SV165 != SV54 )
= $false )
| ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| SV193 )
| SV193 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[850]) ).
thf(910,plain,
! [SV54: $i,SV129: $i,SV165: $i,SV193: $o] :
( ( SV193 = $false )
| ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| SV193 )
| SV193 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[850]) ).
thf(911,plain,
! [SV129: $i,SV54: $i,SV165: $i] :
( ( ( SV165 != SV54 )
= $false )
| ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| $true )
| $true )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[851]) ).
thf(912,plain,
! [SV54: $i,SV129: $i,SV165: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| $true )
| $true )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[851]) ).
thf(913,plain,
! [SV129: $i,SV54: $i,SV165: $i] :
( ( ( SV165 != SV54 )
= $false )
| ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| $false )
| $false )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(914,plain,
! [SV54: $i,SV129: $i,SV165: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| $false )
| $false )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[852]) ).
thf(915,plain,
! [SV55: $i,SV182: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY715 @ SV182 @ SV55 ) @ SV55 )
| ~ ~ ~ ! [SY958: $i] :
~ ~ ( ~ ( in @ SY958 @ ( sK25_SY715 @ SV182 @ SV55 ) )
| ~ ( in @ SY958 @ SV55 ) ) ) )
= $true )
| ( ( in @ SV182 @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[853]) ).
thf(916,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[854]) ).
thf(917,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ( ~ ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
| ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
| ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[855]) ).
thf(918,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(919,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
| ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
| ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[857]) ).
thf(920,plain,
! [SV133: $i > $o,SV59: $i,SV166: $i] :
( ( ( ~ ( in @ SV166
@ ( dsetconstr @ SV59
@ ^ [SY885: $i] : ( SV133 @ SY885 ) ) ) )
= $true )
| ( ( SV133 @ SV166 )
= $true )
| ( ( in @ SV166 @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[858]) ).
thf(921,plain,
! [SV59: $i,SV166: $i,SV133: $i > $o] :
( ( ( ~ ( SV133 @ SV166 ) )
= $true )
| ( ( in @ SV166
@ ( dsetconstr @ SV59
@ ^ [SY886: $i] : ( SV133 @ SY886 ) ) )
= $true )
| ( ( in @ SV166 @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(922,plain,
! [SV61: $i] :
( ( ~ ~ ( ~ ! [SY913: $i] :
( ~ ( in @ SY913 @ ( sK2_SY743 @ SV61 ) )
| ! [SY745: $i] :
( ~ ( in @ SY745 @ SY913 )
| ( in @ SY745 @ SV61 ) ) )
| ~ ! [SY915: $i,SY916: $i] :
( ~ ~ ( ~ ( in @ SY915 @ SV61 )
| ~ ( in @ SY916 @ SV61 ) )
| ~ ! [SY917: $i] :
( ~ ( in @ SY917 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SY915 @ SY917 )
| ( in @ SY916 @ SY917 ) )
| ~ ( ~ ( in @ SY916 @ SY917 )
| ( in @ SY915 @ SY917 ) ) ) )
| ( SY915 = SY916 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[860]) ).
thf(923,plain,
! [SV61: $i] :
( ( ~ ! [SY918: $i,SY919: $i] :
( ~ ~ ( ~ ( in @ SY918 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY919 @ ( sK2_SY743 @ SV61 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY918 )
| ( in @ SX4 @ SY919 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY919 )
| ( in @ SX4 @ SY918 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[860]) ).
thf(924,plain,
! [SV61: $i,SV199: $i] :
( ( ( ~ ~ ( ~ ! [SY959: $i] :
( ~ ( in @ SY959 @ SV199 )
| ( in @ SY959 @ SV61 ) )
| ~ ~ ! [SY960: $i] :
~ ( in @ SY960 @ SV199 ) ) )
= $true )
| ( ( ~ ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[861]) ).
thf(925,plain,
! [SV68: $i,SV138: $i] :
( ( ( ! [SY889: $i] :
( ~ ( in @ SY889 @ SV138 )
| ( in @ SY889 @ SV68 ) ) )
= $false )
| ( ( SV68 = SV138 )
= $true )
| ( ( in @ ( sK11_SY888 @ SV138 @ SV68 ) @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[862]) ).
thf(926,plain,
! [SV138: $i,SV68: $i] :
( ( ( ~ ( in @ ( sK30_SY889 @ SV68 @ SV138 ) @ SV138 )
| ( in @ ( sK30_SY889 @ SV68 @ SV138 ) @ SV68 ) )
= $false )
| ( ( SV68 = SV138 )
= $true )
| ( ( in @ ( sK11_SY888 @ SV138 @ SV68 ) @ SV138 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[863]) ).
thf(927,plain,
! [SV139: $i > $o,SV69: $i,SV194: $i] :
( ( ( ~ ( in @ SV194 @ SV69 ) )
= $true )
| ( ( ~ ( SV139 @ SV194 ) )
= $true )
| ( ( ( ( dsetconstr @ SV69
@ ^ [SY891: $i] : ( SV139 @ SY891 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[864]) ).
thf(928,plain,
! [SV71: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK26_SY775 @ SV71 ) @ omega )
| ~ ( in @ ( sK26_SY775 @ SV71 ) @ SV71 ) ) )
= $false )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( ! [SY776: $i] :
( ~ ( in @ SY776 @ omega )
| ( in @ SY776 @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[866]) ).
thf(929,plain,
! [SV71: $i] :
( ( ( in @ ( setadjoin @ ( sK26_SY775 @ SV71 ) @ ( sK26_SY775 @ SV71 ) ) @ SV71 )
= $false )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( ! [SY776: $i] :
( ~ ( in @ SY776 @ omega )
| ( in @ SY776 @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[866]) ).
thf(930,plain,
! [SV73: $i,SV141: $i > $o] :
( ( ( ~ ( in @ ( sK19_SY894 @ SV141 @ SV73 ) @ SV73 )
| ~ ( SV141 @ ( sK19_SY894 @ SV141 @ SV73 ) ) )
= $false )
| ( ( ! [SY895: $i] :
( ~ ( in @ SY895 @ SV73 )
| ~ ( SV141 @ SY895 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(931,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ( ~ ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
| ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 ) ) )
= $true )
| ( ( ~ ( ( ( sK20_SY949 @ SV184 @ SV77 )
!= SV184 )
| ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) ) ) )
= $true )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[868]) ).
thf(932,plain,
! [SV146: $i > $o,SV79: $i] :
( ( ( ! [SY901: $i] :
~ ~ ( ~ ( in @ SY901 @ SV79 )
| ~ ( SV146 @ SY901 ) ) )
= $true )
| ( ( in @ ( sK13_SY900 @ SV146 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[869]) ).
thf(933,plain,
! [SV146: $i > $o,SV79: $i] :
( ( ( ! [SY901: $i] :
~ ~ ( ~ ( in @ SY901 @ SV79 )
| ~ ( SV146 @ SY901 ) ) )
= $true )
| ( ( SV146 @ ( sK13_SY900 @ SV146 @ SV79 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[870]) ).
thf(934,plain,
! [SV185: $i,SV81: $i > $o] :
( ( ( SV81 @ SV185 )
= $false )
| ( ( ~ ! [SY950: $i] :
( ~ ( SV81 @ SY950 )
| ( SV185 = SY950 ) ) )
= $true )
| ( ( ~ ! [SY799: $i] :
~ ! [SY800: $i] :
~ ( ~ ( ~ ( SV81 @ SY800 )
| ( SY800 = SY799 ) )
| ~ ( ( SY800 != SY799 )
| ( SV81 @ SY800 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(935,plain,
! [SV196: $i,SV148: $i > $o,SV83: $i] :
( ( ( ! [SY903: $i] :
~ ~ ( ~ ( in @ SY903 @ SV83 )
| ~ ~ ( SV148 @ SY903 ) ) )
= $false )
| ( ( SV148 @ SV196 )
= $true )
| ( ( in @ SV196 @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(936,plain,
! [SV186: $i,SV84: $i > $o] :
( ( ( SV84 @ SV186 )
= $false )
| ( ( ~ ! [SY951: $i] :
( ~ ( SV84 @ SY951 )
| ( SV186 = SY951 ) ) )
= $true )
| ( ( ! [SY807: $i,SY808: $i] :
( ~ ( SV84 @ SY807 )
| ~ ( SV84 @ SY808 )
| ( SY807 = SY808 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(937,plain,
! [SV87: $i,SV150: $i] :
( ( ( ~ ~ ( ~ ( in @ SV150 @ ( sK31_SY906 @ SV87 @ SV150 ) )
| ~ ( in @ ( sK31_SY906 @ SV87 @ SV150 ) @ SV87 ) ) )
= $false )
| ( ( in @ SV150 @ ( setunion @ SV87 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[874]) ).
thf(938,plain,
! [SV87: $i,SV200: $i,SV150: $i] :
( ( ( ~ ~ ( ~ ( in @ SV150 @ SV200 )
| ~ ( in @ SV200 @ SV87 ) ) )
= $true )
| ( ( in @ SV150 @ ( setunion @ SV87 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(939,plain,
! [SV187: $i,SV90: $i > $o] :
( ( ( SV90 @ SV187 )
= $false )
| ( ( ~ ! [SY952: $i] :
( ~ ( SV90 @ SY952 )
| ( SV187 = SY952 ) ) )
= $true )
| ( ( SV90
@ ( descr
@ ^ [SY819: $i] : ( SV90 @ SY819 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(940,plain,
! [SV172: $i,SV17: $i > $o] :
( ( ( ! [SY932: $i] :
( ~ ( SV17 @ SY932 )
| ( SV172 = SY932 ) ) )
= $false )
| ( ( SV17 @ SV172 )
= $false )
| ( ( ~ ! [SY622: $i] :
~ ( SV17 @ SY622 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[880]) ).
thf(941,plain,
! [SV19: $i,SV103: $i > $o] :
( ( ( ~ ( in @ ( sK18_SY823 @ SV103 @ SV19 ) @ SV19 ) )
= $false )
| ( ( ! [SY824: $i] :
( ~ ( in @ SY824 @ SV19 )
| ~ ( SV103 @ SY824 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[881]) ).
thf(942,plain,
! [SV19: $i,SV103: $i > $o] :
( ( ( ~ ( SV103 @ ( sK18_SY823 @ SV103 @ SV19 ) ) )
= $false )
| ( ( ! [SY824: $i] :
( ~ ( in @ SY824 @ SV19 )
| ~ ( SV103 @ SY824 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[881]) ).
thf(943,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ! [SY933: $i] :
( ~ ( SV21 @ SY933 )
| ( SV173 = SY933 ) ) )
= $false )
| ( ( SV21 @ SV173 )
= $false )
| ( ( ~ ! [SY630: $i] :
~ ~ ( ~ ( SV21 @ SY630 )
| ~ ! [SY631: $i] :
( ~ ( SV21 @ SY631 )
| ( SY630 = SY631 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(944,plain,
! [SV106: $i > $o,SV24: $i,SV188: $i] :
( ( ( in @ SV188 @ SV24 )
= $false )
| ( ( ~ ~ ( SV106 @ SV188 ) )
= $true )
| ( ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ SV24 )
| ( SV106 @ SY827 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(945,plain,
! [SV26: $i] :
( ( ( in @ ( sK14_SY640 @ SV26 ) @ SV26 )
= $true )
| ( ( SV26 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[885]) ).
thf(946,plain,
! [SV26: $i] :
( ( $true = $true )
| ( ( SV26 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[886]) ).
thf(947,plain,
! [SV27: $i,SV174: $o,SV108: $i] :
( ( ( in @ SV108 @ ( sK21_SY934 @ SV174 @ SV27 @ SV108 ) )
= $true )
| ( SV174 = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[887]) ).
thf(948,plain,
! [SV108: $i,SV27: $i,SV174: $o] :
( ( ( ~ ( in @ ( sK21_SY934 @ SV174 @ SV27 @ SV108 ) @ SV27 ) )
= $false )
| ( SV174 = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[888]) ).
thf(949,plain,
! [SV27: $i,SV108: $i,SV174: $o] :
( ( SV174 = $false )
| ( SV174 = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[888]) ).
thf(950,plain,
! [SV27: $i,SV108: $i] :
( ( ( in @ SV108 @ ( sK22_SX0 @ SV27 @ SV108 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[889]) ).
thf(951,plain,
! [SV108: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK22_SX0 @ SV27 @ SV108 ) @ SV27 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[890]) ).
thf(952,plain,
! [SV27: $i,SV108: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[890]) ).
thf(953,plain,
! [SV27: $i,SV108: $i] :
( ( ( in @ SV108 @ ( sK23_SX0 @ SV27 @ SV108 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[891]) ).
thf(954,plain,
! [SV108: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK23_SX0 @ SV27 @ SV108 ) @ SV27 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(955,plain,
! [SV27: $i,SV108: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(956,plain,
! [SV30: $i,SV111: $i] :
( ( ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 )
| ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 ) ) )
= $true )
| ( ( SV30 = SV111 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[893]) ).
thf(957,plain,
! [SV30: $i,SV111: $i] :
( ( ( ~ ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 )
| ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 ) )
= $false )
| ( ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 )
= $false )
| ( ( SV30 = SV111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(958,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ( SV32 @ ( sK27_SY651 @ SV175 @ SV32 ) )
| ~ ( SV32 @ ( sK32_SY966 @ SV175 @ SV32 ) )
| ( ( sK27_SY651 @ SV175 @ SV32 )
= ( sK32_SY966 @ SV175 @ SV32 ) ) )
= $false )
| ( ( ~ ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[895]) ).
thf(959,plain,
! [SV37: $i,SV117: $i,SV197: $i] :
( ( ( in @ SV197 @ SV117 )
= $false )
| ( ( in @ SV197 @ SV37 )
= $true )
| ( ( in @ SV117 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(960,plain,
! [SV117: $i,SV37: $i] :
( ( ( in @ ( sK24_SY839 @ SV37 @ SV117 ) @ SV117 )
= $true )
| ( ( in @ SV117 @ ( powerset @ SV37 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[897]) ).
thf(961,plain,
! [SV39: $i,SV119: $i > $o,SV189: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK33_SY842 @ SV189 @ SV119 @ SV39 ) @ SV39 )
| ~ ~ ( SV119 @ ( sK33_SY842 @ SV189 @ SV119 @ SV39 ) ) ) )
= $false )
| ( ( SV119 @ SV189 )
= $true )
| ( ( in @ SV189 @ SV39 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[900]) ).
thf(962,plain,
! [SV176: $i,SV40: $i > $o] :
( ( ( ! [SY935: $i] :
( ~ ( SV40 @ SY935 )
| ( SV176 = SY935 ) ) )
= $false )
| ( ( SV40 @ SV176 )
= $false )
| ( ( ! [SY674: $i,SY675: $i] :
( ~ ( SV40 @ SY674 )
| ~ ( SV40 @ SY675 )
| ( SY674 = SY675 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(963,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ! [SY936: $i] :
( ~ ( SV43 @ SY936 )
| ( SV177 = SY936 ) ) )
= $false )
| ( ( SV43 @ SV177 )
= $false )
| ( ( ~ ! [SY681: $i] :
~ ~ ( ~ ( SV43 @ SY681 )
| ~ ! [SY682: $i] :
( ~ ( SV43 @ SY682 )
| ( SY681 = SY682 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(964,plain,
! [SV123: $i,SV45: $i > $i > $o] :
( ( ( ! [SY967: $i] :
~ ( ~ ( ~ ( in @ SY967 @ ( sK28_SY848 @ SV45 @ SV123 ) )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY967 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY967 ) )
| ( in @ SY967 @ ( sK28_SY848 @ SV45 @ SV123 ) ) ) ) )
= $true )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[904]) ).
thf(965,plain,
! [SV198: $i,SV123: $i,SV45: $i > $i > $o] :
( ( ( ~ ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
| ~ ! [SY957: $i] :
( ~ ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SY957 )
| ( SV198 = SY957 ) ) )
= $true )
| ( ( ~ ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[905]) ).
thf(966,plain,
! [SV124: $i,SV190: $i,SV46: $i,SV178: $i] :
( ( ( in @ SV178 @ SV46 )
= $false )
| ( ( in @ SV190 @ SV124 )
= $true )
| ( ( SV178 = SV190 )
= $false )
| ( ( SV46 = SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(967,plain,
! [SV125: $i,SV191: $i,SV48: $i,SV180: $i] :
( ( ( ~ ( ~ ( in @ SV180 @ SV48 )
| ( in @ SV191 @ SV125 ) ) )
= $false )
| ( ( SV180 = SV191 )
= $false )
| ( ( SV48 = SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[907]) ).
thf(968,plain,
! [SV48: $i,SV180: $i,SV125: $i,SV191: $i] :
( ( ( ~ ( ~ ( in @ SV191 @ SV125 )
| ( in @ SV180 @ SV48 ) ) )
= $false )
| ( ( SV180 = SV191 )
= $false )
| ( ( SV48 = SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[907]) ).
thf(969,plain,
! [SV53: $i,SV128: $i,SV181: $i > $o,SV192: $i > $o] :
( ( ( ~ ( in @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) @ SV53 ) )
= $false )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(970,plain,
! [SV53: $i,SV181: $i > $o,SV192: $i > $o,SV128: $i] :
( ( ( ! [SY970: $i] :
( ~ ( in @ SY970 @ SV128 )
| ( ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 )
!= SY970 )
| ~ ( ~ ( ~ ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) )
| ( SV192 @ SY970 ) )
| ~ ( ~ ( SV192 @ SY970 )
| ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(971,plain,
! [SV193: $o,SV129: $i,SV54: $i,SV165: $i] :
( ( ( SV165 = SV54 )
= $true )
| ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| SV193 )
| SV193 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[909]) ).
thf(972,plain,
! [SV54: $i,SV193: $o,SV129: $i,SV165: $i] :
( ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| SV193 ) )
= $true )
| ( SV193 = $true )
| ( SV193 = $false )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(973,plain,
! [SV129: $i,SV54: $i,SV165: $i] :
( ( ( SV165 = SV54 )
= $true )
| ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| $true )
| $true )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[911]) ).
thf(974,plain,
! [SV54: $i,SV129: $i,SV165: $i] :
( ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(975,plain,
! [SV129: $i,SV54: $i,SV165: $i] :
( ( ( SV165 = SV54 )
= $true )
| ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| $false )
| $false )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[913]) ).
thf(976,plain,
! [SV54: $i,SV129: $i,SV165: $i] :
( ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(977,plain,
! [SV55: $i,SV182: $i] :
( ( ( ~ ( in @ ( sK25_SY715 @ SV182 @ SV55 ) @ SV55 )
| ~ ~ ~ ! [SY958: $i] :
~ ~ ( ~ ( in @ SY958 @ ( sK25_SY715 @ SV182 @ SV55 ) )
| ~ ( in @ SY958 @ SV55 ) ) )
= $false )
| ( ( in @ SV182 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(978,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[916]) ).
thf(979,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
| ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
| ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(980,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[918]) ).
thf(981,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[918]) ).
thf(982,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
| ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) ) )
= $false )
| ( ( ~ ( ~ ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
| ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(983,plain,
! [SV133: $i > $o,SV59: $i,SV166: $i] :
( ( ( in @ SV166
@ ( dsetconstr @ SV59
@ ^ [SY885: $i] : ( SV133 @ SY885 ) ) )
= $false )
| ( ( SV133 @ SV166 )
= $true )
| ( ( in @ SV166 @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(984,plain,
! [SV59: $i,SV166: $i,SV133: $i > $o] :
( ( ( SV133 @ SV166 )
= $false )
| ( ( in @ SV166
@ ( dsetconstr @ SV59
@ ^ [SY886: $i] : ( SV133 @ SY886 ) ) )
= $true )
| ( ( in @ SV166 @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(985,plain,
! [SV61: $i] :
( ( ~ ( ~ ! [SY913: $i] :
( ~ ( in @ SY913 @ ( sK2_SY743 @ SV61 ) )
| ! [SY745: $i] :
( ~ ( in @ SY745 @ SY913 )
| ( in @ SY745 @ SV61 ) ) )
| ~ ! [SY915: $i,SY916: $i] :
( ~ ~ ( ~ ( in @ SY915 @ SV61 )
| ~ ( in @ SY916 @ SV61 ) )
| ~ ! [SY917: $i] :
( ~ ( in @ SY917 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SY915 @ SY917 )
| ( in @ SY916 @ SY917 ) )
| ~ ( ~ ( in @ SY916 @ SY917 )
| ( in @ SY915 @ SY917 ) ) ) )
| ( SY915 = SY916 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[922]) ).
thf(986,plain,
! [SV61: $i] :
( ( ! [SY918: $i,SY919: $i] :
( ~ ~ ( ~ ( in @ SY918 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY919 @ ( sK2_SY743 @ SV61 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY918 )
| ( in @ SX4 @ SY919 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY919 )
| ( in @ SX4 @ SY918 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[923]) ).
thf(987,plain,
! [SV61: $i,SV199: $i] :
( ( ( ~ ( ~ ! [SY959: $i] :
( ~ ( in @ SY959 @ SV199 )
| ( in @ SY959 @ SV61 ) )
| ~ ~ ! [SY960: $i] :
~ ( in @ SY960 @ SV199 ) ) )
= $false )
| ( ( ~ ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[924]) ).
thf(988,plain,
! [SV138: $i,SV68: $i] :
( ( ( ~ ( in @ ( sK34_SY889 @ SV68 @ SV138 ) @ SV138 )
| ( in @ ( sK34_SY889 @ SV68 @ SV138 ) @ SV68 ) )
= $false )
| ( ( SV68 = SV138 )
= $true )
| ( ( in @ ( sK11_SY888 @ SV138 @ SV68 ) @ SV68 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[925]) ).
thf(989,plain,
! [SV138: $i,SV68: $i] :
( ( ( ~ ( in @ ( sK30_SY889 @ SV68 @ SV138 ) @ SV138 ) )
= $false )
| ( ( SV68 = SV138 )
= $true )
| ( ( in @ ( sK11_SY888 @ SV138 @ SV68 ) @ SV138 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[926]) ).
thf(990,plain,
! [SV138: $i,SV68: $i] :
( ( ( in @ ( sK30_SY889 @ SV68 @ SV138 ) @ SV68 )
= $false )
| ( ( SV68 = SV138 )
= $true )
| ( ( in @ ( sK11_SY888 @ SV138 @ SV68 ) @ SV138 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[926]) ).
thf(991,plain,
! [SV139: $i > $o,SV69: $i,SV194: $i] :
( ( ( in @ SV194 @ SV69 )
= $false )
| ( ( ~ ( SV139 @ SV194 ) )
= $true )
| ( ( ( ( dsetconstr @ SV69
@ ^ [SY891: $i] : ( SV139 @ SY891 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(992,plain,
! [SV71: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_SY775 @ SV71 ) @ omega )
| ~ ( in @ ( sK26_SY775 @ SV71 ) @ SV71 ) ) )
= $true )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( ! [SY776: $i] :
( ~ ( in @ SY776 @ omega )
| ( in @ SY776 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[928]) ).
thf(993,plain,
! [SV71: $i,SV201: $i] :
( ( ( ~ ( in @ SV201 @ omega )
| ( in @ SV201 @ SV71 ) )
= $true )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( in @ ( setadjoin @ ( sK26_SY775 @ SV71 ) @ ( sK26_SY775 @ SV71 ) ) @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(994,plain,
! [SV73: $i,SV141: $i > $o] :
( ( ( ~ ( in @ ( sK19_SY894 @ SV141 @ SV73 ) @ SV73 ) )
= $false )
| ( ( ! [SY895: $i] :
( ~ ( in @ SY895 @ SV73 )
| ~ ( SV141 @ SY895 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[930]) ).
thf(995,plain,
! [SV73: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK19_SY894 @ SV141 @ SV73 ) ) )
= $false )
| ( ( ! [SY895: $i] :
( ~ ( in @ SY895 @ SV73 )
| ~ ( SV141 @ SY895 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[930]) ).
thf(996,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
| ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 ) )
= $false )
| ( ( ~ ( ( ( sK20_SY949 @ SV184 @ SV77 )
!= SV184 )
| ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) ) ) )
= $true )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(997,plain,
! [SV146: $i > $o,SV79: $i,SV202: $i] :
( ( ( ~ ~ ( ~ ( in @ SV202 @ SV79 )
| ~ ( SV146 @ SV202 ) ) )
= $true )
| ( ( in @ ( sK13_SY900 @ SV146 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(998,plain,
! [SV146: $i > $o,SV79: $i,SV203: $i] :
( ( ( ~ ~ ( ~ ( in @ SV203 @ SV79 )
| ~ ( SV146 @ SV203 ) ) )
= $true )
| ( ( SV146 @ ( sK13_SY900 @ SV146 @ SV79 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(999,plain,
! [SV185: $i,SV81: $i > $o] :
( ( ( ! [SY950: $i] :
( ~ ( SV81 @ SY950 )
| ( SV185 = SY950 ) ) )
= $false )
| ( ( SV81 @ SV185 )
= $false )
| ( ( ~ ! [SY799: $i] :
~ ! [SY800: $i] :
~ ( ~ ( ~ ( SV81 @ SY800 )
| ( SY800 = SY799 ) )
| ~ ( ( SY800 != SY799 )
| ( SV81 @ SY800 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(1000,plain,
! [SV83: $i,SV148: $i > $o,SV196: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK35_SY903 @ SV196 @ SV148 @ SV83 ) @ SV83 )
| ~ ~ ( SV148 @ ( sK35_SY903 @ SV196 @ SV148 @ SV83 ) ) ) )
= $false )
| ( ( SV148 @ SV196 )
= $true )
| ( ( in @ SV196 @ SV83 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[935]) ).
thf(1001,plain,
! [SV186: $i,SV84: $i > $o] :
( ( ( ! [SY951: $i] :
( ~ ( SV84 @ SY951 )
| ( SV186 = SY951 ) ) )
= $false )
| ( ( SV84 @ SV186 )
= $false )
| ( ( ! [SY807: $i,SY808: $i] :
( ~ ( SV84 @ SY807 )
| ~ ( SV84 @ SY808 )
| ( SY807 = SY808 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(1002,plain,
! [SV87: $i,SV150: $i] :
( ( ( ~ ( ~ ( in @ SV150 @ ( sK31_SY906 @ SV87 @ SV150 ) )
| ~ ( in @ ( sK31_SY906 @ SV87 @ SV150 ) @ SV87 ) ) )
= $true )
| ( ( in @ SV150 @ ( setunion @ SV87 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[937]) ).
thf(1003,plain,
! [SV87: $i,SV200: $i,SV150: $i] :
( ( ( ~ ( ~ ( in @ SV150 @ SV200 )
| ~ ( in @ SV200 @ SV87 ) ) )
= $false )
| ( ( in @ SV150 @ ( setunion @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(1004,plain,
! [SV187: $i,SV90: $i > $o] :
( ( ( ! [SY952: $i] :
( ~ ( SV90 @ SY952 )
| ( SV187 = SY952 ) ) )
= $false )
| ( ( SV90 @ SV187 )
= $false )
| ( ( SV90
@ ( descr
@ ^ [SY819: $i] : ( SV90 @ SY819 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(1005,plain,
! [SV172: $i,SV17: $i > $o] :
( ( ( ~ ( SV17 @ ( sK36_SY932 @ SV172 @ SV17 ) )
| ( SV172
= ( sK36_SY932 @ SV172 @ SV17 ) ) )
= $false )
| ( ( SV17 @ SV172 )
= $false )
| ( ( ~ ! [SY622: $i] :
~ ( SV17 @ SY622 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[940]) ).
thf(1006,plain,
! [SV19: $i,SV103: $i > $o] :
( ( ( in @ ( sK18_SY823 @ SV103 @ SV19 ) @ SV19 )
= $true )
| ( ( ! [SY824: $i] :
( ~ ( in @ SY824 @ SV19 )
| ~ ( SV103 @ SY824 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[941]) ).
thf(1007,plain,
! [SV19: $i,SV103: $i > $o] :
( ( ( SV103 @ ( sK18_SY823 @ SV103 @ SV19 ) )
= $true )
| ( ( ! [SY824: $i] :
( ~ ( in @ SY824 @ SV19 )
| ~ ( SV103 @ SY824 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[942]) ).
thf(1008,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ ( sK37_SY933 @ SV173 @ SV21 ) )
| ( SV173
= ( sK37_SY933 @ SV173 @ SV21 ) ) )
= $false )
| ( ( SV21 @ SV173 )
= $false )
| ( ( ~ ! [SY630: $i] :
~ ~ ( ~ ( SV21 @ SY630 )
| ~ ! [SY631: $i] :
( ~ ( SV21 @ SY631 )
| ( SY630 = SY631 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[943]) ).
thf(1009,plain,
! [SV24: $i,SV188: $i,SV106: $i > $o] :
( ( ( ~ ( SV106 @ SV188 ) )
= $false )
| ( ( in @ SV188 @ SV24 )
= $false )
| ( ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ SV24 )
| ( SV106 @ SY827 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(1010,plain,
! [SV108: $i,SV27: $i,SV174: $o] :
( ( ( in @ ( sK21_SY934 @ SV174 @ SV27 @ SV108 ) @ SV27 )
= $true )
| ( SV174 = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[948]) ).
thf(1011,plain,
! [SV108: $i,SV27: $i] :
( ( ( in @ ( sK22_SX0 @ SV27 @ SV108 ) @ SV27 )
= $true )
| ( $true = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[951]) ).
thf(1012,plain,
! [SV108: $i,SV27: $i] :
( ( ( in @ ( sK23_SX0 @ SV27 @ SV108 ) @ SV27 )
= $true )
| ( $false = $true )
| ( ( in @ SV108 @ ( setunion @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[954]) ).
thf(1013,plain,
! [SV30: $i,SV111: $i] :
( ( ( ~ ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 )
| ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 ) )
= $false )
| ( ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 )
= $true )
| ( ( SV30 = SV111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(1014,plain,
! [SV30: $i,SV111: $i] :
( ( ( ~ ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 ) )
= $false )
| ( ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 )
= $false )
| ( ( SV30 = SV111 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[957]) ).
thf(1015,plain,
! [SV30: $i,SV111: $i] :
( ( ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 )
= $false )
| ( ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 )
= $false )
| ( ( SV30 = SV111 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[957]) ).
thf(1016,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ( SV32 @ ( sK27_SY651 @ SV175 @ SV32 ) ) )
= $false )
| ( ( ~ ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[958]) ).
thf(1017,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ( SV32 @ ( sK32_SY966 @ SV175 @ SV32 ) )
| ( ( sK27_SY651 @ SV175 @ SV32 )
= ( sK32_SY966 @ SV175 @ SV32 ) ) )
= $false )
| ( ( ~ ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[958]) ).
thf(1018,plain,
! [SV39: $i,SV119: $i > $o,SV189: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY842 @ SV189 @ SV119 @ SV39 ) @ SV39 )
| ~ ~ ( SV119 @ ( sK33_SY842 @ SV189 @ SV119 @ SV39 ) ) ) )
= $true )
| ( ( SV119 @ SV189 )
= $true )
| ( ( in @ SV189 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[961]) ).
thf(1019,plain,
! [SV176: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ ( sK38_SY935 @ SV176 @ SV40 ) )
| ( SV176
= ( sK38_SY935 @ SV176 @ SV40 ) ) )
= $false )
| ( ( SV40 @ SV176 )
= $false )
| ( ( ! [SY674: $i,SY675: $i] :
( ~ ( SV40 @ SY674 )
| ~ ( SV40 @ SY675 )
| ( SY674 = SY675 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[962]) ).
thf(1020,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ ( sK39_SY936 @ SV177 @ SV43 ) )
| ( SV177
= ( sK39_SY936 @ SV177 @ SV43 ) ) )
= $false )
| ( ( SV43 @ SV177 )
= $false )
| ( ( ~ ! [SY681: $i] :
~ ~ ( ~ ( SV43 @ SY681 )
| ~ ! [SY682: $i] :
( ~ ( SV43 @ SY682 )
| ( SY681 = SY682 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[963]) ).
thf(1021,plain,
! [SV123: $i,SV45: $i > $i > $o,SV204: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
| ~ ! [SY971: $i] :
~ ~ ( ~ ( in @ SY971 @ SV123 )
| ~ ( SV45 @ SY971 @ SV204 ) ) )
| ~ ( ~ ~ ! [SY972: $i] :
~ ~ ( ~ ( in @ SY972 @ SV123 )
| ~ ( SV45 @ SY972 @ SV204 ) )
| ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) ) ) ) )
= $true )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1022,plain,
! [SV198: $i,SV123: $i,SV45: $i > $i > $o] :
( ( ( ~ ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 ) )
= $true )
| ( ( ~ ! [SY957: $i] :
( ~ ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SY957 )
| ( SV198 = SY957 ) ) )
= $true )
| ( ( ~ ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1023,plain,
! [SV125: $i,SV191: $i,SV48: $i,SV180: $i] :
( ( ( ~ ( in @ SV180 @ SV48 )
| ( in @ SV191 @ SV125 ) )
= $true )
| ( ( SV180 = SV191 )
= $false )
| ( ( SV48 = SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[967]) ).
thf(1024,plain,
! [SV48: $i,SV180: $i,SV125: $i,SV191: $i] :
( ( ( ~ ( in @ SV191 @ SV125 )
| ( in @ SV180 @ SV48 ) )
= $true )
| ( ( SV180 = SV191 )
= $false )
| ( ( SV48 = SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[968]) ).
thf(1025,plain,
! [SV53: $i,SV128: $i,SV181: $i > $o,SV192: $i > $o] :
( ( ( in @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) @ SV53 )
= $true )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[969]) ).
thf(1026,plain,
! [SV128: $i,SV192: $i > $o,SV181: $i > $o,SV53: $i] :
( ( ( ~ ( in @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) @ SV128 )
| ( ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 )
!= ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
| ~ ( ~ ( ~ ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) )
| ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) ) )
| ~ ( ~ ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
| ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[970]) ).
thf(1027,plain,
! [SV54: $i,SV193: $o,SV129: $i,SV165: $i] :
( ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| SV193 ) )
= $true )
| ( SV193 = $true )
| ( ( SV165 = SV54 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1028,plain,
! [SV54: $i,SV193: $o,SV129: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ SV129 )
| SV193 )
= $false )
| ( SV193 = $true )
| ( SV193 = $false )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1029,plain,
! [SV54: $i,SV129: $i,SV165: $i] :
( ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( SV165 = SV54 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[973]) ).
thf(1030,plain,
! [SV54: $i,SV129: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ SV129 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1031,plain,
! [SV54: $i,SV129: $i,SV165: $i] :
( ( ( ~ ( ~ ( in @ SV165 @ SV129 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( SV165 = SV54 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[975]) ).
thf(1032,plain,
! [SV54: $i,SV129: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ SV129 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1033,plain,
! [SV55: $i,SV182: $i] :
( ( ( ~ ( in @ ( sK25_SY715 @ SV182 @ SV55 ) @ SV55 ) )
= $false )
| ( ( in @ SV182 @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[977]) ).
thf(1034,plain,
! [SV55: $i,SV182: $i] :
( ( ( ~ ~ ~ ! [SY958: $i] :
~ ~ ( ~ ( in @ SY958 @ ( sK25_SY715 @ SV182 @ SV55 ) )
| ~ ( in @ SY958 @ SV55 ) ) )
= $false )
| ( ( in @ SV182 @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[977]) ).
thf(1035,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[978]) ).
thf(1036,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
| ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1037,plain,
! [SV56: $i > $o,SV130: $i > $o] :
( ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
| ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1038,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[980]) ).
thf(1039,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[981]) ).
thf(1040,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) ) )
= $false )
| ( ( ~ ( ~ ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
| ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[982]) ).
thf(1041,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( ~ ( ~ ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
| ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[982]) ).
thf(1042,plain,
! [SV61: $i] :
( ( ~ ! [SY913: $i] :
( ~ ( in @ SY913 @ ( sK2_SY743 @ SV61 ) )
| ! [SY745: $i] :
( ~ ( in @ SY745 @ SY913 )
| ( in @ SY745 @ SV61 ) ) )
| ~ ! [SY915: $i,SY916: $i] :
( ~ ~ ( ~ ( in @ SY915 @ SV61 )
| ~ ( in @ SY916 @ SV61 ) )
| ~ ! [SY917: $i] :
( ~ ( in @ SY917 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SY915 @ SY917 )
| ( in @ SY916 @ SY917 ) )
| ~ ( ~ ( in @ SY916 @ SY917 )
| ( in @ SY915 @ SY917 ) ) ) )
| ( SY915 = SY916 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1043,plain,
! [SV61: $i,SV205: $i] :
( ( ! [SY973: $i] :
( ~ ~ ( ~ ( in @ SV205 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY973 @ ( sK2_SY743 @ SV61 ) ) )
| ! [SY974: $i] :
( ~ ( in @ SY974 @ SV205 )
| ( in @ SY974 @ SY973 ) )
| ! [SY975: $i] :
( ~ ( in @ SY975 @ SY973 )
| ( in @ SY975 @ SV205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1044,plain,
! [SV61: $i,SV199: $i] :
( ( ( ~ ! [SY959: $i] :
( ~ ( in @ SY959 @ SV199 )
| ( in @ SY959 @ SV61 ) )
| ~ ~ ! [SY960: $i] :
~ ( in @ SY960 @ SV199 ) )
= $true )
| ( ( ~ ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[987]) ).
thf(1045,plain,
! [SV138: $i,SV68: $i] :
( ( ( ~ ( in @ ( sK34_SY889 @ SV68 @ SV138 ) @ SV138 ) )
= $false )
| ( ( SV68 = SV138 )
= $true )
| ( ( in @ ( sK11_SY888 @ SV138 @ SV68 ) @ SV68 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[988]) ).
thf(1046,plain,
! [SV138: $i,SV68: $i] :
( ( ( in @ ( sK34_SY889 @ SV68 @ SV138 ) @ SV68 )
= $false )
| ( ( SV68 = SV138 )
= $true )
| ( ( in @ ( sK11_SY888 @ SV138 @ SV68 ) @ SV68 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[988]) ).
thf(1047,plain,
! [SV138: $i,SV68: $i] :
( ( ( in @ ( sK30_SY889 @ SV68 @ SV138 ) @ SV138 )
= $true )
| ( ( SV68 = SV138 )
= $true )
| ( ( in @ ( sK11_SY888 @ SV138 @ SV68 ) @ SV138 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[989]) ).
thf(1048,plain,
! [SV69: $i,SV194: $i,SV139: $i > $o] :
( ( ( SV139 @ SV194 )
= $false )
| ( ( in @ SV194 @ SV69 )
= $false )
| ( ( ( ( dsetconstr @ SV69
@ ^ [SY891: $i] : ( SV139 @ SY891 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1049,plain,
! [SV71: $i] :
( ( ( ~ ( in @ ( sK26_SY775 @ SV71 ) @ omega )
| ~ ( in @ ( sK26_SY775 @ SV71 ) @ SV71 ) )
= $false )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( ! [SY776: $i] :
( ~ ( in @ SY776 @ omega )
| ( in @ SY776 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1050,plain,
! [SV71: $i,SV201: $i] :
( ( ( ~ ( in @ SV201 @ omega ) )
= $true )
| ( ( in @ SV201 @ SV71 )
= $true )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( in @ ( setadjoin @ ( sK26_SY775 @ SV71 ) @ ( sK26_SY775 @ SV71 ) ) @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1051,plain,
! [SV73: $i,SV141: $i > $o] :
( ( ( in @ ( sK19_SY894 @ SV141 @ SV73 ) @ SV73 )
= $true )
| ( ( ! [SY895: $i] :
( ~ ( in @ SY895 @ SV73 )
| ~ ( SV141 @ SY895 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[994]) ).
thf(1052,plain,
! [SV73: $i,SV141: $i > $o] :
( ( ( SV141 @ ( sK19_SY894 @ SV141 @ SV73 ) )
= $true )
| ( ( ! [SY895: $i] :
( ~ ( in @ SY895 @ SV73 )
| ~ ( SV141 @ SY895 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[995]) ).
thf(1053,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) ) )
= $false )
| ( ( ~ ( ( ( sK20_SY949 @ SV184 @ SV77 )
!= SV184 )
| ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) ) ) )
= $true )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[996]) ).
thf(1054,plain,
! [SV77: $i > $o,SV184: $i] :
( ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( ~ ( ( ( sK20_SY949 @ SV184 @ SV77 )
!= SV184 )
| ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) ) ) )
= $true )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[996]) ).
thf(1055,plain,
! [SV146: $i > $o,SV79: $i,SV202: $i] :
( ( ( ~ ( ~ ( in @ SV202 @ SV79 )
| ~ ( SV146 @ SV202 ) ) )
= $false )
| ( ( in @ ( sK13_SY900 @ SV146 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1056,plain,
! [SV146: $i > $o,SV79: $i,SV203: $i] :
( ( ( ~ ( ~ ( in @ SV203 @ SV79 )
| ~ ( SV146 @ SV203 ) ) )
= $false )
| ( ( SV146 @ ( sK13_SY900 @ SV146 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[998]) ).
thf(1057,plain,
! [SV185: $i,SV81: $i > $o] :
( ( ( ~ ( SV81 @ ( sK41_SY950 @ SV185 @ SV81 ) )
| ( SV185
= ( sK41_SY950 @ SV185 @ SV81 ) ) )
= $false )
| ( ( SV81 @ SV185 )
= $false )
| ( ( ~ ! [SY799: $i] :
~ ! [SY800: $i] :
~ ( ~ ( ~ ( SV81 @ SY800 )
| ( SY800 = SY799 ) )
| ~ ( ( SY800 != SY799 )
| ( SV81 @ SY800 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[999]) ).
thf(1058,plain,
! [SV83: $i,SV148: $i > $o,SV196: $i] :
( ( ( ~ ( ~ ( in @ ( sK35_SY903 @ SV196 @ SV148 @ SV83 ) @ SV83 )
| ~ ~ ( SV148 @ ( sK35_SY903 @ SV196 @ SV148 @ SV83 ) ) ) )
= $true )
| ( ( SV148 @ SV196 )
= $true )
| ( ( in @ SV196 @ SV83 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1059,plain,
! [SV186: $i,SV84: $i > $o] :
( ( ( ~ ( SV84 @ ( sK42_SY951 @ SV186 @ SV84 ) )
| ( SV186
= ( sK42_SY951 @ SV186 @ SV84 ) ) )
= $false )
| ( ( SV84 @ SV186 )
= $false )
| ( ( ! [SY807: $i,SY808: $i] :
( ~ ( SV84 @ SY807 )
| ~ ( SV84 @ SY808 )
| ( SY807 = SY808 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1001]) ).
thf(1060,plain,
! [SV87: $i,SV150: $i] :
( ( ( ~ ( in @ SV150 @ ( sK31_SY906 @ SV87 @ SV150 ) )
| ~ ( in @ ( sK31_SY906 @ SV87 @ SV150 ) @ SV87 ) )
= $false )
| ( ( in @ SV150 @ ( setunion @ SV87 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1061,plain,
! [SV87: $i,SV200: $i,SV150: $i] :
( ( ( ~ ( in @ SV150 @ SV200 )
| ~ ( in @ SV200 @ SV87 ) )
= $true )
| ( ( in @ SV150 @ ( setunion @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1003]) ).
thf(1062,plain,
! [SV187: $i,SV90: $i > $o] :
( ( ( ~ ( SV90 @ ( sK43_SY952 @ SV187 @ SV90 ) )
| ( SV187
= ( sK43_SY952 @ SV187 @ SV90 ) ) )
= $false )
| ( ( SV90 @ SV187 )
= $false )
| ( ( SV90
@ ( descr
@ ^ [SY819: $i] : ( SV90 @ SY819 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1004]) ).
thf(1063,plain,
! [SV172: $i,SV17: $i > $o] :
( ( ( ~ ( SV17 @ ( sK36_SY932 @ SV172 @ SV17 ) ) )
= $false )
| ( ( SV17 @ SV172 )
= $false )
| ( ( ~ ! [SY622: $i] :
~ ( SV17 @ SY622 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1005]) ).
thf(1064,plain,
! [SV17: $i > $o,SV172: $i] :
( ( ( SV172
= ( sK36_SY932 @ SV172 @ SV17 ) )
= $false )
| ( ( SV17 @ SV172 )
= $false )
| ( ( ~ ! [SY622: $i] :
~ ( SV17 @ SY622 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1005]) ).
thf(1065,plain,
! [SV103: $i > $o,SV19: $i,SV206: $i] :
( ( ( ~ ( in @ SV206 @ SV19 )
| ~ ( SV103 @ SV206 ) )
= $true )
| ( ( in @ ( sK18_SY823 @ SV103 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1066,plain,
! [SV103: $i > $o,SV19: $i,SV207: $i] :
( ( ( ~ ( in @ SV207 @ SV19 )
| ~ ( SV103 @ SV207 ) )
= $true )
| ( ( SV103 @ ( sK18_SY823 @ SV103 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1067,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ ( sK37_SY933 @ SV173 @ SV21 ) ) )
= $false )
| ( ( SV21 @ SV173 )
= $false )
| ( ( ~ ! [SY630: $i] :
~ ~ ( ~ ( SV21 @ SY630 )
| ~ ! [SY631: $i] :
( ~ ( SV21 @ SY631 )
| ( SY630 = SY631 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1008]) ).
thf(1068,plain,
! [SV21: $i > $o,SV173: $i] :
( ( ( SV173
= ( sK37_SY933 @ SV173 @ SV21 ) )
= $false )
| ( ( SV21 @ SV173 )
= $false )
| ( ( ~ ! [SY630: $i] :
~ ~ ( ~ ( SV21 @ SY630 )
| ~ ! [SY631: $i] :
( ~ ( SV21 @ SY631 )
| ( SY630 = SY631 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1008]) ).
thf(1069,plain,
! [SV24: $i,SV188: $i,SV106: $i > $o] :
( ( ( SV106 @ SV188 )
= $true )
| ( ( in @ SV188 @ SV24 )
= $false )
| ( ( ~ ! [SY827: $i] :
( ~ ( in @ SY827 @ SV24 )
| ( SV106 @ SY827 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1009]) ).
thf(1070,plain,
! [SV30: $i,SV111: $i] :
( ( ( ~ ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 ) )
= $false )
| ( ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 )
= $true )
| ( ( SV30 = SV111 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1013]) ).
thf(1071,plain,
! [SV30: $i,SV111: $i] :
( ( ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 )
= $false )
| ( ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 )
= $true )
| ( ( SV30 = SV111 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1013]) ).
thf(1072,plain,
! [SV30: $i,SV111: $i] :
( ( ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 )
= $true )
| ( ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 )
= $false )
| ( ( SV30 = SV111 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1014]) ).
thf(1073,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( SV32 @ ( sK27_SY651 @ SV175 @ SV32 ) )
= $true )
| ( ( ~ ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1016]) ).
thf(1074,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ( SV32 @ ( sK32_SY966 @ SV175 @ SV32 ) ) )
= $false )
| ( ( ~ ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1017]) ).
thf(1075,plain,
! [SV32: $i > $o,SV175: $i] :
( ( ( ( sK27_SY651 @ SV175 @ SV32 )
= ( sK32_SY966 @ SV175 @ SV32 ) )
= $false )
| ( ( ~ ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1017]) ).
thf(1076,plain,
! [SV39: $i,SV119: $i > $o,SV189: $i] :
( ( ( ~ ( in @ ( sK33_SY842 @ SV189 @ SV119 @ SV39 ) @ SV39 )
| ~ ~ ( SV119 @ ( sK33_SY842 @ SV189 @ SV119 @ SV39 ) ) )
= $false )
| ( ( SV119 @ SV189 )
= $true )
| ( ( in @ SV189 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1077,plain,
! [SV176: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ ( sK38_SY935 @ SV176 @ SV40 ) ) )
= $false )
| ( ( SV40 @ SV176 )
= $false )
| ( ( ! [SY674: $i,SY675: $i] :
( ~ ( SV40 @ SY674 )
| ~ ( SV40 @ SY675 )
| ( SY674 = SY675 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1019]) ).
thf(1078,plain,
! [SV40: $i > $o,SV176: $i] :
( ( ( SV176
= ( sK38_SY935 @ SV176 @ SV40 ) )
= $false )
| ( ( SV40 @ SV176 )
= $false )
| ( ( ! [SY674: $i,SY675: $i] :
( ~ ( SV40 @ SY674 )
| ~ ( SV40 @ SY675 )
| ( SY674 = SY675 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1019]) ).
thf(1079,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ ( sK39_SY936 @ SV177 @ SV43 ) ) )
= $false )
| ( ( SV43 @ SV177 )
= $false )
| ( ( ~ ! [SY681: $i] :
~ ~ ( ~ ( SV43 @ SY681 )
| ~ ! [SY682: $i] :
( ~ ( SV43 @ SY682 )
| ( SY681 = SY682 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1080,plain,
! [SV43: $i > $o,SV177: $i] :
( ( ( SV177
= ( sK39_SY936 @ SV177 @ SV43 ) )
= $false )
| ( ( SV43 @ SV177 )
= $false )
| ( ( ~ ! [SY681: $i] :
~ ~ ( ~ ( SV43 @ SY681 )
| ~ ! [SY682: $i] :
( ~ ( SV43 @ SY682 )
| ( SY681 = SY682 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1081,plain,
! [SV123: $i,SV45: $i > $i > $o,SV204: $i] :
( ( ( ~ ( ~ ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
| ~ ! [SY971: $i] :
~ ~ ( ~ ( in @ SY971 @ SV123 )
| ~ ( SV45 @ SY971 @ SV204 ) ) )
| ~ ( ~ ~ ! [SY972: $i] :
~ ~ ( ~ ( in @ SY972 @ SV123 )
| ~ ( SV45 @ SY972 @ SV204 ) )
| ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1082,plain,
! [SV198: $i,SV123: $i,SV45: $i > $i > $o] :
( ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( ~ ! [SY957: $i] :
( ~ ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SY957 )
| ( SV198 = SY957 ) ) )
= $true )
| ( ( ~ ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1083,plain,
! [SV125: $i,SV191: $i,SV48: $i,SV180: $i] :
( ( ( ~ ( in @ SV180 @ SV48 ) )
= $true )
| ( ( in @ SV191 @ SV125 )
= $true )
| ( ( SV180 = SV191 )
= $false )
| ( ( SV48 = SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1084,plain,
! [SV48: $i,SV180: $i,SV125: $i,SV191: $i] :
( ( ( ~ ( in @ SV191 @ SV125 ) )
= $true )
| ( ( in @ SV180 @ SV48 )
= $true )
| ( ( SV180 = SV191 )
= $false )
| ( ( SV48 = SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1085,plain,
! [SV128: $i,SV192: $i > $o,SV181: $i > $o,SV53: $i] :
( ( ( ~ ( in @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) @ SV128 ) )
= $false )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1026]) ).
thf(1086,plain,
! [SV53: $i,SV128: $i,SV181: $i > $o,SV192: $i > $o] :
( ( ( ( ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 )
!= ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
| ~ ( ~ ( ~ ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) )
| ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) ) )
| ~ ( ~ ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
| ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1026]) ).
thf(1087,plain,
! [SV54: $i,SV193: $o,SV129: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ SV129 )
| SV193 )
= $false )
| ( SV193 = $true )
| ( ( SV165 = SV54 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1088,plain,
! [SV54: $i,SV193: $o,SV129: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ SV129 ) )
= $false )
| ( SV193 = $true )
| ( SV193 = $false )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1028]) ).
thf(1089,plain,
! [SV129: $i,SV54: $i,SV165: $i,SV193: $o] :
( ( SV193 = $false )
| ( SV193 = $true )
| ( SV193 = $false )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1028]) ).
thf(1090,plain,
! [SV54: $i,SV129: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ SV129 )
| $true )
= $false )
| ( $true = $true )
| ( ( SV165 = SV54 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1091,plain,
! [SV54: $i,SV129: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ SV129 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1030]) ).
thf(1092,plain,
! [SV129: $i,SV54: $i,SV165: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1030]) ).
thf(1093,plain,
! [SV54: $i,SV129: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ SV129 )
| $false )
= $false )
| ( $false = $true )
| ( ( SV165 = SV54 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1094,plain,
! [SV54: $i,SV129: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ SV129 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1032]) ).
thf(1095,plain,
! [SV129: $i,SV54: $i,SV165: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1032]) ).
thf(1096,plain,
! [SV55: $i,SV182: $i] :
( ( ( in @ ( sK25_SY715 @ SV182 @ SV55 ) @ SV55 )
= $true )
| ( ( in @ SV182 @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1033]) ).
thf(1097,plain,
! [SV55: $i,SV182: $i] :
( ( ( ~ ~ ! [SY958: $i] :
~ ~ ( ~ ( in @ SY958 @ ( sK25_SY715 @ SV182 @ SV55 ) )
| ~ ( in @ SY958 @ SV55 ) ) )
= $true )
| ( ( in @ SV182 @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1034]) ).
thf(1098,plain,
! [SV130: $i > $o,SV208: $i,SV56: $i > $o] :
( ( ( ~ ~ ( ~ ( SV56 @ SV208 )
| ~ ! [SY976: $i] :
( ~ ( SV56 @ SY976 )
| ( SV208 = SY976 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1099,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( ~ ( ~ ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
| ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1036]) ).
thf(1100,plain,
! [SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
| ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1101,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1102,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1039]) ).
thf(1103,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( ~ ( ~ ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
| ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1040]) ).
thf(1104,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
| ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1105,plain,
! [SV61: $i] :
( ( ~ ! [SY913: $i] :
( ~ ( in @ SY913 @ ( sK2_SY743 @ SV61 ) )
| ! [SY745: $i] :
( ~ ( in @ SY745 @ SY913 )
| ( in @ SY745 @ SV61 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1042]) ).
thf(1106,plain,
! [SV61: $i] :
( ( ~ ! [SY915: $i,SY916: $i] :
( ~ ~ ( ~ ( in @ SY915 @ SV61 )
| ~ ( in @ SY916 @ SV61 ) )
| ~ ! [SY917: $i] :
( ~ ( in @ SY917 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SY915 @ SY917 )
| ( in @ SY916 @ SY917 ) )
| ~ ( ~ ( in @ SY916 @ SY917 )
| ( in @ SY915 @ SY917 ) ) ) )
| ( SY915 = SY916 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1042]) ).
thf(1107,plain,
! [SV209: $i,SV61: $i,SV205: $i] :
( ( ~ ~ ( ~ ( in @ SV205 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SV209 @ ( sK2_SY743 @ SV61 ) ) )
| ! [SY977: $i] :
( ~ ( in @ SY977 @ SV205 )
| ( in @ SY977 @ SV209 ) )
| ! [SY978: $i] :
( ~ ( in @ SY978 @ SV209 )
| ( in @ SY978 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1108,plain,
! [SV61: $i,SV199: $i] :
( ( ( ~ ! [SY959: $i] :
( ~ ( in @ SY959 @ SV199 )
| ( in @ SY959 @ SV61 ) ) )
= $true )
| ( ( ~ ~ ! [SY960: $i] :
~ ( in @ SY960 @ SV199 ) )
= $true )
| ( ( ~ ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1044]) ).
thf(1109,plain,
! [SV138: $i,SV68: $i] :
( ( ( in @ ( sK34_SY889 @ SV68 @ SV138 ) @ SV138 )
= $true )
| ( ( SV68 = SV138 )
= $true )
| ( ( in @ ( sK11_SY888 @ SV138 @ SV68 ) @ SV68 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1045]) ).
thf(1110,plain,
! [SV194: $i,SV139: $i > $o,SV69: $i] :
( ( ( ( dsetconstr @ SV69
@ ^ [SY891: $i] : ( SV139 @ SY891 ) )
!= emptyset )
= $true )
| ( $false = $true )
| ( ( in @ SV194 @ SV69 )
= $false )
| ( ( SV139 @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1111,plain,
! [SV71: $i] :
( ( ( ~ ( in @ ( sK26_SY775 @ SV71 ) @ omega ) )
= $false )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( ! [SY776: $i] :
( ~ ( in @ SY776 @ omega )
| ( in @ SY776 @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1049]) ).
thf(1112,plain,
! [SV71: $i] :
( ( ( ~ ( in @ ( sK26_SY775 @ SV71 ) @ SV71 ) )
= $false )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( ! [SY776: $i] :
( ~ ( in @ SY776 @ omega )
| ( in @ SY776 @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1049]) ).
thf(1113,plain,
! [SV71: $i,SV201: $i] :
( ( ( in @ SV201 @ omega )
= $false )
| ( ( in @ SV201 @ SV71 )
= $true )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( in @ ( setadjoin @ ( sK26_SY775 @ SV71 ) @ ( sK26_SY775 @ SV71 ) ) @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1114,plain,
! [SV141: $i > $o,SV73: $i,SV210: $i] :
( ( ( ~ ( in @ SV210 @ SV73 )
| ~ ( SV141 @ SV210 ) )
= $true )
| ( ( in @ ( sK19_SY894 @ SV141 @ SV73 ) @ SV73 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1115,plain,
! [SV141: $i > $o,SV73: $i,SV211: $i] :
( ( ( ~ ( in @ SV211 @ SV73 )
| ~ ( SV141 @ SV211 ) )
= $true )
| ( ( SV141 @ ( sK19_SY894 @ SV141 @ SV73 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1116,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( ~ ( ( ( sK20_SY949 @ SV184 @ SV77 )
!= SV184 )
| ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) ) ) )
= $true )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1053]) ).
thf(1117,plain,
! [SV77: $i > $o,SV184: $i] :
( ( ( ( ( sK20_SY949 @ SV184 @ SV77 )
!= SV184 )
| ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) ) )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1118,plain,
! [SV146: $i > $o,SV79: $i,SV202: $i] :
( ( ( ~ ( in @ SV202 @ SV79 )
| ~ ( SV146 @ SV202 ) )
= $true )
| ( ( in @ ( sK13_SY900 @ SV146 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1055]) ).
thf(1119,plain,
! [SV146: $i > $o,SV79: $i,SV203: $i] :
( ( ( ~ ( in @ SV203 @ SV79 )
| ~ ( SV146 @ SV203 ) )
= $true )
| ( ( SV146 @ ( sK13_SY900 @ SV146 @ SV79 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1056]) ).
thf(1120,plain,
! [SV185: $i,SV81: $i > $o] :
( ( ( ~ ( SV81 @ ( sK41_SY950 @ SV185 @ SV81 ) ) )
= $false )
| ( ( SV81 @ SV185 )
= $false )
| ( ( ~ ! [SY799: $i] :
~ ! [SY800: $i] :
~ ( ~ ( ~ ( SV81 @ SY800 )
| ( SY800 = SY799 ) )
| ~ ( ( SY800 != SY799 )
| ( SV81 @ SY800 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1121,plain,
! [SV81: $i > $o,SV185: $i] :
( ( ( SV185
= ( sK41_SY950 @ SV185 @ SV81 ) )
= $false )
| ( ( SV81 @ SV185 )
= $false )
| ( ( ~ ! [SY799: $i] :
~ ! [SY800: $i] :
~ ( ~ ( ~ ( SV81 @ SY800 )
| ( SY800 = SY799 ) )
| ~ ( ( SY800 != SY799 )
| ( SV81 @ SY800 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1122,plain,
! [SV83: $i,SV148: $i > $o,SV196: $i] :
( ( ( ~ ( in @ ( sK35_SY903 @ SV196 @ SV148 @ SV83 ) @ SV83 )
| ~ ~ ( SV148 @ ( sK35_SY903 @ SV196 @ SV148 @ SV83 ) ) )
= $false )
| ( ( SV148 @ SV196 )
= $true )
| ( ( in @ SV196 @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1123,plain,
! [SV186: $i,SV84: $i > $o] :
( ( ( ~ ( SV84 @ ( sK42_SY951 @ SV186 @ SV84 ) ) )
= $false )
| ( ( SV84 @ SV186 )
= $false )
| ( ( ! [SY807: $i,SY808: $i] :
( ~ ( SV84 @ SY807 )
| ~ ( SV84 @ SY808 )
| ( SY807 = SY808 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1124,plain,
! [SV84: $i > $o,SV186: $i] :
( ( ( SV186
= ( sK42_SY951 @ SV186 @ SV84 ) )
= $false )
| ( ( SV84 @ SV186 )
= $false )
| ( ( ! [SY807: $i,SY808: $i] :
( ~ ( SV84 @ SY807 )
| ~ ( SV84 @ SY808 )
| ( SY807 = SY808 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1125,plain,
! [SV87: $i,SV150: $i] :
( ( ( ~ ( in @ SV150 @ ( sK31_SY906 @ SV87 @ SV150 ) ) )
= $false )
| ( ( in @ SV150 @ ( setunion @ SV87 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1060]) ).
thf(1126,plain,
! [SV150: $i,SV87: $i] :
( ( ( ~ ( in @ ( sK31_SY906 @ SV87 @ SV150 ) @ SV87 ) )
= $false )
| ( ( in @ SV150 @ ( setunion @ SV87 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1060]) ).
thf(1127,plain,
! [SV87: $i,SV200: $i,SV150: $i] :
( ( ( ~ ( in @ SV150 @ SV200 ) )
= $true )
| ( ( ~ ( in @ SV200 @ SV87 ) )
= $true )
| ( ( in @ SV150 @ ( setunion @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1128,plain,
! [SV187: $i,SV90: $i > $o] :
( ( ( ~ ( SV90 @ ( sK43_SY952 @ SV187 @ SV90 ) ) )
= $false )
| ( ( SV90 @ SV187 )
= $false )
| ( ( SV90
@ ( descr
@ ^ [SY819: $i] : ( SV90 @ SY819 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1062]) ).
thf(1129,plain,
! [SV90: $i > $o,SV187: $i] :
( ( ( SV187
= ( sK43_SY952 @ SV187 @ SV90 ) )
= $false )
| ( ( SV90 @ SV187 )
= $false )
| ( ( SV90
@ ( descr
@ ^ [SY819: $i] : ( SV90 @ SY819 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1062]) ).
thf(1130,plain,
! [SV172: $i,SV17: $i > $o] :
( ( ( SV17 @ ( sK36_SY932 @ SV172 @ SV17 ) )
= $true )
| ( ( SV17 @ SV172 )
= $false )
| ( ( ~ ! [SY622: $i] :
~ ( SV17 @ SY622 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1063]) ).
thf(1131,plain,
! [SV172: $i,SV17: $i > $o] :
( ( ( ! [SY622: $i] :
~ ( SV17 @ SY622 ) )
= $false )
| ( ( SV17 @ SV172 )
= $false )
| ( ( SV172
= ( sK36_SY932 @ SV172 @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1064]) ).
thf(1132,plain,
! [SV103: $i > $o,SV19: $i,SV206: $i] :
( ( ( ~ ( in @ SV206 @ SV19 ) )
= $true )
| ( ( ~ ( SV103 @ SV206 ) )
= $true )
| ( ( in @ ( sK18_SY823 @ SV103 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1133,plain,
! [SV103: $i > $o,SV19: $i,SV207: $i] :
( ( ( ~ ( in @ SV207 @ SV19 ) )
= $true )
| ( ( ~ ( SV103 @ SV207 ) )
= $true )
| ( ( SV103 @ ( sK18_SY823 @ SV103 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1134,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( SV21 @ ( sK37_SY933 @ SV173 @ SV21 ) )
= $true )
| ( ( SV21 @ SV173 )
= $false )
| ( ( ~ ! [SY630: $i] :
~ ~ ( ~ ( SV21 @ SY630 )
| ~ ! [SY631: $i] :
( ~ ( SV21 @ SY631 )
| ( SY630 = SY631 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1067]) ).
thf(1135,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ! [SY630: $i] :
~ ~ ( ~ ( SV21 @ SY630 )
| ~ ! [SY631: $i] :
( ~ ( SV21 @ SY631 )
| ( SY630 = SY631 ) ) ) )
= $false )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV173
= ( sK37_SY933 @ SV173 @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1136,plain,
! [SV188: $i,SV106: $i > $o,SV24: $i] :
( ( ( ! [SY827: $i] :
( ~ ( in @ SY827 @ SV24 )
| ( SV106 @ SY827 ) ) )
= $false )
| ( ( in @ SV188 @ SV24 )
= $false )
| ( ( SV106 @ SV188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1137,plain,
! [SV30: $i,SV111: $i] :
( ( ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV111 )
= $true )
| ( ( in @ ( sK6_SY832 @ SV111 @ SV30 ) @ SV30 )
= $true )
| ( ( SV30 = SV111 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1070]) ).
thf(1138,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $false )
| ( ( SV32 @ ( sK27_SY651 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1073]) ).
thf(1139,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( SV32 @ ( sK32_SY966 @ SV175 @ SV32 ) )
= $true )
| ( ( ~ ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1140,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $false )
| ( ( ( sK27_SY651 @ SV175 @ SV32 )
= ( sK32_SY966 @ SV175 @ SV32 ) )
= $false )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1141,plain,
! [SV39: $i,SV119: $i > $o,SV189: $i] :
( ( ( ~ ( in @ ( sK33_SY842 @ SV189 @ SV119 @ SV39 ) @ SV39 ) )
= $false )
| ( ( SV119 @ SV189 )
= $true )
| ( ( in @ SV189 @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1142,plain,
! [SV39: $i,SV189: $i,SV119: $i > $o] :
( ( ( ~ ~ ( SV119 @ ( sK33_SY842 @ SV189 @ SV119 @ SV39 ) ) )
= $false )
| ( ( SV119 @ SV189 )
= $true )
| ( ( in @ SV189 @ SV39 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1143,plain,
! [SV176: $i,SV40: $i > $o] :
( ( ( SV40 @ ( sK38_SY935 @ SV176 @ SV40 ) )
= $true )
| ( ( SV40 @ SV176 )
= $false )
| ( ( ! [SY674: $i,SY675: $i] :
( ~ ( SV40 @ SY674 )
| ~ ( SV40 @ SY675 )
| ( SY674 = SY675 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1077]) ).
thf(1144,plain,
! [SV176: $i,SV212: $i,SV40: $i > $o] :
( ( ( ! [SY979: $i] :
( ~ ( SV40 @ SV212 )
| ~ ( SV40 @ SY979 )
| ( SV212 = SY979 ) ) )
= $true )
| ( ( SV40 @ SV176 )
= $false )
| ( ( SV176
= ( sK38_SY935 @ SV176 @ SV40 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1145,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( SV43 @ ( sK39_SY936 @ SV177 @ SV43 ) )
= $true )
| ( ( SV43 @ SV177 )
= $false )
| ( ( ~ ! [SY681: $i] :
~ ~ ( ~ ( SV43 @ SY681 )
| ~ ! [SY682: $i] :
( ~ ( SV43 @ SY682 )
| ( SY681 = SY682 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1079]) ).
thf(1146,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ! [SY681: $i] :
~ ~ ( ~ ( SV43 @ SY681 )
| ~ ! [SY682: $i] :
( ~ ( SV43 @ SY682 )
| ( SY681 = SY682 ) ) ) )
= $false )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV177
= ( sK39_SY936 @ SV177 @ SV43 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1147,plain,
! [SV123: $i,SV45: $i > $i > $o,SV204: $i] :
( ( ( ~ ( ~ ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
| ~ ! [SY971: $i] :
~ ~ ( ~ ( in @ SY971 @ SV123 )
| ~ ( SV45 @ SY971 @ SV204 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1081]) ).
thf(1148,plain,
! [SV204: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ~ ( ~ ~ ! [SY972: $i] :
~ ~ ( ~ ( in @ SY972 @ SV123 )
| ~ ( SV45 @ SY972 @ SV204 ) )
| ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) ) ) )
= $false )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1081]) ).
thf(1149,plain,
! [SV198: $i,SV123: $i,SV45: $i > $i > $o] :
( ( ( ! [SY957: $i] :
( ~ ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SY957 )
| ( SV198 = SY957 ) ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( ~ ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1150,plain,
! [SV125: $i,SV191: $i,SV48: $i,SV180: $i] :
( ( ( in @ SV180 @ SV48 )
= $false )
| ( ( in @ SV191 @ SV125 )
= $true )
| ( ( SV180 = SV191 )
= $false )
| ( ( SV48 = SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1151,plain,
! [SV48: $i,SV180: $i,SV125: $i,SV191: $i] :
( ( ( in @ SV191 @ SV125 )
= $false )
| ( ( in @ SV180 @ SV48 )
= $true )
| ( ( SV180 = SV191 )
= $false )
| ( ( SV48 = SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1152,plain,
! [SV128: $i,SV192: $i > $o,SV181: $i > $o,SV53: $i] :
( ( ( in @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) @ SV128 )
= $true )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1085]) ).
thf(1153,plain,
! [SV53: $i,SV128: $i,SV181: $i > $o,SV192: $i > $o] :
( ( ( ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 )
!= ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
= $false )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1086]) ).
thf(1154,plain,
! [SV53: $i,SV128: $i,SV192: $i > $o,SV181: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) )
| ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) ) )
| ~ ( ~ ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
| ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1086]) ).
thf(1155,plain,
! [SV54: $i,SV193: $o,SV129: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ SV129 ) )
= $false )
| ( SV193 = $true )
| ( ( SV165 = SV54 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1087]) ).
thf(1156,plain,
! [SV129: $i,SV54: $i,SV165: $i,SV193: $o] :
( ( SV193 = $false )
| ( SV193 = $true )
| ( ( SV165 = SV54 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1087]) ).
thf(1157,plain,
! [SV54: $i,SV193: $o,SV129: $i,SV165: $i] :
( ( ( in @ SV165 @ SV129 )
= $true )
| ( SV193 = $true )
| ( SV193 = $false )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1088]) ).
thf(1158,plain,
! [SV54: $i,SV129: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ SV129 ) )
= $false )
| ( $true = $true )
| ( ( SV165 = SV54 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1159,plain,
! [SV129: $i,SV54: $i,SV165: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( SV165 = SV54 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1160,plain,
! [SV54: $i,SV129: $i,SV165: $i] :
( ( ( in @ SV165 @ SV129 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1091]) ).
thf(1161,plain,
! [SV54: $i,SV129: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ SV129 ) )
= $false )
| ( $false = $true )
| ( ( SV165 = SV54 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1093]) ).
thf(1162,plain,
! [SV129: $i,SV54: $i,SV165: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( SV165 = SV54 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1093]) ).
thf(1163,plain,
! [SV54: $i,SV129: $i,SV165: $i] :
( ( ( in @ SV165 @ SV129 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1094]) ).
thf(1164,plain,
! [SV55: $i,SV182: $i] :
( ( ( ~ ! [SY958: $i] :
~ ~ ( ~ ( in @ SY958 @ ( sK25_SY715 @ SV182 @ SV55 ) )
| ~ ( in @ SY958 @ SV55 ) ) )
= $false )
| ( ( in @ SV182 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1165,plain,
! [SV130: $i > $o,SV208: $i,SV56: $i > $o] :
( ( ( ~ ( ~ ( SV56 @ SV208 )
| ~ ! [SY976: $i] :
( ~ ( SV56 @ SY976 )
| ( SV208 = SY976 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1098]) ).
thf(1166,plain,
! [SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
| ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1167,plain,
! [SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1100]) ).
thf(1168,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1100]) ).
thf(1169,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) ) )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1170,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) ) )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1171,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
| ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1103]) ).
thf(1172,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1104]) ).
thf(1173,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1104]) ).
thf(1174,plain,
! [SV61: $i] :
( ( ! [SY913: $i] :
( ~ ( in @ SY913 @ ( sK2_SY743 @ SV61 ) )
| ! [SY745: $i] :
( ~ ( in @ SY745 @ SY913 )
| ( in @ SY745 @ SV61 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1105]) ).
thf(1175,plain,
! [SV61: $i] :
( ( ! [SY915: $i,SY916: $i] :
( ~ ~ ( ~ ( in @ SY915 @ SV61 )
| ~ ( in @ SY916 @ SV61 ) )
| ~ ! [SY917: $i] :
( ~ ( in @ SY917 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SY915 @ SY917 )
| ( in @ SY916 @ SY917 ) )
| ~ ( ~ ( in @ SY916 @ SY917 )
| ( in @ SY915 @ SY917 ) ) ) )
| ( SY915 = SY916 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1106]) ).
thf(1176,plain,
! [SV209: $i,SV61: $i,SV205: $i] :
( ( ( ~ ~ ( ~ ( in @ SV205 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SV209 @ ( sK2_SY743 @ SV61 ) ) ) )
= $true )
| ( ( ! [SY977: $i] :
( ~ ( in @ SY977 @ SV205 )
| ( in @ SY977 @ SV209 ) )
| ! [SY978: $i] :
( ~ ( in @ SY978 @ SV209 )
| ( in @ SY978 @ SV205 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1177,plain,
! [SV61: $i,SV199: $i] :
( ( ( ! [SY959: $i] :
( ~ ( in @ SY959 @ SV199 )
| ( in @ SY959 @ SV61 ) ) )
= $false )
| ( ( ~ ~ ! [SY960: $i] :
~ ( in @ SY960 @ SV199 ) )
= $true )
| ( ( ~ ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1178,plain,
! [SV194: $i,SV139: $i > $o,SV69: $i] :
( ( ( ( dsetconstr @ SV69
@ ^ [SY891: $i] : ( SV139 @ SY891 ) )
= emptyset )
= $false )
| ( $false = $true )
| ( ( in @ SV194 @ SV69 )
= $false )
| ( ( SV139 @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1179,plain,
! [SV71: $i] :
( ( ( in @ ( sK26_SY775 @ SV71 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( ! [SY776: $i] :
( ~ ( in @ SY776 @ omega )
| ( in @ SY776 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1180,plain,
! [SV71: $i] :
( ( ( in @ ( sK26_SY775 @ SV71 ) @ SV71 )
= $true )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( ! [SY776: $i] :
( ~ ( in @ SY776 @ omega )
| ( in @ SY776 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1112]) ).
thf(1181,plain,
! [SV141: $i > $o,SV73: $i,SV210: $i] :
( ( ( ~ ( in @ SV210 @ SV73 ) )
= $true )
| ( ( ~ ( SV141 @ SV210 ) )
= $true )
| ( ( in @ ( sK19_SY894 @ SV141 @ SV73 ) @ SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1114]) ).
thf(1182,plain,
! [SV141: $i > $o,SV73: $i,SV211: $i] :
( ( ( ~ ( in @ SV211 @ SV73 ) )
= $true )
| ( ( ~ ( SV141 @ SV211 ) )
= $true )
| ( ( SV141 @ ( sK19_SY894 @ SV141 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1115]) ).
thf(1183,plain,
! [SV77: $i > $o,SV184: $i] :
( ( ( ( ( sK20_SY949 @ SV184 @ SV77 )
!= SV184 )
| ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) ) )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1184,plain,
! [SV77: $i > $o,SV184: $i] :
( ( ( ( sK20_SY949 @ SV184 @ SV77 )
!= SV184 )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1117]) ).
thf(1185,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1117]) ).
thf(1186,plain,
! [SV146: $i > $o,SV79: $i,SV202: $i] :
( ( ( ~ ( in @ SV202 @ SV79 ) )
= $true )
| ( ( ~ ( SV146 @ SV202 ) )
= $true )
| ( ( in @ ( sK13_SY900 @ SV146 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1118]) ).
thf(1187,plain,
! [SV146: $i > $o,SV79: $i,SV203: $i] :
( ( ( ~ ( in @ SV203 @ SV79 ) )
= $true )
| ( ( ~ ( SV146 @ SV203 ) )
= $true )
| ( ( SV146 @ ( sK13_SY900 @ SV146 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1188,plain,
! [SV185: $i,SV81: $i > $o] :
( ( ( SV81 @ ( sK41_SY950 @ SV185 @ SV81 ) )
= $true )
| ( ( SV81 @ SV185 )
= $false )
| ( ( ~ ! [SY799: $i] :
~ ! [SY800: $i] :
~ ( ~ ( ~ ( SV81 @ SY800 )
| ( SY800 = SY799 ) )
| ~ ( ( SY800 != SY799 )
| ( SV81 @ SY800 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1120]) ).
thf(1189,plain,
! [SV185: $i,SV81: $i > $o] :
( ( ( ! [SY799: $i] :
~ ! [SY800: $i] :
~ ( ~ ( ~ ( SV81 @ SY800 )
| ( SY800 = SY799 ) )
| ~ ( ( SY800 != SY799 )
| ( SV81 @ SY800 ) ) ) )
= $false )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV185
= ( sK41_SY950 @ SV185 @ SV81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1190,plain,
! [SV83: $i,SV148: $i > $o,SV196: $i] :
( ( ( ~ ( in @ ( sK35_SY903 @ SV196 @ SV148 @ SV83 ) @ SV83 ) )
= $false )
| ( ( SV148 @ SV196 )
= $true )
| ( ( in @ SV196 @ SV83 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1191,plain,
! [SV83: $i,SV196: $i,SV148: $i > $o] :
( ( ( ~ ~ ( SV148 @ ( sK35_SY903 @ SV196 @ SV148 @ SV83 ) ) )
= $false )
| ( ( SV148 @ SV196 )
= $true )
| ( ( in @ SV196 @ SV83 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1192,plain,
! [SV186: $i,SV84: $i > $o] :
( ( ( SV84 @ ( sK42_SY951 @ SV186 @ SV84 ) )
= $true )
| ( ( SV84 @ SV186 )
= $false )
| ( ( ! [SY807: $i,SY808: $i] :
( ~ ( SV84 @ SY807 )
| ~ ( SV84 @ SY808 )
| ( SY807 = SY808 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1123]) ).
thf(1193,plain,
! [SV186: $i,SV213: $i,SV84: $i > $o] :
( ( ( ! [SY980: $i] :
( ~ ( SV84 @ SV213 )
| ~ ( SV84 @ SY980 )
| ( SV213 = SY980 ) ) )
= $true )
| ( ( SV84 @ SV186 )
= $false )
| ( ( SV186
= ( sK42_SY951 @ SV186 @ SV84 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1194,plain,
! [SV87: $i,SV150: $i] :
( ( ( in @ SV150 @ ( sK31_SY906 @ SV87 @ SV150 ) )
= $true )
| ( ( in @ SV150 @ ( setunion @ SV87 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1125]) ).
thf(1195,plain,
! [SV150: $i,SV87: $i] :
( ( ( in @ ( sK31_SY906 @ SV87 @ SV150 ) @ SV87 )
= $true )
| ( ( in @ SV150 @ ( setunion @ SV87 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1126]) ).
thf(1196,plain,
! [SV87: $i,SV200: $i,SV150: $i] :
( ( ( in @ SV150 @ SV200 )
= $false )
| ( ( ~ ( in @ SV200 @ SV87 ) )
= $true )
| ( ( in @ SV150 @ ( setunion @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1197,plain,
! [SV187: $i,SV90: $i > $o] :
( ( ( SV90 @ ( sK43_SY952 @ SV187 @ SV90 ) )
= $true )
| ( ( SV90 @ SV187 )
= $false )
| ( ( SV90
@ ( descr
@ ^ [SY819: $i] : ( SV90 @ SY819 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1198,plain,
! [SV172: $i,SV17: $i > $o] :
( ( ( ! [SY622: $i] :
~ ( SV17 @ SY622 ) )
= $false )
| ( ( SV17 @ SV172 )
= $false )
| ( ( SV17 @ ( sK36_SY932 @ SV172 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1199,plain,
! [SV172: $i,SV17: $i > $o] :
( ( ( ~ ( SV17 @ ( sK44_SY622 @ SV172 @ SV17 ) ) )
= $false )
| ( ( SV17 @ SV172 )
= $false )
| ( ( SV172
= ( sK36_SY932 @ SV172 @ SV17 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1131]) ).
thf(1200,plain,
! [SV103: $i > $o,SV19: $i,SV206: $i] :
( ( ( in @ SV206 @ SV19 )
= $false )
| ( ( ~ ( SV103 @ SV206 ) )
= $true )
| ( ( in @ ( sK18_SY823 @ SV103 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1201,plain,
! [SV103: $i > $o,SV19: $i,SV207: $i] :
( ( ( in @ SV207 @ SV19 )
= $false )
| ( ( ~ ( SV103 @ SV207 ) )
= $true )
| ( ( SV103 @ ( sK18_SY823 @ SV103 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1202,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ! [SY630: $i] :
~ ~ ( ~ ( SV21 @ SY630 )
| ~ ! [SY631: $i] :
( ~ ( SV21 @ SY631 )
| ( SY630 = SY631 ) ) ) )
= $false )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV21 @ ( sK37_SY933 @ SV173 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1203,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ~ ~ ( ~ ( SV21 @ ( sK45_SY630 @ SV173 @ SV21 ) )
| ~ ! [SY981: $i] :
( ~ ( SV21 @ SY981 )
| ( ( sK45_SY630 @ SV173 @ SV21 )
= SY981 ) ) ) )
= $false )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV173
= ( sK37_SY933 @ SV173 @ SV21 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1135]) ).
thf(1204,plain,
! [SV24: $i,SV106: $i > $o,SV188: $i] :
( ( ( ~ ( in @ ( sK46_SY827 @ SV188 @ SV106 @ SV24 ) @ SV24 )
| ( SV106 @ ( sK46_SY827 @ SV188 @ SV106 @ SV24 ) ) )
= $false )
| ( ( in @ SV188 @ SV24 )
= $false )
| ( ( SV106 @ SV188 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1136]) ).
thf(1205,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ~ ( ~ ( SV32 @ ( sK47_SY653 @ SV175 @ SV32 ) )
| ~ ! [SY982: $i] :
( ~ ( SV32 @ SY982 )
| ( ( sK47_SY653 @ SV175 @ SV32 )
= SY982 ) ) ) )
= $false )
| ( ( SV32 @ ( sK27_SY651 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1138]) ).
thf(1206,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ! [SY653: $i] :
~ ~ ( ~ ( SV32 @ SY653 )
| ~ ! [SY654: $i] :
( ~ ( SV32 @ SY654 )
| ( SY653 = SY654 ) ) ) )
= $false )
| ( ( SV32 @ ( sK32_SY966 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1207,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ~ ( ~ ( SV32 @ ( sK48_SY653 @ SV175 @ SV32 ) )
| ~ ! [SY983: $i] :
( ~ ( SV32 @ SY983 )
| ( ( sK48_SY653 @ SV175 @ SV32 )
= SY983 ) ) ) )
= $false )
| ( ( ( sK27_SY651 @ SV175 @ SV32 )
= ( sK32_SY966 @ SV175 @ SV32 ) )
= $false )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1140]) ).
thf(1208,plain,
! [SV39: $i,SV119: $i > $o,SV189: $i] :
( ( ( in @ ( sK33_SY842 @ SV189 @ SV119 @ SV39 ) @ SV39 )
= $true )
| ( ( SV119 @ SV189 )
= $true )
| ( ( in @ SV189 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1141]) ).
thf(1209,plain,
! [SV39: $i,SV189: $i,SV119: $i > $o] :
( ( ( ~ ( SV119 @ ( sK33_SY842 @ SV189 @ SV119 @ SV39 ) ) )
= $true )
| ( ( SV119 @ SV189 )
= $true )
| ( ( in @ SV189 @ SV39 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1142]) ).
thf(1210,plain,
! [SV176: $i,SV214: $i,SV40: $i > $o] :
( ( ( ! [SY984: $i] :
( ~ ( SV40 @ SV214 )
| ~ ( SV40 @ SY984 )
| ( SV214 = SY984 ) ) )
= $true )
| ( ( SV40 @ SV176 )
= $false )
| ( ( SV40 @ ( sK38_SY935 @ SV176 @ SV40 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1211,plain,
! [SV176: $i,SV215: $i,SV212: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ SV212 )
| ~ ( SV40 @ SV215 )
| ( SV212 = SV215 ) )
= $true )
| ( ( SV40 @ SV176 )
= $false )
| ( ( SV176
= ( sK38_SY935 @ SV176 @ SV40 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1212,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ! [SY681: $i] :
~ ~ ( ~ ( SV43 @ SY681 )
| ~ ! [SY682: $i] :
( ~ ( SV43 @ SY682 )
| ( SY681 = SY682 ) ) ) )
= $false )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV43 @ ( sK39_SY936 @ SV177 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1213,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ~ ~ ( ~ ( SV43 @ ( sK49_SY681 @ SV177 @ SV43 ) )
| ~ ! [SY985: $i] :
( ~ ( SV43 @ SY985 )
| ( ( sK49_SY681 @ SV177 @ SV43 )
= SY985 ) ) ) )
= $false )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV177
= ( sK39_SY936 @ SV177 @ SV43 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1146]) ).
thf(1214,plain,
! [SV123: $i,SV45: $i > $i > $o,SV204: $i] :
( ( ( ~ ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
| ~ ! [SY971: $i] :
~ ~ ( ~ ( in @ SY971 @ SV123 )
| ~ ( SV45 @ SY971 @ SV204 ) ) )
= $true )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1147]) ).
thf(1215,plain,
! [SV204: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ~ ~ ! [SY972: $i] :
~ ~ ( ~ ( in @ SY972 @ SV123 )
| ~ ( SV45 @ SY972 @ SV204 ) )
| ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) ) )
= $true )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1148]) ).
thf(1216,plain,
! [SV198: $i,SV123: $i,SV45: $i > $i > $o] :
( ( ( ~ ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
| ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( ~ ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1149]) ).
thf(1217,plain,
! [SV53: $i,SV128: $i,SV181: $i > $o,SV192: $i > $o] :
( ( ( ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 )
= ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
= $true )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1153]) ).
thf(1218,plain,
! [SV53: $i,SV128: $i,SV192: $i > $o,SV181: $i > $o] :
( ( ( ~ ( ~ ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) )
| ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) ) )
| ~ ( ~ ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
| ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1154]) ).
thf(1219,plain,
! [SV54: $i,SV193: $o,SV129: $i,SV165: $i] :
( ( ( in @ SV165 @ SV129 )
= $true )
| ( SV193 = $true )
| ( ( SV165 = SV54 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1155]) ).
thf(1220,plain,
! [SV54: $i,SV129: $i,SV165: $i] :
( ( ( in @ SV165 @ SV129 )
= $true )
| ( $true = $true )
| ( ( SV165 = SV54 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1158]) ).
thf(1221,plain,
! [SV54: $i,SV129: $i,SV165: $i] :
( ( ( in @ SV165 @ SV129 )
= $true )
| ( $false = $true )
| ( ( SV165 = SV54 )
= $true )
| ( ( in @ SV165 @ ( setadjoin @ SV54 @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1161]) ).
thf(1222,plain,
! [SV55: $i,SV182: $i] :
( ( ( ! [SY958: $i] :
~ ~ ( ~ ( in @ SY958 @ ( sK25_SY715 @ SV182 @ SV55 ) )
| ~ ( in @ SY958 @ SV55 ) ) )
= $true )
| ( ( in @ SV182 @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1164]) ).
thf(1223,plain,
! [SV130: $i > $o,SV208: $i,SV56: $i > $o] :
( ( ( ~ ( SV56 @ SV208 )
| ~ ! [SY976: $i] :
( ~ ( SV56 @ SY976 )
| ( SV208 = SY976 ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1165]) ).
thf(1224,plain,
! [SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1166]) ).
thf(1225,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1166]) ).
thf(1226,plain,
! [SV56: $i > $o,SV130: $i > $o] :
( ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1167]) ).
thf(1227,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1168]) ).
thf(1228,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1169]) ).
thf(1229,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1170]) ).
thf(1230,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1171]) ).
thf(1231,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1171]) ).
thf(1232,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1172]) ).
thf(1233,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1234,plain,
! [SV61: $i,SV216: $i] :
( ( ~ ( in @ SV216 @ ( sK2_SY743 @ SV61 ) )
| ! [SY986: $i] :
( ~ ( in @ SY986 @ SV216 )
| ( in @ SY986 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1235,plain,
! [SV61: $i,SV217: $i] :
( ( ! [SY987: $i] :
( ~ ~ ( ~ ( in @ SV217 @ SV61 )
| ~ ( in @ SY987 @ SV61 ) )
| ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SV217 @ SY988 )
| ( in @ SY987 @ SY988 ) )
| ~ ( ~ ( in @ SY987 @ SY988 )
| ( in @ SV217 @ SY988 ) ) ) )
| ( SV217 = SY987 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1236,plain,
! [SV209: $i,SV61: $i,SV205: $i] :
( ( ( ~ ( ~ ( in @ SV205 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SV209 @ ( sK2_SY743 @ SV61 ) ) ) )
= $false )
| ( ( ! [SY977: $i] :
( ~ ( in @ SY977 @ SV205 )
| ( in @ SY977 @ SV209 ) )
| ! [SY978: $i] :
( ~ ( in @ SY978 @ SV209 )
| ( in @ SY978 @ SV205 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1237,plain,
! [SV199: $i,SV61: $i] :
( ( ( ~ ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
| ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 ) )
= $false )
| ( ( ~ ~ ! [SY960: $i] :
~ ( in @ SY960 @ SV199 ) )
= $true )
| ( ( ~ ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1177]) ).
thf(1238,plain,
! [SV71: $i,SV218: $i] :
( ( ( ~ ( in @ SV218 @ omega )
| ( in @ SV218 @ SV71 ) )
= $true )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( in @ ( sK26_SY775 @ SV71 ) @ omega )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1239,plain,
! [SV71: $i,SV219: $i] :
( ( ( ~ ( in @ SV219 @ omega )
| ( in @ SV219 @ SV71 ) )
= $true )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( in @ ( sK26_SY775 @ SV71 ) @ SV71 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1240,plain,
! [SV141: $i > $o,SV73: $i,SV210: $i] :
( ( ( in @ SV210 @ SV73 )
= $false )
| ( ( ~ ( SV141 @ SV210 ) )
= $true )
| ( ( in @ ( sK19_SY894 @ SV141 @ SV73 ) @ SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1241,plain,
! [SV141: $i > $o,SV73: $i,SV211: $i] :
( ( ( in @ SV211 @ SV73 )
= $false )
| ( ( ~ ( SV141 @ SV211 ) )
= $true )
| ( ( SV141 @ ( sK19_SY894 @ SV141 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1242,plain,
! [SV77: $i > $o,SV184: $i] :
( ( ( ( sK20_SY949 @ SV184 @ SV77 )
!= SV184 )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1183]) ).
thf(1243,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1183]) ).
thf(1244,plain,
! [SV77: $i > $o,SV184: $i] :
( ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1184]) ).
thf(1245,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1246,plain,
! [SV146: $i > $o,SV79: $i,SV202: $i] :
( ( ( in @ SV202 @ SV79 )
= $false )
| ( ( ~ ( SV146 @ SV202 ) )
= $true )
| ( ( in @ ( sK13_SY900 @ SV146 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1247,plain,
! [SV146: $i > $o,SV79: $i,SV203: $i] :
( ( ( in @ SV203 @ SV79 )
= $false )
| ( ( ~ ( SV146 @ SV203 ) )
= $true )
| ( ( SV146 @ ( sK13_SY900 @ SV146 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1248,plain,
! [SV185: $i,SV81: $i > $o] :
( ( ( ! [SY799: $i] :
~ ! [SY800: $i] :
~ ( ~ ( ~ ( SV81 @ SY800 )
| ( SY800 = SY799 ) )
| ~ ( ( SY800 != SY799 )
| ( SV81 @ SY800 ) ) ) )
= $false )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV81 @ ( sK41_SY950 @ SV185 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1188]) ).
thf(1249,plain,
! [SV185: $i,SV81: $i > $o] :
( ( ( ~ ! [SY989: $i] :
~ ( ~ ( ~ ( SV81 @ SY989 )
| ( SY989
= ( sK52_SY799 @ SV185 @ SV81 ) ) )
| ~ ( ( SY989
!= ( sK52_SY799 @ SV185 @ SV81 ) )
| ( SV81 @ SY989 ) ) ) )
= $false )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV185
= ( sK41_SY950 @ SV185 @ SV81 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1189]) ).
thf(1250,plain,
! [SV83: $i,SV148: $i > $o,SV196: $i] :
( ( ( in @ ( sK35_SY903 @ SV196 @ SV148 @ SV83 ) @ SV83 )
= $true )
| ( ( SV148 @ SV196 )
= $true )
| ( ( in @ SV196 @ SV83 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1251,plain,
! [SV83: $i,SV196: $i,SV148: $i > $o] :
( ( ( ~ ( SV148 @ ( sK35_SY903 @ SV196 @ SV148 @ SV83 ) ) )
= $true )
| ( ( SV148 @ SV196 )
= $true )
| ( ( in @ SV196 @ SV83 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1191]) ).
thf(1252,plain,
! [SV186: $i,SV220: $i,SV84: $i > $o] :
( ( ( ! [SY990: $i] :
( ~ ( SV84 @ SV220 )
| ~ ( SV84 @ SY990 )
| ( SV220 = SY990 ) ) )
= $true )
| ( ( SV84 @ SV186 )
= $false )
| ( ( SV84 @ ( sK42_SY951 @ SV186 @ SV84 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1253,plain,
! [SV186: $i,SV221: $i,SV213: $i,SV84: $i > $o] :
( ( ( ~ ( SV84 @ SV213 )
| ~ ( SV84 @ SV221 )
| ( SV213 = SV221 ) )
= $true )
| ( ( SV84 @ SV186 )
= $false )
| ( ( SV186
= ( sK42_SY951 @ SV186 @ SV84 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1254,plain,
! [SV150: $i,SV87: $i,SV200: $i] :
( ( ( in @ SV200 @ SV87 )
= $false )
| ( ( in @ SV150 @ SV200 )
= $false )
| ( ( in @ SV150 @ ( setunion @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1255,plain,
! [SV172: $i,SV17: $i > $o] :
( ( ( ~ ( SV17 @ ( sK53_SY622 @ SV172 @ SV17 ) ) )
= $false )
| ( ( SV17 @ SV172 )
= $false )
| ( ( SV17 @ ( sK36_SY932 @ SV172 @ SV17 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1198]) ).
thf(1256,plain,
! [SV172: $i,SV17: $i > $o] :
( ( ( SV17 @ ( sK44_SY622 @ SV172 @ SV17 ) )
= $true )
| ( ( SV17 @ SV172 )
= $false )
| ( ( SV172
= ( sK36_SY932 @ SV172 @ SV17 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1199]) ).
thf(1257,plain,
! [SV19: $i,SV206: $i,SV103: $i > $o] :
( ( ( SV103 @ SV206 )
= $false )
| ( ( in @ SV206 @ SV19 )
= $false )
| ( ( in @ ( sK18_SY823 @ SV103 @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1258,plain,
! [SV19: $i,SV207: $i,SV103: $i > $o] :
( ( ( SV103 @ SV207 )
= $false )
| ( ( in @ SV207 @ SV19 )
= $false )
| ( ( SV103 @ ( sK18_SY823 @ SV103 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1259,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ~ ~ ( ~ ( SV21 @ ( sK54_SY630 @ SV173 @ SV21 ) )
| ~ ! [SY991: $i] :
( ~ ( SV21 @ SY991 )
| ( ( sK54_SY630 @ SV173 @ SV21 )
= SY991 ) ) ) )
= $false )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV21 @ ( sK37_SY933 @ SV173 @ SV21 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1202]) ).
thf(1260,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ~ ( ~ ( SV21 @ ( sK45_SY630 @ SV173 @ SV21 ) )
| ~ ! [SY981: $i] :
( ~ ( SV21 @ SY981 )
| ( ( sK45_SY630 @ SV173 @ SV21 )
= SY981 ) ) ) )
= $true )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV173
= ( sK37_SY933 @ SV173 @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1203]) ).
thf(1261,plain,
! [SV24: $i,SV106: $i > $o,SV188: $i] :
( ( ( ~ ( in @ ( sK46_SY827 @ SV188 @ SV106 @ SV24 ) @ SV24 ) )
= $false )
| ( ( in @ SV188 @ SV24 )
= $false )
| ( ( SV106 @ SV188 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1204]) ).
thf(1262,plain,
! [SV24: $i,SV188: $i,SV106: $i > $o] :
( ( ( SV106 @ ( sK46_SY827 @ SV188 @ SV106 @ SV24 ) )
= $false )
| ( ( in @ SV188 @ SV24 )
= $false )
| ( ( SV106 @ SV188 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1204]) ).
thf(1263,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ( ~ ( SV32 @ ( sK47_SY653 @ SV175 @ SV32 ) )
| ~ ! [SY982: $i] :
( ~ ( SV32 @ SY982 )
| ( ( sK47_SY653 @ SV175 @ SV32 )
= SY982 ) ) ) )
= $true )
| ( ( SV32 @ ( sK27_SY651 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1205]) ).
thf(1264,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ~ ( ~ ( SV32 @ ( sK55_SY653 @ SV175 @ SV32 ) )
| ~ ! [SY992: $i] :
( ~ ( SV32 @ SY992 )
| ( ( sK55_SY653 @ SV175 @ SV32 )
= SY992 ) ) ) )
= $false )
| ( ( SV32 @ ( sK32_SY966 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1206]) ).
thf(1265,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ( ~ ( SV32 @ ( sK48_SY653 @ SV175 @ SV32 ) )
| ~ ! [SY983: $i] :
( ~ ( SV32 @ SY983 )
| ( ( sK48_SY653 @ SV175 @ SV32 )
= SY983 ) ) ) )
= $true )
| ( ( ( sK27_SY651 @ SV175 @ SV32 )
= ( sK32_SY966 @ SV175 @ SV32 ) )
= $false )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1207]) ).
thf(1266,plain,
! [SV39: $i,SV189: $i,SV119: $i > $o] :
( ( ( SV119 @ ( sK33_SY842 @ SV189 @ SV119 @ SV39 ) )
= $false )
| ( ( SV119 @ SV189 )
= $true )
| ( ( in @ SV189 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1209]) ).
thf(1267,plain,
! [SV176: $i,SV222: $i,SV214: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ SV214 )
| ~ ( SV40 @ SV222 )
| ( SV214 = SV222 ) )
= $true )
| ( ( SV40 @ SV176 )
= $false )
| ( ( SV40 @ ( sK38_SY935 @ SV176 @ SV40 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1268,plain,
! [SV176: $i,SV215: $i,SV212: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ SV212 ) )
= $true )
| ( ( ~ ( SV40 @ SV215 )
| ( SV212 = SV215 ) )
= $true )
| ( ( SV40 @ SV176 )
= $false )
| ( ( SV176
= ( sK38_SY935 @ SV176 @ SV40 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1269,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ~ ~ ( ~ ( SV43 @ ( sK56_SY681 @ SV177 @ SV43 ) )
| ~ ! [SY993: $i] :
( ~ ( SV43 @ SY993 )
| ( ( sK56_SY681 @ SV177 @ SV43 )
= SY993 ) ) ) )
= $false )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV43 @ ( sK39_SY936 @ SV177 @ SV43 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1212]) ).
thf(1270,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ~ ( ~ ( SV43 @ ( sK49_SY681 @ SV177 @ SV43 ) )
| ~ ! [SY985: $i] :
( ~ ( SV43 @ SY985 )
| ( ( sK49_SY681 @ SV177 @ SV43 )
= SY985 ) ) ) )
= $true )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV177
= ( sK39_SY936 @ SV177 @ SV43 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1213]) ).
thf(1271,plain,
! [SV123: $i,SV45: $i > $i > $o,SV204: $i] :
( ( ( ~ ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) ) )
= $true )
| ( ( ~ ! [SY971: $i] :
~ ~ ( ~ ( in @ SY971 @ SV123 )
| ~ ( SV45 @ SY971 @ SV204 ) ) )
= $true )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1272,plain,
! [SV204: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ~ ~ ! [SY972: $i] :
~ ~ ( ~ ( in @ SY972 @ SV123 )
| ~ ( SV45 @ SY972 @ SV204 ) ) )
= $true )
| ( ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
= $true )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1273,plain,
! [SV198: $i,SV123: $i,SV45: $i > $i > $o] :
( ( ( ~ ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( ~ ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1216]) ).
thf(1274,plain,
! [SV45: $i > $i > $o,SV123: $i,SV198: $i] :
( ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( ~ ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1216]) ).
thf(1275,plain,
! [SV53: $i,SV128: $i,SV192: $i > $o,SV181: $i > $o] :
( ( ( ~ ( ~ ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) )
| ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
| ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1276,plain,
! [SV55: $i,SV182: $i,SV223: $i] :
( ( ( ~ ~ ( ~ ( in @ SV223 @ ( sK25_SY715 @ SV182 @ SV55 ) )
| ~ ( in @ SV223 @ SV55 ) ) )
= $true )
| ( ( in @ SV182 @ SV55 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1277,plain,
! [SV130: $i > $o,SV208: $i,SV56: $i > $o] :
( ( ( ~ ( SV56 @ SV208 ) )
= $true )
| ( ( ~ ! [SY976: $i] :
( ~ ( SV56 @ SY976 )
| ( SV208 = SY976 ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1278,plain,
! [SV56: $i > $o,SV130: $i > $o] :
( ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) )
| ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1224]) ).
thf(1279,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1225]) ).
thf(1280,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1226]) ).
thf(1281,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1282,plain,
! [SV132: $i > $o,SV224: $i,SV58: $i > $o] :
( ( ( ~ ~ ( ~ ( SV58 @ SV224 )
| ~ ! [SY994: $i] :
( ~ ( SV58 @ SY994 )
| ( SV224 = SY994 ) ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1283,plain,
! [SV58: $i > $o,SV225: $i,SV132: $i > $o] :
( ( ( ~ ~ ( ~ ( SV132 @ SV225 )
| ~ ! [SY995: $i] :
( ~ ( SV132 @ SY995 )
| ( SV225 = SY995 ) ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1284,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1230]) ).
thf(1285,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1286,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1287,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1233]) ).
thf(1288,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1233]) ).
thf(1289,plain,
! [SV61: $i,SV216: $i] :
( ( ( ~ ( in @ SV216 @ ( sK2_SY743 @ SV61 ) ) )
= $true )
| ( ( ! [SY986: $i] :
( ~ ( in @ SY986 @ SV216 )
| ( in @ SY986 @ SV61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1290,plain,
! [SV226: $i,SV61: $i,SV217: $i] :
( ( ~ ~ ( ~ ( in @ SV217 @ SV61 )
| ~ ( in @ SV226 @ SV61 ) )
| ~ ! [SY996: $i] :
( ~ ( in @ SY996 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SV217 @ SY996 )
| ( in @ SV226 @ SY996 ) )
| ~ ( ~ ( in @ SV226 @ SY996 )
| ( in @ SV217 @ SY996 ) ) ) )
| ( SV217 = SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1291,plain,
! [SV209: $i,SV61: $i,SV205: $i] :
( ( ( ~ ( in @ SV205 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SV209 @ ( sK2_SY743 @ SV61 ) ) )
= $true )
| ( ( ! [SY977: $i] :
( ~ ( in @ SY977 @ SV205 )
| ( in @ SY977 @ SV209 ) )
| ! [SY978: $i] :
( ~ ( in @ SY978 @ SV209 )
| ( in @ SY978 @ SV205 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1236]) ).
thf(1292,plain,
! [SV199: $i,SV61: $i] :
( ( ( ~ ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 ) )
= $false )
| ( ( ~ ~ ! [SY960: $i] :
~ ( in @ SY960 @ SV199 ) )
= $true )
| ( ( ~ ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1237]) ).
thf(1293,plain,
! [SV199: $i,SV61: $i] :
( ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( ~ ~ ! [SY960: $i] :
~ ( in @ SY960 @ SV199 ) )
= $true )
| ( ( ~ ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1237]) ).
thf(1294,plain,
! [SV71: $i,SV218: $i] :
( ( ( ~ ( in @ SV218 @ omega ) )
= $true )
| ( ( in @ SV218 @ SV71 )
= $true )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( in @ ( sK26_SY775 @ SV71 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1295,plain,
! [SV71: $i,SV219: $i] :
( ( ( ~ ( in @ SV219 @ omega ) )
= $true )
| ( ( in @ SV219 @ SV71 )
= $true )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( in @ ( sK26_SY775 @ SV71 ) @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1296,plain,
! [SV73: $i,SV210: $i,SV141: $i > $o] :
( ( ( SV141 @ SV210 )
= $false )
| ( ( in @ SV210 @ SV73 )
= $false )
| ( ( in @ ( sK19_SY894 @ SV141 @ SV73 ) @ SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1297,plain,
! [SV73: $i,SV211: $i,SV141: $i > $o] :
( ( ( SV141 @ SV211 )
= $false )
| ( ( in @ SV211 @ SV73 )
= $false )
| ( ( SV141 @ ( sK19_SY894 @ SV141 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1298,plain,
! [SV77: $i > $o,SV184: $i] :
( ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( ~ ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1242]) ).
thf(1299,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1300,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1301,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ~ ( ~ ( SV77 @ ( sK57_SY789 @ SV184 @ SV77 ) )
| ~ ! [SY997: $i] :
( ~ ( SV77 @ SY997 )
| ( ( sK57_SY789 @ SV184 @ SV77 )
= SY997 ) ) ) )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1245]) ).
thf(1302,plain,
! [SV79: $i,SV202: $i,SV146: $i > $o] :
( ( ( SV146 @ SV202 )
= $false )
| ( ( in @ SV202 @ SV79 )
= $false )
| ( ( in @ ( sK13_SY900 @ SV146 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1303,plain,
! [SV79: $i,SV203: $i,SV146: $i > $o] :
( ( ( SV146 @ SV203 )
= $false )
| ( ( in @ SV203 @ SV79 )
= $false )
| ( ( SV146 @ ( sK13_SY900 @ SV146 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1304,plain,
! [SV185: $i,SV81: $i > $o] :
( ( ( ~ ! [SY998: $i] :
~ ( ~ ( ~ ( SV81 @ SY998 )
| ( SY998
= ( sK58_SY799 @ SV185 @ SV81 ) ) )
| ~ ( ( SY998
!= ( sK58_SY799 @ SV185 @ SV81 ) )
| ( SV81 @ SY998 ) ) ) )
= $false )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV81 @ ( sK41_SY950 @ SV185 @ SV81 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1248]) ).
thf(1305,plain,
! [SV185: $i,SV81: $i > $o] :
( ( ( ! [SY989: $i] :
~ ( ~ ( ~ ( SV81 @ SY989 )
| ( SY989
= ( sK52_SY799 @ SV185 @ SV81 ) ) )
| ~ ( ( SY989
!= ( sK52_SY799 @ SV185 @ SV81 ) )
| ( SV81 @ SY989 ) ) ) )
= $true )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV185
= ( sK41_SY950 @ SV185 @ SV81 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1249]) ).
thf(1306,plain,
! [SV83: $i,SV196: $i,SV148: $i > $o] :
( ( ( SV148 @ ( sK35_SY903 @ SV196 @ SV148 @ SV83 ) )
= $false )
| ( ( SV148 @ SV196 )
= $true )
| ( ( in @ SV196 @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1307,plain,
! [SV186: $i,SV227: $i,SV220: $i,SV84: $i > $o] :
( ( ( ~ ( SV84 @ SV220 )
| ~ ( SV84 @ SV227 )
| ( SV220 = SV227 ) )
= $true )
| ( ( SV84 @ SV186 )
= $false )
| ( ( SV84 @ ( sK42_SY951 @ SV186 @ SV84 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1308,plain,
! [SV186: $i,SV221: $i,SV213: $i,SV84: $i > $o] :
( ( ( ~ ( SV84 @ SV213 ) )
= $true )
| ( ( ~ ( SV84 @ SV221 )
| ( SV213 = SV221 ) )
= $true )
| ( ( SV84 @ SV186 )
= $false )
| ( ( SV186
= ( sK42_SY951 @ SV186 @ SV84 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1253]) ).
thf(1309,plain,
! [SV172: $i,SV17: $i > $o] :
( ( ( SV17 @ ( sK53_SY622 @ SV172 @ SV17 ) )
= $true )
| ( ( SV17 @ SV172 )
= $false )
| ( ( SV17 @ ( sK36_SY932 @ SV172 @ SV17 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1255]) ).
thf(1310,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ~ ( ~ ( SV21 @ ( sK54_SY630 @ SV173 @ SV21 ) )
| ~ ! [SY991: $i] :
( ~ ( SV21 @ SY991 )
| ( ( sK54_SY630 @ SV173 @ SV21 )
= SY991 ) ) ) )
= $true )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV21 @ ( sK37_SY933 @ SV173 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1259]) ).
thf(1311,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ ( sK45_SY630 @ SV173 @ SV21 ) )
| ~ ! [SY981: $i] :
( ~ ( SV21 @ SY981 )
| ( ( sK45_SY630 @ SV173 @ SV21 )
= SY981 ) ) )
= $false )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV173
= ( sK37_SY933 @ SV173 @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1312,plain,
! [SV24: $i,SV106: $i > $o,SV188: $i] :
( ( ( in @ ( sK46_SY827 @ SV188 @ SV106 @ SV24 ) @ SV24 )
= $true )
| ( ( in @ SV188 @ SV24 )
= $false )
| ( ( SV106 @ SV188 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1261]) ).
thf(1313,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ( SV32 @ ( sK47_SY653 @ SV175 @ SV32 ) )
| ~ ! [SY982: $i] :
( ~ ( SV32 @ SY982 )
| ( ( sK47_SY653 @ SV175 @ SV32 )
= SY982 ) ) )
= $false )
| ( ( SV32 @ ( sK27_SY651 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1314,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ( ~ ( SV32 @ ( sK55_SY653 @ SV175 @ SV32 ) )
| ~ ! [SY992: $i] :
( ~ ( SV32 @ SY992 )
| ( ( sK55_SY653 @ SV175 @ SV32 )
= SY992 ) ) ) )
= $true )
| ( ( SV32 @ ( sK32_SY966 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1264]) ).
thf(1315,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ( SV32 @ ( sK48_SY653 @ SV175 @ SV32 ) )
| ~ ! [SY983: $i] :
( ~ ( SV32 @ SY983 )
| ( ( sK48_SY653 @ SV175 @ SV32 )
= SY983 ) ) )
= $false )
| ( ( ( sK27_SY651 @ SV175 @ SV32 )
= ( sK32_SY966 @ SV175 @ SV32 ) )
= $false )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1316,plain,
! [SV176: $i,SV222: $i,SV214: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ SV214 ) )
= $true )
| ( ( ~ ( SV40 @ SV222 )
| ( SV214 = SV222 ) )
= $true )
| ( ( SV40 @ SV176 )
= $false )
| ( ( SV40 @ ( sK38_SY935 @ SV176 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1267]) ).
thf(1317,plain,
! [SV176: $i,SV215: $i,SV212: $i,SV40: $i > $o] :
( ( ( SV40 @ SV212 )
= $false )
| ( ( ~ ( SV40 @ SV215 )
| ( SV212 = SV215 ) )
= $true )
| ( ( SV40 @ SV176 )
= $false )
| ( ( SV176
= ( sK38_SY935 @ SV176 @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1318,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ~ ( ~ ( SV43 @ ( sK56_SY681 @ SV177 @ SV43 ) )
| ~ ! [SY993: $i] :
( ~ ( SV43 @ SY993 )
| ( ( sK56_SY681 @ SV177 @ SV43 )
= SY993 ) ) ) )
= $true )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV43 @ ( sK39_SY936 @ SV177 @ SV43 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1269]) ).
thf(1319,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ ( sK49_SY681 @ SV177 @ SV43 ) )
| ~ ! [SY985: $i] :
( ~ ( SV43 @ SY985 )
| ( ( sK49_SY681 @ SV177 @ SV43 )
= SY985 ) ) )
= $false )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV177
= ( sK39_SY936 @ SV177 @ SV43 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1320,plain,
! [SV123: $i,SV45: $i > $i > $o,SV204: $i] :
( ( ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
= $false )
| ( ( ~ ! [SY971: $i] :
~ ~ ( ~ ( in @ SY971 @ SV123 )
| ~ ( SV45 @ SY971 @ SV204 ) ) )
= $true )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1321,plain,
! [SV204: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ~ ! [SY972: $i] :
~ ~ ( ~ ( in @ SY972 @ SV123 )
| ~ ( SV45 @ SY972 @ SV204 ) ) )
= $false )
| ( ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
= $true )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1272]) ).
thf(1322,plain,
! [SV198: $i,SV123: $i,SV45: $i > $i > $o] :
( ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( ~ ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1273]) ).
thf(1323,plain,
! [SV198: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1324,plain,
! [SV53: $i,SV128: $i,SV192: $i > $o,SV181: $i > $o] :
( ( ( ~ ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) )
| ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) ) )
= $false )
| ( ( ~ ( ~ ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
| ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1325,plain,
! [SV55: $i,SV182: $i,SV223: $i] :
( ( ( ~ ( ~ ( in @ SV223 @ ( sK25_SY715 @ SV182 @ SV55 ) )
| ~ ( in @ SV223 @ SV55 ) ) )
= $false )
| ( ( in @ SV182 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1326,plain,
! [SV130: $i > $o,SV208: $i,SV56: $i > $o] :
( ( ( SV56 @ SV208 )
= $false )
| ( ( ~ ! [SY976: $i] :
( ~ ( SV56 @ SY976 )
| ( SV208 = SY976 ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1327,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1278]) ).
thf(1328,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1329,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1330,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1281]) ).
thf(1331,plain,
! [SV132: $i > $o,SV224: $i,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ SV224 )
| ~ ! [SY994: $i] :
( ~ ( SV58 @ SY994 )
| ( SV224 = SY994 ) ) ) )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1332,plain,
! [SV58: $i > $o,SV225: $i,SV132: $i > $o] :
( ( ( ~ ( ~ ( SV132 @ SV225 )
| ~ ! [SY995: $i] :
( ~ ( SV132 @ SY995 )
| ( SV225 = SY995 ) ) ) )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1283]) ).
thf(1333,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
| ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1334,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1285]) ).
thf(1335,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1285]) ).
thf(1336,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1286]) ).
thf(1337,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1286]) ).
thf(1338,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1287]) ).
thf(1339,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1288]) ).
thf(1340,plain,
! [SV61: $i,SV216: $i] :
( ( ( in @ SV216 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( ! [SY986: $i] :
( ~ ( in @ SY986 @ SV216 )
| ( in @ SY986 @ SV61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1341,plain,
! [SV226: $i,SV61: $i,SV217: $i] :
( ( ( ~ ~ ( ~ ( in @ SV217 @ SV61 )
| ~ ( in @ SV226 @ SV61 ) ) )
= $true )
| ( ( ~ ! [SY996: $i] :
( ~ ( in @ SY996 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SV217 @ SY996 )
| ( in @ SV226 @ SY996 ) )
| ~ ( ~ ( in @ SV226 @ SY996 )
| ( in @ SV217 @ SY996 ) ) ) )
| ( SV217 = SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1342,plain,
! [SV209: $i,SV61: $i,SV205: $i] :
( ( ( ~ ( in @ SV205 @ ( sK2_SY743 @ SV61 ) ) )
= $true )
| ( ( ~ ( in @ SV209 @ ( sK2_SY743 @ SV61 ) ) )
= $true )
| ( ( ! [SY977: $i] :
( ~ ( in @ SY977 @ SV205 )
| ( in @ SY977 @ SV209 ) )
| ! [SY978: $i] :
( ~ ( in @ SY978 @ SV209 )
| ( in @ SY978 @ SV205 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1291]) ).
thf(1343,plain,
! [SV199: $i,SV61: $i] :
( ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( ~ ~ ! [SY960: $i] :
~ ( in @ SY960 @ SV199 ) )
= $true )
| ( ( ~ ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1292]) ).
thf(1344,plain,
! [SV61: $i,SV199: $i] :
( ( ( ~ ! [SY960: $i] :
~ ( in @ SY960 @ SV199 ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( ~ ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1345,plain,
! [SV71: $i,SV218: $i] :
( ( ( in @ SV218 @ omega )
= $false )
| ( ( in @ SV218 @ SV71 )
= $true )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( in @ ( sK26_SY775 @ SV71 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1346,plain,
! [SV71: $i,SV219: $i] :
( ( ( in @ SV219 @ omega )
= $false )
| ( ( in @ SV219 @ SV71 )
= $true )
| ( ( in @ emptyset @ SV71 )
= $false )
| ( ( in @ ( sK26_SY775 @ SV71 ) @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1347,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ! [SY789: $i] :
~ ~ ( ~ ( SV77 @ SY789 )
| ~ ! [SY790: $i] :
( ~ ( SV77 @ SY790 )
| ( SY789 = SY790 ) ) ) )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1348,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ~ ( ~ ( SV77 @ ( sK59_SY789 @ SV184 @ SV77 ) )
| ~ ! [SY999: $i] :
( ~ ( SV77 @ SY999 )
| ( ( sK59_SY789 @ SV184 @ SV77 )
= SY999 ) ) ) )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1299]) ).
thf(1349,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ~ ( ~ ( SV77 @ ( sK60_SY789 @ SV184 @ SV77 ) )
| ~ ! [SY1000: $i] :
( ~ ( SV77 @ SY1000 )
| ( ( sK60_SY789 @ SV184 @ SV77 )
= SY1000 ) ) ) )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1300]) ).
thf(1350,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ( ~ ( SV77 @ ( sK57_SY789 @ SV184 @ SV77 ) )
| ~ ! [SY997: $i] :
( ~ ( SV77 @ SY997 )
| ( ( sK57_SY789 @ SV184 @ SV77 )
= SY997 ) ) ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1301]) ).
thf(1351,plain,
! [SV185: $i,SV81: $i > $o] :
( ( ( ! [SY998: $i] :
~ ( ~ ( ~ ( SV81 @ SY998 )
| ( SY998
= ( sK58_SY799 @ SV185 @ SV81 ) ) )
| ~ ( ( SY998
!= ( sK58_SY799 @ SV185 @ SV81 ) )
| ( SV81 @ SY998 ) ) ) )
= $true )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV81 @ ( sK41_SY950 @ SV185 @ SV81 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1304]) ).
thf(1352,plain,
! [SV185: $i,SV228: $i,SV81: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV81 @ SV228 )
| ( SV228
= ( sK52_SY799 @ SV185 @ SV81 ) ) )
| ~ ( ( SV228
!= ( sK52_SY799 @ SV185 @ SV81 ) )
| ( SV81 @ SV228 ) ) ) )
= $true )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV185
= ( sK41_SY950 @ SV185 @ SV81 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1353,plain,
! [SV186: $i,SV227: $i,SV220: $i,SV84: $i > $o] :
( ( ( ~ ( SV84 @ SV220 ) )
= $true )
| ( ( ~ ( SV84 @ SV227 )
| ( SV220 = SV227 ) )
= $true )
| ( ( SV84 @ SV186 )
= $false )
| ( ( SV84 @ ( sK42_SY951 @ SV186 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1307]) ).
thf(1354,plain,
! [SV186: $i,SV221: $i,SV213: $i,SV84: $i > $o] :
( ( ( SV84 @ SV213 )
= $false )
| ( ( ~ ( SV84 @ SV221 )
| ( SV213 = SV221 ) )
= $true )
| ( ( SV84 @ SV186 )
= $false )
| ( ( SV186
= ( sK42_SY951 @ SV186 @ SV84 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1355,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ ( sK54_SY630 @ SV173 @ SV21 ) )
| ~ ! [SY991: $i] :
( ~ ( SV21 @ SY991 )
| ( ( sK54_SY630 @ SV173 @ SV21 )
= SY991 ) ) )
= $false )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV21 @ ( sK37_SY933 @ SV173 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1356,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ ( sK45_SY630 @ SV173 @ SV21 ) ) )
= $false )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV173
= ( sK37_SY933 @ SV173 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1311]) ).
thf(1357,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ~ ! [SY981: $i] :
( ~ ( SV21 @ SY981 )
| ( ( sK45_SY630 @ SV173 @ SV21 )
= SY981 ) ) )
= $false )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV173
= ( sK37_SY933 @ SV173 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1311]) ).
thf(1358,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ( SV32 @ ( sK47_SY653 @ SV175 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK27_SY651 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1313]) ).
thf(1359,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ! [SY982: $i] :
( ~ ( SV32 @ SY982 )
| ( ( sK47_SY653 @ SV175 @ SV32 )
= SY982 ) ) )
= $false )
| ( ( SV32 @ ( sK27_SY651 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1313]) ).
thf(1360,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ( SV32 @ ( sK55_SY653 @ SV175 @ SV32 ) )
| ~ ! [SY992: $i] :
( ~ ( SV32 @ SY992 )
| ( ( sK55_SY653 @ SV175 @ SV32 )
= SY992 ) ) )
= $false )
| ( ( SV32 @ ( sK32_SY966 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1314]) ).
thf(1361,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ( SV32 @ ( sK48_SY653 @ SV175 @ SV32 ) ) )
= $false )
| ( ( ( sK27_SY651 @ SV175 @ SV32 )
= ( sK32_SY966 @ SV175 @ SV32 ) )
= $false )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1315]) ).
thf(1362,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ! [SY983: $i] :
( ~ ( SV32 @ SY983 )
| ( ( sK48_SY653 @ SV175 @ SV32 )
= SY983 ) ) )
= $false )
| ( ( ( sK27_SY651 @ SV175 @ SV32 )
= ( sK32_SY966 @ SV175 @ SV32 ) )
= $false )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1315]) ).
thf(1363,plain,
! [SV176: $i,SV222: $i,SV214: $i,SV40: $i > $o] :
( ( ( SV40 @ SV214 )
= $false )
| ( ( ~ ( SV40 @ SV222 )
| ( SV214 = SV222 ) )
= $true )
| ( ( SV40 @ SV176 )
= $false )
| ( ( SV40 @ ( sK38_SY935 @ SV176 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1316]) ).
thf(1364,plain,
! [SV176: $i,SV212: $i,SV215: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ SV215 ) )
= $true )
| ( ( SV212 = SV215 )
= $true )
| ( ( SV40 @ SV212 )
= $false )
| ( ( SV40 @ SV176 )
= $false )
| ( ( SV176
= ( sK38_SY935 @ SV176 @ SV40 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1317]) ).
thf(1365,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ ( sK56_SY681 @ SV177 @ SV43 ) )
| ~ ! [SY993: $i] :
( ~ ( SV43 @ SY993 )
| ( ( sK56_SY681 @ SV177 @ SV43 )
= SY993 ) ) )
= $false )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV43 @ ( sK39_SY936 @ SV177 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1366,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ ( sK49_SY681 @ SV177 @ SV43 ) ) )
= $false )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV177
= ( sK39_SY936 @ SV177 @ SV43 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1319]) ).
thf(1367,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ~ ! [SY985: $i] :
( ~ ( SV43 @ SY985 )
| ( ( sK49_SY681 @ SV177 @ SV43 )
= SY985 ) ) )
= $false )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV177
= ( sK39_SY936 @ SV177 @ SV43 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1319]) ).
thf(1368,plain,
! [SV204: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ! [SY971: $i] :
~ ~ ( ~ ( in @ SY971 @ SV123 )
| ~ ( SV45 @ SY971 @ SV204 ) ) )
= $false )
| ( ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
= $false )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1369,plain,
! [SV204: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ! [SY972: $i] :
~ ~ ( ~ ( in @ SY972 @ SV123 )
| ~ ( SV45 @ SY972 @ SV204 ) ) )
= $true )
| ( ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
= $true )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1321]) ).
thf(1370,plain,
! [SV198: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ! [SY848: $i] :
~ ! [SY849: $i] :
~ ( ~ ( ~ ( in @ SY849 @ SY848 )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY849 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY849 ) )
| ( in @ SY849 @ SY848 ) ) ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1322]) ).
thf(1371,plain,
! [SV123: $i,SV45: $i > $i > $o,SV198: $i] :
( ( ( ~ ! [SY1001: $i] :
~ ( ~ ( ~ ( in @ SY1001 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY1001 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY1001 ) )
| ( in @ SY1001 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) ) ) ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1323]) ).
thf(1372,plain,
! [SV53: $i,SV128: $i,SV192: $i > $o,SV181: $i > $o] :
( ( ( ~ ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) ) )
= $false )
| ( ( ~ ( ~ ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
| ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1324]) ).
thf(1373,plain,
! [SV128: $i,SV181: $i > $o,SV53: $i,SV192: $i > $o] :
( ( ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
= $false )
| ( ( ~ ( ~ ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
| ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1324]) ).
thf(1374,plain,
! [SV55: $i,SV182: $i,SV223: $i] :
( ( ( ~ ( in @ SV223 @ ( sK25_SY715 @ SV182 @ SV55 ) )
| ~ ( in @ SV223 @ SV55 ) )
= $true )
| ( ( in @ SV182 @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1325]) ).
thf(1375,plain,
! [SV130: $i > $o,SV208: $i,SV56: $i > $o] :
( ( ( ! [SY976: $i] :
( ~ ( SV56 @ SY976 )
| ( SV208 = SY976 ) ) )
= $false )
| ( ( SV56 @ SV208 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1376,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1377,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1328]) ).
thf(1378,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1329]) ).
thf(1379,plain,
! [SV130: $i > $o,SV229: $i,SV56: $i > $o] :
( ( ( ~ ~ ( ~ ( SV56 @ SV229 )
| ~ ! [SY1004: $i] :
( ~ ( SV56 @ SY1004 )
| ( SV229 = SY1004 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1380,plain,
! [SV132: $i > $o,SV224: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV224 )
| ~ ! [SY994: $i] :
( ~ ( SV58 @ SY994 )
| ( SV224 = SY994 ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1331]) ).
thf(1381,plain,
! [SV58: $i > $o,SV225: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV225 )
| ~ ! [SY995: $i] :
( ~ ( SV132 @ SY995 )
| ( SV225 = SY995 ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1332]) ).
thf(1382,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1333]) ).
thf(1383,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1333]) ).
thf(1384,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1385,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1335]) ).
thf(1386,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1336]) ).
thf(1387,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1337]) ).
thf(1388,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1338]) ).
thf(1389,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1339]) ).
thf(1390,plain,
! [SV61: $i,SV216: $i,SV230: $i] :
( ( ( ~ ( in @ SV230 @ SV216 )
| ( in @ SV230 @ SV61 ) )
= $true )
| ( ( in @ SV216 @ ( sK2_SY743 @ SV61 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1391,plain,
! [SV226: $i,SV61: $i,SV217: $i] :
( ( ( ~ ( ~ ( in @ SV217 @ SV61 )
| ~ ( in @ SV226 @ SV61 ) ) )
= $false )
| ( ( ~ ! [SY996: $i] :
( ~ ( in @ SY996 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SV217 @ SY996 )
| ( in @ SV226 @ SY996 ) )
| ~ ( ~ ( in @ SV226 @ SY996 )
| ( in @ SV217 @ SY996 ) ) ) )
| ( SV217 = SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1392,plain,
! [SV209: $i,SV61: $i,SV205: $i] :
( ( ( in @ SV205 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( ~ ( in @ SV209 @ ( sK2_SY743 @ SV61 ) ) )
= $true )
| ( ( ! [SY977: $i] :
( ~ ( in @ SY977 @ SV205 )
| ( in @ SY977 @ SV209 ) )
| ! [SY978: $i] :
( ~ ( in @ SY978 @ SV209 )
| ( in @ SY978 @ SV205 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1393,plain,
! [SV61: $i,SV199: $i] :
( ( ( ~ ! [SY960: $i] :
~ ( in @ SY960 @ SV199 ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( ~ ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1394,plain,
! [SV61: $i,SV199: $i] :
( ( ( ! [SY960: $i] :
~ ( in @ SY960 @ SV199 ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( ~ ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1344]) ).
thf(1395,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ~ ( ~ ( SV77 @ ( sK62_SY789 @ SV184 @ SV77 ) )
| ~ ! [SY1005: $i] :
( ~ ( SV77 @ SY1005 )
| ( ( sK62_SY789 @ SV184 @ SV77 )
= SY1005 ) ) ) )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1347]) ).
thf(1396,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ( ~ ( SV77 @ ( sK59_SY789 @ SV184 @ SV77 ) )
| ~ ! [SY999: $i] :
( ~ ( SV77 @ SY999 )
| ( ( sK59_SY789 @ SV184 @ SV77 )
= SY999 ) ) ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1348]) ).
thf(1397,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ( ~ ( SV77 @ ( sK60_SY789 @ SV184 @ SV77 ) )
| ~ ! [SY1000: $i] :
( ~ ( SV77 @ SY1000 )
| ( ( sK60_SY789 @ SV184 @ SV77 )
= SY1000 ) ) ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1349]) ).
thf(1398,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ( SV77 @ ( sK57_SY789 @ SV184 @ SV77 ) )
| ~ ! [SY997: $i] :
( ~ ( SV77 @ SY997 )
| ( ( sK57_SY789 @ SV184 @ SV77 )
= SY997 ) ) )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1399,plain,
! [SV185: $i,SV231: $i,SV81: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV81 @ SV231 )
| ( SV231
= ( sK58_SY799 @ SV185 @ SV81 ) ) )
| ~ ( ( SV231
!= ( sK58_SY799 @ SV185 @ SV81 ) )
| ( SV81 @ SV231 ) ) ) )
= $true )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV81 @ ( sK41_SY950 @ SV185 @ SV81 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1400,plain,
! [SV185: $i,SV228: $i,SV81: $i > $o] :
( ( ( ~ ( ~ ( SV81 @ SV228 )
| ( SV228
= ( sK52_SY799 @ SV185 @ SV81 ) ) )
| ~ ( ( SV228
!= ( sK52_SY799 @ SV185 @ SV81 ) )
| ( SV81 @ SV228 ) ) )
= $false )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV185
= ( sK41_SY950 @ SV185 @ SV81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1352]) ).
thf(1401,plain,
! [SV186: $i,SV227: $i,SV220: $i,SV84: $i > $o] :
( ( ( SV84 @ SV220 )
= $false )
| ( ( ~ ( SV84 @ SV227 )
| ( SV220 = SV227 ) )
= $true )
| ( ( SV84 @ SV186 )
= $false )
| ( ( SV84 @ ( sK42_SY951 @ SV186 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1402,plain,
! [SV186: $i,SV213: $i,SV221: $i,SV84: $i > $o] :
( ( ( ~ ( SV84 @ SV221 ) )
= $true )
| ( ( SV213 = SV221 )
= $true )
| ( ( SV84 @ SV213 )
= $false )
| ( ( SV84 @ SV186 )
= $false )
| ( ( SV186
= ( sK42_SY951 @ SV186 @ SV84 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1354]) ).
thf(1403,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ ( sK54_SY630 @ SV173 @ SV21 ) ) )
= $false )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV21 @ ( sK37_SY933 @ SV173 @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1355]) ).
thf(1404,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ~ ! [SY991: $i] :
( ~ ( SV21 @ SY991 )
| ( ( sK54_SY630 @ SV173 @ SV21 )
= SY991 ) ) )
= $false )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV21 @ ( sK37_SY933 @ SV173 @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1355]) ).
thf(1405,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( SV21 @ ( sK45_SY630 @ SV173 @ SV21 ) )
= $true )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV173
= ( sK37_SY933 @ SV173 @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1356]) ).
thf(1406,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ! [SY981: $i] :
( ~ ( SV21 @ SY981 )
| ( ( sK45_SY630 @ SV173 @ SV21 )
= SY981 ) ) )
= $true )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV173
= ( sK37_SY933 @ SV173 @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1357]) ).
thf(1407,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( SV32 @ ( sK47_SY653 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK27_SY651 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1358]) ).
thf(1408,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ! [SY982: $i] :
( ~ ( SV32 @ SY982 )
| ( ( sK47_SY653 @ SV175 @ SV32 )
= SY982 ) ) )
= $true )
| ( ( SV32 @ ( sK27_SY651 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1359]) ).
thf(1409,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ( SV32 @ ( sK55_SY653 @ SV175 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK32_SY966 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1360]) ).
thf(1410,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ~ ! [SY992: $i] :
( ~ ( SV32 @ SY992 )
| ( ( sK55_SY653 @ SV175 @ SV32 )
= SY992 ) ) )
= $false )
| ( ( SV32 @ ( sK32_SY966 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1360]) ).
thf(1411,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( SV32 @ ( sK48_SY653 @ SV175 @ SV32 ) )
= $true )
| ( ( ( sK27_SY651 @ SV175 @ SV32 )
= ( sK32_SY966 @ SV175 @ SV32 ) )
= $false )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1361]) ).
thf(1412,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ! [SY983: $i] :
( ~ ( SV32 @ SY983 )
| ( ( sK48_SY653 @ SV175 @ SV32 )
= SY983 ) ) )
= $true )
| ( ( ( sK27_SY651 @ SV175 @ SV32 )
= ( sK32_SY966 @ SV175 @ SV32 ) )
= $false )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1362]) ).
thf(1413,plain,
! [SV176: $i,SV214: $i,SV222: $i,SV40: $i > $o] :
( ( ( ~ ( SV40 @ SV222 ) )
= $true )
| ( ( SV214 = SV222 )
= $true )
| ( ( SV40 @ SV214 )
= $false )
| ( ( SV40 @ SV176 )
= $false )
| ( ( SV40 @ ( sK38_SY935 @ SV176 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1363]) ).
thf(1414,plain,
! [SV176: $i,SV212: $i,SV215: $i,SV40: $i > $o] :
( ( ( SV40 @ SV215 )
= $false )
| ( ( SV212 = SV215 )
= $true )
| ( ( SV40 @ SV212 )
= $false )
| ( ( SV40 @ SV176 )
= $false )
| ( ( SV176
= ( sK38_SY935 @ SV176 @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1415,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ ( sK56_SY681 @ SV177 @ SV43 ) ) )
= $false )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV43 @ ( sK39_SY936 @ SV177 @ SV43 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1416,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ~ ! [SY993: $i] :
( ~ ( SV43 @ SY993 )
| ( ( sK56_SY681 @ SV177 @ SV43 )
= SY993 ) ) )
= $false )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV43 @ ( sK39_SY936 @ SV177 @ SV43 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1365]) ).
thf(1417,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( SV43 @ ( sK49_SY681 @ SV177 @ SV43 ) )
= $true )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV177
= ( sK39_SY936 @ SV177 @ SV43 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1366]) ).
thf(1418,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ! [SY985: $i] :
( ~ ( SV43 @ SY985 )
| ( ( sK49_SY681 @ SV177 @ SV43 )
= SY985 ) ) )
= $true )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV177
= ( sK39_SY936 @ SV177 @ SV43 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1367]) ).
thf(1419,plain,
! [SV123: $i,SV45: $i > $i > $o,SV204: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK63_SY971 @ SV204 @ SV45 @ SV123 ) @ SV123 )
| ~ ( SV45 @ ( sK63_SY971 @ SV204 @ SV45 @ SV123 ) @ SV204 ) ) )
= $false )
| ( ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
= $false )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1368]) ).
thf(1420,plain,
! [SV204: $i,SV45: $i > $i > $o,SV123: $i,SV232: $i] :
( ( ( ~ ~ ( ~ ( in @ SV232 @ SV123 )
| ~ ( SV45 @ SV232 @ SV204 ) ) )
= $true )
| ( ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
= $true )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1421,plain,
! [SV123: $i,SV45: $i > $i > $o,SV198: $i] :
( ( ( ~ ! [SY1006: $i] :
~ ( ~ ( ~ ( in @ SY1006 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY1006 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY1006 ) )
| ( in @ SY1006 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) ) ) ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1370]) ).
thf(1422,plain,
! [SV123: $i,SV45: $i > $i > $o,SV198: $i] :
( ( ( ! [SY1001: $i] :
~ ( ~ ( ~ ( in @ SY1001 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY1001 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY1001 ) )
| ( in @ SY1001 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) ) ) ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1371]) ).
thf(1423,plain,
! [SV53: $i,SV128: $i,SV192: $i > $o,SV181: $i > $o] :
( ( ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) )
= $true )
| ( ( ~ ( ~ ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
| ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1372]) ).
thf(1424,plain,
! [SV128: $i,SV181: $i > $o,SV53: $i,SV192: $i > $o] :
( ( ( ~ ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
| ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) ) )
= $false )
| ( ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
= $false )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1425,plain,
! [SV55: $i,SV182: $i,SV223: $i] :
( ( ( ~ ( in @ SV223 @ ( sK25_SY715 @ SV182 @ SV55 ) ) )
= $true )
| ( ( ~ ( in @ SV223 @ SV55 ) )
= $true )
| ( ( in @ SV182 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1426,plain,
! [SV208: $i,SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ( SV56 @ ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
| ( SV208
= ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) ) )
= $false )
| ( ( SV56 @ SV208 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1375]) ).
thf(1427,plain,
! [SV130: $i > $o,SV56: $i > $o] :
( ( ( ! [SY720: $i] :
~ ~ ( ~ ( SV56 @ SY720 )
| ~ ! [SY721: $i] :
( ~ ( SV56 @ SY721 )
| ( SY720 = SY721 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1376]) ).
thf(1428,plain,
! [SV130: $i > $o,SV233: $i,SV56: $i > $o] :
( ( ( ~ ~ ( ~ ( SV56 @ SV233 )
| ~ ! [SY1009: $i] :
( ~ ( SV56 @ SY1009 )
| ( SV233 = SY1009 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1429,plain,
! [SV130: $i > $o,SV234: $i,SV56: $i > $o] :
( ( ( ~ ~ ( ~ ( SV56 @ SV234 )
| ~ ! [SY1010: $i] :
( ~ ( SV56 @ SY1010 )
| ( SV234 = SY1010 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1430,plain,
! [SV130: $i > $o,SV229: $i,SV56: $i > $o] :
( ( ( ~ ( ~ ( SV56 @ SV229 )
| ~ ! [SY1004: $i] :
( ~ ( SV56 @ SY1004 )
| ( SV229 = SY1004 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1431,plain,
! [SV132: $i > $o,SV224: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV224 ) )
= $true )
| ( ( ~ ! [SY994: $i] :
( ~ ( SV58 @ SY994 )
| ( SV224 = SY994 ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1380]) ).
thf(1432,plain,
! [SV58: $i > $o,SV225: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV225 ) )
= $true )
| ( ( ~ ! [SY995: $i] :
( ~ ( SV132 @ SY995 )
| ( SV225 = SY995 ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1433,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) )
| ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1382]) ).
thf(1434,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) )
| ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1383]) ).
thf(1435,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1384]) ).
thf(1436,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1437,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1438,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1439,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) ) )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1440,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) ) )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1441,plain,
! [SV61: $i,SV216: $i,SV230: $i] :
( ( ( ~ ( in @ SV230 @ SV216 ) )
= $true )
| ( ( in @ SV230 @ SV61 )
= $true )
| ( ( in @ SV216 @ ( sK2_SY743 @ SV61 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1442,plain,
! [SV226: $i,SV61: $i,SV217: $i] :
( ( ( ~ ( in @ SV217 @ SV61 )
| ~ ( in @ SV226 @ SV61 ) )
= $true )
| ( ( ~ ! [SY996: $i] :
( ~ ( in @ SY996 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SV217 @ SY996 )
| ( in @ SV226 @ SY996 ) )
| ~ ( ~ ( in @ SV226 @ SY996 )
| ( in @ SV217 @ SY996 ) ) ) )
| ( SV217 = SV226 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1391]) ).
thf(1443,plain,
! [SV205: $i,SV61: $i,SV209: $i] :
( ( ( in @ SV209 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( in @ SV205 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( ! [SY977: $i] :
( ~ ( in @ SY977 @ SV205 )
| ( in @ SY977 @ SV209 ) )
| ! [SY978: $i] :
( ~ ( in @ SY978 @ SV209 )
| ( in @ SY978 @ SV205 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1444,plain,
! [SV61: $i,SV199: $i] :
( ( ( ! [SY960: $i] :
~ ( in @ SY960 @ SV199 ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( ~ ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1393]) ).
thf(1445,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( ~ ( in @ SV235 @ SV199 ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( ~ ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1446,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ( ~ ( SV77 @ ( sK62_SY789 @ SV184 @ SV77 ) )
| ~ ! [SY1005: $i] :
( ~ ( SV77 @ SY1005 )
| ( ( sK62_SY789 @ SV184 @ SV77 )
= SY1005 ) ) ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1395]) ).
thf(1447,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ( SV77 @ ( sK59_SY789 @ SV184 @ SV77 ) )
| ~ ! [SY999: $i] :
( ~ ( SV77 @ SY999 )
| ( ( sK59_SY789 @ SV184 @ SV77 )
= SY999 ) ) )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1448,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ( SV77 @ ( sK60_SY789 @ SV184 @ SV77 ) )
| ~ ! [SY1000: $i] :
( ~ ( SV77 @ SY1000 )
| ( ( sK60_SY789 @ SV184 @ SV77 )
= SY1000 ) ) )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1397]) ).
thf(1449,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ( SV77 @ ( sK57_SY789 @ SV184 @ SV77 ) ) )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1398]) ).
thf(1450,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ! [SY997: $i] :
( ~ ( SV77 @ SY997 )
| ( ( sK57_SY789 @ SV184 @ SV77 )
= SY997 ) ) )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1398]) ).
thf(1451,plain,
! [SV185: $i,SV231: $i,SV81: $i > $o] :
( ( ( ~ ( ~ ( SV81 @ SV231 )
| ( SV231
= ( sK58_SY799 @ SV185 @ SV81 ) ) )
| ~ ( ( SV231
!= ( sK58_SY799 @ SV185 @ SV81 ) )
| ( SV81 @ SV231 ) ) )
= $false )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV81 @ ( sK41_SY950 @ SV185 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1452,plain,
! [SV185: $i,SV228: $i,SV81: $i > $o] :
( ( ( ~ ( ~ ( SV81 @ SV228 )
| ( SV228
= ( sK52_SY799 @ SV185 @ SV81 ) ) ) )
= $false )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV185
= ( sK41_SY950 @ SV185 @ SV81 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1400]) ).
thf(1453,plain,
! [SV81: $i > $o,SV185: $i,SV228: $i] :
( ( ( ~ ( ( SV228
!= ( sK52_SY799 @ SV185 @ SV81 ) )
| ( SV81 @ SV228 ) ) )
= $false )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV185
= ( sK41_SY950 @ SV185 @ SV81 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1400]) ).
thf(1454,plain,
! [SV186: $i,SV220: $i,SV227: $i,SV84: $i > $o] :
( ( ( ~ ( SV84 @ SV227 ) )
= $true )
| ( ( SV220 = SV227 )
= $true )
| ( ( SV84 @ SV220 )
= $false )
| ( ( SV84 @ SV186 )
= $false )
| ( ( SV84 @ ( sK42_SY951 @ SV186 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1401]) ).
thf(1455,plain,
! [SV186: $i,SV213: $i,SV221: $i,SV84: $i > $o] :
( ( ( SV84 @ SV221 )
= $false )
| ( ( SV213 = SV221 )
= $true )
| ( ( SV84 @ SV213 )
= $false )
| ( ( SV84 @ SV186 )
= $false )
| ( ( SV186
= ( sK42_SY951 @ SV186 @ SV84 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1456,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( SV21 @ ( sK54_SY630 @ SV173 @ SV21 ) )
= $true )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV21 @ ( sK37_SY933 @ SV173 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1403]) ).
thf(1457,plain,
! [SV173: $i,SV21: $i > $o] :
( ( ( ! [SY991: $i] :
( ~ ( SV21 @ SY991 )
| ( ( sK54_SY630 @ SV173 @ SV21 )
= SY991 ) ) )
= $true )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV21 @ ( sK37_SY933 @ SV173 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1404]) ).
thf(1458,plain,
! [SV173: $i,SV236: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ SV236 )
| ( ( sK45_SY630 @ SV173 @ SV21 )
= SV236 ) )
= $true )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV173
= ( sK37_SY933 @ SV173 @ SV21 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1459,plain,
! [SV175: $i,SV237: $i,SV32: $i > $o] :
( ( ( ~ ( SV32 @ SV237 )
| ( ( sK47_SY653 @ SV175 @ SV32 )
= SV237 ) )
= $true )
| ( ( SV32 @ ( sK27_SY651 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1460,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( SV32 @ ( sK55_SY653 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK32_SY966 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1409]) ).
thf(1461,plain,
! [SV175: $i,SV32: $i > $o] :
( ( ( ! [SY992: $i] :
( ~ ( SV32 @ SY992 )
| ( ( sK55_SY653 @ SV175 @ SV32 )
= SY992 ) ) )
= $true )
| ( ( SV32 @ ( sK32_SY966 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1410]) ).
thf(1462,plain,
! [SV175: $i,SV238: $i,SV32: $i > $o] :
( ( ( ~ ( SV32 @ SV238 )
| ( ( sK48_SY653 @ SV175 @ SV32 )
= SV238 ) )
= $true )
| ( ( ( sK27_SY651 @ SV175 @ SV32 )
= ( sK32_SY966 @ SV175 @ SV32 ) )
= $false )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1463,plain,
! [SV176: $i,SV214: $i,SV222: $i,SV40: $i > $o] :
( ( ( SV40 @ SV222 )
= $false )
| ( ( SV214 = SV222 )
= $true )
| ( ( SV40 @ SV214 )
= $false )
| ( ( SV40 @ SV176 )
= $false )
| ( ( SV40 @ ( sK38_SY935 @ SV176 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1413]) ).
thf(1464,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( SV43 @ ( sK56_SY681 @ SV177 @ SV43 ) )
= $true )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV43 @ ( sK39_SY936 @ SV177 @ SV43 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1415]) ).
thf(1465,plain,
! [SV177: $i,SV43: $i > $o] :
( ( ( ! [SY993: $i] :
( ~ ( SV43 @ SY993 )
| ( ( sK56_SY681 @ SV177 @ SV43 )
= SY993 ) ) )
= $true )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV43 @ ( sK39_SY936 @ SV177 @ SV43 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1416]) ).
thf(1466,plain,
! [SV177: $i,SV239: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ SV239 )
| ( ( sK49_SY681 @ SV177 @ SV43 )
= SV239 ) )
= $true )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV177
= ( sK39_SY936 @ SV177 @ SV43 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1467,plain,
! [SV123: $i,SV45: $i > $i > $o,SV204: $i] :
( ( ( ~ ( ~ ( in @ ( sK63_SY971 @ SV204 @ SV45 @ SV123 ) @ SV123 )
| ~ ( SV45 @ ( sK63_SY971 @ SV204 @ SV45 @ SV123 ) @ SV204 ) ) )
= $true )
| ( ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
= $false )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1419]) ).
thf(1468,plain,
! [SV204: $i,SV45: $i > $i > $o,SV123: $i,SV232: $i] :
( ( ( ~ ( ~ ( in @ SV232 @ SV123 )
| ~ ( SV45 @ SV232 @ SV204 ) ) )
= $false )
| ( ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
= $true )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1420]) ).
thf(1469,plain,
! [SV123: $i,SV45: $i > $i > $o,SV198: $i] :
( ( ( ! [SY1006: $i] :
~ ( ~ ( ~ ( in @ SY1006 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
| ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV123 )
| ~ ( SV45 @ SY850 @ SY1006 ) ) )
| ~ ( ~ ~ ! [SY851: $i] :
~ ~ ( ~ ( in @ SY851 @ SV123 )
| ~ ( SV45 @ SY851 @ SY1006 ) )
| ( in @ SY1006 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) ) ) ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1421]) ).
thf(1470,plain,
! [SV123: $i,SV45: $i > $i > $o,SV198: $i,SV240: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
| ~ ! [SY1011: $i] :
~ ~ ( ~ ( in @ SY1011 @ SV123 )
| ~ ( SV45 @ SY1011 @ SV240 ) ) )
| ~ ( ~ ~ ! [SY1012: $i] :
~ ~ ( ~ ( in @ SY1012 @ SV123 )
| ~ ( SV45 @ SY1012 @ SV240 ) )
| ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) ) ) ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1471,plain,
! [SV128: $i,SV181: $i > $o,SV53: $i,SV192: $i > $o] :
( ( ( ~ ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
| ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) ) )
= $false )
| ( ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) )
= $true )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1472,plain,
! [SV128: $i,SV181: $i > $o,SV53: $i,SV192: $i > $o] :
( ( ( ~ ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) ) )
= $false )
| ( ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
= $false )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1424]) ).
thf(1473,plain,
! [SV53: $i,SV128: $i,SV192: $i > $o,SV181: $i > $o] :
( ( ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) )
= $false )
| ( ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
= $false )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1424]) ).
thf(1474,plain,
! [SV55: $i,SV182: $i,SV223: $i] :
( ( ( in @ SV223 @ ( sK25_SY715 @ SV182 @ SV55 ) )
= $false )
| ( ( ~ ( in @ SV223 @ SV55 ) )
= $true )
| ( ( in @ SV182 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1475,plain,
! [SV208: $i,SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ( SV56 @ ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) ) )
= $false )
| ( ( SV56 @ SV208 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1476,plain,
! [SV56: $i > $o,SV130: $i > $o,SV208: $i] :
( ( ( SV208
= ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $false )
| ( ( SV56 @ SV208 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1477,plain,
! [SV130: $i > $o,SV241: $i,SV56: $i > $o] :
( ( ( ~ ~ ( ~ ( SV56 @ SV241 )
| ~ ! [SY1013: $i] :
( ~ ( SV56 @ SY1013 )
| ( SV241 = SY1013 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1478,plain,
! [SV130: $i > $o,SV233: $i,SV56: $i > $o] :
( ( ( ~ ( ~ ( SV56 @ SV233 )
| ~ ! [SY1009: $i] :
( ~ ( SV56 @ SY1009 )
| ( SV233 = SY1009 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1428]) ).
thf(1479,plain,
! [SV130: $i > $o,SV234: $i,SV56: $i > $o] :
( ( ( ~ ( ~ ( SV56 @ SV234 )
| ~ ! [SY1010: $i] :
( ~ ( SV56 @ SY1010 )
| ( SV234 = SY1010 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1480,plain,
! [SV130: $i > $o,SV229: $i,SV56: $i > $o] :
( ( ( ~ ( SV56 @ SV229 )
| ~ ! [SY1004: $i] :
( ~ ( SV56 @ SY1004 )
| ( SV229 = SY1004 ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1430]) ).
thf(1481,plain,
! [SV132: $i > $o,SV224: $i,SV58: $i > $o] :
( ( ( SV58 @ SV224 )
= $false )
| ( ( ~ ! [SY994: $i] :
( ~ ( SV58 @ SY994 )
| ( SV224 = SY994 ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1482,plain,
! [SV58: $i > $o,SV225: $i,SV132: $i > $o] :
( ( ( SV132 @ SV225 )
= $false )
| ( ( ~ ! [SY995: $i] :
( ~ ( SV132 @ SY995 )
| ( SV225 = SY995 ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1483,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1433]) ).
thf(1484,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1434]) ).
thf(1485,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) ) )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1435]) ).
thf(1486,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) ) )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1487,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) ) )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1437]) ).
thf(1488,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) ) )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1438]) ).
thf(1489,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1439]) ).
thf(1490,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1440]) ).
thf(1491,plain,
! [SV61: $i,SV216: $i,SV230: $i] :
( ( ( in @ SV230 @ SV216 )
= $false )
| ( ( in @ SV230 @ SV61 )
= $true )
| ( ( in @ SV216 @ ( sK2_SY743 @ SV61 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1492,plain,
! [SV226: $i,SV61: $i,SV217: $i] :
( ( ( ~ ( in @ SV217 @ SV61 ) )
= $true )
| ( ( ~ ( in @ SV226 @ SV61 ) )
= $true )
| ( ( ~ ! [SY996: $i] :
( ~ ( in @ SY996 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SV217 @ SY996 )
| ( in @ SV226 @ SY996 ) )
| ~ ( ~ ( in @ SV226 @ SY996 )
| ( in @ SV217 @ SY996 ) ) ) )
| ( SV217 = SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1442]) ).
thf(1493,plain,
! [SV61: $i,SV209: $i,SV205: $i] :
( ( ( ! [SY977: $i] :
( ~ ( in @ SY977 @ SV205 )
| ( in @ SY977 @ SV209 ) ) )
= $true )
| ( ( ! [SY978: $i] :
( ~ ( in @ SY978 @ SV209 )
| ( in @ SY978 @ SV205 ) ) )
= $true )
| ( ( in @ SV205 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( in @ SV209 @ ( sK2_SY743 @ SV61 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1443]) ).
thf(1494,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ SV199 ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( ~ ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1495,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( in @ SV235 @ SV199 )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( ~ ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1496,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ( SV77 @ ( sK62_SY789 @ SV184 @ SV77 ) )
| ~ ! [SY1005: $i] :
( ~ ( SV77 @ SY1005 )
| ( ( sK62_SY789 @ SV184 @ SV77 )
= SY1005 ) ) )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1497,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ( SV77 @ ( sK59_SY789 @ SV184 @ SV77 ) ) )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1498,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ! [SY999: $i] :
( ~ ( SV77 @ SY999 )
| ( ( sK59_SY789 @ SV184 @ SV77 )
= SY999 ) ) )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1499,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ( SV77 @ ( sK60_SY789 @ SV184 @ SV77 ) ) )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1448]) ).
thf(1500,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ! [SY1000: $i] :
( ~ ( SV77 @ SY1000 )
| ( ( sK60_SY789 @ SV184 @ SV77 )
= SY1000 ) ) )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1448]) ).
thf(1501,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( SV77 @ ( sK57_SY789 @ SV184 @ SV77 ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1449]) ).
thf(1502,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ! [SY997: $i] :
( ~ ( SV77 @ SY997 )
| ( ( sK57_SY789 @ SV184 @ SV77 )
= SY997 ) ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1450]) ).
thf(1503,plain,
! [SV185: $i,SV231: $i,SV81: $i > $o] :
( ( ( ~ ( ~ ( SV81 @ SV231 )
| ( SV231
= ( sK58_SY799 @ SV185 @ SV81 ) ) ) )
= $false )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV81 @ ( sK41_SY950 @ SV185 @ SV81 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1451]) ).
thf(1504,plain,
! [SV81: $i > $o,SV185: $i,SV231: $i] :
( ( ( ~ ( ( SV231
!= ( sK58_SY799 @ SV185 @ SV81 ) )
| ( SV81 @ SV231 ) ) )
= $false )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV81 @ ( sK41_SY950 @ SV185 @ SV81 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1451]) ).
thf(1505,plain,
! [SV185: $i,SV228: $i,SV81: $i > $o] :
( ( ( ~ ( SV81 @ SV228 )
| ( SV228
= ( sK52_SY799 @ SV185 @ SV81 ) ) )
= $true )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV185
= ( sK41_SY950 @ SV185 @ SV81 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1452]) ).
thf(1506,plain,
! [SV81: $i > $o,SV185: $i,SV228: $i] :
( ( ( ( SV228
!= ( sK52_SY799 @ SV185 @ SV81 ) )
| ( SV81 @ SV228 ) )
= $true )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV185
= ( sK41_SY950 @ SV185 @ SV81 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1453]) ).
thf(1507,plain,
! [SV186: $i,SV220: $i,SV227: $i,SV84: $i > $o] :
( ( ( SV84 @ SV227 )
= $false )
| ( ( SV220 = SV227 )
= $true )
| ( ( SV84 @ SV220 )
= $false )
| ( ( SV84 @ SV186 )
= $false )
| ( ( SV84 @ ( sK42_SY951 @ SV186 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1454]) ).
thf(1508,plain,
! [SV173: $i,SV243: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ SV243 )
| ( ( sK54_SY630 @ SV173 @ SV21 )
= SV243 ) )
= $true )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV21 @ ( sK37_SY933 @ SV173 @ SV21 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1509,plain,
! [SV173: $i,SV236: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ SV236 ) )
= $true )
| ( ( ( sK45_SY630 @ SV173 @ SV21 )
= SV236 )
= $true )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV173
= ( sK37_SY933 @ SV173 @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1510,plain,
! [SV175: $i,SV237: $i,SV32: $i > $o] :
( ( ( ~ ( SV32 @ SV237 ) )
= $true )
| ( ( ( sK47_SY653 @ SV175 @ SV32 )
= SV237 )
= $true )
| ( ( SV32 @ ( sK27_SY651 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1459]) ).
thf(1511,plain,
! [SV175: $i,SV244: $i,SV32: $i > $o] :
( ( ( ~ ( SV32 @ SV244 )
| ( ( sK55_SY653 @ SV175 @ SV32 )
= SV244 ) )
= $true )
| ( ( SV32 @ ( sK32_SY966 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1512,plain,
! [SV175: $i,SV238: $i,SV32: $i > $o] :
( ( ( ~ ( SV32 @ SV238 ) )
= $true )
| ( ( ( sK48_SY653 @ SV175 @ SV32 )
= SV238 )
= $true )
| ( ( ( sK27_SY651 @ SV175 @ SV32 )
= ( sK32_SY966 @ SV175 @ SV32 ) )
= $false )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1513,plain,
! [SV177: $i,SV245: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ SV245 )
| ( ( sK56_SY681 @ SV177 @ SV43 )
= SV245 ) )
= $true )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV43 @ ( sK39_SY936 @ SV177 @ SV43 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1514,plain,
! [SV177: $i,SV239: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ SV239 ) )
= $true )
| ( ( ( sK49_SY681 @ SV177 @ SV43 )
= SV239 )
= $true )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV177
= ( sK39_SY936 @ SV177 @ SV43 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1466]) ).
thf(1515,plain,
! [SV123: $i,SV45: $i > $i > $o,SV204: $i] :
( ( ( ~ ( in @ ( sK63_SY971 @ SV204 @ SV45 @ SV123 ) @ SV123 )
| ~ ( SV45 @ ( sK63_SY971 @ SV204 @ SV45 @ SV123 ) @ SV204 ) )
= $false )
| ( ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
= $false )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1516,plain,
! [SV204: $i,SV45: $i > $i > $o,SV123: $i,SV232: $i] :
( ( ( ~ ( in @ SV232 @ SV123 )
| ~ ( SV45 @ SV232 @ SV204 ) )
= $true )
| ( ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
= $true )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1468]) ).
thf(1517,plain,
! [SV123: $i,SV45: $i > $i > $o,SV198: $i,SV246: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
| ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SV123 )
| ~ ( SV45 @ SY1014 @ SV246 ) ) )
| ~ ( ~ ~ ! [SY1015: $i] :
~ ~ ( ~ ( in @ SY1015 @ SV123 )
| ~ ( SV45 @ SY1015 @ SV246 ) )
| ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) ) ) ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1518,plain,
! [SV123: $i,SV45: $i > $i > $o,SV198: $i,SV240: $i] :
( ( ( ~ ( ~ ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
| ~ ! [SY1011: $i] :
~ ~ ( ~ ( in @ SY1011 @ SV123 )
| ~ ( SV45 @ SY1011 @ SV240 ) ) )
| ~ ( ~ ~ ! [SY1012: $i] :
~ ~ ( ~ ( in @ SY1012 @ SV123 )
| ~ ( SV45 @ SY1012 @ SV240 ) )
| ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) ) ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1519,plain,
! [SV128: $i,SV181: $i > $o,SV53: $i,SV192: $i > $o] :
( ( ( ~ ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) ) )
= $false )
| ( ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) )
= $true )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1471]) ).
thf(1520,plain,
! [SV53: $i,SV128: $i,SV192: $i > $o,SV181: $i > $o] :
( ( ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) )
= $false )
| ( ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) )
= $true )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1471]) ).
thf(1521,plain,
! [SV128: $i,SV181: $i > $o,SV53: $i,SV192: $i > $o] :
( ( ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
= $true )
| ( ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
= $false )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1472]) ).
thf(1522,plain,
! [SV182: $i,SV55: $i,SV223: $i] :
( ( ( in @ SV223 @ SV55 )
= $false )
| ( ( in @ SV223 @ ( sK25_SY715 @ SV182 @ SV55 ) )
= $false )
| ( ( in @ SV182 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1523,plain,
! [SV208: $i,SV130: $i > $o,SV56: $i > $o] :
( ( ( SV56 @ ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1475]) ).
thf(1524,plain,
! [SV208: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV208
= ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $false )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1476]) ).
thf(1525,plain,
! [SV130: $i > $o,SV241: $i,SV56: $i > $o] :
( ( ( ~ ( ~ ( SV56 @ SV241 )
| ~ ! [SY1013: $i] :
( ~ ( SV56 @ SY1013 )
| ( SV241 = SY1013 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1477]) ).
thf(1526,plain,
! [SV130: $i > $o,SV233: $i,SV56: $i > $o] :
( ( ( ~ ( SV56 @ SV233 )
| ~ ! [SY1009: $i] :
( ~ ( SV56 @ SY1009 )
| ( SV233 = SY1009 ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1478]) ).
thf(1527,plain,
! [SV130: $i > $o,SV234: $i,SV56: $i > $o] :
( ( ( ~ ( SV56 @ SV234 )
| ~ ! [SY1010: $i] :
( ~ ( SV56 @ SY1010 )
| ( SV234 = SY1010 ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1479]) ).
thf(1528,plain,
! [SV130: $i > $o,SV229: $i,SV56: $i > $o] :
( ( ( ~ ( SV56 @ SV229 ) )
= $true )
| ( ( ~ ! [SY1004: $i] :
( ~ ( SV56 @ SY1004 )
| ( SV229 = SY1004 ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1529,plain,
! [SV132: $i > $o,SV224: $i,SV58: $i > $o] :
( ( ( ! [SY994: $i] :
( ~ ( SV58 @ SY994 )
| ( SV224 = SY994 ) ) )
= $false )
| ( ( SV58 @ SV224 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1530,plain,
! [SV58: $i > $o,SV225: $i,SV132: $i > $o] :
( ( ( ! [SY995: $i] :
( ~ ( SV132 @ SY995 )
| ( SV225 = SY995 ) ) )
= $false )
| ( ( SV132 @ SV225 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1531,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) ) )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1532,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) ) )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1484]) ).
thf(1533,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1485]) ).
thf(1534,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1486]) ).
thf(1535,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1487]) ).
thf(1536,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1488]) ).
thf(1537,plain,
! [SV132: $i > $o,SV247: $i,SV58: $i > $o] :
( ( ( ~ ~ ( ~ ( SV58 @ SV247 )
| ~ ! [SY1016: $i] :
( ~ ( SV58 @ SY1016 )
| ( SV247 = SY1016 ) ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1538,plain,
! [SV58: $i > $o,SV248: $i,SV132: $i > $o] :
( ( ( ~ ~ ( ~ ( SV132 @ SV248 )
| ~ ! [SY1017: $i] :
( ~ ( SV132 @ SY1017 )
| ( SV248 = SY1017 ) ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1539,plain,
! [SV226: $i,SV61: $i,SV217: $i] :
( ( ( in @ SV217 @ SV61 )
= $false )
| ( ( ~ ( in @ SV226 @ SV61 ) )
= $true )
| ( ( ~ ! [SY996: $i] :
( ~ ( in @ SY996 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SV217 @ SY996 )
| ( in @ SV226 @ SY996 ) )
| ~ ( ~ ( in @ SV226 @ SY996 )
| ( in @ SV217 @ SY996 ) ) ) )
| ( SV217 = SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1540,plain,
! [SV61: $i,SV209: $i,SV205: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV205 )
| ( in @ SV249 @ SV209 ) )
= $true )
| ( ( ! [SY978: $i] :
( ~ ( in @ SY978 @ SV209 )
| ( in @ SY978 @ SV205 ) ) )
= $true )
| ( ( in @ SV205 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( in @ SV209 @ ( sK2_SY743 @ SV61 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1541,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( in @ SV242 @ SV199 )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( ~ ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1494]) ).
thf(1542,plain,
! [SV235: $i,SV199: $i,SV61: $i] :
( ( ( ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1543,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ( SV77 @ ( sK62_SY789 @ SV184 @ SV77 ) ) )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1496]) ).
thf(1544,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ~ ! [SY1005: $i] :
( ~ ( SV77 @ SY1005 )
| ( ( sK62_SY789 @ SV184 @ SV77 )
= SY1005 ) ) )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1496]) ).
thf(1545,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( SV77 @ ( sK59_SY789 @ SV184 @ SV77 ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1497]) ).
thf(1546,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ! [SY999: $i] :
( ~ ( SV77 @ SY999 )
| ( ( sK59_SY789 @ SV184 @ SV77 )
= SY999 ) ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1498]) ).
thf(1547,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( SV77 @ ( sK60_SY789 @ SV184 @ SV77 ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1499]) ).
thf(1548,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ! [SY1000: $i] :
( ~ ( SV77 @ SY1000 )
| ( ( sK60_SY789 @ SV184 @ SV77 )
= SY1000 ) ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1500]) ).
thf(1549,plain,
! [SV184: $i,SV250: $i,SV77: $i > $o] :
( ( ( ~ ( SV77 @ SV250 )
| ( ( sK57_SY789 @ SV184 @ SV77 )
= SV250 ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1550,plain,
! [SV185: $i,SV231: $i,SV81: $i > $o] :
( ( ( ~ ( SV81 @ SV231 )
| ( SV231
= ( sK58_SY799 @ SV185 @ SV81 ) ) )
= $true )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV81 @ ( sK41_SY950 @ SV185 @ SV81 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1503]) ).
thf(1551,plain,
! [SV81: $i > $o,SV185: $i,SV231: $i] :
( ( ( ( SV231
!= ( sK58_SY799 @ SV185 @ SV81 ) )
| ( SV81 @ SV231 ) )
= $true )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV81 @ ( sK41_SY950 @ SV185 @ SV81 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1504]) ).
thf(1552,plain,
! [SV185: $i,SV228: $i,SV81: $i > $o] :
( ( ( ~ ( SV81 @ SV228 ) )
= $true )
| ( ( SV228
= ( sK52_SY799 @ SV185 @ SV81 ) )
= $true )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV185
= ( sK41_SY950 @ SV185 @ SV81 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1505]) ).
thf(1553,plain,
! [SV81: $i > $o,SV185: $i,SV228: $i] :
( ( ( SV228
!= ( sK52_SY799 @ SV185 @ SV81 ) )
= $true )
| ( ( SV81 @ SV228 )
= $true )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV185
= ( sK41_SY950 @ SV185 @ SV81 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1506]) ).
thf(1554,plain,
! [SV173: $i,SV243: $i,SV21: $i > $o] :
( ( ( ~ ( SV21 @ SV243 ) )
= $true )
| ( ( ( sK54_SY630 @ SV173 @ SV21 )
= SV243 )
= $true )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV21 @ ( sK37_SY933 @ SV173 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1508]) ).
thf(1555,plain,
! [SV173: $i,SV236: $i,SV21: $i > $o] :
( ( ( SV21 @ SV236 )
= $false )
| ( ( ( sK45_SY630 @ SV173 @ SV21 )
= SV236 )
= $true )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV173
= ( sK37_SY933 @ SV173 @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1556,plain,
! [SV175: $i,SV237: $i,SV32: $i > $o] :
( ( ( SV32 @ SV237 )
= $false )
| ( ( ( sK47_SY653 @ SV175 @ SV32 )
= SV237 )
= $true )
| ( ( SV32 @ ( sK27_SY651 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1557,plain,
! [SV175: $i,SV244: $i,SV32: $i > $o] :
( ( ( ~ ( SV32 @ SV244 ) )
= $true )
| ( ( ( sK55_SY653 @ SV175 @ SV32 )
= SV244 )
= $true )
| ( ( SV32 @ ( sK32_SY966 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1511]) ).
thf(1558,plain,
! [SV175: $i,SV238: $i,SV32: $i > $o] :
( ( ( SV32 @ SV238 )
= $false )
| ( ( ( sK48_SY653 @ SV175 @ SV32 )
= SV238 )
= $true )
| ( ( ( sK27_SY651 @ SV175 @ SV32 )
= ( sK32_SY966 @ SV175 @ SV32 ) )
= $false )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1559,plain,
! [SV177: $i,SV245: $i,SV43: $i > $o] :
( ( ( ~ ( SV43 @ SV245 ) )
= $true )
| ( ( ( sK56_SY681 @ SV177 @ SV43 )
= SV245 )
= $true )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV43 @ ( sK39_SY936 @ SV177 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1513]) ).
thf(1560,plain,
! [SV177: $i,SV239: $i,SV43: $i > $o] :
( ( ( SV43 @ SV239 )
= $false )
| ( ( ( sK49_SY681 @ SV177 @ SV43 )
= SV239 )
= $true )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV177
= ( sK39_SY936 @ SV177 @ SV43 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1561,plain,
! [SV123: $i,SV45: $i > $i > $o,SV204: $i] :
( ( ( ~ ( in @ ( sK63_SY971 @ SV204 @ SV45 @ SV123 ) @ SV123 ) )
= $false )
| ( ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
= $false )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1515]) ).
thf(1562,plain,
! [SV123: $i,SV204: $i,SV45: $i > $i > $o] :
( ( ( ~ ( SV45 @ ( sK63_SY971 @ SV204 @ SV45 @ SV123 ) @ SV204 ) )
= $false )
| ( ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
= $false )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1515]) ).
thf(1563,plain,
! [SV204: $i,SV45: $i > $i > $o,SV123: $i,SV232: $i] :
( ( ( ~ ( in @ SV232 @ SV123 ) )
= $true )
| ( ( ~ ( SV45 @ SV232 @ SV204 ) )
= $true )
| ( ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
= $true )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1516]) ).
thf(1564,plain,
! [SV123: $i,SV45: $i > $i > $o,SV198: $i,SV246: $i] :
( ( ( ~ ( ~ ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
| ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SV123 )
| ~ ( SV45 @ SY1014 @ SV246 ) ) )
| ~ ( ~ ~ ! [SY1015: $i] :
~ ~ ( ~ ( in @ SY1015 @ SV123 )
| ~ ( SV45 @ SY1015 @ SV246 ) )
| ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) ) ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1565,plain,
! [SV123: $i,SV45: $i > $i > $o,SV198: $i,SV240: $i] :
( ( ( ~ ( ~ ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
| ~ ! [SY1011: $i] :
~ ~ ( ~ ( in @ SY1011 @ SV123 )
| ~ ( SV45 @ SY1011 @ SV240 ) ) ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1518]) ).
thf(1566,plain,
! [SV198: $i,SV240: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ~ ( ~ ~ ! [SY1012: $i] :
~ ~ ( ~ ( in @ SY1012 @ SV123 )
| ~ ( SV45 @ SY1012 @ SV240 ) )
| ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) ) ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1518]) ).
thf(1567,plain,
! [SV128: $i,SV181: $i > $o,SV53: $i,SV192: $i > $o] :
( ( ( SV192 @ ( sK40_SY970 @ SV53 @ SV181 @ SV192 @ SV128 ) )
= $true )
| ( ( SV181 @ ( sK29_SY953 @ SV192 @ SV181 @ SV128 @ SV53 ) )
= $true )
| ( ( ( dsetconstr @ SV53
@ ^ [SY944: $i] : ( SV181 @ SY944 ) )
= ( dsetconstr @ SV128
@ ^ [SY956: $i] : ( SV192 @ SY956 ) ) )
= $true )
| ( ( SV53 = SV128 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1519]) ).
thf(1568,plain,
! [SV208: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV56 @ ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1523]) ).
thf(1569,plain,
! [SV208: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV208
= ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $false )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1570,plain,
! [SV130: $i > $o,SV241: $i,SV56: $i > $o] :
( ( ( ~ ( SV56 @ SV241 )
| ~ ! [SY1013: $i] :
( ~ ( SV56 @ SY1013 )
| ( SV241 = SY1013 ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1525]) ).
thf(1571,plain,
! [SV130: $i > $o,SV233: $i,SV56: $i > $o] :
( ( ( ~ ( SV56 @ SV233 ) )
= $true )
| ( ( ~ ! [SY1009: $i] :
( ~ ( SV56 @ SY1009 )
| ( SV233 = SY1009 ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1526]) ).
thf(1572,plain,
! [SV130: $i > $o,SV234: $i,SV56: $i > $o] :
( ( ( ~ ( SV56 @ SV234 ) )
= $true )
| ( ( ~ ! [SY1010: $i] :
( ~ ( SV56 @ SY1010 )
| ( SV234 = SY1010 ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1527]) ).
thf(1573,plain,
! [SV130: $i > $o,SV229: $i,SV56: $i > $o] :
( ( ( SV56 @ SV229 )
= $false )
| ( ( ~ ! [SY1004: $i] :
( ~ ( SV56 @ SY1004 )
| ( SV229 = SY1004 ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1528]) ).
thf(1574,plain,
! [SV224: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
| ( SV224
= ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) ) )
= $false )
| ( ( SV58 @ SV224 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1529]) ).
thf(1575,plain,
! [SV225: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
| ( SV225
= ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) ) )
= $false )
| ( ( SV132 @ SV225 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1530]) ).
thf(1576,plain,
! [SV132: $i > $o,SV58: $i > $o] :
( ( ( ! [SY730: $i] :
~ ~ ( ~ ( SV58 @ SY730 )
| ~ ! [SY731: $i] :
( ~ ( SV58 @ SY731 )
| ( SY730 = SY731 ) ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1531]) ).
thf(1577,plain,
! [SV58: $i > $o,SV132: $i > $o] :
( ( ( ! [SY880: $i] :
~ ~ ( ~ ( SV132 @ SY880 )
| ~ ! [SY881: $i] :
( ~ ( SV132 @ SY881 )
| ( SY880 = SY881 ) ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1532]) ).
thf(1578,plain,
! [SV132: $i > $o,SV251: $i,SV58: $i > $o] :
( ( ( ~ ~ ( ~ ( SV58 @ SV251 )
| ~ ! [SY1018: $i] :
( ~ ( SV58 @ SY1018 )
| ( SV251 = SY1018 ) ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1579,plain,
! [SV58: $i > $o,SV252: $i,SV132: $i > $o] :
( ( ( ~ ~ ( ~ ( SV132 @ SV252 )
| ~ ! [SY1019: $i] :
( ~ ( SV132 @ SY1019 )
| ( SV252 = SY1019 ) ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1580,plain,
! [SV132: $i > $o,SV253: $i,SV58: $i > $o] :
( ( ( ~ ~ ( ~ ( SV58 @ SV253 )
| ~ ! [SY1020: $i] :
( ~ ( SV58 @ SY1020 )
| ( SV253 = SY1020 ) ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1581,plain,
! [SV58: $i > $o,SV254: $i,SV132: $i > $o] :
( ( ( ~ ~ ( ~ ( SV132 @ SV254 )
| ~ ! [SY1021: $i] :
( ~ ( SV132 @ SY1021 )
| ( SV254 = SY1021 ) ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1582,plain,
! [SV132: $i > $o,SV247: $i,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ SV247 )
| ~ ! [SY1016: $i] :
( ~ ( SV58 @ SY1016 )
| ( SV247 = SY1016 ) ) ) )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1583,plain,
! [SV58: $i > $o,SV248: $i,SV132: $i > $o] :
( ( ( ~ ( ~ ( SV132 @ SV248 )
| ~ ! [SY1017: $i] :
( ~ ( SV132 @ SY1017 )
| ( SV248 = SY1017 ) ) ) )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1584,plain,
! [SV217: $i,SV61: $i,SV226: $i] :
( ( ( in @ SV226 @ SV61 )
= $false )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( ~ ! [SY996: $i] :
( ~ ( in @ SY996 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SV217 @ SY996 )
| ( in @ SV226 @ SY996 ) )
| ~ ( ~ ( in @ SV226 @ SY996 )
| ( in @ SV217 @ SY996 ) ) ) )
| ( SV217 = SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1585,plain,
! [SV61: $i,SV209: $i,SV205: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ SV205 ) )
= $true )
| ( ( in @ SV249 @ SV209 )
= $true )
| ( ( ! [SY978: $i] :
( ~ ( in @ SY978 @ SV209 )
| ( in @ SY978 @ SV205 ) ) )
= $true )
| ( ( in @ SV205 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( in @ SV209 @ ( sK2_SY743 @ SV61 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1540]) ).
thf(1586,plain,
! [SV242: $i,SV199: $i,SV61: $i] :
( ( ( ! [SY961: $i] :
~ ~ ! [SY962: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY961 @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY962 @ SV199 ) )
| ~ ~ ~ ! [SY963: $i] :
~ ~ ( ~ ( in @ SY963 @ SY961 )
| ~ ( in @ SY963 @ SV199 ) ) )
| ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ ( sK2_SY743 @ SV61 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY928 )
| ( in @ SX6 @ SY961 ) )
| ( in @ SY962 @ SY928 ) ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1541]) ).
thf(1587,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( ~ ~ ! [SY1022: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY1022 @ SV199 ) )
| ~ ~ ~ ! [SY1023: $i] :
~ ~ ( ~ ( in @ SY1023 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
| ~ ( in @ SY1023 @ SV199 ) ) )
| ~ ! [SY1024: $i] :
( ~ ( in @ SY1024 @ ( sK2_SY743 @ SV61 ) )
| ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SY1024 )
| ( in @ SY1025 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) ) )
| ( in @ SY1022 @ SY1024 ) ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1542]) ).
thf(1588,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( SV77 @ ( sK62_SY789 @ SV184 @ SV77 ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1543]) ).
thf(1589,plain,
! [SV184: $i,SV77: $i > $o] :
( ( ( ! [SY1005: $i] :
( ~ ( SV77 @ SY1005 )
| ( ( sK62_SY789 @ SV184 @ SV77 )
= SY1005 ) ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1544]) ).
thf(1590,plain,
! [SV184: $i,SV255: $i,SV77: $i > $o] :
( ( ( ~ ( SV77 @ SV255 )
| ( ( sK59_SY789 @ SV184 @ SV77 )
= SV255 ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1591,plain,
! [SV184: $i,SV256: $i,SV77: $i > $o] :
( ( ( ~ ( SV77 @ SV256 )
| ( ( sK60_SY789 @ SV184 @ SV77 )
= SV256 ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1592,plain,
! [SV184: $i,SV250: $i,SV77: $i > $o] :
( ( ( ~ ( SV77 @ SV250 ) )
= $true )
| ( ( ( sK57_SY789 @ SV184 @ SV77 )
= SV250 )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1549]) ).
thf(1593,plain,
! [SV185: $i,SV231: $i,SV81: $i > $o] :
( ( ( ~ ( SV81 @ SV231 ) )
= $true )
| ( ( SV231
= ( sK58_SY799 @ SV185 @ SV81 ) )
= $true )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV81 @ ( sK41_SY950 @ SV185 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1550]) ).
thf(1594,plain,
! [SV81: $i > $o,SV185: $i,SV231: $i] :
( ( ( SV231
!= ( sK58_SY799 @ SV185 @ SV81 ) )
= $true )
| ( ( SV81 @ SV231 )
= $true )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV81 @ ( sK41_SY950 @ SV185 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1551]) ).
thf(1595,plain,
! [SV185: $i,SV228: $i,SV81: $i > $o] :
( ( ( SV81 @ SV228 )
= $false )
| ( ( SV228
= ( sK52_SY799 @ SV185 @ SV81 ) )
= $true )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV185
= ( sK41_SY950 @ SV185 @ SV81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1552]) ).
thf(1596,plain,
! [SV81: $i > $o,SV185: $i,SV228: $i] :
( ( ( SV228
= ( sK52_SY799 @ SV185 @ SV81 ) )
= $false )
| ( ( SV81 @ SV228 )
= $true )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV185
= ( sK41_SY950 @ SV185 @ SV81 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1597,plain,
! [SV173: $i,SV243: $i,SV21: $i > $o] :
( ( ( SV21 @ SV243 )
= $false )
| ( ( ( sK54_SY630 @ SV173 @ SV21 )
= SV243 )
= $true )
| ( ( SV21 @ SV173 )
= $false )
| ( ( SV21 @ ( sK37_SY933 @ SV173 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1598,plain,
! [SV175: $i,SV244: $i,SV32: $i > $o] :
( ( ( SV32 @ SV244 )
= $false )
| ( ( ( sK55_SY653 @ SV175 @ SV32 )
= SV244 )
= $true )
| ( ( SV32 @ ( sK32_SY966 @ SV175 @ SV32 ) )
= $true )
| ( ( SV32 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1557]) ).
thf(1599,plain,
! [SV177: $i,SV245: $i,SV43: $i > $o] :
( ( ( SV43 @ SV245 )
= $false )
| ( ( ( sK56_SY681 @ SV177 @ SV43 )
= SV245 )
= $true )
| ( ( SV43 @ SV177 )
= $false )
| ( ( SV43 @ ( sK39_SY936 @ SV177 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1600,plain,
! [SV123: $i,SV45: $i > $i > $o,SV204: $i] :
( ( ( in @ ( sK63_SY971 @ SV204 @ SV45 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
= $false )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1561]) ).
thf(1601,plain,
! [SV123: $i,SV204: $i,SV45: $i > $i > $o] :
( ( ( SV45 @ ( sK63_SY971 @ SV204 @ SV45 @ SV123 ) @ SV204 )
= $true )
| ( ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
= $false )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1562]) ).
thf(1602,plain,
! [SV204: $i,SV45: $i > $i > $o,SV123: $i,SV232: $i] :
( ( ( in @ SV232 @ SV123 )
= $false )
| ( ( ~ ( SV45 @ SV232 @ SV204 ) )
= $true )
| ( ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
= $true )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1563]) ).
thf(1603,plain,
! [SV123: $i,SV45: $i > $i > $o,SV198: $i,SV246: $i] :
( ( ( ~ ( ~ ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
| ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SV123 )
| ~ ( SV45 @ SY1014 @ SV246 ) ) ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1564]) ).
thf(1604,plain,
! [SV198: $i,SV246: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ~ ( ~ ~ ! [SY1015: $i] :
~ ~ ( ~ ( in @ SY1015 @ SV123 )
| ~ ( SV45 @ SY1015 @ SV246 ) )
| ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) ) ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1564]) ).
thf(1605,plain,
! [SV123: $i,SV45: $i > $i > $o,SV198: $i,SV240: $i] :
( ( ( ~ ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
| ~ ! [SY1011: $i] :
~ ~ ( ~ ( in @ SY1011 @ SV123 )
| ~ ( SV45 @ SY1011 @ SV240 ) ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1565]) ).
thf(1606,plain,
! [SV198: $i,SV240: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ~ ~ ! [SY1012: $i] :
~ ~ ( ~ ( in @ SY1012 @ SV123 )
| ~ ( SV45 @ SY1012 @ SV240 ) )
| ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1566]) ).
thf(1607,plain,
! [SV208: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV56 @ ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1568]) ).
thf(1608,plain,
! [SV208: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV208
= ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $false )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1569]) ).
thf(1609,plain,
! [SV130: $i > $o,SV241: $i,SV56: $i > $o] :
( ( ( ~ ( SV56 @ SV241 ) )
= $true )
| ( ( ~ ! [SY1013: $i] :
( ~ ( SV56 @ SY1013 )
| ( SV241 = SY1013 ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1570]) ).
thf(1610,plain,
! [SV130: $i > $o,SV233: $i,SV56: $i > $o] :
( ( ( SV56 @ SV233 )
= $false )
| ( ( ~ ! [SY1009: $i] :
( ~ ( SV56 @ SY1009 )
| ( SV233 = SY1009 ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1611,plain,
! [SV130: $i > $o,SV234: $i,SV56: $i > $o] :
( ( ( SV56 @ SV234 )
= $false )
| ( ( ~ ! [SY1010: $i] :
( ~ ( SV56 @ SY1010 )
| ( SV234 = SY1010 ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1572]) ).
thf(1612,plain,
! [SV130: $i > $o,SV229: $i,SV56: $i > $o] :
( ( ( ! [SY1004: $i] :
( ~ ( SV56 @ SY1004 )
| ( SV229 = SY1004 ) ) )
= $false )
| ( ( SV56 @ SV229 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1573]) ).
thf(1613,plain,
! [SV224: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) ) )
= $false )
| ( ( SV58 @ SV224 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1574]) ).
thf(1614,plain,
! [SV58: $i > $o,SV132: $i > $o,SV224: $i] :
( ( ( SV224
= ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $false )
| ( ( SV58 @ SV224 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1574]) ).
thf(1615,plain,
! [SV225: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) ) )
= $false )
| ( ( SV132 @ SV225 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1575]) ).
thf(1616,plain,
! [SV132: $i > $o,SV58: $i > $o,SV225: $i] :
( ( ( SV225
= ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $false )
| ( ( SV132 @ SV225 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1575]) ).
thf(1617,plain,
! [SV132: $i > $o,SV257: $i,SV58: $i > $o] :
( ( ( ~ ~ ( ~ ( SV58 @ SV257 )
| ~ ! [SY1026: $i] :
( ~ ( SV58 @ SY1026 )
| ( SV257 = SY1026 ) ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1618,plain,
! [SV58: $i > $o,SV258: $i,SV132: $i > $o] :
( ( ( ~ ~ ( ~ ( SV132 @ SV258 )
| ~ ! [SY1027: $i] :
( ~ ( SV132 @ SY1027 )
| ( SV258 = SY1027 ) ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1619,plain,
! [SV132: $i > $o,SV251: $i,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ SV251 )
| ~ ! [SY1018: $i] :
( ~ ( SV58 @ SY1018 )
| ( SV251 = SY1018 ) ) ) )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1620,plain,
! [SV58: $i > $o,SV252: $i,SV132: $i > $o] :
( ( ( ~ ( ~ ( SV132 @ SV252 )
| ~ ! [SY1019: $i] :
( ~ ( SV132 @ SY1019 )
| ( SV252 = SY1019 ) ) ) )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1579]) ).
thf(1621,plain,
! [SV132: $i > $o,SV253: $i,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ SV253 )
| ~ ! [SY1020: $i] :
( ~ ( SV58 @ SY1020 )
| ( SV253 = SY1020 ) ) ) )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1622,plain,
! [SV58: $i > $o,SV254: $i,SV132: $i > $o] :
( ( ( ~ ( ~ ( SV132 @ SV254 )
| ~ ! [SY1021: $i] :
( ~ ( SV132 @ SY1021 )
| ( SV254 = SY1021 ) ) ) )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1581]) ).
thf(1623,plain,
! [SV132: $i > $o,SV247: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV247 )
| ~ ! [SY1016: $i] :
( ~ ( SV58 @ SY1016 )
| ( SV247 = SY1016 ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1582]) ).
thf(1624,plain,
! [SV58: $i > $o,SV248: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV248 )
| ~ ! [SY1017: $i] :
( ~ ( SV132 @ SY1017 )
| ( SV248 = SY1017 ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1583]) ).
thf(1625,plain,
! [SV226: $i,SV217: $i,SV61: $i] :
( ( ( ~ ! [SY996: $i] :
( ~ ( in @ SY996 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SV217 @ SY996 )
| ( in @ SV226 @ SY996 ) )
| ~ ( ~ ( in @ SV226 @ SY996 )
| ( in @ SV217 @ SY996 ) ) ) ) )
= $true )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1584]) ).
thf(1626,plain,
! [SV61: $i,SV209: $i,SV205: $i,SV249: $i] :
( ( ( in @ SV249 @ SV205 )
= $false )
| ( ( in @ SV249 @ SV209 )
= $true )
| ( ( ! [SY978: $i] :
( ~ ( in @ SY978 @ SV209 )
| ( in @ SY978 @ SV205 ) ) )
= $true )
| ( ( in @ SV205 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( in @ SV209 @ ( sK2_SY743 @ SV61 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1627,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( ~ ~ ! [SY1028: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY1028 @ SV199 ) )
| ~ ~ ~ ! [SY1029: $i] :
~ ~ ( ~ ( in @ SY1029 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
| ~ ( in @ SY1029 @ SV199 ) ) )
| ~ ! [SY1030: $i] :
( ~ ( in @ SY1030 @ ( sK2_SY743 @ SV61 ) )
| ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SY1030 )
| ( in @ SY1031 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) ) )
| ( in @ SY1028 @ SY1030 ) ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1586]) ).
thf(1628,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( ~ ! [SY1022: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY1022 @ SV199 ) )
| ~ ~ ~ ! [SY1023: $i] :
~ ~ ( ~ ( in @ SY1023 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
| ~ ( in @ SY1023 @ SV199 ) ) )
| ~ ! [SY1024: $i] :
( ~ ( in @ SY1024 @ ( sK2_SY743 @ SV61 ) )
| ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SY1024 )
| ( in @ SY1025 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) ) )
| ( in @ SY1022 @ SY1024 ) ) ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1587]) ).
thf(1629,plain,
! [SV184: $i,SV259: $i,SV77: $i > $o] :
( ( ( ~ ( SV77 @ SV259 )
| ( ( sK62_SY789 @ SV184 @ SV77 )
= SV259 ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(1630,plain,
! [SV184: $i,SV255: $i,SV77: $i > $o] :
( ( ( ~ ( SV77 @ SV255 ) )
= $true )
| ( ( ( sK59_SY789 @ SV184 @ SV77 )
= SV255 )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1590]) ).
thf(1631,plain,
! [SV184: $i,SV256: $i,SV77: $i > $o] :
( ( ( ~ ( SV77 @ SV256 ) )
= $true )
| ( ( ( sK60_SY789 @ SV184 @ SV77 )
= SV256 )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1591]) ).
thf(1632,plain,
! [SV184: $i,SV250: $i,SV77: $i > $o] :
( ( ( SV77 @ SV250 )
= $false )
| ( ( ( sK57_SY789 @ SV184 @ SV77 )
= SV250 )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1633,plain,
! [SV185: $i,SV231: $i,SV81: $i > $o] :
( ( ( SV81 @ SV231 )
= $false )
| ( ( SV231
= ( sK58_SY799 @ SV185 @ SV81 ) )
= $true )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV81 @ ( sK41_SY950 @ SV185 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1593]) ).
thf(1634,plain,
! [SV81: $i > $o,SV185: $i,SV231: $i] :
( ( ( SV231
= ( sK58_SY799 @ SV185 @ SV81 ) )
= $false )
| ( ( SV81 @ SV231 )
= $true )
| ( ( SV81 @ SV185 )
= $false )
| ( ( SV81 @ ( sK41_SY950 @ SV185 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1635,plain,
! [SV123: $i,SV204: $i,SV232: $i,SV45: $i > $i > $o] :
( ( ( SV45 @ SV232 @ SV204 )
= $false )
| ( ( in @ SV232 @ SV123 )
= $false )
| ( ( in @ SV204 @ ( sK28_SY848 @ SV45 @ SV123 ) )
= $true )
| ( ( in @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1636,plain,
! [SV123: $i,SV45: $i > $i > $o,SV198: $i,SV246: $i] :
( ( ( ~ ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
| ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SV123 )
| ~ ( SV45 @ SY1014 @ SV246 ) ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1603]) ).
thf(1637,plain,
! [SV198: $i,SV246: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ~ ~ ! [SY1015: $i] :
~ ~ ( ~ ( in @ SY1015 @ SV123 )
| ~ ( SV45 @ SY1015 @ SV246 ) )
| ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1604]) ).
thf(1638,plain,
! [SV123: $i,SV45: $i > $i > $o,SV198: $i,SV240: $i] :
( ( ( ~ ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) ) )
= $true )
| ( ( ~ ! [SY1011: $i] :
~ ~ ( ~ ( in @ SY1011 @ SV123 )
| ~ ( SV45 @ SY1011 @ SV240 ) ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1605]) ).
thf(1639,plain,
! [SV198: $i,SV240: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ~ ~ ! [SY1012: $i] :
~ ~ ( ~ ( in @ SY1012 @ SV123 )
| ~ ( SV45 @ SY1012 @ SV240 ) ) )
= $true )
| ( ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1606]) ).
thf(1640,plain,
! [SV208: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV56 @ ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1607]) ).
thf(1641,plain,
! [SV208: $i,SV56: $i > $o,SV260: $i,SV130: $i > $o] :
( ( ( ~ ~ ( ~ ( SV130 @ SV260 )
| ~ ! [SY1032: $i] :
( ~ ( SV130 @ SY1032 )
| ( SV260 = SY1032 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV208
= ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $false )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(1642,plain,
! [SV130: $i > $o,SV241: $i,SV56: $i > $o] :
( ( ( SV56 @ SV241 )
= $false )
| ( ( ~ ! [SY1013: $i] :
( ~ ( SV56 @ SY1013 )
| ( SV241 = SY1013 ) ) )
= $true )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1609]) ).
thf(1643,plain,
! [SV130: $i > $o,SV233: $i,SV56: $i > $o] :
( ( ( ! [SY1009: $i] :
( ~ ( SV56 @ SY1009 )
| ( SV233 = SY1009 ) ) )
= $false )
| ( ( SV56 @ SV233 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1644,plain,
! [SV130: $i > $o,SV234: $i,SV56: $i > $o] :
( ( ( ! [SY1010: $i] :
( ~ ( SV56 @ SY1010 )
| ( SV234 = SY1010 ) ) )
= $false )
| ( ( SV56 @ SV234 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1611]) ).
thf(1645,plain,
! [SV229: $i,SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ( SV56 @ ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
| ( SV229
= ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) ) )
= $false )
| ( ( SV56 @ SV229 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1612]) ).
thf(1646,plain,
! [SV224: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( SV58 @ ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $true )
| ( ( SV58 @ SV224 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1613]) ).
thf(1647,plain,
! [SV224: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $false )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV224
= ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1648,plain,
! [SV225: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( SV132 @ ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $true )
| ( ( SV132 @ SV225 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1615]) ).
thf(1649,plain,
! [SV225: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $false )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV225
= ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1650,plain,
! [SV132: $i > $o,SV257: $i,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ SV257 )
| ~ ! [SY1026: $i] :
( ~ ( SV58 @ SY1026 )
| ( SV257 = SY1026 ) ) ) )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1651,plain,
! [SV58: $i > $o,SV258: $i,SV132: $i > $o] :
( ( ( ~ ( ~ ( SV132 @ SV258 )
| ~ ! [SY1027: $i] :
( ~ ( SV132 @ SY1027 )
| ( SV258 = SY1027 ) ) ) )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1652,plain,
! [SV132: $i > $o,SV251: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV251 )
| ~ ! [SY1018: $i] :
( ~ ( SV58 @ SY1018 )
| ( SV251 = SY1018 ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1619]) ).
thf(1653,plain,
! [SV58: $i > $o,SV252: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV252 )
| ~ ! [SY1019: $i] :
( ~ ( SV132 @ SY1019 )
| ( SV252 = SY1019 ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1620]) ).
thf(1654,plain,
! [SV132: $i > $o,SV253: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV253 )
| ~ ! [SY1020: $i] :
( ~ ( SV58 @ SY1020 )
| ( SV253 = SY1020 ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1621]) ).
thf(1655,plain,
! [SV58: $i > $o,SV254: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV254 )
| ~ ! [SY1021: $i] :
( ~ ( SV132 @ SY1021 )
| ( SV254 = SY1021 ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1622]) ).
thf(1656,plain,
! [SV132: $i > $o,SV247: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV247 ) )
= $true )
| ( ( ~ ! [SY1016: $i] :
( ~ ( SV58 @ SY1016 )
| ( SV247 = SY1016 ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1623]) ).
thf(1657,plain,
! [SV58: $i > $o,SV248: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV248 ) )
= $true )
| ( ( ~ ! [SY1017: $i] :
( ~ ( SV132 @ SY1017 )
| ( SV248 = SY1017 ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1624]) ).
thf(1658,plain,
! [SV226: $i,SV217: $i,SV61: $i] :
( ( ( ! [SY996: $i] :
( ~ ( in @ SY996 @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SV217 @ SY996 )
| ( in @ SV226 @ SY996 ) )
| ~ ( ~ ( in @ SV226 @ SY996 )
| ( in @ SV217 @ SY996 ) ) ) ) )
= $false )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1659,plain,
! [SV61: $i,SV249: $i,SV205: $i,SV209: $i,SV261: $i] :
( ( ( ~ ( in @ SV261 @ SV209 )
| ( in @ SV261 @ SV205 ) )
= $true )
| ( ( in @ SV249 @ SV209 )
= $true )
| ( ( in @ SV249 @ SV205 )
= $false )
| ( ( in @ SV205 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( in @ SV209 @ ( sK2_SY743 @ SV61 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(1660,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( ~ ! [SY1028: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY1028 @ SV199 ) )
| ~ ~ ~ ! [SY1029: $i] :
~ ~ ( ~ ( in @ SY1029 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
| ~ ( in @ SY1029 @ SV199 ) ) )
| ~ ! [SY1030: $i] :
( ~ ( in @ SY1030 @ ( sK2_SY743 @ SV61 ) )
| ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SY1030 )
| ( in @ SY1031 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) ) )
| ( in @ SY1028 @ SY1030 ) ) ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1627]) ).
thf(1661,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( ! [SY1022: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY1022 @ SV199 ) )
| ~ ~ ~ ! [SY1023: $i] :
~ ~ ( ~ ( in @ SY1023 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
| ~ ( in @ SY1023 @ SV199 ) ) )
| ~ ! [SY1024: $i] :
( ~ ( in @ SY1024 @ ( sK2_SY743 @ SV61 ) )
| ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SY1024 )
| ( in @ SY1025 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) ) )
| ( in @ SY1022 @ SY1024 ) ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1628]) ).
thf(1662,plain,
! [SV184: $i,SV259: $i,SV77: $i > $o] :
( ( ( ~ ( SV77 @ SV259 ) )
= $true )
| ( ( ( sK62_SY789 @ SV184 @ SV77 )
= SV259 )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1629]) ).
thf(1663,plain,
! [SV184: $i,SV255: $i,SV77: $i > $o] :
( ( ( SV77 @ SV255 )
= $false )
| ( ( ( sK59_SY789 @ SV184 @ SV77 )
= SV255 )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1630]) ).
thf(1664,plain,
! [SV184: $i,SV256: $i,SV77: $i > $o] :
( ( ( SV77 @ SV256 )
= $false )
| ( ( ( sK60_SY789 @ SV184 @ SV77 )
= SV256 )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $false )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1631]) ).
thf(1665,plain,
! [SV123: $i,SV45: $i > $i > $o,SV198: $i,SV246: $i] :
( ( ( ~ ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) ) )
= $true )
| ( ( ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SV123 )
| ~ ( SV45 @ SY1014 @ SV246 ) ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1636]) ).
thf(1666,plain,
! [SV198: $i,SV246: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ~ ~ ! [SY1015: $i] :
~ ~ ( ~ ( in @ SY1015 @ SV123 )
| ~ ( SV45 @ SY1015 @ SV246 ) ) )
= $true )
| ( ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1637]) ).
thf(1667,plain,
! [SV123: $i,SV45: $i > $i > $o,SV198: $i,SV240: $i] :
( ( ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
= $false )
| ( ( ~ ! [SY1011: $i] :
~ ~ ( ~ ( in @ SY1011 @ SV123 )
| ~ ( SV45 @ SY1011 @ SV240 ) ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1668,plain,
! [SV198: $i,SV240: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( in @ SY1012 @ SV123 )
| ~ ( SV45 @ SY1012 @ SV240 ) ) )
= $false )
| ( ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1669,plain,
! [SV208: $i,SV56: $i > $o,SV262: $i,SV130: $i > $o] :
( ( ( ~ ~ ( ~ ( SV130 @ SV262 )
| ~ ! [SY1033: $i] :
( ~ ( SV130 @ SY1033 )
| ( SV262 = SY1033 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV56 @ ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1670,plain,
! [SV208: $i,SV56: $i > $o,SV260: $i,SV130: $i > $o] :
( ( ( ~ ( ~ ( SV130 @ SV260 )
| ~ ! [SY1032: $i] :
( ~ ( SV130 @ SY1032 )
| ( SV260 = SY1032 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV208
= ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $false )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1671,plain,
! [SV130: $i > $o,SV241: $i,SV56: $i > $o] :
( ( ( ! [SY1013: $i] :
( ~ ( SV56 @ SY1013 )
| ( SV241 = SY1013 ) ) )
= $false )
| ( ( SV56 @ SV241 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1642]) ).
thf(1672,plain,
! [SV233: $i,SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ( SV56 @ ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
| ( SV233
= ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) ) )
= $false )
| ( ( SV56 @ SV233 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1643]) ).
thf(1673,plain,
! [SV234: $i,SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ( SV56 @ ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
| ( SV234
= ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) ) )
= $false )
| ( ( SV56 @ SV234 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1644]) ).
thf(1674,plain,
! [SV229: $i,SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ( SV56 @ ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) ) )
= $false )
| ( ( SV56 @ SV229 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1645]) ).
thf(1675,plain,
! [SV56: $i > $o,SV130: $i > $o,SV229: $i] :
( ( ( SV229
= ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $false )
| ( ( SV56 @ SV229 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1645]) ).
thf(1676,plain,
! [SV224: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $false )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV58 @ ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1677,plain,
! [SV58: $i > $o,SV224: $i,SV132: $i > $o] :
( ( ( ~ ~ ( ~ ( SV132 @ ( sK73_SY878 @ SV224 @ SV58 @ SV132 ) )
| ~ ! [SY1034: $i] :
( ~ ( SV132 @ SY1034 )
| ( ( sK73_SY878 @ SV224 @ SV58 @ SV132 )
= SY1034 ) ) ) )
= $false )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV224
= ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1647]) ).
thf(1678,plain,
! [SV225: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $false )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV132 @ ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1648]) ).
thf(1679,plain,
! [SV132: $i > $o,SV225: $i,SV58: $i > $o] :
( ( ( ~ ~ ( ~ ( SV58 @ ( sK74_SY736 @ SV225 @ SV132 @ SV58 ) )
| ~ ! [SY1035: $i] :
( ~ ( SV58 @ SY1035 )
| ( ( sK74_SY736 @ SV225 @ SV132 @ SV58 )
= SY1035 ) ) ) )
= $false )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV225
= ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1649]) ).
thf(1680,plain,
! [SV132: $i > $o,SV257: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV257 )
| ~ ! [SY1026: $i] :
( ~ ( SV58 @ SY1026 )
| ( SV257 = SY1026 ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1650]) ).
thf(1681,plain,
! [SV58: $i > $o,SV258: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV258 )
| ~ ! [SY1027: $i] :
( ~ ( SV132 @ SY1027 )
| ( SV258 = SY1027 ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1651]) ).
thf(1682,plain,
! [SV132: $i > $o,SV251: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV251 ) )
= $true )
| ( ( ~ ! [SY1018: $i] :
( ~ ( SV58 @ SY1018 )
| ( SV251 = SY1018 ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1652]) ).
thf(1683,plain,
! [SV58: $i > $o,SV252: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV252 ) )
= $true )
| ( ( ~ ! [SY1019: $i] :
( ~ ( SV132 @ SY1019 )
| ( SV252 = SY1019 ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1653]) ).
thf(1684,plain,
! [SV132: $i > $o,SV253: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV253 ) )
= $true )
| ( ( ~ ! [SY1020: $i] :
( ~ ( SV58 @ SY1020 )
| ( SV253 = SY1020 ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1654]) ).
thf(1685,plain,
! [SV58: $i > $o,SV254: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV254 ) )
= $true )
| ( ( ~ ! [SY1021: $i] :
( ~ ( SV132 @ SY1021 )
| ( SV254 = SY1021 ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1655]) ).
thf(1686,plain,
! [SV132: $i > $o,SV247: $i,SV58: $i > $o] :
( ( ( SV58 @ SV247 )
= $false )
| ( ( ~ ! [SY1016: $i] :
( ~ ( SV58 @ SY1016 )
| ( SV247 = SY1016 ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1656]) ).
thf(1687,plain,
! [SV58: $i > $o,SV248: $i,SV132: $i > $o] :
( ( ( SV132 @ SV248 )
= $false )
| ( ( ~ ! [SY1017: $i] :
( ~ ( SV132 @ SY1017 )
| ( SV248 = SY1017 ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1688,plain,
! [SV61: $i,SV217: $i,SV226: $i] :
( ( ( ~ ( in @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( ~ ( ~ ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
| ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) ) )
| ~ ( ~ ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
| ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) ) ) ) )
= $false )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1658]) ).
thf(1689,plain,
! [SV61: $i,SV249: $i,SV205: $i,SV209: $i,SV261: $i] :
( ( ( ~ ( in @ SV261 @ SV209 ) )
= $true )
| ( ( in @ SV261 @ SV205 )
= $true )
| ( ( in @ SV249 @ SV209 )
= $true )
| ( ( in @ SV249 @ SV205 )
= $false )
| ( ( in @ SV205 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( in @ SV209 @ ( sK2_SY743 @ SV61 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1659]) ).
thf(1690,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( ! [SY1028: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ SY1028 @ SV199 ) )
| ~ ~ ~ ! [SY1029: $i] :
~ ~ ( ~ ( in @ SY1029 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
| ~ ( in @ SY1029 @ SV199 ) ) )
| ~ ! [SY1030: $i] :
( ~ ( in @ SY1030 @ ( sK2_SY743 @ SV61 ) )
| ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SY1030 )
| ( in @ SY1031 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) ) )
| ( in @ SY1028 @ SY1030 ) ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1660]) ).
thf(1691,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SV199 ) )
| ~ ~ ~ ! [SY1023: $i] :
~ ~ ( ~ ( in @ SY1023 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
| ~ ( in @ SY1023 @ SV199 ) ) )
| ~ ! [SY1037: $i] :
( ~ ( in @ SY1037 @ ( sK2_SY743 @ SV61 ) )
| ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SY1037 )
| ( in @ SY1025 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) ) )
| ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SY1037 ) ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1661]) ).
thf(1692,plain,
! [SV184: $i,SV259: $i,SV77: $i > $o] :
( ( ( SV77 @ SV259 )
= $false )
| ( ( ( sK62_SY789 @ SV184 @ SV77 )
= SV259 )
= $true )
| ( ( SV77 @ ( sK20_SY949 @ SV184 @ SV77 ) )
= $true )
| ( ( ( sK20_SY949 @ SV184 @ SV77 )
= SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1693,plain,
! [SV123: $i,SV45: $i > $i > $o,SV198: $i,SV246: $i] :
( ( ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
= $false )
| ( ( ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SV123 )
| ~ ( SV45 @ SY1014 @ SV246 ) ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1665]) ).
thf(1694,plain,
! [SV198: $i,SV246: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ~ ! [SY1015: $i] :
~ ~ ( ~ ( in @ SY1015 @ SV123 )
| ~ ( SV45 @ SY1015 @ SV246 ) ) )
= $false )
| ( ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1666]) ).
thf(1695,plain,
! [SV198: $i,SV240: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ! [SY1011: $i] :
~ ~ ( ~ ( in @ SY1011 @ SV123 )
| ~ ( SV45 @ SY1011 @ SV240 ) ) )
= $false )
| ( ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1696,plain,
! [SV198: $i,SV240: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ! [SY1012: $i] :
~ ~ ( ~ ( in @ SY1012 @ SV123 )
| ~ ( SV45 @ SY1012 @ SV240 ) ) )
= $true )
| ( ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1668]) ).
thf(1697,plain,
! [SV208: $i,SV56: $i > $o,SV262: $i,SV130: $i > $o] :
( ( ( ~ ( ~ ( SV130 @ SV262 )
| ~ ! [SY1033: $i] :
( ~ ( SV130 @ SY1033 )
| ( SV262 = SY1033 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV56 @ ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1669]) ).
thf(1698,plain,
! [SV208: $i,SV56: $i > $o,SV260: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV260 )
| ~ ! [SY1032: $i] :
( ~ ( SV130 @ SY1032 )
| ( SV260 = SY1032 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV208
= ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $false )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1670]) ).
thf(1699,plain,
! [SV241: $i,SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ( SV56 @ ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
| ( SV241
= ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) ) )
= $false )
| ( ( SV56 @ SV241 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1671]) ).
thf(1700,plain,
! [SV233: $i,SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ( SV56 @ ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) ) )
= $false )
| ( ( SV56 @ SV233 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1672]) ).
thf(1701,plain,
! [SV56: $i > $o,SV130: $i > $o,SV233: $i] :
( ( ( SV233
= ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $false )
| ( ( SV56 @ SV233 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1672]) ).
thf(1702,plain,
! [SV234: $i,SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ( SV56 @ ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) ) )
= $false )
| ( ( SV56 @ SV234 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1673]) ).
thf(1703,plain,
! [SV56: $i > $o,SV130: $i > $o,SV234: $i] :
( ( ( SV234
= ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $false )
| ( ( SV56 @ SV234 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1673]) ).
thf(1704,plain,
! [SV229: $i,SV130: $i > $o,SV56: $i > $o] :
( ( ( SV56 @ ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1705,plain,
! [SV229: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV229
= ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1675]) ).
thf(1706,plain,
! [SV58: $i > $o,SV224: $i,SV132: $i > $o] :
( ( ( ~ ~ ( ~ ( SV132 @ ( sK78_SY878 @ SV224 @ SV58 @ SV132 ) )
| ~ ! [SY1039: $i] :
( ~ ( SV132 @ SY1039 )
| ( ( sK78_SY878 @ SV224 @ SV58 @ SV132 )
= SY1039 ) ) ) )
= $false )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV58 @ ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1676]) ).
thf(1707,plain,
! [SV58: $i > $o,SV224: $i,SV132: $i > $o] :
( ( ( ~ ( ~ ( SV132 @ ( sK73_SY878 @ SV224 @ SV58 @ SV132 ) )
| ~ ! [SY1034: $i] :
( ~ ( SV132 @ SY1034 )
| ( ( sK73_SY878 @ SV224 @ SV58 @ SV132 )
= SY1034 ) ) ) )
= $true )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV224
= ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1677]) ).
thf(1708,plain,
! [SV132: $i > $o,SV225: $i,SV58: $i > $o] :
( ( ( ~ ~ ( ~ ( SV58 @ ( sK79_SY736 @ SV225 @ SV132 @ SV58 ) )
| ~ ! [SY1040: $i] :
( ~ ( SV58 @ SY1040 )
| ( ( sK79_SY736 @ SV225 @ SV132 @ SV58 )
= SY1040 ) ) ) )
= $false )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV132 @ ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1678]) ).
thf(1709,plain,
! [SV132: $i > $o,SV225: $i,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ ( sK74_SY736 @ SV225 @ SV132 @ SV58 ) )
| ~ ! [SY1035: $i] :
( ~ ( SV58 @ SY1035 )
| ( ( sK74_SY736 @ SV225 @ SV132 @ SV58 )
= SY1035 ) ) ) )
= $true )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV225
= ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1679]) ).
thf(1710,plain,
! [SV132: $i > $o,SV257: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV257 ) )
= $true )
| ( ( ~ ! [SY1026: $i] :
( ~ ( SV58 @ SY1026 )
| ( SV257 = SY1026 ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1680]) ).
thf(1711,plain,
! [SV58: $i > $o,SV258: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV258 ) )
= $true )
| ( ( ~ ! [SY1027: $i] :
( ~ ( SV132 @ SY1027 )
| ( SV258 = SY1027 ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1681]) ).
thf(1712,plain,
! [SV132: $i > $o,SV251: $i,SV58: $i > $o] :
( ( ( SV58 @ SV251 )
= $false )
| ( ( ~ ! [SY1018: $i] :
( ~ ( SV58 @ SY1018 )
| ( SV251 = SY1018 ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1682]) ).
thf(1713,plain,
! [SV58: $i > $o,SV252: $i,SV132: $i > $o] :
( ( ( SV132 @ SV252 )
= $false )
| ( ( ~ ! [SY1019: $i] :
( ~ ( SV132 @ SY1019 )
| ( SV252 = SY1019 ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1683]) ).
thf(1714,plain,
! [SV132: $i > $o,SV253: $i,SV58: $i > $o] :
( ( ( SV58 @ SV253 )
= $false )
| ( ( ~ ! [SY1020: $i] :
( ~ ( SV58 @ SY1020 )
| ( SV253 = SY1020 ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1684]) ).
thf(1715,plain,
! [SV58: $i > $o,SV254: $i,SV132: $i > $o] :
( ( ( SV132 @ SV254 )
= $false )
| ( ( ~ ! [SY1021: $i] :
( ~ ( SV132 @ SY1021 )
| ( SV254 = SY1021 ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1716,plain,
! [SV132: $i > $o,SV247: $i,SV58: $i > $o] :
( ( ( ! [SY1016: $i] :
( ~ ( SV58 @ SY1016 )
| ( SV247 = SY1016 ) ) )
= $false )
| ( ( SV58 @ SV247 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1686]) ).
thf(1717,plain,
! [SV58: $i > $o,SV248: $i,SV132: $i > $o] :
( ( ( ! [SY1017: $i] :
( ~ ( SV132 @ SY1017 )
| ( SV248 = SY1017 ) ) )
= $false )
| ( ( SV132 @ SV248 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1687]) ).
thf(1718,plain,
! [SV61: $i,SV217: $i,SV226: $i] :
( ( ( ~ ( in @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) @ ( sK2_SY743 @ SV61 ) ) )
= $false )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1688]) ).
thf(1719,plain,
! [SV61: $i,SV226: $i,SV217: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
| ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) ) )
| ~ ( ~ ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
| ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) ) ) ) )
= $false )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1688]) ).
thf(1720,plain,
! [SV61: $i,SV249: $i,SV205: $i,SV209: $i,SV261: $i] :
( ( ( in @ SV261 @ SV209 )
= $false )
| ( ( in @ SV261 @ SV205 )
= $true )
| ( ( in @ SV249 @ SV209 )
= $true )
| ( ( in @ SV249 @ SV205 )
= $false )
| ( ( in @ SV205 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( in @ SV209 @ ( sK2_SY743 @ SV61 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1689]) ).
thf(1721,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SV199 ) )
| ~ ~ ~ ! [SY1029: $i] :
~ ~ ( ~ ( in @ SY1029 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
| ~ ( in @ SY1029 @ SV199 ) ) )
| ~ ! [SY1042: $i] :
( ~ ( in @ SY1042 @ ( sK2_SY743 @ SV61 ) )
| ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SY1042 )
| ( in @ SY1031 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) ) )
| ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SY1042 ) ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1690]) ).
thf(1722,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SV199 ) )
| ~ ~ ~ ! [SY1023: $i] :
~ ~ ( ~ ( in @ SY1023 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
| ~ ( in @ SY1023 @ SV199 ) ) )
| ~ ! [SY1037: $i] :
( ~ ( in @ SY1037 @ ( sK2_SY743 @ SV61 ) )
| ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SY1037 )
| ( in @ SY1025 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) ) )
| ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SY1037 ) ) ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1691]) ).
thf(1723,plain,
! [SV198: $i,SV246: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SV123 )
| ~ ( SV45 @ SY1014 @ SV246 ) ) )
= $false )
| ( ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1724,plain,
! [SV198: $i,SV246: $i,SV45: $i > $i > $o,SV123: $i] :
( ( ( ! [SY1015: $i] :
~ ~ ( ~ ( in @ SY1015 @ SV123 )
| ~ ( SV45 @ SY1015 @ SV246 ) ) )
= $true )
| ( ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1694]) ).
thf(1725,plain,
! [SV123: $i,SV45: $i > $i > $o,SV240: $i,SV198: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK81_SY1011 @ SV198 @ SV240 @ SV45 @ SV123 ) @ SV123 )
| ~ ( SV45 @ ( sK81_SY1011 @ SV198 @ SV240 @ SV45 @ SV123 ) @ SV240 ) ) )
= $false )
| ( ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1695]) ).
thf(1726,plain,
! [SV198: $i,SV240: $i,SV45: $i > $i > $o,SV123: $i,SV263: $i] :
( ( ( ~ ~ ( ~ ( in @ SV263 @ SV123 )
| ~ ( SV45 @ SV263 @ SV240 ) ) )
= $true )
| ( ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(1727,plain,
! [SV208: $i,SV56: $i > $o,SV262: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV262 )
| ~ ! [SY1033: $i] :
( ~ ( SV130 @ SY1033 )
| ( SV262 = SY1033 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV56 @ ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1697]) ).
thf(1728,plain,
! [SV208: $i,SV56: $i > $o,SV260: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV260 ) )
= $true )
| ( ( ~ ! [SY1032: $i] :
( ~ ( SV130 @ SY1032 )
| ( SV260 = SY1032 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV208
= ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $false )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1698]) ).
thf(1729,plain,
! [SV241: $i,SV130: $i > $o,SV56: $i > $o] :
( ( ( ~ ( SV56 @ ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) ) )
= $false )
| ( ( SV56 @ SV241 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1699]) ).
thf(1730,plain,
! [SV56: $i > $o,SV130: $i > $o,SV241: $i] :
( ( ( SV241
= ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $false )
| ( ( SV56 @ SV241 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1699]) ).
thf(1731,plain,
! [SV233: $i,SV130: $i > $o,SV56: $i > $o] :
( ( ( SV56 @ ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1700]) ).
thf(1732,plain,
! [SV233: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV233
= ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1701]) ).
thf(1733,plain,
! [SV234: $i,SV130: $i > $o,SV56: $i > $o] :
( ( ( SV56 @ ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1702]) ).
thf(1734,plain,
! [SV234: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV234
= ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1703]) ).
thf(1735,plain,
! [SV229: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV56 @ ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(1736,plain,
! [SV229: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV229
= ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1705]) ).
thf(1737,plain,
! [SV58: $i > $o,SV224: $i,SV132: $i > $o] :
( ( ( ~ ( ~ ( SV132 @ ( sK78_SY878 @ SV224 @ SV58 @ SV132 ) )
| ~ ! [SY1039: $i] :
( ~ ( SV132 @ SY1039 )
| ( ( sK78_SY878 @ SV224 @ SV58 @ SV132 )
= SY1039 ) ) ) )
= $true )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV58 @ ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1706]) ).
thf(1738,plain,
! [SV58: $i > $o,SV224: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK73_SY878 @ SV224 @ SV58 @ SV132 ) )
| ~ ! [SY1034: $i] :
( ~ ( SV132 @ SY1034 )
| ( ( sK73_SY878 @ SV224 @ SV58 @ SV132 )
= SY1034 ) ) )
= $false )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV224
= ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1707]) ).
thf(1739,plain,
! [SV132: $i > $o,SV225: $i,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ ( sK79_SY736 @ SV225 @ SV132 @ SV58 ) )
| ~ ! [SY1040: $i] :
( ~ ( SV58 @ SY1040 )
| ( ( sK79_SY736 @ SV225 @ SV132 @ SV58 )
= SY1040 ) ) ) )
= $true )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV132 @ ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1708]) ).
thf(1740,plain,
! [SV132: $i > $o,SV225: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK74_SY736 @ SV225 @ SV132 @ SV58 ) )
| ~ ! [SY1035: $i] :
( ~ ( SV58 @ SY1035 )
| ( ( sK74_SY736 @ SV225 @ SV132 @ SV58 )
= SY1035 ) ) )
= $false )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV225
= ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(1741,plain,
! [SV132: $i > $o,SV257: $i,SV58: $i > $o] :
( ( ( SV58 @ SV257 )
= $false )
| ( ( ~ ! [SY1026: $i] :
( ~ ( SV58 @ SY1026 )
| ( SV257 = SY1026 ) ) )
= $true )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1710]) ).
thf(1742,plain,
! [SV58: $i > $o,SV258: $i,SV132: $i > $o] :
( ( ( SV132 @ SV258 )
= $false )
| ( ( ~ ! [SY1027: $i] :
( ~ ( SV132 @ SY1027 )
| ( SV258 = SY1027 ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(1743,plain,
! [SV132: $i > $o,SV251: $i,SV58: $i > $o] :
( ( ( ! [SY1018: $i] :
( ~ ( SV58 @ SY1018 )
| ( SV251 = SY1018 ) ) )
= $false )
| ( ( SV58 @ SV251 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1744,plain,
! [SV58: $i > $o,SV252: $i,SV132: $i > $o] :
( ( ( ! [SY1019: $i] :
( ~ ( SV132 @ SY1019 )
| ( SV252 = SY1019 ) ) )
= $false )
| ( ( SV132 @ SV252 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1713]) ).
thf(1745,plain,
! [SV132: $i > $o,SV253: $i,SV58: $i > $o] :
( ( ( ! [SY1020: $i] :
( ~ ( SV58 @ SY1020 )
| ( SV253 = SY1020 ) ) )
= $false )
| ( ( SV58 @ SV253 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1714]) ).
thf(1746,plain,
! [SV58: $i > $o,SV254: $i,SV132: $i > $o] :
( ( ( ! [SY1021: $i] :
( ~ ( SV132 @ SY1021 )
| ( SV254 = SY1021 ) ) )
= $false )
| ( ( SV132 @ SV254 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1747,plain,
! [SV247: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
| ( SV247
= ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) ) )
= $false )
| ( ( SV58 @ SV247 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1716]) ).
thf(1748,plain,
! [SV248: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
| ( SV248
= ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) ) )
= $false )
| ( ( SV132 @ SV248 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1717]) ).
thf(1749,plain,
! [SV61: $i,SV217: $i,SV226: $i] :
( ( ( in @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
= $true )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1718]) ).
thf(1750,plain,
! [SV61: $i,SV226: $i,SV217: $i] :
( ( ( ~ ( ~ ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
| ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) ) )
| ~ ( ~ ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
| ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) ) ) )
= $true )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1719]) ).
thf(1751,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SV199 ) )
| ~ ~ ~ ! [SY1029: $i] :
~ ~ ( ~ ( in @ SY1029 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
| ~ ( in @ SY1029 @ SV199 ) ) )
| ~ ! [SY1042: $i] :
( ~ ( in @ SY1042 @ ( sK2_SY743 @ SV61 ) )
| ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SY1042 )
| ( in @ SY1031 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) ) )
| ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SY1042 ) ) ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1721]) ).
thf(1752,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SV199 ) )
| ~ ~ ~ ! [SY1023: $i] :
~ ~ ( ~ ( in @ SY1023 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
| ~ ( in @ SY1023 @ SV199 ) ) )
| ~ ! [SY1037: $i] :
( ~ ( in @ SY1037 @ ( sK2_SY743 @ SV61 ) )
| ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SY1037 )
| ( in @ SY1025 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) ) )
| ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SY1037 ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1753,plain,
! [SV123: $i,SV45: $i > $i > $o,SV246: $i,SV198: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK84_SY1014 @ SV198 @ SV246 @ SV45 @ SV123 ) @ SV123 )
| ~ ( SV45 @ ( sK84_SY1014 @ SV198 @ SV246 @ SV45 @ SV123 ) @ SV246 ) ) )
= $false )
| ( ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1723]) ).
thf(1754,plain,
! [SV198: $i,SV246: $i,SV45: $i > $i > $o,SV123: $i,SV264: $i] :
( ( ( ~ ~ ( ~ ( in @ SV264 @ SV123 )
| ~ ( SV45 @ SV264 @ SV246 ) ) )
= $true )
| ( ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(1755,plain,
! [SV123: $i,SV45: $i > $i > $o,SV240: $i,SV198: $i] :
( ( ( ~ ( ~ ( in @ ( sK81_SY1011 @ SV198 @ SV240 @ SV45 @ SV123 ) @ SV123 )
| ~ ( SV45 @ ( sK81_SY1011 @ SV198 @ SV240 @ SV45 @ SV123 ) @ SV240 ) ) )
= $true )
| ( ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1725]) ).
thf(1756,plain,
! [SV198: $i,SV240: $i,SV45: $i > $i > $o,SV123: $i,SV263: $i] :
( ( ( ~ ( ~ ( in @ SV263 @ SV123 )
| ~ ( SV45 @ SV263 @ SV240 ) ) )
= $false )
| ( ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1726]) ).
thf(1757,plain,
! [SV208: $i,SV56: $i > $o,SV262: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV262 ) )
= $true )
| ( ( ~ ! [SY1033: $i] :
( ~ ( SV130 @ SY1033 )
| ( SV262 = SY1033 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV56 @ ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(1758,plain,
! [SV208: $i,SV56: $i > $o,SV260: $i,SV130: $i > $o] :
( ( ( SV130 @ SV260 )
= $false )
| ( ( ~ ! [SY1032: $i] :
( ~ ( SV130 @ SY1032 )
| ( SV260 = SY1032 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV208
= ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $false )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1728]) ).
thf(1759,plain,
! [SV241: $i,SV130: $i > $o,SV56: $i > $o] :
( ( ( SV56 @ ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) )
| ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1729]) ).
thf(1760,plain,
! [SV241: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV241
= ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1730]) ).
thf(1761,plain,
! [SV233: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV56 @ ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1731]) ).
thf(1762,plain,
! [SV233: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV233
= ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(1763,plain,
! [SV234: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV56 @ ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1733]) ).
thf(1764,plain,
! [SV234: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV234
= ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1734]) ).
thf(1765,plain,
! [SV229: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV56 @ ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1735]) ).
thf(1766,plain,
! [SV229: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV229
= ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1736]) ).
thf(1767,plain,
! [SV58: $i > $o,SV224: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK78_SY878 @ SV224 @ SV58 @ SV132 ) )
| ~ ! [SY1039: $i] :
( ~ ( SV132 @ SY1039 )
| ( ( sK78_SY878 @ SV224 @ SV58 @ SV132 )
= SY1039 ) ) )
= $false )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV58 @ ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1768,plain,
! [SV58: $i > $o,SV224: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK73_SY878 @ SV224 @ SV58 @ SV132 ) ) )
= $false )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV224
= ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1738]) ).
thf(1769,plain,
! [SV58: $i > $o,SV224: $i,SV132: $i > $o] :
( ( ( ~ ! [SY1034: $i] :
( ~ ( SV132 @ SY1034 )
| ( ( sK73_SY878 @ SV224 @ SV58 @ SV132 )
= SY1034 ) ) )
= $false )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV224
= ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1738]) ).
thf(1770,plain,
! [SV132: $i > $o,SV225: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK79_SY736 @ SV225 @ SV132 @ SV58 ) )
| ~ ! [SY1040: $i] :
( ~ ( SV58 @ SY1040 )
| ( ( sK79_SY736 @ SV225 @ SV132 @ SV58 )
= SY1040 ) ) )
= $false )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV132 @ ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1739]) ).
thf(1771,plain,
! [SV132: $i > $o,SV225: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK74_SY736 @ SV225 @ SV132 @ SV58 ) ) )
= $false )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV225
= ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1740]) ).
thf(1772,plain,
! [SV132: $i > $o,SV225: $i,SV58: $i > $o] :
( ( ( ~ ! [SY1035: $i] :
( ~ ( SV58 @ SY1035 )
| ( ( sK74_SY736 @ SV225 @ SV132 @ SV58 )
= SY1035 ) ) )
= $false )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV225
= ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1740]) ).
thf(1773,plain,
! [SV132: $i > $o,SV257: $i,SV58: $i > $o] :
( ( ( ! [SY1026: $i] :
( ~ ( SV58 @ SY1026 )
| ( SV257 = SY1026 ) ) )
= $false )
| ( ( SV58 @ SV257 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1774,plain,
! [SV58: $i > $o,SV258: $i,SV132: $i > $o] :
( ( ( ! [SY1027: $i] :
( ~ ( SV132 @ SY1027 )
| ( SV258 = SY1027 ) ) )
= $false )
| ( ( SV132 @ SV258 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1742]) ).
thf(1775,plain,
! [SV251: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
| ( SV251
= ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) ) )
= $false )
| ( ( SV58 @ SV251 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1743]) ).
thf(1776,plain,
! [SV252: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
| ( SV252
= ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) ) )
= $false )
| ( ( SV132 @ SV252 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1744]) ).
thf(1777,plain,
! [SV253: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
| ( SV253
= ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) ) )
= $false )
| ( ( SV58 @ SV253 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1745]) ).
thf(1778,plain,
! [SV254: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
| ( SV254
= ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) ) )
= $false )
| ( ( SV132 @ SV254 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1746]) ).
thf(1779,plain,
! [SV247: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) ) )
= $false )
| ( ( SV58 @ SV247 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1747]) ).
thf(1780,plain,
! [SV58: $i > $o,SV132: $i > $o,SV247: $i] :
( ( ( SV247
= ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $false )
| ( ( SV58 @ SV247 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1747]) ).
thf(1781,plain,
! [SV248: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) ) )
= $false )
| ( ( SV132 @ SV248 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1748]) ).
thf(1782,plain,
! [SV132: $i > $o,SV58: $i > $o,SV248: $i] :
( ( ( SV248
= ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $false )
| ( ( SV132 @ SV248 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1748]) ).
thf(1783,plain,
! [SV61: $i,SV226: $i,SV217: $i] :
( ( ( ~ ( ~ ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
| ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
| ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) ) ) )
= $true )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1750]) ).
thf(1784,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SV199 ) )
| ~ ~ ~ ! [SY1029: $i] :
~ ~ ( ~ ( in @ SY1029 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
| ~ ( in @ SY1029 @ SV199 ) ) )
| ~ ! [SY1042: $i] :
( ~ ( in @ SY1042 @ ( sK2_SY743 @ SV61 ) )
| ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SY1042 )
| ( in @ SY1031 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) ) )
| ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SY1042 ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1751]) ).
thf(1785,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SV199 ) )
| ~ ~ ~ ! [SY1023: $i] :
~ ~ ( ~ ( in @ SY1023 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
| ~ ( in @ SY1023 @ SV199 ) ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1752]) ).
thf(1786,plain,
! [SV199: $i,SV235: $i,SV61: $i] :
( ( ( ~ ! [SY1037: $i] :
( ~ ( in @ SY1037 @ ( sK2_SY743 @ SV61 ) )
| ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SY1037 )
| ( in @ SY1025 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) ) )
| ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SY1037 ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1752]) ).
thf(1787,plain,
! [SV123: $i,SV45: $i > $i > $o,SV246: $i,SV198: $i] :
( ( ( ~ ( ~ ( in @ ( sK84_SY1014 @ SV198 @ SV246 @ SV45 @ SV123 ) @ SV123 )
| ~ ( SV45 @ ( sK84_SY1014 @ SV198 @ SV246 @ SV45 @ SV123 ) @ SV246 ) ) )
= $true )
| ( ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1753]) ).
thf(1788,plain,
! [SV198: $i,SV246: $i,SV45: $i > $i > $o,SV123: $i,SV264: $i] :
( ( ( ~ ( ~ ( in @ SV264 @ SV123 )
| ~ ( SV45 @ SV264 @ SV246 ) ) )
= $false )
| ( ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1754]) ).
thf(1789,plain,
! [SV123: $i,SV45: $i > $i > $o,SV240: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK81_SY1011 @ SV198 @ SV240 @ SV45 @ SV123 ) @ SV123 )
| ~ ( SV45 @ ( sK81_SY1011 @ SV198 @ SV240 @ SV45 @ SV123 ) @ SV240 ) )
= $false )
| ( ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(1790,plain,
! [SV198: $i,SV240: $i,SV45: $i > $i > $o,SV123: $i,SV263: $i] :
( ( ( ~ ( in @ SV263 @ SV123 )
| ~ ( SV45 @ SV263 @ SV240 ) )
= $true )
| ( ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1756]) ).
thf(1791,plain,
! [SV208: $i,SV56: $i > $o,SV262: $i,SV130: $i > $o] :
( ( ( SV130 @ SV262 )
= $false )
| ( ( ~ ! [SY1033: $i] :
( ~ ( SV130 @ SY1033 )
| ( SV262 = SY1033 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV56 @ ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1792,plain,
! [SV208: $i,SV56: $i > $o,SV260: $i,SV130: $i > $o] :
( ( ( ! [SY1032: $i] :
( ~ ( SV130 @ SY1032 )
| ( SV260 = SY1032 ) ) )
= $false )
| ( ( SV130 @ SV260 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV208
= ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $false )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1793,plain,
! [SV241: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV56 @ ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1759]) ).
thf(1794,plain,
! [SV241: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV241
= ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1760]) ).
thf(1795,plain,
! [SV233: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV56 @ ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1761]) ).
thf(1796,plain,
! [SV233: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV233
= ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1762]) ).
thf(1797,plain,
! [SV234: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV56 @ ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1798,plain,
! [SV234: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV234
= ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1764]) ).
thf(1799,plain,
! [SV229: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV56 @ ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1765]) ).
thf(1800,plain,
! [SV229: $i,SV56: $i > $o,SV265: $i,SV130: $i > $o] :
( ( ( ~ ~ ( ~ ( SV130 @ SV265 )
| ~ ! [SY1044: $i] :
( ~ ( SV130 @ SY1044 )
| ( SV265 = SY1044 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV229
= ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(1801,plain,
! [SV58: $i > $o,SV224: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK78_SY878 @ SV224 @ SV58 @ SV132 ) ) )
= $false )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV58 @ ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1767]) ).
thf(1802,plain,
! [SV58: $i > $o,SV224: $i,SV132: $i > $o] :
( ( ( ~ ! [SY1039: $i] :
( ~ ( SV132 @ SY1039 )
| ( ( sK78_SY878 @ SV224 @ SV58 @ SV132 )
= SY1039 ) ) )
= $false )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV58 @ ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1767]) ).
thf(1803,plain,
! [SV58: $i > $o,SV224: $i,SV132: $i > $o] :
( ( ( SV132 @ ( sK73_SY878 @ SV224 @ SV58 @ SV132 ) )
= $true )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV224
= ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1768]) ).
thf(1804,plain,
! [SV58: $i > $o,SV224: $i,SV132: $i > $o] :
( ( ( ! [SY1034: $i] :
( ~ ( SV132 @ SY1034 )
| ( ( sK73_SY878 @ SV224 @ SV58 @ SV132 )
= SY1034 ) ) )
= $true )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV224
= ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1769]) ).
thf(1805,plain,
! [SV132: $i > $o,SV225: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK79_SY736 @ SV225 @ SV132 @ SV58 ) ) )
= $false )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV132 @ ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1770]) ).
thf(1806,plain,
! [SV132: $i > $o,SV225: $i,SV58: $i > $o] :
( ( ( ~ ! [SY1040: $i] :
( ~ ( SV58 @ SY1040 )
| ( ( sK79_SY736 @ SV225 @ SV132 @ SV58 )
= SY1040 ) ) )
= $false )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV132 @ ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1770]) ).
thf(1807,plain,
! [SV132: $i > $o,SV225: $i,SV58: $i > $o] :
( ( ( SV58 @ ( sK74_SY736 @ SV225 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV225
= ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1771]) ).
thf(1808,plain,
! [SV132: $i > $o,SV225: $i,SV58: $i > $o] :
( ( ( ! [SY1035: $i] :
( ~ ( SV58 @ SY1035 )
| ( ( sK74_SY736 @ SV225 @ SV132 @ SV58 )
= SY1035 ) ) )
= $true )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV225
= ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1772]) ).
thf(1809,plain,
! [SV257: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
| ( SV257
= ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) ) )
= $false )
| ( ( SV58 @ SV257 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1773]) ).
thf(1810,plain,
! [SV258: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
| ( SV258
= ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) ) )
= $false )
| ( ( SV132 @ SV258 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1774]) ).
thf(1811,plain,
! [SV251: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) ) )
= $false )
| ( ( SV58 @ SV251 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1775]) ).
thf(1812,plain,
! [SV58: $i > $o,SV132: $i > $o,SV251: $i] :
( ( ( SV251
= ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $false )
| ( ( SV58 @ SV251 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1775]) ).
thf(1813,plain,
! [SV252: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) ) )
= $false )
| ( ( SV132 @ SV252 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1776]) ).
thf(1814,plain,
! [SV132: $i > $o,SV58: $i > $o,SV252: $i] :
( ( ( SV252
= ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $false )
| ( ( SV132 @ SV252 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1776]) ).
thf(1815,plain,
! [SV253: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) ) )
= $false )
| ( ( SV58 @ SV253 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1777]) ).
thf(1816,plain,
! [SV58: $i > $o,SV132: $i > $o,SV253: $i] :
( ( ( SV253
= ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $false )
| ( ( SV58 @ SV253 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1777]) ).
thf(1817,plain,
! [SV254: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) ) )
= $false )
| ( ( SV132 @ SV254 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1778]) ).
thf(1818,plain,
! [SV132: $i > $o,SV58: $i > $o,SV254: $i] :
( ( ( SV254
= ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $false )
| ( ( SV132 @ SV254 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1778]) ).
thf(1819,plain,
! [SV247: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( SV58 @ ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $true )
| ( ( SV58 @ SV247 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1779]) ).
thf(1820,plain,
! [SV247: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $false )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV247
= ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1780]) ).
thf(1821,plain,
! [SV248: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( SV132 @ ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $true )
| ( ( SV132 @ SV248 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1781]) ).
thf(1822,plain,
! [SV248: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $false )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV248
= ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(1823,plain,
! [SV61: $i,SV226: $i,SV217: $i] :
( ( ( ~ ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
| ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
| ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) ) ) )
= $true )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(1824,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SV199 ) )
| ~ ~ ~ ! [SY1029: $i] :
~ ~ ( ~ ( in @ SY1029 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
| ~ ( in @ SY1029 @ SV199 ) ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1784]) ).
thf(1825,plain,
! [SV199: $i,SV242: $i,SV61: $i] :
( ( ( ~ ! [SY1042: $i] :
( ~ ( in @ SY1042 @ ( sK2_SY743 @ SV61 ) )
| ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SY1042 )
| ( in @ SY1031 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) ) )
| ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SY1042 ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1784]) ).
thf(1826,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SV199 ) )
| ~ ~ ~ ! [SY1023: $i] :
~ ~ ( ~ ( in @ SY1023 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
| ~ ( in @ SY1023 @ SV199 ) ) ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1785]) ).
thf(1827,plain,
! [SV199: $i,SV235: $i,SV61: $i] :
( ( ( ! [SY1037: $i] :
( ~ ( in @ SY1037 @ ( sK2_SY743 @ SV61 ) )
| ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SY1037 )
| ( in @ SY1025 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) ) )
| ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SY1037 ) ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1786]) ).
thf(1828,plain,
! [SV123: $i,SV45: $i > $i > $o,SV246: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK84_SY1014 @ SV198 @ SV246 @ SV45 @ SV123 ) @ SV123 )
| ~ ( SV45 @ ( sK84_SY1014 @ SV198 @ SV246 @ SV45 @ SV123 ) @ SV246 ) )
= $false )
| ( ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1829,plain,
! [SV198: $i,SV246: $i,SV45: $i > $i > $o,SV123: $i,SV264: $i] :
( ( ( ~ ( in @ SV264 @ SV123 )
| ~ ( SV45 @ SV264 @ SV246 ) )
= $true )
| ( ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1788]) ).
thf(1830,plain,
! [SV123: $i,SV45: $i > $i > $o,SV240: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK81_SY1011 @ SV198 @ SV240 @ SV45 @ SV123 ) @ SV123 ) )
= $false )
| ( ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1789]) ).
thf(1831,plain,
! [SV123: $i,SV240: $i,SV198: $i,SV45: $i > $i > $o] :
( ( ( ~ ( SV45 @ ( sK81_SY1011 @ SV198 @ SV240 @ SV45 @ SV123 ) @ SV240 ) )
= $false )
| ( ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1789]) ).
thf(1832,plain,
! [SV198: $i,SV240: $i,SV45: $i > $i > $o,SV123: $i,SV263: $i] :
( ( ( ~ ( in @ SV263 @ SV123 ) )
= $true )
| ( ( ~ ( SV45 @ SV263 @ SV240 ) )
= $true )
| ( ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(1833,plain,
! [SV208: $i,SV56: $i > $o,SV262: $i,SV130: $i > $o] :
( ( ( ! [SY1033: $i] :
( ~ ( SV130 @ SY1033 )
| ( SV262 = SY1033 ) ) )
= $false )
| ( ( SV130 @ SV262 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV56 @ ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(1834,plain,
! [SV260: $i,SV56: $i > $o,SV208: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK91_SY1032 @ SV208 @ SV56 @ SV260 @ SV130 ) )
| ( SV260
= ( sK91_SY1032 @ SV208 @ SV56 @ SV260 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV260 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV208
= ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $false )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1792]) ).
thf(1835,plain,
! [SV241: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ~ ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV56 @ ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(1836,plain,
! [SV241: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV241
= ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1794]) ).
thf(1837,plain,
! [SV233: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV56 @ ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1795]) ).
thf(1838,plain,
! [SV233: $i,SV56: $i > $o,SV266: $i,SV130: $i > $o] :
( ( ( ~ ~ ( ~ ( SV130 @ SV266 )
| ~ ! [SY1045: $i] :
( ~ ( SV130 @ SY1045 )
| ( SV266 = SY1045 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV233
= ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(1839,plain,
! [SV234: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV56 @ ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1797]) ).
thf(1840,plain,
! [SV234: $i,SV56: $i > $o,SV267: $i,SV130: $i > $o] :
( ( ( ~ ~ ( ~ ( SV130 @ SV267 )
| ~ ! [SY1046: $i] :
( ~ ( SV130 @ SY1046 )
| ( SV267 = SY1046 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV234
= ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(1841,plain,
! [SV229: $i,SV56: $i > $o,SV268: $i,SV130: $i > $o] :
( ( ( ~ ~ ( ~ ( SV130 @ SV268 )
| ~ ! [SY1047: $i] :
( ~ ( SV130 @ SY1047 )
| ( SV268 = SY1047 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV56 @ ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(1842,plain,
! [SV229: $i,SV56: $i > $o,SV265: $i,SV130: $i > $o] :
( ( ( ~ ( ~ ( SV130 @ SV265 )
| ~ ! [SY1044: $i] :
( ~ ( SV130 @ SY1044 )
| ( SV265 = SY1044 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV229
= ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(1843,plain,
! [SV58: $i > $o,SV224: $i,SV132: $i > $o] :
( ( ( SV132 @ ( sK78_SY878 @ SV224 @ SV58 @ SV132 ) )
= $true )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV58 @ ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1801]) ).
thf(1844,plain,
! [SV58: $i > $o,SV224: $i,SV132: $i > $o] :
( ( ( ! [SY1039: $i] :
( ~ ( SV132 @ SY1039 )
| ( ( sK78_SY878 @ SV224 @ SV58 @ SV132 )
= SY1039 ) ) )
= $true )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV58 @ ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1802]) ).
thf(1845,plain,
! [SV58: $i > $o,SV224: $i,SV269: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV269 )
| ( ( sK73_SY878 @ SV224 @ SV58 @ SV132 )
= SV269 ) )
= $true )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV224
= ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(1846,plain,
! [SV132: $i > $o,SV225: $i,SV58: $i > $o] :
( ( ( SV58 @ ( sK79_SY736 @ SV225 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV132 @ ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1805]) ).
thf(1847,plain,
! [SV132: $i > $o,SV225: $i,SV58: $i > $o] :
( ( ( ! [SY1040: $i] :
( ~ ( SV58 @ SY1040 )
| ( ( sK79_SY736 @ SV225 @ SV132 @ SV58 )
= SY1040 ) ) )
= $true )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV132 @ ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1806]) ).
thf(1848,plain,
! [SV132: $i > $o,SV225: $i,SV270: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV270 )
| ( ( sK74_SY736 @ SV225 @ SV132 @ SV58 )
= SV270 ) )
= $true )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV225
= ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(1849,plain,
! [SV257: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) ) )
= $false )
| ( ( SV58 @ SV257 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1809]) ).
thf(1850,plain,
! [SV58: $i > $o,SV132: $i > $o,SV257: $i] :
( ( ( SV257
= ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $false )
| ( ( SV58 @ SV257 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1809]) ).
thf(1851,plain,
! [SV258: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) ) )
= $false )
| ( ( SV132 @ SV258 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1810]) ).
thf(1852,plain,
! [SV132: $i > $o,SV58: $i > $o,SV258: $i] :
( ( ( SV258
= ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $false )
| ( ( SV132 @ SV258 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1810]) ).
thf(1853,plain,
! [SV251: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( SV58 @ ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $true )
| ( ( SV58 @ SV251 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1811]) ).
thf(1854,plain,
! [SV251: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $false )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV251
= ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(1855,plain,
! [SV252: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( SV132 @ ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $true )
| ( ( SV132 @ SV252 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1813]) ).
thf(1856,plain,
! [SV252: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $false )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV252
= ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1857,plain,
! [SV253: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( SV58 @ ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $true )
| ( ( SV58 @ SV253 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1815]) ).
thf(1858,plain,
! [SV253: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $false )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV253
= ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(1859,plain,
! [SV254: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( SV132 @ ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $true )
| ( ( SV132 @ SV254 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1817]) ).
thf(1860,plain,
! [SV254: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $false )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV254
= ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1818]) ).
thf(1861,plain,
! [SV247: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $false )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV58 @ ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(1862,plain,
! [SV58: $i > $o,SV247: $i,SV132: $i > $o] :
( ( ( ~ ~ ( ~ ( SV132 @ ( sK92_SY878 @ SV247 @ SV58 @ SV132 ) )
| ~ ! [SY1048: $i] :
( ~ ( SV132 @ SY1048 )
| ( ( sK92_SY878 @ SV247 @ SV58 @ SV132 )
= SY1048 ) ) ) )
= $false )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV247
= ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1820]) ).
thf(1863,plain,
! [SV248: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $false )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV132 @ ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1821]) ).
thf(1864,plain,
! [SV132: $i > $o,SV248: $i,SV58: $i > $o] :
( ( ( ~ ~ ( ~ ( SV58 @ ( sK93_SY736 @ SV248 @ SV132 @ SV58 ) )
| ~ ! [SY1049: $i] :
( ~ ( SV58 @ SY1049 )
| ( ( sK93_SY736 @ SV248 @ SV132 @ SV58 )
= SY1049 ) ) ) )
= $false )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV248
= ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1822]) ).
thf(1865,plain,
! [SV61: $i,SV226: $i,SV217: $i] :
( ( ( ~ ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
| ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) ) ) )
= $true )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1823]) ).
thf(1866,plain,
! [SV61: $i,SV217: $i,SV226: $i] :
( ( ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
| ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) ) ) )
= $true )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1823]) ).
thf(1867,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SV199 ) )
| ~ ~ ~ ! [SY1029: $i] :
~ ~ ( ~ ( in @ SY1029 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
| ~ ( in @ SY1029 @ SV199 ) ) ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1824]) ).
thf(1868,plain,
! [SV199: $i,SV242: $i,SV61: $i] :
( ( ( ! [SY1042: $i] :
( ~ ( in @ SY1042 @ ( sK2_SY743 @ SV61 ) )
| ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SY1042 )
| ( in @ SY1031 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) ) )
| ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SY1042 ) ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1825]) ).
thf(1869,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SV199 ) )
| ~ ~ ~ ! [SY1023: $i] :
~ ~ ( ~ ( in @ SY1023 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
| ~ ( in @ SY1023 @ SV199 ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1826]) ).
thf(1870,plain,
! [SV199: $i,SV235: $i,SV61: $i,SV271: $i] :
( ( ( ~ ( in @ SV271 @ ( sK2_SY743 @ SV61 ) )
| ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV271 )
| ( in @ SY1050 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) ) )
| ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SV271 ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(1871,plain,
! [SV123: $i,SV45: $i > $i > $o,SV246: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK84_SY1014 @ SV198 @ SV246 @ SV45 @ SV123 ) @ SV123 ) )
= $false )
| ( ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1828]) ).
thf(1872,plain,
! [SV123: $i,SV246: $i,SV198: $i,SV45: $i > $i > $o] :
( ( ( ~ ( SV45 @ ( sK84_SY1014 @ SV198 @ SV246 @ SV45 @ SV123 ) @ SV246 ) )
= $false )
| ( ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1828]) ).
thf(1873,plain,
! [SV198: $i,SV246: $i,SV45: $i > $i > $o,SV123: $i,SV264: $i] :
( ( ( ~ ( in @ SV264 @ SV123 ) )
= $true )
| ( ( ~ ( SV45 @ SV264 @ SV246 ) )
= $true )
| ( ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(1874,plain,
! [SV123: $i,SV45: $i > $i > $o,SV240: $i,SV198: $i] :
( ( ( in @ ( sK81_SY1011 @ SV198 @ SV240 @ SV45 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1830]) ).
thf(1875,plain,
! [SV123: $i,SV240: $i,SV198: $i,SV45: $i > $i > $o] :
( ( ( SV45 @ ( sK81_SY1011 @ SV198 @ SV240 @ SV45 @ SV123 ) @ SV240 )
= $true )
| ( ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1831]) ).
thf(1876,plain,
! [SV198: $i,SV240: $i,SV45: $i > $i > $o,SV123: $i,SV263: $i] :
( ( ( in @ SV263 @ SV123 )
= $false )
| ( ( ~ ( SV45 @ SV263 @ SV240 ) )
= $true )
| ( ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1832]) ).
thf(1877,plain,
! [SV262: $i,SV56: $i > $o,SV208: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK94_SY1033 @ SV208 @ SV56 @ SV262 @ SV130 ) )
| ( SV262
= ( sK94_SY1033 @ SV208 @ SV56 @ SV262 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV262 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV56 @ ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1833]) ).
thf(1878,plain,
! [SV260: $i,SV56: $i > $o,SV208: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK91_SY1032 @ SV208 @ SV56 @ SV260 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV260 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV208
= ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $false )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1834]) ).
thf(1879,plain,
! [SV130: $i > $o,SV56: $i > $o,SV208: $i,SV260: $i] :
( ( ( SV260
= ( sK91_SY1032 @ SV208 @ SV56 @ SV260 @ SV130 ) )
= $false )
| ( ( SV130 @ SV260 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV208
= ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $false )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1834]) ).
thf(1880,plain,
! [SV241: $i,SV56: $i > $o,SV130: $i > $o] :
( ( ( ! [SY870: $i] :
~ ~ ( ~ ( SV130 @ SY870 )
| ~ ! [SY871: $i] :
( ~ ( SV130 @ SY871 )
| ( SY870 = SY871 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV56 @ ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1835]) ).
thf(1881,plain,
! [SV241: $i,SV56: $i > $o,SV272: $i,SV130: $i > $o] :
( ( ( ~ ~ ( ~ ( SV130 @ SV272 )
| ~ ! [SY1051: $i] :
( ~ ( SV130 @ SY1051 )
| ( SV272 = SY1051 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV241
= ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(1882,plain,
! [SV233: $i,SV56: $i > $o,SV273: $i,SV130: $i > $o] :
( ( ( ~ ~ ( ~ ( SV130 @ SV273 )
| ~ ! [SY1052: $i] :
( ~ ( SV130 @ SY1052 )
| ( SV273 = SY1052 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV56 @ ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(1883,plain,
! [SV233: $i,SV56: $i > $o,SV266: $i,SV130: $i > $o] :
( ( ( ~ ( ~ ( SV130 @ SV266 )
| ~ ! [SY1045: $i] :
( ~ ( SV130 @ SY1045 )
| ( SV266 = SY1045 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV233
= ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(1884,plain,
! [SV234: $i,SV56: $i > $o,SV274: $i,SV130: $i > $o] :
( ( ( ~ ~ ( ~ ( SV130 @ SV274 )
| ~ ! [SY1053: $i] :
( ~ ( SV130 @ SY1053 )
| ( SV274 = SY1053 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV56 @ ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(1885,plain,
! [SV234: $i,SV56: $i > $o,SV267: $i,SV130: $i > $o] :
( ( ( ~ ( ~ ( SV130 @ SV267 )
| ~ ! [SY1046: $i] :
( ~ ( SV130 @ SY1046 )
| ( SV267 = SY1046 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV234
= ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1840]) ).
thf(1886,plain,
! [SV229: $i,SV56: $i > $o,SV268: $i,SV130: $i > $o] :
( ( ( ~ ( ~ ( SV130 @ SV268 )
| ~ ! [SY1047: $i] :
( ~ ( SV130 @ SY1047 )
| ( SV268 = SY1047 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV56 @ ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1841]) ).
thf(1887,plain,
! [SV229: $i,SV56: $i > $o,SV265: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV265 )
| ~ ! [SY1044: $i] :
( ~ ( SV130 @ SY1044 )
| ( SV265 = SY1044 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV229
= ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1842]) ).
thf(1888,plain,
! [SV58: $i > $o,SV224: $i,SV275: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV275 )
| ( ( sK78_SY878 @ SV224 @ SV58 @ SV132 )
= SV275 ) )
= $true )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV58 @ ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(1889,plain,
! [SV58: $i > $o,SV224: $i,SV269: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV269 ) )
= $true )
| ( ( ( sK73_SY878 @ SV224 @ SV58 @ SV132 )
= SV269 )
= $true )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV224
= ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1845]) ).
thf(1890,plain,
! [SV132: $i > $o,SV225: $i,SV276: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV276 )
| ( ( sK79_SY736 @ SV225 @ SV132 @ SV58 )
= SV276 ) )
= $true )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV132 @ ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(1891,plain,
! [SV132: $i > $o,SV225: $i,SV270: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV270 ) )
= $true )
| ( ( ( sK74_SY736 @ SV225 @ SV132 @ SV58 )
= SV270 )
= $true )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV225
= ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(1892,plain,
! [SV257: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( SV58 @ ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $true )
| ( ( SV58 @ SV257 )
= $false )
| ( ( ~ ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1849]) ).
thf(1893,plain,
! [SV257: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $false )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV257
= ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(1894,plain,
! [SV258: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( SV132 @ ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $true )
| ( ( SV132 @ SV258 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1851]) ).
thf(1895,plain,
! [SV258: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $false )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV258
= ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1852]) ).
thf(1896,plain,
! [SV251: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $false )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV58 @ ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1853]) ).
thf(1897,plain,
! [SV58: $i > $o,SV251: $i,SV132: $i > $o] :
( ( ( ~ ~ ( ~ ( SV132 @ ( sK95_SY878 @ SV251 @ SV58 @ SV132 ) )
| ~ ! [SY1054: $i] :
( ~ ( SV132 @ SY1054 )
| ( ( sK95_SY878 @ SV251 @ SV58 @ SV132 )
= SY1054 ) ) ) )
= $false )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV251
= ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1854]) ).
thf(1898,plain,
! [SV252: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $false )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV132 @ ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1855]) ).
thf(1899,plain,
! [SV132: $i > $o,SV252: $i,SV58: $i > $o] :
( ( ( ~ ~ ( ~ ( SV58 @ ( sK96_SY736 @ SV252 @ SV132 @ SV58 ) )
| ~ ! [SY1055: $i] :
( ~ ( SV58 @ SY1055 )
| ( ( sK96_SY736 @ SV252 @ SV132 @ SV58 )
= SY1055 ) ) ) )
= $false )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV252
= ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1856]) ).
thf(1900,plain,
! [SV253: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $false )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV58 @ ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(1901,plain,
! [SV58: $i > $o,SV253: $i,SV132: $i > $o] :
( ( ( ~ ~ ( ~ ( SV132 @ ( sK97_SY878 @ SV253 @ SV58 @ SV132 ) )
| ~ ! [SY1056: $i] :
( ~ ( SV132 @ SY1056 )
| ( ( sK97_SY878 @ SV253 @ SV58 @ SV132 )
= SY1056 ) ) ) )
= $false )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV253
= ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1858]) ).
thf(1902,plain,
! [SV254: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $false )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV132 @ ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(1903,plain,
! [SV132: $i > $o,SV254: $i,SV58: $i > $o] :
( ( ( ~ ~ ( ~ ( SV58 @ ( sK98_SY736 @ SV254 @ SV132 @ SV58 ) )
| ~ ! [SY1057: $i] :
( ~ ( SV58 @ SY1057 )
| ( ( sK98_SY736 @ SV254 @ SV132 @ SV58 )
= SY1057 ) ) ) )
= $false )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV254
= ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1860]) ).
thf(1904,plain,
! [SV58: $i > $o,SV247: $i,SV132: $i > $o] :
( ( ( ~ ~ ( ~ ( SV132 @ ( sK99_SY878 @ SV247 @ SV58 @ SV132 ) )
| ~ ! [SY1058: $i] :
( ~ ( SV132 @ SY1058 )
| ( ( sK99_SY878 @ SV247 @ SV58 @ SV132 )
= SY1058 ) ) ) )
= $false )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV58 @ ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1861]) ).
thf(1905,plain,
! [SV58: $i > $o,SV247: $i,SV132: $i > $o] :
( ( ( ~ ( ~ ( SV132 @ ( sK92_SY878 @ SV247 @ SV58 @ SV132 ) )
| ~ ! [SY1048: $i] :
( ~ ( SV132 @ SY1048 )
| ( ( sK92_SY878 @ SV247 @ SV58 @ SV132 )
= SY1048 ) ) ) )
= $true )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV247
= ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1862]) ).
thf(1906,plain,
! [SV132: $i > $o,SV248: $i,SV58: $i > $o] :
( ( ( ~ ~ ( ~ ( SV58 @ ( sK100_SY736 @ SV248 @ SV132 @ SV58 ) )
| ~ ! [SY1059: $i] :
( ~ ( SV58 @ SY1059 )
| ( ( sK100_SY736 @ SV248 @ SV132 @ SV58 )
= SY1059 ) ) ) )
= $false )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV132 @ ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1863]) ).
thf(1907,plain,
! [SV132: $i > $o,SV248: $i,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ ( sK93_SY736 @ SV248 @ SV132 @ SV58 ) )
| ~ ! [SY1049: $i] :
( ~ ( SV58 @ SY1049 )
| ( ( sK93_SY736 @ SV248 @ SV132 @ SV58 )
= SY1049 ) ) ) )
= $true )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV248
= ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1864]) ).
thf(1908,plain,
! [SV61: $i,SV226: $i,SV217: $i] :
( ( ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
| ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) ) ) )
= $true )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1865]) ).
thf(1909,plain,
! [SV61: $i,SV217: $i,SV226: $i] :
( ( ( ~ ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
| ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) ) )
= $false )
| ( ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
= $false )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1866]) ).
thf(1910,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SV199 ) )
| ~ ~ ~ ! [SY1029: $i] :
~ ~ ( ~ ( in @ SY1029 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
| ~ ( in @ SY1029 @ SV199 ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(1911,plain,
! [SV199: $i,SV242: $i,SV61: $i,SV277: $i] :
( ( ( ~ ( in @ SV277 @ ( sK2_SY743 @ SV61 ) )
| ! [SY1060: $i] :
( ~ ( in @ SY1060 @ SV277 )
| ( in @ SY1060 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) ) )
| ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SV277 ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(1912,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SV199 ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1869]) ).
thf(1913,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( ~ ~ ~ ! [SY1023: $i] :
~ ~ ( ~ ( in @ SY1023 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
| ~ ( in @ SY1023 @ SV199 ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1869]) ).
thf(1914,plain,
! [SV199: $i,SV235: $i,SV61: $i,SV271: $i] :
( ( ( ~ ( in @ SV271 @ ( sK2_SY743 @ SV61 ) ) )
= $true )
| ( ( ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV271 )
| ( in @ SY1050 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) ) )
| ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SV271 ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1870]) ).
thf(1915,plain,
! [SV123: $i,SV45: $i > $i > $o,SV246: $i,SV198: $i] :
( ( ( in @ ( sK84_SY1014 @ SV198 @ SV246 @ SV45 @ SV123 ) @ SV123 )
= $true )
| ( ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1871]) ).
thf(1916,plain,
! [SV123: $i,SV246: $i,SV198: $i,SV45: $i > $i > $o] :
( ( ( SV45 @ ( sK84_SY1014 @ SV198 @ SV246 @ SV45 @ SV123 ) @ SV246 )
= $true )
| ( ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1872]) ).
thf(1917,plain,
! [SV198: $i,SV246: $i,SV45: $i > $i > $o,SV123: $i,SV264: $i] :
( ( ( in @ SV264 @ SV123 )
= $false )
| ( ( ~ ( SV45 @ SV264 @ SV246 ) )
= $true )
| ( ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1873]) ).
thf(1918,plain,
! [SV198: $i,SV123: $i,SV240: $i,SV263: $i,SV45: $i > $i > $o] :
( ( ( SV45 @ SV263 @ SV240 )
= $false )
| ( ( in @ SV263 @ SV123 )
= $false )
| ( ( in @ SV240 @ ( sK61_SY848 @ SV198 @ SV45 @ SV123 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV198
= ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(1919,plain,
! [SV262: $i,SV56: $i > $o,SV208: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK94_SY1033 @ SV208 @ SV56 @ SV262 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV262 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV56 @ ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1877]) ).
thf(1920,plain,
! [SV130: $i > $o,SV56: $i > $o,SV208: $i,SV262: $i] :
( ( ( SV262
= ( sK94_SY1033 @ SV208 @ SV56 @ SV262 @ SV130 ) )
= $false )
| ( ( SV130 @ SV262 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV56 @ ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1877]) ).
thf(1921,plain,
! [SV260: $i,SV56: $i > $o,SV208: $i,SV130: $i > $o] :
( ( ( SV130 @ ( sK91_SY1032 @ SV208 @ SV56 @ SV260 @ SV130 ) )
= $true )
| ( ( SV130 @ SV260 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV208
= ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $false )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1878]) ).
thf(1922,plain,
! [SV241: $i,SV56: $i > $o,SV278: $i,SV130: $i > $o] :
( ( ( ~ ~ ( ~ ( SV130 @ SV278 )
| ~ ! [SY1061: $i] :
( ~ ( SV130 @ SY1061 )
| ( SV278 = SY1061 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV56 @ ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(1923,plain,
! [SV241: $i,SV56: $i > $o,SV272: $i,SV130: $i > $o] :
( ( ( ~ ( ~ ( SV130 @ SV272 )
| ~ ! [SY1051: $i] :
( ~ ( SV130 @ SY1051 )
| ( SV272 = SY1051 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV241
= ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1881]) ).
thf(1924,plain,
! [SV233: $i,SV56: $i > $o,SV273: $i,SV130: $i > $o] :
( ( ( ~ ( ~ ( SV130 @ SV273 )
| ~ ! [SY1052: $i] :
( ~ ( SV130 @ SY1052 )
| ( SV273 = SY1052 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV56 @ ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1882]) ).
thf(1925,plain,
! [SV233: $i,SV56: $i > $o,SV266: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV266 )
| ~ ! [SY1045: $i] :
( ~ ( SV130 @ SY1045 )
| ( SV266 = SY1045 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV233
= ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1883]) ).
thf(1926,plain,
! [SV234: $i,SV56: $i > $o,SV274: $i,SV130: $i > $o] :
( ( ( ~ ( ~ ( SV130 @ SV274 )
| ~ ! [SY1053: $i] :
( ~ ( SV130 @ SY1053 )
| ( SV274 = SY1053 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV56 @ ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(1927,plain,
! [SV234: $i,SV56: $i > $o,SV267: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV267 )
| ~ ! [SY1046: $i] :
( ~ ( SV130 @ SY1046 )
| ( SV267 = SY1046 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV234
= ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1885]) ).
thf(1928,plain,
! [SV229: $i,SV56: $i > $o,SV268: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV268 )
| ~ ! [SY1047: $i] :
( ~ ( SV130 @ SY1047 )
| ( SV268 = SY1047 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV56 @ ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1886]) ).
thf(1929,plain,
! [SV229: $i,SV56: $i > $o,SV265: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV265 ) )
= $true )
| ( ( ~ ! [SY1044: $i] :
( ~ ( SV130 @ SY1044 )
| ( SV265 = SY1044 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV229
= ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1887]) ).
thf(1930,plain,
! [SV58: $i > $o,SV224: $i,SV275: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV275 ) )
= $true )
| ( ( ( sK78_SY878 @ SV224 @ SV58 @ SV132 )
= SV275 )
= $true )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV58 @ ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1888]) ).
thf(1931,plain,
! [SV58: $i > $o,SV224: $i,SV269: $i,SV132: $i > $o] :
( ( ( SV132 @ SV269 )
= $false )
| ( ( ( sK73_SY878 @ SV224 @ SV58 @ SV132 )
= SV269 )
= $true )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV224
= ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(1932,plain,
! [SV132: $i > $o,SV225: $i,SV276: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV276 ) )
= $true )
| ( ( ( sK79_SY736 @ SV225 @ SV132 @ SV58 )
= SV276 )
= $true )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV132 @ ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1890]) ).
thf(1933,plain,
! [SV132: $i > $o,SV225: $i,SV270: $i,SV58: $i > $o] :
( ( ( SV58 @ SV270 )
= $false )
| ( ( ( sK74_SY736 @ SV225 @ SV132 @ SV58 )
= SV270 )
= $true )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV225
= ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $false )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(1934,plain,
! [SV257: $i,SV58: $i > $o,SV132: $i > $o] :
( ( ( ! [SY878: $i] :
~ ~ ( ~ ( SV132 @ SY878 )
| ~ ! [SY879: $i] :
( ~ ( SV132 @ SY879 )
| ( SY878 = SY879 ) ) ) )
= $false )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV58 @ ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1892]) ).
thf(1935,plain,
! [SV58: $i > $o,SV257: $i,SV132: $i > $o] :
( ( ( ~ ~ ( ~ ( SV132 @ ( sK101_SY878 @ SV257 @ SV58 @ SV132 ) )
| ~ ! [SY1062: $i] :
( ~ ( SV132 @ SY1062 )
| ( ( sK101_SY878 @ SV257 @ SV58 @ SV132 )
= SY1062 ) ) ) )
= $false )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV257
= ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1893]) ).
thf(1936,plain,
! [SV258: $i,SV132: $i > $o,SV58: $i > $o] :
( ( ( ! [SY736: $i] :
~ ~ ( ~ ( SV58 @ SY736 )
| ~ ! [SY737: $i] :
( ~ ( SV58 @ SY737 )
| ( SY736 = SY737 ) ) ) )
= $false )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV132 @ ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1894]) ).
thf(1937,plain,
! [SV132: $i > $o,SV258: $i,SV58: $i > $o] :
( ( ( ~ ~ ( ~ ( SV58 @ ( sK102_SY736 @ SV258 @ SV132 @ SV58 ) )
| ~ ! [SY1063: $i] :
( ~ ( SV58 @ SY1063 )
| ( ( sK102_SY736 @ SV258 @ SV132 @ SV58 )
= SY1063 ) ) ) )
= $false )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV258
= ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1895]) ).
thf(1938,plain,
! [SV58: $i > $o,SV251: $i,SV132: $i > $o] :
( ( ( ~ ~ ( ~ ( SV132 @ ( sK103_SY878 @ SV251 @ SV58 @ SV132 ) )
| ~ ! [SY1064: $i] :
( ~ ( SV132 @ SY1064 )
| ( ( sK103_SY878 @ SV251 @ SV58 @ SV132 )
= SY1064 ) ) ) )
= $false )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV58 @ ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1896]) ).
thf(1939,plain,
! [SV58: $i > $o,SV251: $i,SV132: $i > $o] :
( ( ( ~ ( ~ ( SV132 @ ( sK95_SY878 @ SV251 @ SV58 @ SV132 ) )
| ~ ! [SY1054: $i] :
( ~ ( SV132 @ SY1054 )
| ( ( sK95_SY878 @ SV251 @ SV58 @ SV132 )
= SY1054 ) ) ) )
= $true )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV251
= ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1897]) ).
thf(1940,plain,
! [SV132: $i > $o,SV252: $i,SV58: $i > $o] :
( ( ( ~ ~ ( ~ ( SV58 @ ( sK104_SY736 @ SV252 @ SV132 @ SV58 ) )
| ~ ! [SY1065: $i] :
( ~ ( SV58 @ SY1065 )
| ( ( sK104_SY736 @ SV252 @ SV132 @ SV58 )
= SY1065 ) ) ) )
= $false )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV132 @ ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1898]) ).
thf(1941,plain,
! [SV132: $i > $o,SV252: $i,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ ( sK96_SY736 @ SV252 @ SV132 @ SV58 ) )
| ~ ! [SY1055: $i] :
( ~ ( SV58 @ SY1055 )
| ( ( sK96_SY736 @ SV252 @ SV132 @ SV58 )
= SY1055 ) ) ) )
= $true )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV252
= ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1899]) ).
thf(1942,plain,
! [SV58: $i > $o,SV253: $i,SV132: $i > $o] :
( ( ( ~ ~ ( ~ ( SV132 @ ( sK105_SY878 @ SV253 @ SV58 @ SV132 ) )
| ~ ! [SY1066: $i] :
( ~ ( SV132 @ SY1066 )
| ( ( sK105_SY878 @ SV253 @ SV58 @ SV132 )
= SY1066 ) ) ) )
= $false )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV58 @ ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1900]) ).
thf(1943,plain,
! [SV58: $i > $o,SV253: $i,SV132: $i > $o] :
( ( ( ~ ( ~ ( SV132 @ ( sK97_SY878 @ SV253 @ SV58 @ SV132 ) )
| ~ ! [SY1056: $i] :
( ~ ( SV132 @ SY1056 )
| ( ( sK97_SY878 @ SV253 @ SV58 @ SV132 )
= SY1056 ) ) ) )
= $true )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV253
= ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1901]) ).
thf(1944,plain,
! [SV132: $i > $o,SV254: $i,SV58: $i > $o] :
( ( ( ~ ~ ( ~ ( SV58 @ ( sK106_SY736 @ SV254 @ SV132 @ SV58 ) )
| ~ ! [SY1067: $i] :
( ~ ( SV58 @ SY1067 )
| ( ( sK106_SY736 @ SV254 @ SV132 @ SV58 )
= SY1067 ) ) ) )
= $false )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV132 @ ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1902]) ).
thf(1945,plain,
! [SV132: $i > $o,SV254: $i,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ ( sK98_SY736 @ SV254 @ SV132 @ SV58 ) )
| ~ ! [SY1057: $i] :
( ~ ( SV58 @ SY1057 )
| ( ( sK98_SY736 @ SV254 @ SV132 @ SV58 )
= SY1057 ) ) ) )
= $true )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV254
= ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1903]) ).
thf(1946,plain,
! [SV58: $i > $o,SV247: $i,SV132: $i > $o] :
( ( ( ~ ( ~ ( SV132 @ ( sK99_SY878 @ SV247 @ SV58 @ SV132 ) )
| ~ ! [SY1058: $i] :
( ~ ( SV132 @ SY1058 )
| ( ( sK99_SY878 @ SV247 @ SV58 @ SV132 )
= SY1058 ) ) ) )
= $true )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV58 @ ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1904]) ).
thf(1947,plain,
! [SV58: $i > $o,SV247: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK92_SY878 @ SV247 @ SV58 @ SV132 ) )
| ~ ! [SY1048: $i] :
( ~ ( SV132 @ SY1048 )
| ( ( sK92_SY878 @ SV247 @ SV58 @ SV132 )
= SY1048 ) ) )
= $false )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV247
= ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1905]) ).
thf(1948,plain,
! [SV132: $i > $o,SV248: $i,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ ( sK100_SY736 @ SV248 @ SV132 @ SV58 ) )
| ~ ! [SY1059: $i] :
( ~ ( SV58 @ SY1059 )
| ( ( sK100_SY736 @ SV248 @ SV132 @ SV58 )
= SY1059 ) ) ) )
= $true )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV132 @ ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1906]) ).
thf(1949,plain,
! [SV132: $i > $o,SV248: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK93_SY736 @ SV248 @ SV132 @ SV58 ) )
| ~ ! [SY1049: $i] :
( ~ ( SV58 @ SY1049 )
| ( ( sK93_SY736 @ SV248 @ SV132 @ SV58 )
= SY1049 ) ) )
= $false )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV248
= ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1907]) ).
thf(1950,plain,
! [SV61: $i,SV217: $i,SV226: $i] :
( ( ( ~ ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
| ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) ) )
= $false )
| ( ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
= $true )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(1951,plain,
! [SV61: $i,SV217: $i,SV226: $i] :
( ( ( ~ ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) ) )
= $false )
| ( ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
= $false )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1909]) ).
thf(1952,plain,
! [SV61: $i,SV226: $i,SV217: $i] :
( ( ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
= $false )
| ( ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
= $false )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1909]) ).
thf(1953,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SV199 ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1910]) ).
thf(1954,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( ~ ~ ~ ! [SY1029: $i] :
~ ~ ( ~ ( in @ SY1029 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
| ~ ( in @ SY1029 @ SV199 ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1910]) ).
thf(1955,plain,
! [SV199: $i,SV242: $i,SV61: $i,SV277: $i] :
( ( ( ~ ( in @ SV277 @ ( sK2_SY743 @ SV61 ) ) )
= $true )
| ( ( ! [SY1060: $i] :
( ~ ( in @ SY1060 @ SV277 )
| ( in @ SY1060 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) ) )
| ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SV277 ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(1956,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( ~ ( ~ ( in @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SV199 ) ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1912]) ).
thf(1957,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( ~ ~ ! [SY1023: $i] :
~ ~ ( ~ ( in @ SY1023 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
| ~ ( in @ SY1023 @ SV199 ) ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1913]) ).
thf(1958,plain,
! [SV199: $i,SV235: $i,SV61: $i,SV271: $i] :
( ( ( in @ SV271 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV271 )
| ( in @ SY1050 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) ) )
| ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SV271 ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(1959,plain,
! [SV198: $i,SV123: $i,SV246: $i,SV264: $i,SV45: $i > $i > $o] :
( ( ( SV45 @ SV264 @ SV246 )
= $false )
| ( ( in @ SV264 @ SV123 )
= $false )
| ( ( in @ SV246 @ ( sK64_SY848 @ SV198 @ SV45 @ SV123 ) )
= $true )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ SV198 )
= $false )
| ( ( SV45 @ ( sK8_SY845 @ SV45 @ SV123 ) @ ( sK50_SY957 @ SV198 @ SV123 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(1960,plain,
! [SV262: $i,SV56: $i > $o,SV208: $i,SV130: $i > $o] :
( ( ( SV130 @ ( sK94_SY1033 @ SV208 @ SV56 @ SV262 @ SV130 ) )
= $true )
| ( ( SV130 @ SV262 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV208 )
= $false )
| ( ( SV56 @ ( sK65_SY976 @ SV130 @ SV208 @ SV56 ) )
= $true )
| ( ( ( sK9_SY866 @ SV130 @ SV56 )
= ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1919]) ).
thf(1961,plain,
! [SV241: $i,SV56: $i > $o,SV278: $i,SV130: $i > $o] :
( ( ( ~ ( ~ ( SV130 @ SV278 )
| ~ ! [SY1061: $i] :
( ~ ( SV130 @ SY1061 )
| ( SV278 = SY1061 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV56 @ ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(1962,plain,
! [SV241: $i,SV56: $i > $o,SV272: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV272 )
| ~ ! [SY1051: $i] :
( ~ ( SV130 @ SY1051 )
| ( SV272 = SY1051 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV241
= ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1923]) ).
thf(1963,plain,
! [SV233: $i,SV56: $i > $o,SV273: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV273 )
| ~ ! [SY1052: $i] :
( ~ ( SV130 @ SY1052 )
| ( SV273 = SY1052 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV56 @ ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1924]) ).
thf(1964,plain,
! [SV233: $i,SV56: $i > $o,SV266: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV266 ) )
= $true )
| ( ( ~ ! [SY1045: $i] :
( ~ ( SV130 @ SY1045 )
| ( SV266 = SY1045 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV233
= ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1925]) ).
thf(1965,plain,
! [SV234: $i,SV56: $i > $o,SV274: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV274 )
| ~ ! [SY1053: $i] :
( ~ ( SV130 @ SY1053 )
| ( SV274 = SY1053 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV56 @ ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1926]) ).
thf(1966,plain,
! [SV234: $i,SV56: $i > $o,SV267: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV267 ) )
= $true )
| ( ( ~ ! [SY1046: $i] :
( ~ ( SV130 @ SY1046 )
| ( SV267 = SY1046 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV234
= ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1927]) ).
thf(1967,plain,
! [SV229: $i,SV56: $i > $o,SV268: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV268 ) )
= $true )
| ( ( ~ ! [SY1047: $i] :
( ~ ( SV130 @ SY1047 )
| ( SV268 = SY1047 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV56 @ ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1928]) ).
thf(1968,plain,
! [SV229: $i,SV56: $i > $o,SV265: $i,SV130: $i > $o] :
( ( ( SV130 @ SV265 )
= $false )
| ( ( ~ ! [SY1044: $i] :
( ~ ( SV130 @ SY1044 )
| ( SV265 = SY1044 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV229
= ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1929]) ).
thf(1969,plain,
! [SV58: $i > $o,SV224: $i,SV275: $i,SV132: $i > $o] :
( ( ( SV132 @ SV275 )
= $false )
| ( ( ( sK78_SY878 @ SV224 @ SV58 @ SV132 )
= SV275 )
= $true )
| ( ( SV58 @ SV224 )
= $false )
| ( ( SV58 @ ( sK66_SY994 @ SV132 @ SV224 @ SV58 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(1970,plain,
! [SV132: $i > $o,SV225: $i,SV276: $i,SV58: $i > $o] :
( ( ( SV58 @ SV276 )
= $false )
| ( ( ( sK79_SY736 @ SV225 @ SV132 @ SV58 )
= SV276 )
= $true )
| ( ( SV132 @ SV225 )
= $false )
| ( ( SV132 @ ( sK67_SY995 @ SV58 @ SV225 @ SV132 ) )
= $true )
| ( ( ( sK10_SY874 @ SV132 @ SV58 )
= ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1932]) ).
thf(1971,plain,
! [SV58: $i > $o,SV257: $i,SV132: $i > $o] :
( ( ( ~ ~ ( ~ ( SV132 @ ( sK107_SY878 @ SV257 @ SV58 @ SV132 ) )
| ~ ! [SY1068: $i] :
( ~ ( SV132 @ SY1068 )
| ( ( sK107_SY878 @ SV257 @ SV58 @ SV132 )
= SY1068 ) ) ) )
= $false )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV58 @ ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1934]) ).
thf(1972,plain,
! [SV58: $i > $o,SV257: $i,SV132: $i > $o] :
( ( ( ~ ( ~ ( SV132 @ ( sK101_SY878 @ SV257 @ SV58 @ SV132 ) )
| ~ ! [SY1062: $i] :
( ~ ( SV132 @ SY1062 )
| ( ( sK101_SY878 @ SV257 @ SV58 @ SV132 )
= SY1062 ) ) ) )
= $true )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV257
= ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1935]) ).
thf(1973,plain,
! [SV132: $i > $o,SV258: $i,SV58: $i > $o] :
( ( ( ~ ~ ( ~ ( SV58 @ ( sK108_SY736 @ SV258 @ SV132 @ SV58 ) )
| ~ ! [SY1069: $i] :
( ~ ( SV58 @ SY1069 )
| ( ( sK108_SY736 @ SV258 @ SV132 @ SV58 )
= SY1069 ) ) ) )
= $false )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV132 @ ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1936]) ).
thf(1974,plain,
! [SV132: $i > $o,SV258: $i,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ ( sK102_SY736 @ SV258 @ SV132 @ SV58 ) )
| ~ ! [SY1063: $i] :
( ~ ( SV58 @ SY1063 )
| ( ( sK102_SY736 @ SV258 @ SV132 @ SV58 )
= SY1063 ) ) ) )
= $true )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV258
= ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1937]) ).
thf(1975,plain,
! [SV58: $i > $o,SV251: $i,SV132: $i > $o] :
( ( ( ~ ( ~ ( SV132 @ ( sK103_SY878 @ SV251 @ SV58 @ SV132 ) )
| ~ ! [SY1064: $i] :
( ~ ( SV132 @ SY1064 )
| ( ( sK103_SY878 @ SV251 @ SV58 @ SV132 )
= SY1064 ) ) ) )
= $true )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV58 @ ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1938]) ).
thf(1976,plain,
! [SV58: $i > $o,SV251: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK95_SY878 @ SV251 @ SV58 @ SV132 ) )
| ~ ! [SY1054: $i] :
( ~ ( SV132 @ SY1054 )
| ( ( sK95_SY878 @ SV251 @ SV58 @ SV132 )
= SY1054 ) ) )
= $false )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV251
= ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1939]) ).
thf(1977,plain,
! [SV132: $i > $o,SV252: $i,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ ( sK104_SY736 @ SV252 @ SV132 @ SV58 ) )
| ~ ! [SY1065: $i] :
( ~ ( SV58 @ SY1065 )
| ( ( sK104_SY736 @ SV252 @ SV132 @ SV58 )
= SY1065 ) ) ) )
= $true )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV132 @ ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1940]) ).
thf(1978,plain,
! [SV132: $i > $o,SV252: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK96_SY736 @ SV252 @ SV132 @ SV58 ) )
| ~ ! [SY1055: $i] :
( ~ ( SV58 @ SY1055 )
| ( ( sK96_SY736 @ SV252 @ SV132 @ SV58 )
= SY1055 ) ) )
= $false )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV252
= ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(1979,plain,
! [SV58: $i > $o,SV253: $i,SV132: $i > $o] :
( ( ( ~ ( ~ ( SV132 @ ( sK105_SY878 @ SV253 @ SV58 @ SV132 ) )
| ~ ! [SY1066: $i] :
( ~ ( SV132 @ SY1066 )
| ( ( sK105_SY878 @ SV253 @ SV58 @ SV132 )
= SY1066 ) ) ) )
= $true )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV58 @ ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1942]) ).
thf(1980,plain,
! [SV58: $i > $o,SV253: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK97_SY878 @ SV253 @ SV58 @ SV132 ) )
| ~ ! [SY1056: $i] :
( ~ ( SV132 @ SY1056 )
| ( ( sK97_SY878 @ SV253 @ SV58 @ SV132 )
= SY1056 ) ) )
= $false )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV253
= ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1943]) ).
thf(1981,plain,
! [SV132: $i > $o,SV254: $i,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ ( sK106_SY736 @ SV254 @ SV132 @ SV58 ) )
| ~ ! [SY1067: $i] :
( ~ ( SV58 @ SY1067 )
| ( ( sK106_SY736 @ SV254 @ SV132 @ SV58 )
= SY1067 ) ) ) )
= $true )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV132 @ ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1944]) ).
thf(1982,plain,
! [SV132: $i > $o,SV254: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK98_SY736 @ SV254 @ SV132 @ SV58 ) )
| ~ ! [SY1057: $i] :
( ~ ( SV58 @ SY1057 )
| ( ( sK98_SY736 @ SV254 @ SV132 @ SV58 )
= SY1057 ) ) )
= $false )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV254
= ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1945]) ).
thf(1983,plain,
! [SV58: $i > $o,SV247: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK99_SY878 @ SV247 @ SV58 @ SV132 ) )
| ~ ! [SY1058: $i] :
( ~ ( SV132 @ SY1058 )
| ( ( sK99_SY878 @ SV247 @ SV58 @ SV132 )
= SY1058 ) ) )
= $false )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV58 @ ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1946]) ).
thf(1984,plain,
! [SV58: $i > $o,SV247: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK92_SY878 @ SV247 @ SV58 @ SV132 ) ) )
= $false )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV247
= ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1947]) ).
thf(1985,plain,
! [SV58: $i > $o,SV247: $i,SV132: $i > $o] :
( ( ( ~ ! [SY1048: $i] :
( ~ ( SV132 @ SY1048 )
| ( ( sK92_SY878 @ SV247 @ SV58 @ SV132 )
= SY1048 ) ) )
= $false )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV247
= ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1947]) ).
thf(1986,plain,
! [SV132: $i > $o,SV248: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK100_SY736 @ SV248 @ SV132 @ SV58 ) )
| ~ ! [SY1059: $i] :
( ~ ( SV58 @ SY1059 )
| ( ( sK100_SY736 @ SV248 @ SV132 @ SV58 )
= SY1059 ) ) )
= $false )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV132 @ ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1948]) ).
thf(1987,plain,
! [SV132: $i > $o,SV248: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK93_SY736 @ SV248 @ SV132 @ SV58 ) ) )
= $false )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV248
= ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1949]) ).
thf(1988,plain,
! [SV132: $i > $o,SV248: $i,SV58: $i > $o] :
( ( ( ~ ! [SY1049: $i] :
( ~ ( SV58 @ SY1049 )
| ( ( sK93_SY736 @ SV248 @ SV132 @ SV58 )
= SY1049 ) ) )
= $false )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV248
= ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1949]) ).
thf(1989,plain,
! [SV61: $i,SV217: $i,SV226: $i] :
( ( ( ~ ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) ) )
= $false )
| ( ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
= $true )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1950]) ).
thf(1990,plain,
! [SV61: $i,SV226: $i,SV217: $i] :
( ( ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
= $false )
| ( ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
= $true )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1950]) ).
thf(1991,plain,
! [SV61: $i,SV217: $i,SV226: $i] :
( ( ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
= $true )
| ( ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
= $false )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1951]) ).
thf(1992,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( ~ ( ~ ( in @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SV199 ) ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1953]) ).
thf(1993,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( ~ ~ ! [SY1029: $i] :
~ ~ ( ~ ( in @ SY1029 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
| ~ ( in @ SY1029 @ SV199 ) ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1954]) ).
thf(1994,plain,
! [SV199: $i,SV242: $i,SV61: $i,SV277: $i] :
( ( ( in @ SV277 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( ! [SY1060: $i] :
( ~ ( in @ SY1060 @ SV277 )
| ( in @ SY1060 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) ) )
| ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SV277 ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1955]) ).
thf(1995,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( ~ ( in @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SV199 ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1956]) ).
thf(1996,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( ~ ! [SY1023: $i] :
~ ~ ( ~ ( in @ SY1023 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
| ~ ( in @ SY1023 @ SV199 ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1957]) ).
thf(1997,plain,
! [SV61: $i,SV199: $i,SV235: $i,SV271: $i] :
( ( ( ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV271 )
| ( in @ SY1050 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) ) ) )
= $true )
| ( ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SV271 )
= $true )
| ( ( in @ SV271 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1958]) ).
thf(1998,plain,
! [SV241: $i,SV56: $i > $o,SV278: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV278 )
| ~ ! [SY1061: $i] :
( ~ ( SV130 @ SY1061 )
| ( SV278 = SY1061 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV56 @ ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1961]) ).
thf(1999,plain,
! [SV241: $i,SV56: $i > $o,SV272: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV272 ) )
= $true )
| ( ( ~ ! [SY1051: $i] :
( ~ ( SV130 @ SY1051 )
| ( SV272 = SY1051 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV241
= ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1962]) ).
thf(2000,plain,
! [SV233: $i,SV56: $i > $o,SV273: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV273 ) )
= $true )
| ( ( ~ ! [SY1052: $i] :
( ~ ( SV130 @ SY1052 )
| ( SV273 = SY1052 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV56 @ ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1963]) ).
thf(2001,plain,
! [SV233: $i,SV56: $i > $o,SV266: $i,SV130: $i > $o] :
( ( ( SV130 @ SV266 )
= $false )
| ( ( ~ ! [SY1045: $i] :
( ~ ( SV130 @ SY1045 )
| ( SV266 = SY1045 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV233
= ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2002,plain,
! [SV234: $i,SV56: $i > $o,SV274: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV274 ) )
= $true )
| ( ( ~ ! [SY1053: $i] :
( ~ ( SV130 @ SY1053 )
| ( SV274 = SY1053 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV56 @ ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1965]) ).
thf(2003,plain,
! [SV234: $i,SV56: $i > $o,SV267: $i,SV130: $i > $o] :
( ( ( SV130 @ SV267 )
= $false )
| ( ( ~ ! [SY1046: $i] :
( ~ ( SV130 @ SY1046 )
| ( SV267 = SY1046 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV234
= ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(2004,plain,
! [SV229: $i,SV56: $i > $o,SV268: $i,SV130: $i > $o] :
( ( ( SV130 @ SV268 )
= $false )
| ( ( ~ ! [SY1047: $i] :
( ~ ( SV130 @ SY1047 )
| ( SV268 = SY1047 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV56 @ ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1967]) ).
thf(2005,plain,
! [SV229: $i,SV56: $i > $o,SV265: $i,SV130: $i > $o] :
( ( ( ! [SY1044: $i] :
( ~ ( SV130 @ SY1044 )
| ( SV265 = SY1044 ) ) )
= $false )
| ( ( SV130 @ SV265 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV229
= ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(2006,plain,
! [SV58: $i > $o,SV257: $i,SV132: $i > $o] :
( ( ( ~ ( ~ ( SV132 @ ( sK107_SY878 @ SV257 @ SV58 @ SV132 ) )
| ~ ! [SY1068: $i] :
( ~ ( SV132 @ SY1068 )
| ( ( sK107_SY878 @ SV257 @ SV58 @ SV132 )
= SY1068 ) ) ) )
= $true )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV58 @ ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1971]) ).
thf(2007,plain,
! [SV58: $i > $o,SV257: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK101_SY878 @ SV257 @ SV58 @ SV132 ) )
| ~ ! [SY1062: $i] :
( ~ ( SV132 @ SY1062 )
| ( ( sK101_SY878 @ SV257 @ SV58 @ SV132 )
= SY1062 ) ) )
= $false )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV257
= ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2008,plain,
! [SV132: $i > $o,SV258: $i,SV58: $i > $o] :
( ( ( ~ ( ~ ( SV58 @ ( sK108_SY736 @ SV258 @ SV132 @ SV58 ) )
| ~ ! [SY1069: $i] :
( ~ ( SV58 @ SY1069 )
| ( ( sK108_SY736 @ SV258 @ SV132 @ SV58 )
= SY1069 ) ) ) )
= $true )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV132 @ ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1973]) ).
thf(2009,plain,
! [SV132: $i > $o,SV258: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK102_SY736 @ SV258 @ SV132 @ SV58 ) )
| ~ ! [SY1063: $i] :
( ~ ( SV58 @ SY1063 )
| ( ( sK102_SY736 @ SV258 @ SV132 @ SV58 )
= SY1063 ) ) )
= $false )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV258
= ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1974]) ).
thf(2010,plain,
! [SV58: $i > $o,SV251: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK103_SY878 @ SV251 @ SV58 @ SV132 ) )
| ~ ! [SY1064: $i] :
( ~ ( SV132 @ SY1064 )
| ( ( sK103_SY878 @ SV251 @ SV58 @ SV132 )
= SY1064 ) ) )
= $false )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV58 @ ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1975]) ).
thf(2011,plain,
! [SV58: $i > $o,SV251: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK95_SY878 @ SV251 @ SV58 @ SV132 ) ) )
= $false )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV251
= ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1976]) ).
thf(2012,plain,
! [SV58: $i > $o,SV251: $i,SV132: $i > $o] :
( ( ( ~ ! [SY1054: $i] :
( ~ ( SV132 @ SY1054 )
| ( ( sK95_SY878 @ SV251 @ SV58 @ SV132 )
= SY1054 ) ) )
= $false )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV251
= ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1976]) ).
thf(2013,plain,
! [SV132: $i > $o,SV252: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK104_SY736 @ SV252 @ SV132 @ SV58 ) )
| ~ ! [SY1065: $i] :
( ~ ( SV58 @ SY1065 )
| ( ( sK104_SY736 @ SV252 @ SV132 @ SV58 )
= SY1065 ) ) )
= $false )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV132 @ ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1977]) ).
thf(2014,plain,
! [SV132: $i > $o,SV252: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK96_SY736 @ SV252 @ SV132 @ SV58 ) ) )
= $false )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV252
= ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1978]) ).
thf(2015,plain,
! [SV132: $i > $o,SV252: $i,SV58: $i > $o] :
( ( ( ~ ! [SY1055: $i] :
( ~ ( SV58 @ SY1055 )
| ( ( sK96_SY736 @ SV252 @ SV132 @ SV58 )
= SY1055 ) ) )
= $false )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV252
= ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1978]) ).
thf(2016,plain,
! [SV58: $i > $o,SV253: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK105_SY878 @ SV253 @ SV58 @ SV132 ) )
| ~ ! [SY1066: $i] :
( ~ ( SV132 @ SY1066 )
| ( ( sK105_SY878 @ SV253 @ SV58 @ SV132 )
= SY1066 ) ) )
= $false )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV58 @ ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1979]) ).
thf(2017,plain,
! [SV58: $i > $o,SV253: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK97_SY878 @ SV253 @ SV58 @ SV132 ) ) )
= $false )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV253
= ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1980]) ).
thf(2018,plain,
! [SV58: $i > $o,SV253: $i,SV132: $i > $o] :
( ( ( ~ ! [SY1056: $i] :
( ~ ( SV132 @ SY1056 )
| ( ( sK97_SY878 @ SV253 @ SV58 @ SV132 )
= SY1056 ) ) )
= $false )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV253
= ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1980]) ).
thf(2019,plain,
! [SV132: $i > $o,SV254: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK106_SY736 @ SV254 @ SV132 @ SV58 ) )
| ~ ! [SY1067: $i] :
( ~ ( SV58 @ SY1067 )
| ( ( sK106_SY736 @ SV254 @ SV132 @ SV58 )
= SY1067 ) ) )
= $false )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV132 @ ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1981]) ).
thf(2020,plain,
! [SV132: $i > $o,SV254: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK98_SY736 @ SV254 @ SV132 @ SV58 ) ) )
= $false )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV254
= ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1982]) ).
thf(2021,plain,
! [SV132: $i > $o,SV254: $i,SV58: $i > $o] :
( ( ( ~ ! [SY1057: $i] :
( ~ ( SV58 @ SY1057 )
| ( ( sK98_SY736 @ SV254 @ SV132 @ SV58 )
= SY1057 ) ) )
= $false )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV254
= ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1982]) ).
thf(2022,plain,
! [SV58: $i > $o,SV247: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK99_SY878 @ SV247 @ SV58 @ SV132 ) ) )
= $false )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV58 @ ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1983]) ).
thf(2023,plain,
! [SV58: $i > $o,SV247: $i,SV132: $i > $o] :
( ( ( ~ ! [SY1058: $i] :
( ~ ( SV132 @ SY1058 )
| ( ( sK99_SY878 @ SV247 @ SV58 @ SV132 )
= SY1058 ) ) )
= $false )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV58 @ ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1983]) ).
thf(2024,plain,
! [SV58: $i > $o,SV247: $i,SV132: $i > $o] :
( ( ( SV132 @ ( sK92_SY878 @ SV247 @ SV58 @ SV132 ) )
= $true )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV247
= ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1984]) ).
thf(2025,plain,
! [SV58: $i > $o,SV247: $i,SV132: $i > $o] :
( ( ( ! [SY1048: $i] :
( ~ ( SV132 @ SY1048 )
| ( ( sK92_SY878 @ SV247 @ SV58 @ SV132 )
= SY1048 ) ) )
= $true )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV247
= ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1985]) ).
thf(2026,plain,
! [SV132: $i > $o,SV248: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK100_SY736 @ SV248 @ SV132 @ SV58 ) ) )
= $false )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV132 @ ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1986]) ).
thf(2027,plain,
! [SV132: $i > $o,SV248: $i,SV58: $i > $o] :
( ( ( ~ ! [SY1059: $i] :
( ~ ( SV58 @ SY1059 )
| ( ( sK100_SY736 @ SV248 @ SV132 @ SV58 )
= SY1059 ) ) )
= $false )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV132 @ ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1986]) ).
thf(2028,plain,
! [SV132: $i > $o,SV248: $i,SV58: $i > $o] :
( ( ( SV58 @ ( sK93_SY736 @ SV248 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV248
= ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1987]) ).
thf(2029,plain,
! [SV132: $i > $o,SV248: $i,SV58: $i > $o] :
( ( ( ! [SY1049: $i] :
( ~ ( SV58 @ SY1049 )
| ( ( sK93_SY736 @ SV248 @ SV132 @ SV58 )
= SY1049 ) ) )
= $true )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV248
= ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1988]) ).
thf(2030,plain,
! [SV61: $i,SV217: $i,SV226: $i] :
( ( ( in @ SV226 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
= $true )
| ( ( in @ SV217 @ ( sK75_SY996 @ SV226 @ SV217 @ SV61 ) )
= $true )
| ( ( SV217 = SV226 )
= $true )
| ( ( in @ SV217 @ SV61 )
= $false )
| ( ( in @ SV226 @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1989]) ).
thf(2031,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( ~ ( in @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
| ~ ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SV199 ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1992]) ).
thf(2032,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( ~ ! [SY1029: $i] :
~ ~ ( ~ ( in @ SY1029 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
| ~ ( in @ SY1029 @ SV199 ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1993]) ).
thf(2033,plain,
! [SV61: $i,SV199: $i,SV242: $i,SV277: $i] :
( ( ( ! [SY1060: $i] :
( ~ ( in @ SY1060 @ SV277 )
| ( in @ SY1060 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) ) ) )
= $true )
| ( ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SV277 )
= $true )
| ( ( in @ SV277 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1994]) ).
thf(2034,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( ~ ( in @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1995]) ).
thf(2035,plain,
! [SV235: $i,SV199: $i,SV61: $i] :
( ( ( ~ ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SV199 ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1995]) ).
thf(2036,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( ! [SY1023: $i] :
~ ~ ( ~ ( in @ SY1023 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
| ~ ( in @ SY1023 @ SV199 ) ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1996]) ).
thf(2037,plain,
! [SV61: $i,SV199: $i,SV235: $i,SV271: $i,SV279: $i] :
( ( ( ~ ( in @ SV279 @ SV271 )
| ( in @ SV279 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) ) )
= $true )
| ( ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SV271 )
= $true )
| ( ( in @ SV271 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2038,plain,
! [SV241: $i,SV56: $i > $o,SV278: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV278 ) )
= $true )
| ( ( ~ ! [SY1061: $i] :
( ~ ( SV130 @ SY1061 )
| ( SV278 = SY1061 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV56 @ ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1998]) ).
thf(2039,plain,
! [SV241: $i,SV56: $i > $o,SV272: $i,SV130: $i > $o] :
( ( ( SV130 @ SV272 )
= $false )
| ( ( ~ ! [SY1051: $i] :
( ~ ( SV130 @ SY1051 )
| ( SV272 = SY1051 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV241
= ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1999]) ).
thf(2040,plain,
! [SV233: $i,SV56: $i > $o,SV273: $i,SV130: $i > $o] :
( ( ( SV130 @ SV273 )
= $false )
| ( ( ~ ! [SY1052: $i] :
( ~ ( SV130 @ SY1052 )
| ( SV273 = SY1052 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV56 @ ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2000]) ).
thf(2041,plain,
! [SV233: $i,SV56: $i > $o,SV266: $i,SV130: $i > $o] :
( ( ( ! [SY1045: $i] :
( ~ ( SV130 @ SY1045 )
| ( SV266 = SY1045 ) ) )
= $false )
| ( ( SV130 @ SV266 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV233
= ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2001]) ).
thf(2042,plain,
! [SV234: $i,SV56: $i > $o,SV274: $i,SV130: $i > $o] :
( ( ( SV130 @ SV274 )
= $false )
| ( ( ~ ! [SY1053: $i] :
( ~ ( SV130 @ SY1053 )
| ( SV274 = SY1053 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV56 @ ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2002]) ).
thf(2043,plain,
! [SV234: $i,SV56: $i > $o,SV267: $i,SV130: $i > $o] :
( ( ( ! [SY1046: $i] :
( ~ ( SV130 @ SY1046 )
| ( SV267 = SY1046 ) ) )
= $false )
| ( ( SV130 @ SV267 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV234
= ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2044,plain,
! [SV229: $i,SV56: $i > $o,SV268: $i,SV130: $i > $o] :
( ( ( ! [SY1047: $i] :
( ~ ( SV130 @ SY1047 )
| ( SV268 = SY1047 ) ) )
= $false )
| ( ( SV130 @ SV268 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV56 @ ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2045,plain,
! [SV265: $i,SV56: $i > $o,SV229: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK109_SY1044 @ SV229 @ SV56 @ SV265 @ SV130 ) )
| ( SV265
= ( sK109_SY1044 @ SV229 @ SV56 @ SV265 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV265 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV229
= ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2005]) ).
thf(2046,plain,
! [SV58: $i > $o,SV257: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK107_SY878 @ SV257 @ SV58 @ SV132 ) )
| ~ ! [SY1068: $i] :
( ~ ( SV132 @ SY1068 )
| ( ( sK107_SY878 @ SV257 @ SV58 @ SV132 )
= SY1068 ) ) )
= $false )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV58 @ ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2006]) ).
thf(2047,plain,
! [SV58: $i > $o,SV257: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK101_SY878 @ SV257 @ SV58 @ SV132 ) ) )
= $false )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV257
= ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2007]) ).
thf(2048,plain,
! [SV58: $i > $o,SV257: $i,SV132: $i > $o] :
( ( ( ~ ! [SY1062: $i] :
( ~ ( SV132 @ SY1062 )
| ( ( sK101_SY878 @ SV257 @ SV58 @ SV132 )
= SY1062 ) ) )
= $false )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV257
= ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2007]) ).
thf(2049,plain,
! [SV132: $i > $o,SV258: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK108_SY736 @ SV258 @ SV132 @ SV58 ) )
| ~ ! [SY1069: $i] :
( ~ ( SV58 @ SY1069 )
| ( ( sK108_SY736 @ SV258 @ SV132 @ SV58 )
= SY1069 ) ) )
= $false )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV132 @ ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2008]) ).
thf(2050,plain,
! [SV132: $i > $o,SV258: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK102_SY736 @ SV258 @ SV132 @ SV58 ) ) )
= $false )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV258
= ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2009]) ).
thf(2051,plain,
! [SV132: $i > $o,SV258: $i,SV58: $i > $o] :
( ( ( ~ ! [SY1063: $i] :
( ~ ( SV58 @ SY1063 )
| ( ( sK102_SY736 @ SV258 @ SV132 @ SV58 )
= SY1063 ) ) )
= $false )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV258
= ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2009]) ).
thf(2052,plain,
! [SV58: $i > $o,SV251: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK103_SY878 @ SV251 @ SV58 @ SV132 ) ) )
= $false )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV58 @ ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2010]) ).
thf(2053,plain,
! [SV58: $i > $o,SV251: $i,SV132: $i > $o] :
( ( ( ~ ! [SY1064: $i] :
( ~ ( SV132 @ SY1064 )
| ( ( sK103_SY878 @ SV251 @ SV58 @ SV132 )
= SY1064 ) ) )
= $false )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV58 @ ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2010]) ).
thf(2054,plain,
! [SV58: $i > $o,SV251: $i,SV132: $i > $o] :
( ( ( SV132 @ ( sK95_SY878 @ SV251 @ SV58 @ SV132 ) )
= $true )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV251
= ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2011]) ).
thf(2055,plain,
! [SV58: $i > $o,SV251: $i,SV132: $i > $o] :
( ( ( ! [SY1054: $i] :
( ~ ( SV132 @ SY1054 )
| ( ( sK95_SY878 @ SV251 @ SV58 @ SV132 )
= SY1054 ) ) )
= $true )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV251
= ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2012]) ).
thf(2056,plain,
! [SV132: $i > $o,SV252: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK104_SY736 @ SV252 @ SV132 @ SV58 ) ) )
= $false )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV132 @ ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2013]) ).
thf(2057,plain,
! [SV132: $i > $o,SV252: $i,SV58: $i > $o] :
( ( ( ~ ! [SY1065: $i] :
( ~ ( SV58 @ SY1065 )
| ( ( sK104_SY736 @ SV252 @ SV132 @ SV58 )
= SY1065 ) ) )
= $false )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV132 @ ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2013]) ).
thf(2058,plain,
! [SV132: $i > $o,SV252: $i,SV58: $i > $o] :
( ( ( SV58 @ ( sK96_SY736 @ SV252 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV252
= ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2014]) ).
thf(2059,plain,
! [SV132: $i > $o,SV252: $i,SV58: $i > $o] :
( ( ( ! [SY1055: $i] :
( ~ ( SV58 @ SY1055 )
| ( ( sK96_SY736 @ SV252 @ SV132 @ SV58 )
= SY1055 ) ) )
= $true )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV252
= ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2015]) ).
thf(2060,plain,
! [SV58: $i > $o,SV253: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK105_SY878 @ SV253 @ SV58 @ SV132 ) ) )
= $false )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV58 @ ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2016]) ).
thf(2061,plain,
! [SV58: $i > $o,SV253: $i,SV132: $i > $o] :
( ( ( ~ ! [SY1066: $i] :
( ~ ( SV132 @ SY1066 )
| ( ( sK105_SY878 @ SV253 @ SV58 @ SV132 )
= SY1066 ) ) )
= $false )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV58 @ ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2016]) ).
thf(2062,plain,
! [SV58: $i > $o,SV253: $i,SV132: $i > $o] :
( ( ( SV132 @ ( sK97_SY878 @ SV253 @ SV58 @ SV132 ) )
= $true )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV253
= ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2017]) ).
thf(2063,plain,
! [SV58: $i > $o,SV253: $i,SV132: $i > $o] :
( ( ( ! [SY1056: $i] :
( ~ ( SV132 @ SY1056 )
| ( ( sK97_SY878 @ SV253 @ SV58 @ SV132 )
= SY1056 ) ) )
= $true )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV253
= ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2018]) ).
thf(2064,plain,
! [SV132: $i > $o,SV254: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK106_SY736 @ SV254 @ SV132 @ SV58 ) ) )
= $false )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV132 @ ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2019]) ).
thf(2065,plain,
! [SV132: $i > $o,SV254: $i,SV58: $i > $o] :
( ( ( ~ ! [SY1067: $i] :
( ~ ( SV58 @ SY1067 )
| ( ( sK106_SY736 @ SV254 @ SV132 @ SV58 )
= SY1067 ) ) )
= $false )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV132 @ ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2019]) ).
thf(2066,plain,
! [SV132: $i > $o,SV254: $i,SV58: $i > $o] :
( ( ( SV58 @ ( sK98_SY736 @ SV254 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV254
= ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2020]) ).
thf(2067,plain,
! [SV132: $i > $o,SV254: $i,SV58: $i > $o] :
( ( ( ! [SY1057: $i] :
( ~ ( SV58 @ SY1057 )
| ( ( sK98_SY736 @ SV254 @ SV132 @ SV58 )
= SY1057 ) ) )
= $true )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV254
= ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2021]) ).
thf(2068,plain,
! [SV58: $i > $o,SV247: $i,SV132: $i > $o] :
( ( ( SV132 @ ( sK99_SY878 @ SV247 @ SV58 @ SV132 ) )
= $true )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV58 @ ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2022]) ).
thf(2069,plain,
! [SV58: $i > $o,SV247: $i,SV132: $i > $o] :
( ( ( ! [SY1058: $i] :
( ~ ( SV132 @ SY1058 )
| ( ( sK99_SY878 @ SV247 @ SV58 @ SV132 )
= SY1058 ) ) )
= $true )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV58 @ ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2023]) ).
thf(2070,plain,
! [SV58: $i > $o,SV247: $i,SV280: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV280 )
| ( ( sK92_SY878 @ SV247 @ SV58 @ SV132 )
= SV280 ) )
= $true )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV247
= ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2071,plain,
! [SV132: $i > $o,SV248: $i,SV58: $i > $o] :
( ( ( SV58 @ ( sK100_SY736 @ SV248 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV132 @ ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2026]) ).
thf(2072,plain,
! [SV132: $i > $o,SV248: $i,SV58: $i > $o] :
( ( ( ! [SY1059: $i] :
( ~ ( SV58 @ SY1059 )
| ( ( sK100_SY736 @ SV248 @ SV132 @ SV58 )
= SY1059 ) ) )
= $true )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV132 @ ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2027]) ).
thf(2073,plain,
! [SV132: $i > $o,SV248: $i,SV281: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV281 )
| ( ( sK93_SY736 @ SV248 @ SV132 @ SV58 )
= SV281 ) )
= $true )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV248
= ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2074,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( ~ ( in @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2031]) ).
thf(2075,plain,
! [SV242: $i,SV199: $i,SV61: $i] :
( ( ( ~ ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SV199 ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2031]) ).
thf(2076,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( ! [SY1029: $i] :
~ ~ ( ~ ( in @ SY1029 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
| ~ ( in @ SY1029 @ SV199 ) ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2032]) ).
thf(2077,plain,
! [SV61: $i,SV199: $i,SV242: $i,SV277: $i,SV282: $i] :
( ( ( ~ ( in @ SV282 @ SV277 )
| ( in @ SV282 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) ) )
= $true )
| ( ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SV277 )
= $true )
| ( ( in @ SV277 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2078,plain,
! [SV61: $i,SV199: $i,SV235: $i] :
( ( ( in @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2034]) ).
thf(2079,plain,
! [SV235: $i,SV199: $i,SV61: $i] :
( ( ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SV199 )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2035]) ).
thf(2080,plain,
! [SV61: $i,SV199: $i,SV235: $i,SV283: $i] :
( ( ( ~ ~ ( ~ ( in @ SV283 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
| ~ ( in @ SV283 @ SV199 ) ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2081,plain,
! [SV61: $i,SV199: $i,SV235: $i,SV271: $i,SV279: $i] :
( ( ( ~ ( in @ SV279 @ SV271 ) )
= $true )
| ( ( in @ SV279 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
= $true )
| ( ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SV271 )
= $true )
| ( ( in @ SV271 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2037]) ).
thf(2082,plain,
! [SV241: $i,SV56: $i > $o,SV278: $i,SV130: $i > $o] :
( ( ( SV130 @ SV278 )
= $false )
| ( ( ~ ! [SY1061: $i] :
( ~ ( SV130 @ SY1061 )
| ( SV278 = SY1061 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV56 @ ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2038]) ).
thf(2083,plain,
! [SV241: $i,SV56: $i > $o,SV272: $i,SV130: $i > $o] :
( ( ( ! [SY1051: $i] :
( ~ ( SV130 @ SY1051 )
| ( SV272 = SY1051 ) ) )
= $false )
| ( ( SV130 @ SV272 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV241
= ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2039]) ).
thf(2084,plain,
! [SV233: $i,SV56: $i > $o,SV273: $i,SV130: $i > $o] :
( ( ( ! [SY1052: $i] :
( ~ ( SV130 @ SY1052 )
| ( SV273 = SY1052 ) ) )
= $false )
| ( ( SV130 @ SV273 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV56 @ ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2040]) ).
thf(2085,plain,
! [SV266: $i,SV56: $i > $o,SV233: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK110_SY1045 @ SV233 @ SV56 @ SV266 @ SV130 ) )
| ( SV266
= ( sK110_SY1045 @ SV233 @ SV56 @ SV266 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV266 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV233
= ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2041]) ).
thf(2086,plain,
! [SV234: $i,SV56: $i > $o,SV274: $i,SV130: $i > $o] :
( ( ( ! [SY1053: $i] :
( ~ ( SV130 @ SY1053 )
| ( SV274 = SY1053 ) ) )
= $false )
| ( ( SV130 @ SV274 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV56 @ ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2042]) ).
thf(2087,plain,
! [SV267: $i,SV56: $i > $o,SV234: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK111_SY1046 @ SV234 @ SV56 @ SV267 @ SV130 ) )
| ( SV267
= ( sK111_SY1046 @ SV234 @ SV56 @ SV267 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV267 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV234
= ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2043]) ).
thf(2088,plain,
! [SV268: $i,SV56: $i > $o,SV229: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK112_SY1047 @ SV229 @ SV56 @ SV268 @ SV130 ) )
| ( SV268
= ( sK112_SY1047 @ SV229 @ SV56 @ SV268 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV268 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV56 @ ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2044]) ).
thf(2089,plain,
! [SV265: $i,SV56: $i > $o,SV229: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK109_SY1044 @ SV229 @ SV56 @ SV265 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV265 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV229
= ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2045]) ).
thf(2090,plain,
! [SV130: $i > $o,SV56: $i > $o,SV229: $i,SV265: $i] :
( ( ( SV265
= ( sK109_SY1044 @ SV229 @ SV56 @ SV265 @ SV130 ) )
= $false )
| ( ( SV130 @ SV265 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV229
= ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2045]) ).
thf(2091,plain,
! [SV58: $i > $o,SV257: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ ( sK107_SY878 @ SV257 @ SV58 @ SV132 ) ) )
= $false )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV58 @ ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2046]) ).
thf(2092,plain,
! [SV58: $i > $o,SV257: $i,SV132: $i > $o] :
( ( ( ~ ! [SY1068: $i] :
( ~ ( SV132 @ SY1068 )
| ( ( sK107_SY878 @ SV257 @ SV58 @ SV132 )
= SY1068 ) ) )
= $false )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV58 @ ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2046]) ).
thf(2093,plain,
! [SV58: $i > $o,SV257: $i,SV132: $i > $o] :
( ( ( SV132 @ ( sK101_SY878 @ SV257 @ SV58 @ SV132 ) )
= $true )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV257
= ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2047]) ).
thf(2094,plain,
! [SV58: $i > $o,SV257: $i,SV132: $i > $o] :
( ( ( ! [SY1062: $i] :
( ~ ( SV132 @ SY1062 )
| ( ( sK101_SY878 @ SV257 @ SV58 @ SV132 )
= SY1062 ) ) )
= $true )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV257
= ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2048]) ).
thf(2095,plain,
! [SV132: $i > $o,SV258: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ ( sK108_SY736 @ SV258 @ SV132 @ SV58 ) ) )
= $false )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV132 @ ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2049]) ).
thf(2096,plain,
! [SV132: $i > $o,SV258: $i,SV58: $i > $o] :
( ( ( ~ ! [SY1069: $i] :
( ~ ( SV58 @ SY1069 )
| ( ( sK108_SY736 @ SV258 @ SV132 @ SV58 )
= SY1069 ) ) )
= $false )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV132 @ ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2049]) ).
thf(2097,plain,
! [SV132: $i > $o,SV258: $i,SV58: $i > $o] :
( ( ( SV58 @ ( sK102_SY736 @ SV258 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV258
= ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2050]) ).
thf(2098,plain,
! [SV132: $i > $o,SV258: $i,SV58: $i > $o] :
( ( ( ! [SY1063: $i] :
( ~ ( SV58 @ SY1063 )
| ( ( sK102_SY736 @ SV258 @ SV132 @ SV58 )
= SY1063 ) ) )
= $true )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV258
= ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2051]) ).
thf(2099,plain,
! [SV58: $i > $o,SV251: $i,SV132: $i > $o] :
( ( ( SV132 @ ( sK103_SY878 @ SV251 @ SV58 @ SV132 ) )
= $true )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV58 @ ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2052]) ).
thf(2100,plain,
! [SV58: $i > $o,SV251: $i,SV132: $i > $o] :
( ( ( ! [SY1064: $i] :
( ~ ( SV132 @ SY1064 )
| ( ( sK103_SY878 @ SV251 @ SV58 @ SV132 )
= SY1064 ) ) )
= $true )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV58 @ ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2053]) ).
thf(2101,plain,
! [SV58: $i > $o,SV251: $i,SV284: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV284 )
| ( ( sK95_SY878 @ SV251 @ SV58 @ SV132 )
= SV284 ) )
= $true )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV251
= ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2102,plain,
! [SV132: $i > $o,SV252: $i,SV58: $i > $o] :
( ( ( SV58 @ ( sK104_SY736 @ SV252 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV132 @ ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2056]) ).
thf(2103,plain,
! [SV132: $i > $o,SV252: $i,SV58: $i > $o] :
( ( ( ! [SY1065: $i] :
( ~ ( SV58 @ SY1065 )
| ( ( sK104_SY736 @ SV252 @ SV132 @ SV58 )
= SY1065 ) ) )
= $true )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV132 @ ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2057]) ).
thf(2104,plain,
! [SV132: $i > $o,SV252: $i,SV285: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV285 )
| ( ( sK96_SY736 @ SV252 @ SV132 @ SV58 )
= SV285 ) )
= $true )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV252
= ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2105,plain,
! [SV58: $i > $o,SV253: $i,SV132: $i > $o] :
( ( ( SV132 @ ( sK105_SY878 @ SV253 @ SV58 @ SV132 ) )
= $true )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV58 @ ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2060]) ).
thf(2106,plain,
! [SV58: $i > $o,SV253: $i,SV132: $i > $o] :
( ( ( ! [SY1066: $i] :
( ~ ( SV132 @ SY1066 )
| ( ( sK105_SY878 @ SV253 @ SV58 @ SV132 )
= SY1066 ) ) )
= $true )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV58 @ ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2061]) ).
thf(2107,plain,
! [SV58: $i > $o,SV253: $i,SV286: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV286 )
| ( ( sK97_SY878 @ SV253 @ SV58 @ SV132 )
= SV286 ) )
= $true )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV253
= ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2108,plain,
! [SV132: $i > $o,SV254: $i,SV58: $i > $o] :
( ( ( SV58 @ ( sK106_SY736 @ SV254 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV132 @ ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2064]) ).
thf(2109,plain,
! [SV132: $i > $o,SV254: $i,SV58: $i > $o] :
( ( ( ! [SY1067: $i] :
( ~ ( SV58 @ SY1067 )
| ( ( sK106_SY736 @ SV254 @ SV132 @ SV58 )
= SY1067 ) ) )
= $true )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV132 @ ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2065]) ).
thf(2110,plain,
! [SV132: $i > $o,SV254: $i,SV287: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV287 )
| ( ( sK98_SY736 @ SV254 @ SV132 @ SV58 )
= SV287 ) )
= $true )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV254
= ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2111,plain,
! [SV58: $i > $o,SV247: $i,SV288: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV288 )
| ( ( sK99_SY878 @ SV247 @ SV58 @ SV132 )
= SV288 ) )
= $true )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV58 @ ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2112,plain,
! [SV58: $i > $o,SV247: $i,SV280: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV280 ) )
= $true )
| ( ( ( sK92_SY878 @ SV247 @ SV58 @ SV132 )
= SV280 )
= $true )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV247
= ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2070]) ).
thf(2113,plain,
! [SV132: $i > $o,SV248: $i,SV289: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV289 )
| ( ( sK100_SY736 @ SV248 @ SV132 @ SV58 )
= SV289 ) )
= $true )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV132 @ ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2114,plain,
! [SV132: $i > $o,SV248: $i,SV281: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV281 ) )
= $true )
| ( ( ( sK93_SY736 @ SV248 @ SV132 @ SV58 )
= SV281 )
= $true )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV248
= ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2073]) ).
thf(2115,plain,
! [SV61: $i,SV199: $i,SV242: $i] :
( ( ( in @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) @ ( sK2_SY743 @ SV61 ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2074]) ).
thf(2116,plain,
! [SV242: $i,SV199: $i,SV61: $i] :
( ( ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SV199 )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2075]) ).
thf(2117,plain,
! [SV61: $i,SV199: $i,SV242: $i,SV290: $i] :
( ( ( ~ ~ ( ~ ( in @ SV290 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
| ~ ( in @ SV290 @ SV199 ) ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2118,plain,
! [SV61: $i,SV199: $i,SV242: $i,SV277: $i,SV282: $i] :
( ( ( ~ ( in @ SV282 @ SV277 ) )
= $true )
| ( ( in @ SV282 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
= $true )
| ( ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SV277 )
= $true )
| ( ( in @ SV277 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2077]) ).
thf(2119,plain,
! [SV61: $i,SV199: $i,SV235: $i,SV283: $i] :
( ( ( ~ ( ~ ( in @ SV283 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
| ~ ( in @ SV283 @ SV199 ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2120,plain,
! [SV61: $i,SV199: $i,SV235: $i,SV271: $i,SV279: $i] :
( ( ( in @ SV279 @ SV271 )
= $false )
| ( ( in @ SV279 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
= $true )
| ( ( in @ ( sK76_SY1022 @ SV61 @ SV199 @ SV235 ) @ SV271 )
= $true )
| ( ( in @ SV271 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2081]) ).
thf(2121,plain,
! [SV241: $i,SV56: $i > $o,SV278: $i,SV130: $i > $o] :
( ( ( ! [SY1061: $i] :
( ~ ( SV130 @ SY1061 )
| ( SV278 = SY1061 ) ) )
= $false )
| ( ( SV130 @ SV278 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV56 @ ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2082]) ).
thf(2122,plain,
! [SV272: $i,SV56: $i > $o,SV241: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK113_SY1051 @ SV241 @ SV56 @ SV272 @ SV130 ) )
| ( SV272
= ( sK113_SY1051 @ SV241 @ SV56 @ SV272 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV272 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV241
= ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2083]) ).
thf(2123,plain,
! [SV273: $i,SV56: $i > $o,SV233: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK114_SY1052 @ SV233 @ SV56 @ SV273 @ SV130 ) )
| ( SV273
= ( sK114_SY1052 @ SV233 @ SV56 @ SV273 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV273 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV56 @ ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2084]) ).
thf(2124,plain,
! [SV266: $i,SV56: $i > $o,SV233: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK110_SY1045 @ SV233 @ SV56 @ SV266 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV266 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV233
= ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2085]) ).
thf(2125,plain,
! [SV130: $i > $o,SV56: $i > $o,SV233: $i,SV266: $i] :
( ( ( SV266
= ( sK110_SY1045 @ SV233 @ SV56 @ SV266 @ SV130 ) )
= $false )
| ( ( SV130 @ SV266 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV233
= ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2085]) ).
thf(2126,plain,
! [SV274: $i,SV56: $i > $o,SV234: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK115_SY1053 @ SV234 @ SV56 @ SV274 @ SV130 ) )
| ( SV274
= ( sK115_SY1053 @ SV234 @ SV56 @ SV274 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV274 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV56 @ ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2086]) ).
thf(2127,plain,
! [SV267: $i,SV56: $i > $o,SV234: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK111_SY1046 @ SV234 @ SV56 @ SV267 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV267 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV234
= ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2087]) ).
thf(2128,plain,
! [SV130: $i > $o,SV56: $i > $o,SV234: $i,SV267: $i] :
( ( ( SV267
= ( sK111_SY1046 @ SV234 @ SV56 @ SV267 @ SV130 ) )
= $false )
| ( ( SV130 @ SV267 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV234
= ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2087]) ).
thf(2129,plain,
! [SV268: $i,SV56: $i > $o,SV229: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK112_SY1047 @ SV229 @ SV56 @ SV268 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV268 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV56 @ ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2088]) ).
thf(2130,plain,
! [SV130: $i > $o,SV56: $i > $o,SV229: $i,SV268: $i] :
( ( ( SV268
= ( sK112_SY1047 @ SV229 @ SV56 @ SV268 @ SV130 ) )
= $false )
| ( ( SV130 @ SV268 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV56 @ ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2088]) ).
thf(2131,plain,
! [SV265: $i,SV56: $i > $o,SV229: $i,SV130: $i > $o] :
( ( ( SV130 @ ( sK109_SY1044 @ SV229 @ SV56 @ SV265 @ SV130 ) )
= $true )
| ( ( SV130 @ SV265 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV229
= ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2089]) ).
thf(2132,plain,
! [SV58: $i > $o,SV257: $i,SV132: $i > $o] :
( ( ( SV132 @ ( sK107_SY878 @ SV257 @ SV58 @ SV132 ) )
= $true )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV58 @ ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2091]) ).
thf(2133,plain,
! [SV58: $i > $o,SV257: $i,SV132: $i > $o] :
( ( ( ! [SY1068: $i] :
( ~ ( SV132 @ SY1068 )
| ( ( sK107_SY878 @ SV257 @ SV58 @ SV132 )
= SY1068 ) ) )
= $true )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV58 @ ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2092]) ).
thf(2134,plain,
! [SV58: $i > $o,SV257: $i,SV291: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV291 )
| ( ( sK101_SY878 @ SV257 @ SV58 @ SV132 )
= SV291 ) )
= $true )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV257
= ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2135,plain,
! [SV132: $i > $o,SV258: $i,SV58: $i > $o] :
( ( ( SV58 @ ( sK108_SY736 @ SV258 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV132 @ ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2095]) ).
thf(2136,plain,
! [SV132: $i > $o,SV258: $i,SV58: $i > $o] :
( ( ( ! [SY1069: $i] :
( ~ ( SV58 @ SY1069 )
| ( ( sK108_SY736 @ SV258 @ SV132 @ SV58 )
= SY1069 ) ) )
= $true )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV132 @ ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2096]) ).
thf(2137,plain,
! [SV132: $i > $o,SV258: $i,SV292: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV292 )
| ( ( sK102_SY736 @ SV258 @ SV132 @ SV58 )
= SV292 ) )
= $true )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV258
= ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2138,plain,
! [SV58: $i > $o,SV251: $i,SV293: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV293 )
| ( ( sK103_SY878 @ SV251 @ SV58 @ SV132 )
= SV293 ) )
= $true )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV58 @ ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2139,plain,
! [SV58: $i > $o,SV251: $i,SV284: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV284 ) )
= $true )
| ( ( ( sK95_SY878 @ SV251 @ SV58 @ SV132 )
= SV284 )
= $true )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV251
= ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2101]) ).
thf(2140,plain,
! [SV132: $i > $o,SV252: $i,SV294: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV294 )
| ( ( sK104_SY736 @ SV252 @ SV132 @ SV58 )
= SV294 ) )
= $true )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV132 @ ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2141,plain,
! [SV132: $i > $o,SV252: $i,SV285: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV285 ) )
= $true )
| ( ( ( sK96_SY736 @ SV252 @ SV132 @ SV58 )
= SV285 )
= $true )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV252
= ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2104]) ).
thf(2142,plain,
! [SV58: $i > $o,SV253: $i,SV295: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV295 )
| ( ( sK105_SY878 @ SV253 @ SV58 @ SV132 )
= SV295 ) )
= $true )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV58 @ ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2143,plain,
! [SV58: $i > $o,SV253: $i,SV286: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV286 ) )
= $true )
| ( ( ( sK97_SY878 @ SV253 @ SV58 @ SV132 )
= SV286 )
= $true )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV253
= ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2107]) ).
thf(2144,plain,
! [SV132: $i > $o,SV254: $i,SV296: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV296 )
| ( ( sK106_SY736 @ SV254 @ SV132 @ SV58 )
= SV296 ) )
= $true )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV132 @ ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2145,plain,
! [SV132: $i > $o,SV254: $i,SV287: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV287 ) )
= $true )
| ( ( ( sK98_SY736 @ SV254 @ SV132 @ SV58 )
= SV287 )
= $true )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV254
= ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2110]) ).
thf(2146,plain,
! [SV58: $i > $o,SV247: $i,SV288: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV288 ) )
= $true )
| ( ( ( sK99_SY878 @ SV247 @ SV58 @ SV132 )
= SV288 )
= $true )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV58 @ ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2111]) ).
thf(2147,plain,
! [SV58: $i > $o,SV247: $i,SV280: $i,SV132: $i > $o] :
( ( ( SV132 @ SV280 )
= $false )
| ( ( ( sK92_SY878 @ SV247 @ SV58 @ SV132 )
= SV280 )
= $true )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV247
= ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2112]) ).
thf(2148,plain,
! [SV132: $i > $o,SV248: $i,SV289: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV289 ) )
= $true )
| ( ( ( sK100_SY736 @ SV248 @ SV132 @ SV58 )
= SV289 )
= $true )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV132 @ ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2113]) ).
thf(2149,plain,
! [SV132: $i > $o,SV248: $i,SV281: $i,SV58: $i > $o] :
( ( ( SV58 @ SV281 )
= $false )
| ( ( ( sK93_SY736 @ SV248 @ SV132 @ SV58 )
= SV281 )
= $true )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV248
= ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2150,plain,
! [SV61: $i,SV199: $i,SV242: $i,SV290: $i] :
( ( ( ~ ( ~ ( in @ SV290 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
| ~ ( in @ SV290 @ SV199 ) ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2117]) ).
thf(2151,plain,
! [SV61: $i,SV199: $i,SV242: $i,SV277: $i,SV282: $i] :
( ( ( in @ SV282 @ SV277 )
= $false )
| ( ( in @ SV282 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
= $true )
| ( ( in @ ( sK80_SY1028 @ SV61 @ SV199 @ SV242 ) @ SV277 )
= $true )
| ( ( in @ SV277 @ ( sK2_SY743 @ SV61 ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2152,plain,
! [SV61: $i,SV199: $i,SV235: $i,SV283: $i] :
( ( ( ~ ( in @ SV283 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
| ~ ( in @ SV283 @ SV199 ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2119]) ).
thf(2153,plain,
! [SV278: $i,SV56: $i > $o,SV241: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK116_SY1061 @ SV241 @ SV56 @ SV278 @ SV130 ) )
| ( SV278
= ( sK116_SY1061 @ SV241 @ SV56 @ SV278 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV278 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV56 @ ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2121]) ).
thf(2154,plain,
! [SV272: $i,SV56: $i > $o,SV241: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK113_SY1051 @ SV241 @ SV56 @ SV272 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV272 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV241
= ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2122]) ).
thf(2155,plain,
! [SV130: $i > $o,SV56: $i > $o,SV241: $i,SV272: $i] :
( ( ( SV272
= ( sK113_SY1051 @ SV241 @ SV56 @ SV272 @ SV130 ) )
= $false )
| ( ( SV130 @ SV272 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV241
= ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2122]) ).
thf(2156,plain,
! [SV273: $i,SV56: $i > $o,SV233: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK114_SY1052 @ SV233 @ SV56 @ SV273 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV273 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV56 @ ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2123]) ).
thf(2157,plain,
! [SV130: $i > $o,SV56: $i > $o,SV233: $i,SV273: $i] :
( ( ( SV273
= ( sK114_SY1052 @ SV233 @ SV56 @ SV273 @ SV130 ) )
= $false )
| ( ( SV130 @ SV273 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV56 @ ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2123]) ).
thf(2158,plain,
! [SV266: $i,SV56: $i > $o,SV233: $i,SV130: $i > $o] :
( ( ( SV130 @ ( sK110_SY1045 @ SV233 @ SV56 @ SV266 @ SV130 ) )
= $true )
| ( ( SV130 @ SV266 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV233
= ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2124]) ).
thf(2159,plain,
! [SV274: $i,SV56: $i > $o,SV234: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK115_SY1053 @ SV234 @ SV56 @ SV274 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV274 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV56 @ ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2126]) ).
thf(2160,plain,
! [SV130: $i > $o,SV56: $i > $o,SV234: $i,SV274: $i] :
( ( ( SV274
= ( sK115_SY1053 @ SV234 @ SV56 @ SV274 @ SV130 ) )
= $false )
| ( ( SV130 @ SV274 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV56 @ ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2126]) ).
thf(2161,plain,
! [SV267: $i,SV56: $i > $o,SV234: $i,SV130: $i > $o] :
( ( ( SV130 @ ( sK111_SY1046 @ SV234 @ SV56 @ SV267 @ SV130 ) )
= $true )
| ( ( SV130 @ SV267 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV234
= ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2127]) ).
thf(2162,plain,
! [SV268: $i,SV56: $i > $o,SV229: $i,SV130: $i > $o] :
( ( ( SV130 @ ( sK112_SY1047 @ SV229 @ SV56 @ SV268 @ SV130 ) )
= $true )
| ( ( SV130 @ SV268 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV229 )
= $false )
| ( ( SV56 @ ( sK70_SY1004 @ SV130 @ SV229 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2129]) ).
thf(2163,plain,
! [SV58: $i > $o,SV257: $i,SV297: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV297 )
| ( ( sK107_SY878 @ SV257 @ SV58 @ SV132 )
= SV297 ) )
= $true )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV58 @ ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2133]) ).
thf(2164,plain,
! [SV58: $i > $o,SV257: $i,SV291: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV291 ) )
= $true )
| ( ( ( sK101_SY878 @ SV257 @ SV58 @ SV132 )
= SV291 )
= $true )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV257
= ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2134]) ).
thf(2165,plain,
! [SV132: $i > $o,SV258: $i,SV298: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV298 )
| ( ( sK108_SY736 @ SV258 @ SV132 @ SV58 )
= SV298 ) )
= $true )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV132 @ ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2166,plain,
! [SV132: $i > $o,SV258: $i,SV292: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV292 ) )
= $true )
| ( ( ( sK102_SY736 @ SV258 @ SV132 @ SV58 )
= SV292 )
= $true )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV258
= ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2137]) ).
thf(2167,plain,
! [SV58: $i > $o,SV251: $i,SV293: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV293 ) )
= $true )
| ( ( ( sK103_SY878 @ SV251 @ SV58 @ SV132 )
= SV293 )
= $true )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV58 @ ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2138]) ).
thf(2168,plain,
! [SV58: $i > $o,SV251: $i,SV284: $i,SV132: $i > $o] :
( ( ( SV132 @ SV284 )
= $false )
| ( ( ( sK95_SY878 @ SV251 @ SV58 @ SV132 )
= SV284 )
= $true )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV251
= ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2169,plain,
! [SV132: $i > $o,SV252: $i,SV294: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV294 ) )
= $true )
| ( ( ( sK104_SY736 @ SV252 @ SV132 @ SV58 )
= SV294 )
= $true )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV132 @ ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2140]) ).
thf(2170,plain,
! [SV132: $i > $o,SV252: $i,SV285: $i,SV58: $i > $o] :
( ( ( SV58 @ SV285 )
= $false )
| ( ( ( sK96_SY736 @ SV252 @ SV132 @ SV58 )
= SV285 )
= $true )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV252
= ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2171,plain,
! [SV58: $i > $o,SV253: $i,SV295: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV295 ) )
= $true )
| ( ( ( sK105_SY878 @ SV253 @ SV58 @ SV132 )
= SV295 )
= $true )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV58 @ ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2142]) ).
thf(2172,plain,
! [SV58: $i > $o,SV253: $i,SV286: $i,SV132: $i > $o] :
( ( ( SV132 @ SV286 )
= $false )
| ( ( ( sK97_SY878 @ SV253 @ SV58 @ SV132 )
= SV286 )
= $true )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV253
= ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2143]) ).
thf(2173,plain,
! [SV132: $i > $o,SV254: $i,SV296: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV296 ) )
= $true )
| ( ( ( sK106_SY736 @ SV254 @ SV132 @ SV58 )
= SV296 )
= $true )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV132 @ ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2144]) ).
thf(2174,plain,
! [SV132: $i > $o,SV254: $i,SV287: $i,SV58: $i > $o] :
( ( ( SV58 @ SV287 )
= $false )
| ( ( ( sK98_SY736 @ SV254 @ SV132 @ SV58 )
= SV287 )
= $true )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV254
= ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2175,plain,
! [SV58: $i > $o,SV247: $i,SV288: $i,SV132: $i > $o] :
( ( ( SV132 @ SV288 )
= $false )
| ( ( ( sK99_SY878 @ SV247 @ SV58 @ SV132 )
= SV288 )
= $true )
| ( ( SV58 @ SV247 )
= $false )
| ( ( SV58 @ ( sK82_SY1016 @ SV132 @ SV247 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2146]) ).
thf(2176,plain,
! [SV132: $i > $o,SV248: $i,SV289: $i,SV58: $i > $o] :
( ( ( SV58 @ SV289 )
= $false )
| ( ( ( sK100_SY736 @ SV248 @ SV132 @ SV58 )
= SV289 )
= $true )
| ( ( SV132 @ SV248 )
= $false )
| ( ( SV132 @ ( sK83_SY1017 @ SV58 @ SV248 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2148]) ).
thf(2177,plain,
! [SV61: $i,SV199: $i,SV242: $i,SV290: $i] :
( ( ( ~ ( in @ SV290 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
| ~ ( in @ SV290 @ SV199 ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2150]) ).
thf(2178,plain,
! [SV61: $i,SV199: $i,SV235: $i,SV283: $i] :
( ( ( ~ ( in @ SV283 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) ) )
= $true )
| ( ( ~ ( in @ SV283 @ SV199 ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2152]) ).
thf(2179,plain,
! [SV278: $i,SV56: $i > $o,SV241: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK116_SY1061 @ SV241 @ SV56 @ SV278 @ SV130 ) ) )
= $false )
| ( ( SV130 @ SV278 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV56 @ ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2153]) ).
thf(2180,plain,
! [SV130: $i > $o,SV56: $i > $o,SV241: $i,SV278: $i] :
( ( ( SV278
= ( sK116_SY1061 @ SV241 @ SV56 @ SV278 @ SV130 ) )
= $false )
| ( ( SV130 @ SV278 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV56 @ ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2153]) ).
thf(2181,plain,
! [SV272: $i,SV56: $i > $o,SV241: $i,SV130: $i > $o] :
( ( ( SV130 @ ( sK113_SY1051 @ SV241 @ SV56 @ SV272 @ SV130 ) )
= $true )
| ( ( SV130 @ SV272 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV241
= ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $false )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2154]) ).
thf(2182,plain,
! [SV273: $i,SV56: $i > $o,SV233: $i,SV130: $i > $o] :
( ( ( SV130 @ ( sK114_SY1052 @ SV233 @ SV56 @ SV273 @ SV130 ) )
= $true )
| ( ( SV130 @ SV273 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV233 )
= $false )
| ( ( SV56 @ ( sK71_SY1009 @ SV130 @ SV233 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2156]) ).
thf(2183,plain,
! [SV274: $i,SV56: $i > $o,SV234: $i,SV130: $i > $o] :
( ( ( SV130 @ ( sK115_SY1053 @ SV234 @ SV56 @ SV274 @ SV130 ) )
= $true )
| ( ( SV130 @ SV274 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV234 )
= $false )
| ( ( SV56 @ ( sK72_SY1010 @ SV130 @ SV234 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $false )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2159]) ).
thf(2184,plain,
! [SV58: $i > $o,SV257: $i,SV297: $i,SV132: $i > $o] :
( ( ( ~ ( SV132 @ SV297 ) )
= $true )
| ( ( ( sK107_SY878 @ SV257 @ SV58 @ SV132 )
= SV297 )
= $true )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV58 @ ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2163]) ).
thf(2185,plain,
! [SV58: $i > $o,SV257: $i,SV291: $i,SV132: $i > $o] :
( ( ( SV132 @ SV291 )
= $false )
| ( ( ( sK101_SY878 @ SV257 @ SV58 @ SV132 )
= SV291 )
= $true )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV257
= ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2164]) ).
thf(2186,plain,
! [SV132: $i > $o,SV258: $i,SV298: $i,SV58: $i > $o] :
( ( ( ~ ( SV58 @ SV298 ) )
= $true )
| ( ( ( sK108_SY736 @ SV258 @ SV132 @ SV58 )
= SV298 )
= $true )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV132 @ ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2165]) ).
thf(2187,plain,
! [SV132: $i > $o,SV258: $i,SV292: $i,SV58: $i > $o] :
( ( ( SV58 @ SV292 )
= $false )
| ( ( ( sK102_SY736 @ SV258 @ SV132 @ SV58 )
= SV292 )
= $true )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV258
= ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $false )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2166]) ).
thf(2188,plain,
! [SV58: $i > $o,SV251: $i,SV293: $i,SV132: $i > $o] :
( ( ( SV132 @ SV293 )
= $false )
| ( ( ( sK103_SY878 @ SV251 @ SV58 @ SV132 )
= SV293 )
= $true )
| ( ( SV58 @ SV251 )
= $false )
| ( ( SV58 @ ( sK85_SY1018 @ SV132 @ SV251 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2167]) ).
thf(2189,plain,
! [SV132: $i > $o,SV252: $i,SV294: $i,SV58: $i > $o] :
( ( ( SV58 @ SV294 )
= $false )
| ( ( ( sK104_SY736 @ SV252 @ SV132 @ SV58 )
= SV294 )
= $true )
| ( ( SV132 @ SV252 )
= $false )
| ( ( SV132 @ ( sK86_SY1019 @ SV58 @ SV252 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2169]) ).
thf(2190,plain,
! [SV58: $i > $o,SV253: $i,SV295: $i,SV132: $i > $o] :
( ( ( SV132 @ SV295 )
= $false )
| ( ( ( sK105_SY878 @ SV253 @ SV58 @ SV132 )
= SV295 )
= $true )
| ( ( SV58 @ SV253 )
= $false )
| ( ( SV58 @ ( sK87_SY1020 @ SV132 @ SV253 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2171]) ).
thf(2191,plain,
! [SV132: $i > $o,SV254: $i,SV296: $i,SV58: $i > $o] :
( ( ( SV58 @ SV296 )
= $false )
| ( ( ( sK106_SY736 @ SV254 @ SV132 @ SV58 )
= SV296 )
= $true )
| ( ( SV132 @ SV254 )
= $false )
| ( ( SV132 @ ( sK88_SY1021 @ SV58 @ SV254 @ SV132 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $false )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2173]) ).
thf(2192,plain,
! [SV61: $i,SV199: $i,SV242: $i,SV290: $i] :
( ( ( ~ ( in @ SV290 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) ) )
= $true )
| ( ( ~ ( in @ SV290 @ SV199 ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2177]) ).
thf(2193,plain,
! [SV61: $i,SV199: $i,SV235: $i,SV283: $i] :
( ( ( in @ SV283 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
= $false )
| ( ( ~ ( in @ SV283 @ SV199 ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2178]) ).
thf(2194,plain,
! [SV278: $i,SV56: $i > $o,SV241: $i,SV130: $i > $o] :
( ( ( SV130 @ ( sK116_SY1061 @ SV241 @ SV56 @ SV278 @ SV130 ) )
= $true )
| ( ( SV130 @ SV278 )
= $false )
| ( ( ( descr
@ ^ [SY724: $i] : ( SV56 @ SY724 ) )
= ( descr
@ ^ [SY873: $i] : ( SV130 @ SY873 ) ) )
= $true )
| ( ( SV56 @ SV241 )
= $false )
| ( ( SV56 @ ( sK77_SY1013 @ SV130 @ SV241 @ SV56 ) )
= $true )
| ( ( SV56 @ ( sK9_SY866 @ SV130 @ SV56 ) )
= $true )
| ( ( SV130 @ ( sK15_SY946 @ SV56 @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2179]) ).
thf(2195,plain,
! [SV58: $i > $o,SV257: $i,SV297: $i,SV132: $i > $o] :
( ( ( SV132 @ SV297 )
= $false )
| ( ( ( sK107_SY878 @ SV257 @ SV58 @ SV132 )
= SV297 )
= $true )
| ( ( SV58 @ SV257 )
= $false )
| ( ( SV58 @ ( sK89_SY1026 @ SV132 @ SV257 @ SV58 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2184]) ).
thf(2196,plain,
! [SV132: $i > $o,SV258: $i,SV298: $i,SV58: $i > $o] :
( ( ( SV58 @ SV298 )
= $false )
| ( ( ( sK108_SY736 @ SV258 @ SV132 @ SV58 )
= SV298 )
= $true )
| ( ( SV132 @ SV258 )
= $false )
| ( ( SV132 @ ( sK90_SY1027 @ SV58 @ SV258 @ SV132 ) )
= $true )
| ( ( SV58 @ ( sK10_SY874 @ SV132 @ SV58 ) )
= $true )
| ( ( SV132 @ ( sK16_SY947 @ SV58 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2186]) ).
thf(2197,plain,
! [SV61: $i,SV199: $i,SV242: $i,SV290: $i] :
( ( ( in @ SV290 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
= $false )
| ( ( ~ ( in @ SV290 @ SV199 ) )
= $true )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2198,plain,
! [SV61: $i,SV235: $i,SV199: $i,SV283: $i] :
( ( ( in @ SV283 @ SV199 )
= $false )
| ( ( in @ SV283 @ ( sK68_SY961 @ SV235 @ SV199 @ SV61 ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV61 )
= $false )
| ( ( in @ SV235 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2193]) ).
thf(2199,plain,
! [SV61: $i,SV242: $i,SV199: $i,SV290: $i] :
( ( ( in @ SV290 @ SV199 )
= $false )
| ( ( in @ SV290 @ ( sK69_SY961 @ SV242 @ SV199 @ SV61 ) )
= $false )
| ( ( in @ ( sK51_SY959 @ SV61 @ SV199 ) @ SV199 )
= $true )
| ( ( in @ SV242 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2197]) ).
thf(2200,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[122,2199,2198,2196,2195,2194,2191,2190,2189,2188,2187,2185,2183,2182,2181,2180,2176,2175,2174,2172,2170,2168,2162,2161,2160,2158,2157,2155,2151,2149,2147,2135,2132,2131,2130,2128,2125,2120,2116,2115,2108,2105,2102,2099,2097,2093,2090,2079,2078,2071,2068,2066,2062,2058,2054,2030,2028,2024,1991,1990,1970,1969,1960,1959,1952,1933,1931,1921,1920,1918,1916,1915,1879,1875,1874,1846,1843,1807,1803,1749,1720,1692,1664,1663,1635,1634,1633,1632,1601,1600,1599,1598,1597,1596,1595,1588,1567,1560,1558,1556,1555,1547,1545,1522,1521,1520,1507,1501,1491,1473,1464,1463,1460,1456,1455,1417,1414,1411,1407,1405,1346,1345,1312,1309,1306,1303,1302,1297,1296,1266,1262,1258,1257,1256,1254,1250,1221,1220,1219,1217,1208,1197,1195,1194,1178,1163,1162,1160,1159,1157,1156,1152,1151,1150,1137,1129,1113,1109,1096,1095,1092,1089,1072,1071,1047,1046,1025,1015,1012,1011,1010,990,984,983,966,960,959,955,953,952,950,949,947,946,945,903,899,898,883,879,878,877,865,837,818,814,812,791,785,778,777,774,769,761,759,750,740,722,712,710,695,694,688,679,671,664,637,630,626,617,612,609,608,607,602,601,599,594,589,581,566,558,556,550,549,548,543,522,519,518,517,507,506,505,504,377,376,375,374,373,372,371,281,280,279,276,275,188,164,126]) ).
thf(2201,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU578^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n026.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:31:02 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.05/2.95
% 16.05/2.95 No.of.Axioms: 0
% 16.05/2.95
% 16.05/2.95 Length.of.Defs: 19419
% 16.05/2.95
% 16.05/2.95 Contains.Choice.Funs: true
% 16.05/2.95 .........................................................................
% 16.05/2.95
% 16.05/2.95 ********************************
% 16.05/2.95 * All subproblems solved! *
% 16.05/2.95 ********************************
% 16.05/2.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:94,ps:0,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:2200,loop_count:0,foatp_calls:1,translation:fof_full)
% 16.05/2.95
% 16.05/2.95 %**** Beginning of derivation protocol ****
% 16.05/2.95 % SZS output start CNFRefutation
% See solution above
% 16.05/2.96
% 16.05/2.96 %**** End of derivation protocol ****
% 16.05/2.96 %**** no. of clauses in derivation: 2201 ****
% 16.05/2.96 %**** clause counter: 2200 ****
% 16.05/2.96
% 16.05/2.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:94,ps:0,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:2200,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------