%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU650^1 : 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 : n016.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 10:45:54 AM UTC 2026
% Result : Theorem 219.11s 36.82s
% Output : CNFRefutation 219.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 173
% Syntax : Number of formulae : 3202 (1092 unt; 0 typ; 172 def)
% Number of atoms : 25401 (10729 equ; 0 cnn)
% Maximal formula atoms : 168 ( 7 avg)
% Number of connectives : 59176 (12363 ~;9534 |; 220 &;35520 @)
% ( 56 <=>;1483 =>; 0 <=; 0 <~>)
% Maximal formula depth : 170 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1990 (1990 >; 0 *; 0 +; 0 <<)
% Number of symbols : 346 ( 343 usr; 172 con; 0-4 aty)
% Number of variables : 12738 (1111 ^;11403 !; 224 ?;12738 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_atleast2p,type,
atleast2p: $i > $o ).
thf(tp_atmost1p,type,
atmost1p: $i > $o ).
thf(tp_atmost2p,type,
atmost2p: $i > $o ).
thf(tp_binintersect,type,
binintersect: $i > $i > $i ).
thf(tp_binintersectEL,type,
binintersectEL: $o ).
thf(tp_binintersectER,type,
binintersectER: $o ).
thf(tp_binintersectI,type,
binintersectI: $o ).
thf(tp_binintersectLsub,type,
binintersectLsub: $o ).
thf(tp_binintersectRsub,type,
binintersectRsub: $o ).
thf(tp_binintersectSubset1,type,
binintersectSubset1: $o ).
thf(tp_binintersectSubset2,type,
binintersectSubset2: $o ).
thf(tp_binintersectSubset3,type,
binintersectSubset3: $o ).
thf(tp_binintersectSubset4,type,
binintersectSubset4: $o ).
thf(tp_binintersectSubset5,type,
binintersectSubset5: $o ).
thf(tp_binunion,type,
binunion: $i > $i > $i ).
thf(tp_binunionE,type,
binunionE: $o ).
thf(tp_binunionEcases,type,
binunionEcases: $o ).
thf(tp_binunionIL,type,
binunionIL: $o ).
thf(tp_binunionIR,type,
binunionIR: $o ).
thf(tp_binunionLsub,type,
binunionLsub: $o ).
thf(tp_binunionRsub,type,
binunionRsub: $o ).
thf(tp_bs114d,type,
bs114d: $o ).
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_cartprodfstin,type,
cartprodfstin: $o ).
thf(tp_cartprodmempair,type,
cartprodmempair: $o ).
thf(tp_cartprodmempair1,type,
cartprodmempair1: $o ).
thf(tp_cartprodpairin,type,
cartprodpairin: $o ).
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_disjointsetsI1,type,
disjointsetsI1: $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_ex1,type,
ex1: $i > ( $i > $o ) > $o ).
thf(tp_ex1E1,type,
ex1E1: $o ).
thf(tp_ex1I,type,
ex1I: $o ).
thf(tp_ex1I2,type,
ex1I2: $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_inPowerset,type,
inPowerset: $o ).
thf(tp_in__Cong,type,
in__Cong: $o ).
thf(tp_iskpair,type,
iskpair: $i > $o ).
thf(tp_kfst,type,
kfst: $i > $i ).
thf(tp_kfstpairEq,type,
kfstpairEq: $o ).
thf(tp_kfstsingleton,type,
kfstsingleton: $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_kpairiskpair,type,
kpairiskpair: $o ).
thf(tp_kpairp,type,
kpairp: $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_powersetsubset,type,
powersetsubset: $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_regular,type,
regular: $i > $o ).
thf(tp_replAx,type,
replAx: $o ).
thf(tp_sK100_SY1533,type,
sK100_SY1533: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK101_SY1731,type,
sK101_SY1731: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK102_SY1715,type,
sK102_SY1715: $i > $i > $i > $i ).
thf(tp_sK103_SY1754,type,
sK103_SY1754: $i > $i > $i > $i ).
thf(tp_sK104_SY1517,type,
sK104_SY1517: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK105_SY1253,type,
sK105_SY1253: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK106_SY1739,type,
sK106_SY1739: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK107_SY1740,type,
sK107_SY1740: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK108_SY1770,type,
sK108_SY1770: $i > $i > $i > $i ).
thf(tp_sK109_SY1517,type,
sK109_SY1517: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK10_SY1478,type,
sK10_SY1478: ( $i > $o ) > $i > $i ).
thf(tp_sK110_SY1253,type,
sK110_SY1253: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK111_SY1745,type,
sK111_SY1745: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK112_SY1741,type,
sK112_SY1741: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK113_SY1750,type,
sK113_SY1750: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK114_SY1751,type,
sK114_SY1751: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK115_SY1746,type,
sK115_SY1746: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK116_SY1762,type,
sK116_SY1762: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK117_SY1763,type,
sK117_SY1763: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK118_SY1764,type,
sK118_SY1764: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK119_SY1765,type,
sK119_SY1765: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK11_SY1480,type,
sK11_SY1480: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK120_SY1776,type,
sK120_SY1776: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK121_SY1777,type,
sK121_SY1777: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK122_SY1517,type,
sK122_SY1517: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK123_SY1253,type,
sK123_SY1253: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK124_SY1780,type,
sK124_SY1780: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK125_SY1517,type,
sK125_SY1517: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK126_SY1253,type,
sK126_SY1253: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK127_SY1517,type,
sK127_SY1517: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK128_SY1253,type,
sK128_SY1253: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK129_SY1517,type,
sK129_SY1517: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK12_SY1492,type,
sK12_SY1492: ( $i > $o ) > $i > $i ).
thf(tp_sK130_SY1253,type,
sK130_SY1253: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK131_SY1786,type,
sK131_SY1786: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK132_SY1517,type,
sK132_SY1517: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK133_SY1253,type,
sK133_SY1253: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK134_SY1517,type,
sK134_SY1517: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK135_SY1253,type,
sK135_SY1253: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK136_SY1517,type,
sK136_SY1517: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK137_SY1253,type,
sK137_SY1253: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK138_SY1517,type,
sK138_SY1517: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK139_SY1253,type,
sK139_SY1253: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK13_SY1513,type,
sK13_SY1513: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK140_SY1792,type,
sK140_SY1792: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK141_SY1796,type,
sK141_SY1796: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK142_SY1797,type,
sK142_SY1797: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK143_SY1798,type,
sK143_SY1798: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK144_SY1806,type,
sK144_SY1806: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK145_SY1807,type,
sK145_SY1807: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK146_SY1808,type,
sK146_SY1808: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK147_SY1815,type,
sK147_SY1815: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK14_SY1523,type,
sK14_SY1523: $i > $i > $i ).
thf(tp_sK15_SY1530,type,
sK15_SY1530: ( $i > $o ) > $i > $i ).
thf(tp_sK16_SY1565,type,
sK16_SY1565: $i > $i > $i ).
thf(tp_sK17_SY1575,type,
sK17_SY1575: $i > $i > $i ).
thf(tp_sK18_SY1576,type,
sK18_SY1576: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK19_SY1165,type,
sK19_SY1165: $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK20_SY1658,type,
sK20_SY1658: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK21_SY1385,type,
sK21_SY1385: $i > $i ).
thf(tp_sK22_SY1666,type,
sK22_SY1666: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK23_SY1595,type,
sK23_SY1595: $i > $i > $i ).
thf(tp_sK24_SY1622,type,
sK24_SY1622: $i > $i > $i > $i ).
thf(tp_sK25_SY1654,type,
sK25_SY1654: ( $i > $o ) > $i > $i ).
thf(tp_sK26_SY1527,type,
sK26_SY1527: $i > $i > $i ).
thf(tp_sK27_SY1660,type,
sK27_SY1660: ( $i > $o ) > $i > $i ).
thf(tp_sK28_SY1661,type,
sK28_SY1661: $i > ( $i > $o ) > $i ).
thf(tp_sK29_SY1632,type,
sK29_SY1632: $i > $i > $i > $i ).
thf(tp_sK2_SY1109,type,
sK2_SY1109: $i > $i ).
thf(tp_sK30_SY1550,type,
sK30_SY1550: ( $i > $o ) > $i > $i ).
thf(tp_sK31_SY1588,type,
sK31_SY1588: ( $i > $o ) > $i > $i ).
thf(tp_sK32_SY1655,type,
sK32_SY1655: $o > $i > $i > $i ).
thf(tp_sK33_SX0,type,
sK33_SX0: $i > $i > $i ).
thf(tp_sK34_SX0,type,
sK34_SX0: $i > $i > $i ).
thf(tp_sK35_SY1373,type,
sK35_SY1373: $i > $i ).
thf(tp_sK36_SY1574,type,
sK36_SY1574: $i > $i > $i ).
thf(tp_sK37_SY1383,type,
sK37_SY1383: $i > $i > $i ).
thf(tp_sK38_SY1669,type,
sK38_SY1669: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(tp_sK39_SY1463,type,
sK39_SY1463: $i > $i > $i ).
thf(tp_sK3_SY1491,type,
sK3_SY1491: $i ).
thf(tp_sK40_SY1483,type,
sK40_SY1483: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK41_SY1568,type,
sK41_SY1568: $i > $i > $i ).
thf(tp_sK42_SY1359,type,
sK42_SY1359: $i > ( $i > $o ) > $i ).
thf(tp_sK43_SY1458,type,
sK43_SY1458: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK44_SY1463,type,
sK44_SY1463: $i > $i > $i ).
thf(tp_sK45_SY1643,type,
sK45_SY1643: $i > $i > $i ).
thf(tp_sK46_SY1644,type,
sK46_SY1644: $i > $i > $i ).
thf(tp_sK47_SY1564,type,
sK47_SY1564: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK48_SY1690,type,
sK48_SY1690: $i > ( $i > $o ) > $i ).
thf(tp_sK49_SY1639,type,
sK49_SY1639: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK4_SY1465,type,
sK4_SY1465: $i > $i > $i ).
thf(tp_sK50_SY1686,type,
sK50_SY1686: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(tp_sK51_SY1650,type,
sK51_SY1650: $i > ( $i > $o ) > $i ).
thf(tp_sK52_SY1651,type,
sK52_SY1651: $i > ( $i > $o ) > $i ).
thf(tp_sK53_SY1659,type,
sK53_SY1659: $i > ( $i > $o ) > $i ).
thf(tp_sK54_SY1664,type,
sK54_SY1664: $i > ( $i > $o ) > $i ).
thf(tp_sK55_SY1665,type,
sK55_SY1665: $i > ( $i > $o ) > $i ).
thf(tp_sK56_SY1667,type,
sK56_SY1667: $i > ( $i > $o ) > $i ).
thf(tp_sK57_SY1668,type,
sK57_SY1668: $i > ( $i > $o ) > $i ).
thf(tp_sK58_SY1675,type,
sK58_SY1675: $i > $i > $i > $i ).
thf(tp_sK59_SY1507,type,
sK59_SY1507: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK5_SY1476,type,
sK5_SY1476: $i > $i > $i ).
thf(tp_sK60_SY1676,type,
sK60_SY1676: $i > $i > $i > $i ).
thf(tp_sK61_SY1677,type,
sK61_SY1677: $i > $i > $i ).
thf(tp_sK62_SY1449,type,
sK62_SY1449: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK63_SY1160,type,
sK63_SY1160: $i > ( $i > $o ) > $i ).
thf(tp_sK64_SY1684,type,
sK64_SY1684: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK65_SY1266,type,
sK65_SY1266: $i > ( $i > $o ) > $i ).
thf(tp_sK66_SY1348,type,
sK66_SY1348: $i > ( $i > $o ) > $i ).
thf(tp_sK67_SY1361,type,
sK67_SY1361: $i > ( $i > $o ) > $i ).
thf(tp_sK68_SY1361,type,
sK68_SY1361: $i > ( $i > $o ) > $i ).
thf(tp_sK69_SY1372,type,
sK69_SY1372: $i > ( $i > $o ) > $i ).
thf(tp_sK6_SY1321,type,
sK6_SY1321: $i > $i ).
thf(tp_sK70_SY1598,type,
sK70_SY1598: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK71_SY1598,type,
sK71_SY1598: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK72_SY1160,type,
sK72_SY1160: $i > ( $i > $o ) > $i ).
thf(tp_sK73_SY1266,type,
sK73_SY1266: $i > ( $i > $o ) > $i ).
thf(tp_sK74_SY1292,type,
sK74_SY1292: $i > ( $i > $o ) > $i ).
thf(tp_sK75_SY1348,type,
sK75_SY1348: $i > ( $i > $o ) > $i ).
thf(tp_sK76_SY1361,type,
sK76_SY1361: $i > ( $i > $o ) > $i ).
thf(tp_sK77_SY1372,type,
sK77_SY1372: $i > ( $i > $o ) > $i ).
thf(tp_sK78_SY1598,type,
sK78_SY1598: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK79_SY1292,type,
sK79_SY1292: $i > ( $i > $o ) > $i ).
thf(tp_sK7_SY1357,type,
sK7_SY1357: $i > $i ).
thf(tp_sK80_SY1292,type,
sK80_SY1292: $i > ( $i > $o ) > $i ).
thf(tp_sK81_SY1483,type,
sK81_SY1483: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK82_SY1292,type,
sK82_SY1292: $i > ( $i > $o ) > $i ).
thf(tp_sK83_SY1694,type,
sK83_SY1694: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK84_SY1483,type,
sK84_SY1483: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK85_SY1495,type,
sK85_SY1495: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK86_SY1533,type,
sK86_SY1533: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK87_SY1698,type,
sK87_SY1698: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK88_SY1316,type,
sK88_SY1316: $i > $i > $i > $i ).
thf(tp_sK89_SY1495,type,
sK89_SY1495: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK8_SY1462,type,
sK8_SY1462: $i > $i > $i ).
thf(tp_sK90_SY1533,type,
sK90_SY1533: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK91_SY1679,type,
sK91_SY1679: $i > $i > $i > $i ).
thf(tp_sK92_SY1495,type,
sK92_SY1495: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK93_SY1495,type,
sK93_SY1495: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK94_SY1717,type,
sK94_SY1717: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK95_SY1718,type,
sK95_SY1718: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK96_SY1533,type,
sK96_SY1533: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK97_SY1533,type,
sK97_SY1533: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK98_SY1679,type,
sK98_SY1679: $i > $i > $i > $i ).
thf(tp_sK99_SY1495,type,
sK99_SY1495: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK9_SY1473,type,
sK9_SY1473: $i > $i > $i ).
thf(tp_secondinupair,type,
secondinupair: $o ).
thf(tp_sepInPowerset,type,
sepInPowerset: $o ).
thf(tp_sepSubset,type,
sepSubset: $o ).
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_setminus,type,
setminus: $i > $i > $i ).
thf(tp_setminusEL,type,
setminusEL: $o ).
thf(tp_setminusELneg,type,
setminusELneg: $o ).
thf(tp_setminusER,type,
setminusER: $o ).
thf(tp_setminusERneg,type,
setminusERneg: $o ).
thf(tp_setminusI,type,
setminusI: $o ).
thf(tp_setminusILneg,type,
setminusILneg: $o ).
thf(tp_setminusIRneg,type,
setminusIRneg: $o ).
thf(tp_setminusLsub,type,
setminusLsub: $o ).
thf(tp_setminusSubset1,type,
setminusSubset1: $o ).
thf(tp_setminusSubset2,type,
setminusSubset2: $o ).
thf(tp_setoftrueEq,type,
setoftrueEq: $o ).
thf(tp_setsmeet,type,
setsmeet: $i > $i > $o ).
thf(tp_setukpairIL,type,
setukpairIL: $o ).
thf(tp_setukpairIR,type,
setukpairIR: $o ).
thf(tp_setukpairinjL,type,
setukpairinjL: $o ).
thf(tp_setukpairinjL1,type,
setukpairinjL1: $o ).
thf(tp_setukpairinjL2,type,
setukpairinjL2: $o ).
thf(tp_setukpairinjR11,type,
setukpairinjR11: $o ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunionAx,type,
setunionAx: $o ).
thf(tp_setunionE,type,
setunionE: $o ).
thf(tp_setunionE2,type,
setunionE2: $o ).
thf(tp_setunionI,type,
setunionI: $o ).
thf(tp_setunion__Cong,type,
setunion__Cong: $o ).
thf(tp_setunionsingleton,type,
setunionsingleton: $o ).
thf(tp_setunionsingleton1,type,
setunionsingleton1: $o ).
thf(tp_setunionsingleton2,type,
setunionsingleton2: $o ).
thf(tp_singleton,type,
singleton: $i > $o ).
thf(tp_singletoninpowerset,type,
singletoninpowerset: $o ).
thf(tp_singletoninpowunion,type,
singletoninpowunion: $o ).
thf(tp_singletonprop,type,
singletonprop: $o ).
thf(tp_singletonsswitch,type,
singletonsswitch: $o ).
thf(tp_singletonsubset,type,
singletonsubset: $o ).
thf(tp_singletonsuniq,type,
singletonsuniq: $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_symdiff,type,
symdiff: $i > $i > $i ).
thf(tp_symdiffE,type,
symdiffE: $o ).
thf(tp_symdiffI1,type,
symdiffI1: $o ).
thf(tp_symdiffI2,type,
symdiffI2: $o ).
thf(tp_symdiffIneg1,type,
symdiffIneg1: $o ).
thf(tp_symdiffIneg2,type,
symdiffIneg2: $o ).
thf(tp_theprop,type,
theprop: $o ).
thf(tp_ubforcartprodlem1,type,
ubforcartprodlem1: $o ).
thf(tp_ubforcartprodlem2,type,
ubforcartprodlem2: $o ).
thf(tp_ubforcartprodlem3,type,
ubforcartprodlem3: $o ).
thf(tp_uniqinunit,type,
uniqinunit: $o ).
thf(tp_upairinpowunion,type,
upairinpowunion: $o ).
thf(tp_upairset2E,type,
upairset2E: $o ).
thf(tp_upairset2IR,type,
upairset2IR: $o ).
thf(tp_upairsetE,type,
upairsetE: $o ).
thf(tp_upairsetIL,type,
upairsetIL: $o ).
thf(tp_upairsetIR,type,
upairsetIR: $o ).
thf(tp_upairsetp,type,
upairsetp: $i > $o ).
thf(tp_upairsubunion,type,
upairsubunion: $o ).
thf(tp_vacuousDall,type,
vacuousDall: $o ).
thf(tp_wellorderingAx,type,
wellorderingAx: $o ).
thf(binintersectEL,definition,
( binintersectEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectER,definition,
( binintersectER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER) ).
thf(binintersectI,definition,
( binintersectI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectLsub,definition,
( binintersectLsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectRsub,definition,
( binintersectRsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset1,definition,
( binintersectSubset1
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(binintersectSubset2,definition,
( binintersectSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,definition,
( binintersectSubset3
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectSubset4,definition,
( binintersectSubset4
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset5,definition,
( binintersectSubset5
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binunionE,definition,
( binunionE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(binunionEcases,definition,
( binunionEcases
= ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionIL,definition,
( binunionIL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL) ).
thf(binunionIR,definition,
( binunionIR
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionLsub,definition,
( binunionLsub
= ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,definition,
( binunionRsub
= ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub) ).
thf(bs114d,definition,
( bs114d
= ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bs114d) ).
thf(cartprodfstin,definition,
( cartprodfstin
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstin) ).
thf(cartprodmempair,definition,
( cartprodmempair
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair) ).
thf(cartprodmempair1,definition,
( cartprodmempair1
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodpairin,definition,
( cartprodpairin
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin) ).
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(disjointsetsI1,definition,
( disjointsetsI1
= ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1) ).
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(ex1,definition,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(ex1E1,definition,
( ex1E1
= ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1I,definition,
( ex1I
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xy )
=> ( Xy = Xx ) ) )
=> ( ex1 @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,definition,
( ex1I2
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I2) ).
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(inPowerset,definition,
( inPowerset
= ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).
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(iskpair,definition,
( iskpair
= ( ^ [A: $i] :
? [Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
& ? [Xy: $i] :
( ( in @ Xy @ ( setunion @ A ) )
& ( A
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iskpair) ).
thf(kfstpairEq,definition,
( kfstpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).
thf(kfstsingleton,definition,
( kfstsingleton
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstsingleton) ).
thf(kpair,definition,
( kpair
= ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpair) ).
thf(kpairiskpair,definition,
( kpairiskpair
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,definition,
( kpairp
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
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(powersetsubset,definition,
( powersetsubset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset) ).
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(secondinupair,definition,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
thf(sepInPowerset,definition,
( sepInPowerset
= ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,definition,
( sepSubset
= ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).
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(setminusEL,definition,
( setminusEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusELneg,definition,
( setminusELneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusER,definition,
( setminusER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(setminusERneg,definition,
( setminusERneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusI,definition,
( setminusI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(setminusILneg,definition,
( setminusILneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,definition,
( setminusIRneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,definition,
( setminusLsub
= ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,definition,
( setminusSubset1
= ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1) ).
thf(setminusSubset2,definition,
( setminusSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setoftrueEq,definition,
( setoftrueEq
= ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(setukpairIL,definition,
( setukpairIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,definition,
( setukpairIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIR) ).
thf(setukpairinjL,definition,
( setukpairinjL
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL) ).
thf(setukpairinjL1,definition,
( setukpairinjL1
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(setukpairinjL2,definition,
( setukpairinjL2
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjR11,definition,
( setukpairinjR11
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR11) ).
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(setunionE2,definition,
( setunionE2
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2) ).
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(setunionsingleton,definition,
( setunionsingleton
= ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton) ).
thf(setunionsingleton1,definition,
( setunionsingleton1
= ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,definition,
( setunionsingleton2
= ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(singleton,definition,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( in @ Xx @ A )
& ( A
= ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(singletoninpowerset,definition,
( singletoninpowerset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,definition,
( singletoninpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(singletonprop,definition,
( singletonprop
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonprop) ).
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(singletonsubset,definition,
( singletonsubset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletonsuniq,definition,
( singletonsuniq
= ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsuniq) ).
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(symdiffE,definition,
( symdiffE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,definition,
( symdiffI1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,definition,
( symdiffI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,definition,
( symdiffIneg1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,definition,
( symdiffIneg2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(theprop,definition,
( theprop
= ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop) ).
thf(ubforcartprodlem1,definition,
( ubforcartprodlem1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,definition,
( ubforcartprodlem2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,definition,
( ubforcartprodlem3
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(upairinpowunion,definition,
( upairinpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairinpowunion) ).
thf(upairset2E,definition,
( upairset2E
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E) ).
thf(upairset2IR,definition,
( upairset2IR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).
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(upairsubunion,definition,
( upairsubunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsubunion) ).
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
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR12) ).
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
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $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 ) ) )
=> ( ! [SY19: $i > $i > $o,SY20: $i] :
( ! [SY21: $i] :
( ( in @ SY21 @ SY20 )
=> ? [SY23: $i] :
( ( SY19 @ SY21 @ SY23 )
& ! [SY24: $i] :
( ( SY19 @ SY21 @ SY24 )
=> ( SY23 = SY24 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY20 )
& ( SY19 @ 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 ) ) ) ) ) )
=> ( ! [SY51: $i > $o] :
( ? [SY53: $i] :
( ( SY51 @ SY53 )
& ! [SY54: $i] :
( ( SY51 @ SY54 )
=> ( SY53 = SY54 ) ) )
=> ( SY51
@ ( descr
@ ^ [Xx: $i] : ( SY51 @ 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 ) )
=> ( ! [SY68: $i > $o] :
( ? [SY70: $i] :
( ( SY68 @ SY70 )
& ! [SY71: $i] :
( ( SY68 @ SY71 )
=> ( SY70 = SY71 ) ) )
=> ? [Xx: $i] :
( ( SY68 @ Xx )
& ! [Xy: $i] :
( ( SY68 @ 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 )
=> ( ! [SY80: $i > $o] :
( ? [SY82: $i] :
( ( SY80 @ SY82 )
& ! [SY83: $i] :
( ( SY80 @ SY83 )
=> ( SY82 = SY83 ) ) )
=> ? [Xx: $i] : ( SY80 @ 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 ) ) )
=> ( ! [SY97: $i] :
( ( SY97 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY97 ) )
=> ( ! [SY99: $i,SY100: $i > $o,SY101: $i] :
( ( in @ SY101 @ SY99 )
=> ( ( SY100 @ SY101 )
=> ( ( dsetconstr @ SY99
@ ^ [Xy: $i] : ( SY100 @ Xy ) )
!= emptyset ) ) )
=> ( ! [SY103: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY103 )
=> ( SY103 != 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 ) ) ) )
=> ( ! [SY136: $i > $o] :
( ? [SY138: $i] :
( ( SY136 @ SY138 )
& ! [SY139: $i] :
( ( SY136 @ SY139 )
=> ( SY138 = SY139 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY136 @ Xy )
<=> ( Xy = Xx ) ) )
=> ( ! [SY142: $i] :
( ( SY142 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY142 )
& $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 ) ) )
=> ( ! [SY191: $i > $o] :
( ? [Xx: $i] :
( ( SY191 @ Xx )
& ! [Xy: $i] :
( ( SY191 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY195: $i] :
( ( SY191 @ SY195 )
& ! [SY196: $i] :
( ( SY191 @ SY196 )
=> ( SY195 = SY196 ) ) ) )
=> ( ! [SY197: $i > $o] :
( ? [Xx: $i] : ( SY197 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY197 @ Xx )
=> ( ( SY197 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY202: $i] :
( ( SY197 @ SY202 )
& ! [SY203: $i] :
( ( SY197 @ SY203 )
=> ( SY202 = SY203 ) ) ) ) )
=> ( ! [SY204: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY204 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY208: $i] :
( ( SY204 @ SY208 )
& ! [SY209: $i] :
( ( SY204 @ SY209 )
=> ( SY208 = SY209 ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [SY218: $i > $o] :
( ? [SY220: $i] :
( ( SY218 @ SY220 )
& ! [SY221: $i] :
( ( SY218 @ SY221 )
=> ( SY220 = SY221 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY218 @ Xx )
=> ( ( SY218 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY224: $i > $o,SY225: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY224 @ Xx )
<=> ( SY225 @ Xy ) ) )
=> ( ? [SY229: $i] :
( ( SY224 @ SY229 )
& ! [SY230: $i] :
( ( SY224 @ SY230 )
=> ( SY229 = SY230 ) ) )
<=> ? [SY232: $i] :
( ( SY225 @ SY232 )
& ! [SY233: $i] :
( ( SY225 @ SY233 )
=> ( SY232 = SY233 ) ) ) ) )
=> ( ( 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 )
=> ( ! [SY242: $i > $o] :
( ? [SY244: $i] :
( ( SY242 @ SY244 )
& ! [SY245: $i] :
( ( SY242 @ SY245 )
=> ( SY244 = SY245 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY242 @ Xx )
=> ( ( SY242 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY248: $i > $o,SY249: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY248 @ Xx )
<=> ( SY249 @ Xy ) ) )
=> ( ? [SY253: $i] :
( ( SY248 @ SY253 )
& ! [SY254: $i] :
( ( SY248 @ SY254 )
=> ( SY253 = SY254 ) ) )
=> ( ? [SY256: $i] :
( ( SY249 @ SY256 )
& ! [SY257: $i] :
( ( SY249 @ SY257 )
=> ( SY256 = SY257 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY248 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY249 @ 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 ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) )
=> ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) )
=> ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) )
=> ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B )
=> ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) )
=> ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A )
=> ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [SY418: $i,SY419: $i] :
? [SY420: $i] :
( ( in @ SY420 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY418 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY418 @ ( setadjoin @ SY419 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY421: $i] :
( ( in @ SY421 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY418 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY418 @ ( setadjoin @ SY419 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY418 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY418 @ ( setadjoin @ SY419 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY420 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY420 @ ( setadjoin @ SY421 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ! [SY422: $i,SY423: $i] :
? [SY425: $i] :
( ( in @ SY425 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY422 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY422 @ ( setadjoin @ SY423 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY426: $i] :
( ( in @ SY426 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY422 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY422 @ ( setadjoin @ SY423 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY422 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY422 @ ( setadjoin @ SY423 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY425 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY425 @ ( setadjoin @ SY426 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
=> ( ! [SY453: $i,SY454: $i,SY455: $i] :
( ( in @ SY455 @ SY453 )
=> ! [SY456: $i] :
( ( in @ SY456 @ SY454 )
=> ( in @ ( setadjoin @ ( setadjoin @ SY455 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY455 @ ( setadjoin @ SY456 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SY453 @ SY454 ) ) ) ) ) )
=> ( ! [SY458: $i,SY459: $i,SY460: $i] :
( ( in @ SY460 @ SY458 )
=> ! [SY461: $i] :
( ( in @ SY461 @ SY459 )
=> ( in @ ( setadjoin @ ( setadjoin @ SY460 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY460 @ ( setadjoin @ SY461 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SY458 @ SY459 ) ) ) )
=> ( ! [SY463: $i,SY464: $i,SY465: $i] :
( ( in @ SY465 @ ( cartprod @ SY463 @ SY464 ) )
=> ? [SY466: $i] :
( ( in @ SY466 @ SY463 )
& ? [SY467: $i] :
( ( in @ SY467 @ SY464 )
& ( SY465
= ( setadjoin @ ( setadjoin @ SY466 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY466 @ ( setadjoin @ SY467 @ emptyset ) ) @ emptyset ) ) ) ) ) )
=> ( ! [SY469: $i,SY470: $i,SY471: $i] :
( ( in @ SY471 @ ( cartprod @ SY469 @ SY470 ) )
=> ? [SY472: $i] :
( ( in @ SY472 @ ( setunion @ SY471 ) )
& ? [SY473: $i] :
( ( in @ SY473 @ ( setunion @ SY471 ) )
& ( SY471
= ( setadjoin @ ( setadjoin @ SY472 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY472 @ ( setadjoin @ SY473 @ emptyset ) ) @ emptyset ) ) ) ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) )
=> ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A )
=> ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) )
=> ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx )
=> ( ! [SY480: $i,SY481: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY480 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY480 )
=> ( ( SY481 @ Xx )
=> ( ( SY481 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY480 )
& ( SY481 @ Xx ) )
=> ? [SY486: $i] :
( ( in @ SY486
@ ( dsetconstr @ SY480
@ ^ [Xx: $i] : ( SY481 @ Xx ) ) )
& ( ( dsetconstr @ SY480
@ ^ [Xx: $i] : ( SY481 @ Xx ) )
= ( setadjoin @ SY486 @ emptyset ) ) ) ) )
=> ( ! [SY487: $i,SY488: $i > $o] :
( ? [SY493: $i] :
( ( in @ SY493
@ ( dsetconstr @ SY487
@ ^ [SY494: $i] : ( SY488 @ SY494 ) ) )
& ( ( dsetconstr @ SY487
@ ^ [SY495: $i] : ( SY488 @ SY495 ) )
= ( setadjoin @ SY493 @ emptyset ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY487 )
& ( SY488 @ Xx ) ) )
=> ( ! [SY497: $i,SY498: $i > $o,SY499: $i] :
( ( in @ SY499 @ SY497 )
=> ( ( SY498 @ SY499 )
=> ( ! [Xy: $i] :
( ( in @ Xy @ SY497 )
=> ( ( SY498 @ Xy )
=> ( Xy = SY499 ) ) )
=> ? [SY505: $i] :
( ( in @ SY505
@ ( dsetconstr @ SY497
@ ^ [SY506: $i] : ( SY498 @ SY506 ) ) )
& ( ( dsetconstr @ SY497
@ ^ [SY507: $i] : ( SY498 @ SY507 ) )
= ( setadjoin @ SY505 @ emptyset ) ) ) ) ) )
=> ( ! [SY508: $i,SY509: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY508 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY508 )
=> ( ( SY509 @ Xx )
=> ( ( SY509 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY508 )
& ( SY509 @ Xx ) )
=> ? [SY517: $i] :
( ( in @ SY517
@ ( dsetconstr @ SY508
@ ^ [SY518: $i] : ( SY509 @ SY518 ) ) )
& ( ( dsetconstr @ SY508
@ ^ [SY519: $i] : ( SY509 @ SY519 ) )
= ( setadjoin @ SY517 @ emptyset ) ) ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) )
=> ( ! [SY525: $i] :
( ? [SY526: $i] :
( ( in @ SY526 @ ( setunion @ SY525 ) )
& ? [SY527: $i] :
( ( in @ SY527 @ ( setunion @ SY525 ) )
& ( SY525
= ( setadjoin @ ( setadjoin @ SY526 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY526 @ ( setadjoin @ SY527 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [SY529: $i] :
( ( in @ SY529
@ ( dsetconstr @ ( setunion @ SY525 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY525 ) ) )
& ( ( dsetconstr @ ( setunion @ SY525 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY525 ) )
= ( setadjoin @ SY529 @ emptyset ) ) ) )
=> ( ! [SY530: $i] :
( ? [SY531: $i] :
( ( in @ SY531 @ SY530 )
& ( SY530
= ( setadjoin @ SY531 @ emptyset ) ) )
=> ( in @ ( setunion @ SY530 ) @ SY530 ) )
=> ( ! [SY532: $i,SY533: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ SY532 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY532 @ ( setadjoin @ SY533 @ emptyset ) ) @ emptyset ) ) )
= SY532 )
=> ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) )
=> ( ! [SY542: $i,SY543: $i,SY544: $i,SY545: $i] :
( ( ( setadjoin @ ( setadjoin @ SY542 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY542 @ ( setadjoin @ SY543 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY544 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY544 @ ( setadjoin @ SY545 @ emptyset ) ) @ emptyset ) ) )
=> ( SY542 = SY544 ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,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,
( ( ! [SY19: $i > $i > $o,SY20: $i] :
( ! [SY21: $i] :
( ( in @ SY21 @ SY20 )
=> ? [SY23: $i] :
( ( SY19 @ SY21 @ SY23 )
& ! [SY24: $i] :
( ( SY19 @ SY21 @ SY24 )
=> ( SY23 = SY24 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY20 )
& ( SY19 @ 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,
( ( ! [SY51: $i > $o] :
( ? [SY53: $i] :
( ( SY51 @ SY53 )
& ! [SY54: $i] :
( ( SY51 @ SY54 )
=> ( SY53 = SY54 ) ) )
=> ( SY51
@ ( descr
@ ^ [Xx: $i] : ( SY51 @ 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,
( ( ! [SY68: $i > $o] :
( ? [SY70: $i] :
( ( SY68 @ SY70 )
& ! [SY71: $i] :
( ( SY68 @ SY71 )
=> ( SY70 = SY71 ) ) )
=> ? [Xx: $i] :
( ( SY68 @ Xx )
& ! [Xy: $i] :
( ( SY68 @ 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,
( ( ! [SY80: $i > $o] :
( ? [SY82: $i] :
( ( SY80 @ SY82 )
& ! [SY83: $i] :
( ( SY80 @ SY83 )
=> ( SY82 = SY83 ) ) )
=> ? [Xx: $i] : ( SY80 @ 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,
( ( ! [SY97: $i] :
( ( SY97 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY97 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [SY99: $i,SY100: $i > $o,SY101: $i] :
( ( in @ SY101 @ SY99 )
=> ( ( SY100 @ SY101 )
=> ( ( dsetconstr @ SY99
@ ^ [Xy: $i] : ( SY100 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [SY103: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY103 )
=> ( SY103 != 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,
( ( ! [SY136: $i > $o] :
( ? [SY138: $i] :
( ( SY136 @ SY138 )
& ! [SY139: $i] :
( ( SY136 @ SY139 )
=> ( SY138 = SY139 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY136 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(46,plain,
( ( ! [SY142: $i] :
( ( SY142 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY142 )
& $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,
( ( ! [SY191: $i > $o] :
( ? [Xx: $i] :
( ( SY191 @ Xx )
& ! [Xy: $i] :
( ( SY191 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY195: $i] :
( ( SY191 @ SY195 )
& ! [SY196: $i] :
( ( SY191 @ SY196 )
=> ( SY195 = SY196 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(65,plain,
( ( ! [SY197: $i > $o] :
( ? [Xx: $i] : ( SY197 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY197 @ Xx )
=> ( ( SY197 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY202: $i] :
( ( SY197 @ SY202 )
& ! [SY203: $i] :
( ( SY197 @ SY203 )
=> ( SY202 = SY203 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(66,plain,
( ( ! [SY204: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY204 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY208: $i] :
( ( SY204 @ SY208 )
& ! [SY209: $i] :
( ( SY204 @ SY209 )
=> ( SY208 = SY209 ) ) ) ) )
= $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,
( ( ! [SY218: $i > $o] :
( ? [SY220: $i] :
( ( SY218 @ SY220 )
& ! [SY221: $i] :
( ( SY218 @ SY221 )
=> ( SY220 = SY221 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY218 @ Xx )
=> ( ( SY218 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(70,plain,
( ( ! [SY224: $i > $o,SY225: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY224 @ Xx )
<=> ( SY225 @ Xy ) ) )
=> ( ? [SY229: $i] :
( ( SY224 @ SY229 )
& ! [SY230: $i] :
( ( SY224 @ SY230 )
=> ( SY229 = SY230 ) ) )
<=> ? [SY232: $i] :
( ( SY225 @ SY232 )
& ! [SY233: $i] :
( ( SY225 @ SY233 )
=> ( SY232 = SY233 ) ) ) ) ) )
= $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(76,plain,
( ( ! [SY242: $i > $o] :
( ? [SY244: $i] :
( ( SY242 @ SY244 )
& ! [SY245: $i] :
( ( SY242 @ SY245 )
=> ( SY244 = SY245 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY242 @ Xx )
=> ( ( SY242 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(77,plain,
( ( ! [SY248: $i > $o,SY249: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY248 @ Xx )
<=> ( SY249 @ Xy ) ) )
=> ( ? [SY253: $i] :
( ( SY248 @ SY253 )
& ! [SY254: $i] :
( ( SY248 @ SY254 )
=> ( SY253 = SY254 ) ) )
=> ( ? [SY256: $i] :
( ( SY249 @ SY256 )
& ! [SY257: $i] :
( ( SY249 @ SY257 )
=> ( SY256 = SY257 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY248 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY249 @ 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 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(99,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(100,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(101,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(102,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(103,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(104,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(105,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(106,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(107,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(109,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(110,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(111,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(113,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(114,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(115,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(116,plain,
( ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(117,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(118,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(119,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(120,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(121,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(122,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(123,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(124,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(125,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(126,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(127,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(128,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(129,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(130,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(131,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(132,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(133,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(134,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(135,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(136,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(137,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(138,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(139,plain,
( ( ! [SY418: $i,SY419: $i] :
? [SY420: $i] :
( ( in @ SY420 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY418 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY418 @ ( setadjoin @ SY419 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY421: $i] :
( ( in @ SY421 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY418 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY418 @ ( setadjoin @ SY419 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY418 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY418 @ ( setadjoin @ SY419 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY420 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY420 @ ( setadjoin @ SY421 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(140,plain,
( ( ! [SY422: $i,SY423: $i] :
? [SY425: $i] :
( ( in @ SY425 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY422 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY422 @ ( setadjoin @ SY423 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY426: $i] :
( ( in @ SY426 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY422 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY422 @ ( setadjoin @ SY423 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY422 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY422 @ ( setadjoin @ SY423 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY425 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY425 @ ( setadjoin @ SY426 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(141,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(142,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(143,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(144,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(145,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(146,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(147,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(148,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(149,plain,
( ( ! [SY453: $i,SY454: $i,SY455: $i] :
( ( in @ SY455 @ SY453 )
=> ! [SY456: $i] :
( ( in @ SY456 @ SY454 )
=> ( in @ ( setadjoin @ ( setadjoin @ SY455 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY455 @ ( setadjoin @ SY456 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SY453 @ SY454 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(150,plain,
( ( ! [SY458: $i,SY459: $i,SY460: $i] :
( ( in @ SY460 @ SY458 )
=> ! [SY461: $i] :
( ( in @ SY461 @ SY459 )
=> ( in @ ( setadjoin @ ( setadjoin @ SY460 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY460 @ ( setadjoin @ SY461 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SY458 @ SY459 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(151,plain,
( ( ! [SY463: $i,SY464: $i,SY465: $i] :
( ( in @ SY465 @ ( cartprod @ SY463 @ SY464 ) )
=> ? [SY466: $i] :
( ( in @ SY466 @ SY463 )
& ? [SY467: $i] :
( ( in @ SY467 @ SY464 )
& ( SY465
= ( setadjoin @ ( setadjoin @ SY466 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY466 @ ( setadjoin @ SY467 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(152,plain,
( ( ! [SY469: $i,SY470: $i,SY471: $i] :
( ( in @ SY471 @ ( cartprod @ SY469 @ SY470 ) )
=> ? [SY472: $i] :
( ( in @ SY472 @ ( setunion @ SY471 ) )
& ? [SY473: $i] :
( ( in @ SY473 @ ( setunion @ SY471 ) )
& ( SY471
= ( setadjoin @ ( setadjoin @ SY472 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY472 @ ( setadjoin @ SY473 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(153,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(154,plain,
( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(155,plain,
( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(156,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(157,plain,
( ( ! [SY480: $i,SY481: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY480 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY480 )
=> ( ( SY481 @ Xx )
=> ( ( SY481 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY480 )
& ( SY481 @ Xx ) )
=> ? [SY486: $i] :
( ( in @ SY486
@ ( dsetconstr @ SY480
@ ^ [Xx: $i] : ( SY481 @ Xx ) ) )
& ( ( dsetconstr @ SY480
@ ^ [Xx: $i] : ( SY481 @ Xx ) )
= ( setadjoin @ SY486 @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(158,plain,
( ( ! [SY487: $i,SY488: $i > $o] :
( ? [SY493: $i] :
( ( in @ SY493
@ ( dsetconstr @ SY487
@ ^ [SY494: $i] : ( SY488 @ SY494 ) ) )
& ( ( dsetconstr @ SY487
@ ^ [SY495: $i] : ( SY488 @ SY495 ) )
= ( setadjoin @ SY493 @ emptyset ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY487 )
& ( SY488 @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(159,plain,
( ( ! [SY497: $i,SY498: $i > $o,SY499: $i] :
( ( in @ SY499 @ SY497 )
=> ( ( SY498 @ SY499 )
=> ( ! [Xy: $i] :
( ( in @ Xy @ SY497 )
=> ( ( SY498 @ Xy )
=> ( Xy = SY499 ) ) )
=> ? [SY505: $i] :
( ( in @ SY505
@ ( dsetconstr @ SY497
@ ^ [SY506: $i] : ( SY498 @ SY506 ) ) )
& ( ( dsetconstr @ SY497
@ ^ [SY507: $i] : ( SY498 @ SY507 ) )
= ( setadjoin @ SY505 @ emptyset ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(160,plain,
( ( ! [SY508: $i,SY509: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY508 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY508 )
=> ( ( SY509 @ Xx )
=> ( ( SY509 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY508 )
& ( SY509 @ Xx ) )
=> ? [SY517: $i] :
( ( in @ SY517
@ ( dsetconstr @ SY508
@ ^ [SY518: $i] : ( SY509 @ SY518 ) ) )
& ( ( dsetconstr @ SY508
@ ^ [SY519: $i] : ( SY509 @ SY519 ) )
= ( setadjoin @ SY517 @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(161,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(162,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(163,plain,
( ( ! [SY525: $i] :
( ? [SY526: $i] :
( ( in @ SY526 @ ( setunion @ SY525 ) )
& ? [SY527: $i] :
( ( in @ SY527 @ ( setunion @ SY525 ) )
& ( SY525
= ( setadjoin @ ( setadjoin @ SY526 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY526 @ ( setadjoin @ SY527 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [SY529: $i] :
( ( in @ SY529
@ ( dsetconstr @ ( setunion @ SY525 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY525 ) ) )
& ( ( dsetconstr @ ( setunion @ SY525 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY525 ) )
= ( setadjoin @ SY529 @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(164,plain,
( ( ! [SY530: $i] :
( ? [SY531: $i] :
( ( in @ SY531 @ SY530 )
& ( SY530
= ( setadjoin @ SY531 @ emptyset ) ) )
=> ( in @ ( setunion @ SY530 ) @ SY530 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(165,plain,
( ( ! [SY532: $i,SY533: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ SY532 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY532 @ ( setadjoin @ SY533 @ emptyset ) ) @ emptyset ) ) )
= SY532 ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(166,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(167,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(168,plain,
( ( ! [SY542: $i,SY543: $i,SY544: $i,SY545: $i] :
( ( ( setadjoin @ ( setadjoin @ SY542 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY542 @ ( setadjoin @ SY543 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY544 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY544 @ ( setadjoin @ SY545 @ emptyset ) ) @ emptyset ) ) )
=> ( SY542 = SY544 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(169,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(170,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(171,plain,
( ( ~ ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[170]) ).
thf(172,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(173,plain,
( ( ! [SY542: $i,SY543: $i,SY544: $i,SY545: $i] :
( ( ( setadjoin @ ( setadjoin @ SY542 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY542 @ ( setadjoin @ SY543 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY544 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY544 @ ( setadjoin @ SY545 @ emptyset ) ) @ emptyset ) ) )
=> ( SY542 = SY544 ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(174,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(175,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(176,plain,
( ( ! [SY532: $i,SY533: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ SY532 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY532 @ ( setadjoin @ SY533 @ emptyset ) ) @ emptyset ) ) )
= SY532 ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(177,plain,
( ( ! [SY530: $i] :
( ? [SY531: $i] :
( ( in @ SY531 @ SY530 )
& ( SY530
= ( setadjoin @ SY531 @ emptyset ) ) )
=> ( in @ ( setunion @ SY530 ) @ SY530 ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(178,plain,
( ( ! [SY525: $i] :
( ? [SY526: $i] :
( ( in @ SY526 @ ( setunion @ SY525 ) )
& ? [SY527: $i] :
( ( in @ SY527 @ ( setunion @ SY525 ) )
& ( SY525
= ( setadjoin @ ( setadjoin @ SY526 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY526 @ ( setadjoin @ SY527 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [SY529: $i] :
( ( in @ SY529
@ ( dsetconstr @ ( setunion @ SY525 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY525 ) ) )
& ( ( dsetconstr @ ( setunion @ SY525 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY525 ) )
= ( setadjoin @ SY529 @ emptyset ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(179,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(180,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(181,plain,
( ( ! [SY508: $i,SY509: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY508 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY508 )
=> ( ( SY509 @ Xx )
=> ( ( SY509 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY508 )
& ( SY509 @ Xx ) )
=> ? [SY517: $i] :
( ( in @ SY517
@ ( dsetconstr @ SY508
@ ^ [SY518: $i] : ( SY509 @ SY518 ) ) )
& ( ( dsetconstr @ SY508
@ ^ [SY519: $i] : ( SY509 @ SY519 ) )
= ( setadjoin @ SY517 @ emptyset ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(182,plain,
( ( ! [SY497: $i,SY498: $i > $o,SY499: $i] :
( ( in @ SY499 @ SY497 )
=> ( ( SY498 @ SY499 )
=> ( ! [Xy: $i] :
( ( in @ Xy @ SY497 )
=> ( ( SY498 @ Xy )
=> ( Xy = SY499 ) ) )
=> ? [SY505: $i] :
( ( in @ SY505
@ ( dsetconstr @ SY497
@ ^ [SY506: $i] : ( SY498 @ SY506 ) ) )
& ( ( dsetconstr @ SY497
@ ^ [SY507: $i] : ( SY498 @ SY507 ) )
= ( setadjoin @ SY505 @ emptyset ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(183,plain,
( ( ! [SY487: $i,SY488: $i > $o] :
( ? [SY493: $i] :
( ( in @ SY493
@ ( dsetconstr @ SY487
@ ^ [SY494: $i] : ( SY488 @ SY494 ) ) )
& ( ( dsetconstr @ SY487
@ ^ [SY495: $i] : ( SY488 @ SY495 ) )
= ( setadjoin @ SY493 @ emptyset ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY487 )
& ( SY488 @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(184,plain,
( ( ! [SY480: $i,SY481: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY480 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY480 )
=> ( ( SY481 @ Xx )
=> ( ( SY481 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY480 )
& ( SY481 @ Xx ) )
=> ? [SY486: $i] :
( ( in @ SY486
@ ( dsetconstr @ SY480
@ ^ [Xx: $i] : ( SY481 @ Xx ) ) )
& ( ( dsetconstr @ SY480
@ ^ [Xx: $i] : ( SY481 @ Xx ) )
= ( setadjoin @ SY486 @ emptyset ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(185,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(186,plain,
( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(187,plain,
( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(188,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(189,plain,
( ( ! [SY469: $i,SY470: $i,SY471: $i] :
( ( in @ SY471 @ ( cartprod @ SY469 @ SY470 ) )
=> ? [SY472: $i] :
( ( in @ SY472 @ ( setunion @ SY471 ) )
& ? [SY473: $i] :
( ( in @ SY473 @ ( setunion @ SY471 ) )
& ( SY471
= ( setadjoin @ ( setadjoin @ SY472 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY472 @ ( setadjoin @ SY473 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(190,plain,
( ( ! [SY463: $i,SY464: $i,SY465: $i] :
( ( in @ SY465 @ ( cartprod @ SY463 @ SY464 ) )
=> ? [SY466: $i] :
( ( in @ SY466 @ SY463 )
& ? [SY467: $i] :
( ( in @ SY467 @ SY464 )
& ( SY465
= ( setadjoin @ ( setadjoin @ SY466 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY466 @ ( setadjoin @ SY467 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(191,plain,
( ( ! [SY458: $i,SY459: $i,SY460: $i] :
( ( in @ SY460 @ SY458 )
=> ! [SY461: $i] :
( ( in @ SY461 @ SY459 )
=> ( in @ ( setadjoin @ ( setadjoin @ SY460 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY460 @ ( setadjoin @ SY461 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SY458 @ SY459 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(192,plain,
( ( ! [SY453: $i,SY454: $i,SY455: $i] :
( ( in @ SY455 @ SY453 )
=> ! [SY456: $i] :
( ( in @ SY456 @ SY454 )
=> ( in @ ( setadjoin @ ( setadjoin @ SY455 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY455 @ ( setadjoin @ SY456 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SY453 @ SY454 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(193,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(194,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(195,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(196,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(197,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(198,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(199,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(200,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(201,plain,
( ( ! [SY422: $i,SY423: $i] :
? [SY425: $i] :
( ( in @ SY425 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY422 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY422 @ ( setadjoin @ SY423 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY426: $i] :
( ( in @ SY426 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY422 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY422 @ ( setadjoin @ SY423 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY422 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY422 @ ( setadjoin @ SY423 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY425 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY425 @ ( setadjoin @ SY426 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(202,plain,
( ( ! [SY418: $i,SY419: $i] :
? [SY420: $i] :
( ( in @ SY420 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY418 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY418 @ ( setadjoin @ SY419 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY421: $i] :
( ( in @ SY421 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY418 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY418 @ ( setadjoin @ SY419 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY418 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY418 @ ( setadjoin @ SY419 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY420 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY420 @ ( setadjoin @ SY421 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(203,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(204,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(205,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(206,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(207,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(208,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(209,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(210,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(211,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(212,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(213,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(214,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(215,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(216,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(217,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(218,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(219,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(220,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(221,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(222,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(223,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(224,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(225,plain,
( ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(226,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(227,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(228,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(229,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(230,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(231,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(232,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(233,plain,
( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(234,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(235,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(236,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(237,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(238,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(239,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(240,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(241,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(242,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(243,plain,
( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(244,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(245,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(246,plain,
( ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(247,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(248,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(249,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(250,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(251,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(252,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(253,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(254,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(255,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(256,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(257,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(258,plain,
( ( ! [A: $i] : ( subset @ emptyset @ A ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(259,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(260,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(261,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(262,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(263,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(264,plain,
( ( ! [SY248: $i > $o,SY249: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY248 @ Xx )
<=> ( SY249 @ Xy ) ) )
=> ( ? [SY253: $i] :
( ( SY248 @ SY253 )
& ! [SY254: $i] :
( ( SY248 @ SY254 )
=> ( SY253 = SY254 ) ) )
=> ( ? [SY256: $i] :
( ( SY249 @ SY256 )
& ! [SY257: $i] :
( ( SY249 @ SY257 )
=> ( SY256 = SY257 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY248 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY249 @ Xx ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(265,plain,
( ( ! [SY242: $i > $o] :
( ? [SY244: $i] :
( ( SY242 @ SY244 )
& ! [SY245: $i] :
( ( SY242 @ SY245 )
=> ( SY244 = SY245 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY242 @ Xx )
=> ( ( SY242 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(267,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(268,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(269,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(271,plain,
( ( ! [SY224: $i > $o,SY225: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY224 @ Xx )
<=> ( SY225 @ Xy ) ) )
=> ( ? [SY229: $i] :
( ( SY224 @ SY229 )
& ! [SY230: $i] :
( ( SY224 @ SY230 )
=> ( SY229 = SY230 ) ) )
<=> ? [SY232: $i] :
( ( SY225 @ SY232 )
& ! [SY233: $i] :
( ( SY225 @ SY233 )
=> ( SY232 = SY233 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(272,plain,
( ( ! [SY218: $i > $o] :
( ? [SY220: $i] :
( ( SY218 @ SY220 )
& ! [SY221: $i] :
( ( SY218 @ SY221 )
=> ( SY220 = SY221 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY218 @ Xx )
=> ( ( SY218 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(273,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(274,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(275,plain,
( ( ! [SY204: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY204 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY208: $i] :
( ( SY204 @ SY208 )
& ! [SY209: $i] :
( ( SY204 @ SY209 )
=> ( SY208 = SY209 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(276,plain,
( ( ! [SY197: $i > $o] :
( ? [Xx: $i] : ( SY197 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY197 @ Xx )
=> ( ( SY197 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY202: $i] :
( ( SY197 @ SY202 )
& ! [SY203: $i] :
( ( SY197 @ SY203 )
=> ( SY202 = SY203 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(277,plain,
( ( ! [SY191: $i > $o] :
( ? [Xx: $i] :
( ( SY191 @ Xx )
& ! [Xy: $i] :
( ( SY191 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY195: $i] :
( ( SY191 @ SY195 )
& ! [SY196: $i] :
( ( SY191 @ SY196 )
=> ( SY195 = SY196 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(278,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(279,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(280,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(281,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(282,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(283,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(284,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(285,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(286,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(287,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(288,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(289,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(290,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(291,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(292,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(293,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(294,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(295,plain,
( ( ! [SY142: $i] :
( ( SY142 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY142 )
& $true ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(296,plain,
( ( ! [SY136: $i > $o] :
( ? [SY138: $i] :
( ( SY136 @ SY138 )
& ! [SY139: $i] :
( ( SY136 @ SY139 )
=> ( SY138 = SY139 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY136 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(297,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(298,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(299,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(300,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(301,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(302,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(303,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(304,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(305,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(306,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(307,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(308,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(309,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(310,plain,
( ( ! [SY103: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY103 )
=> ( SY103 != emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(311,plain,
( ( ! [SY99: $i,SY100: $i > $o,SY101: $i] :
( ( in @ SY101 @ SY99 )
=> ( ( SY100 @ SY101 )
=> ( ( dsetconstr @ SY99
@ ^ [Xy: $i] : ( SY100 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(312,plain,
( ( ! [SY97: $i] :
( ( SY97 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY97 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(313,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(314,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(315,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(316,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(317,plain,
( ( ! [SY80: $i > $o] :
( ? [SY82: $i] :
( ( SY80 @ SY82 )
& ! [SY83: $i] :
( ( SY80 @ SY83 )
=> ( SY82 = SY83 ) ) )
=> ? [Xx: $i] : ( SY80 @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(318,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(319,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(320,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(321,plain,
( ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(322,plain,
( ( ! [SY68: $i > $o] :
( ? [SY70: $i] :
( ( SY68 @ SY70 )
& ! [SY71: $i] :
( ( SY68 @ SY71 )
=> ( SY70 = SY71 ) ) )
=> ? [Xx: $i] :
( ( SY68 @ Xx )
& ! [Xy: $i] :
( ( SY68 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(323,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(324,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(325,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(326,plain,
( ( ! [SY51: $i > $o] :
( ? [SY53: $i] :
( ( SY51 @ SY53 )
& ! [SY54: $i] :
( ( SY51 @ SY54 )
=> ( SY53 = SY54 ) ) )
=> ( SY51
@ ( descr
@ ^ [Xx: $i] : ( SY51 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(327,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(328,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(329,plain,
( ( ! [SY19: $i > $i > $o,SY20: $i] :
( ! [SY21: $i] :
( ( in @ SY21 @ SY20 )
=> ? [SY23: $i] :
( ( SY19 @ SY21 @ SY23 )
& ! [SY24: $i] :
( ( SY19 @ SY21 @ SY24 )
=> ( SY23 = SY24 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY20 )
& ( SY19 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(330,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(331,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(332,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(333,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(334,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(335,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(336,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(337,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(338,plain,
( ( ~ ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(339,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)],[263,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(340,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ( SX0
!= ( setadjoin @ SX1 @ emptyset ) ) )
| ( in @ ( setunion @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(341,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)],[287,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(342,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(343,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(344,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( setadjoin @ SX2 @ emptyset ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(345,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)],[327,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(346,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( in @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(347,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)],[265,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(348,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)],[282,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(349,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)],[311,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(350,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(351,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(352,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(353,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setunion @ SX0 )
= ( setunion @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(354,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(355,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)],[278,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(356,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(357,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( ( binintersect @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(358,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(359,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( powerset @ SX0 )
= ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(360,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)],[322,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(361,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)],[316,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(362,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(363,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(364,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(365,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(366,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(367,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(368,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ( SX2
!= ( setadjoin @ ( setadjoin @ SX3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX3 @ ( setadjoin @ SX4 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(369,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)],[337,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(370,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $o] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX0 )
| SX3 )
| ~ ( ~ ( in @ SX2 @ SX1 )
| SX3 )
| SX3 ) )
= $true ),
inference(unfold_def,[status(thm)],[236,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(371,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(372,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)],[284,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(373,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(374,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)],[329,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(375,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(376,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(377,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(378,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(379,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(380,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(381,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= ( setadjoin @ SX2 @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(382,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)],[325,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(383,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)],[298,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(384,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( in @ emptyset @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(385,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)],[274,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(386,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= ( setadjoin @ SX2 @ emptyset ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(387,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[319,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(388,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( subset @ ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(389,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(390,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(391,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)],[269,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(392,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( binintersect @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(393,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(394,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(395,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| ! [SX1: $o] : SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[320,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(396,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)],[271,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(397,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(398,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(399,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(400,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ( ( binintersect @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(401,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)],[296,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(402,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)],[306,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(403,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= ( setadjoin @ SX2 @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(404,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(405,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(406,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(407,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)],[335,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(408,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(409,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)],[275,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(410,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setadjoin @ SX0 @ emptyset )
!= ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(411,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ ( setunion @ SX2 ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ ( setunion @ SX2 ) )
| ( SX2
!= ( setadjoin @ ( setadjoin @ SX3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX3 @ ( setadjoin @ SX4 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(412,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(413,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)],[324,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(414,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(415,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)],[283,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(416,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(417,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(418,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(419,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ ( setunion @ SX0 ) )
| ( SX0
!= ( setadjoin @ ( setadjoin @ SX1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX1 @ ( setadjoin @ SX2 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX2: $i] : ( in @ ( setadjoin @ SX2 @ emptyset ) @ SX0 ) ) )
| ( ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX2: $i] : ( in @ ( setadjoin @ SX2 @ emptyset ) @ SX0 ) )
!= ( setadjoin @ SX1 @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(420,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(421,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(422,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( subset @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ ( binunion @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(423,plain,
( ( ! [SX0: $o,SX1: $i] :
( ~ ( in @ SX1 @ ( prop2set @ SX0 ) )
| SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[321,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(424,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) )
| ! [SX3: $o] :
( ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| SX3 )
| ~ ( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| SX3 )
| SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(425,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(426,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX2 )
| ( subset @ SX0 @ ( setadjoin @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(427,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(428,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(429,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)],[273,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(430,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)],[285,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(431,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(432,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(433,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( setminus @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(434,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(435,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)],[277,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(436,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(437,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)],[333,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(438,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 != emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(439,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(440,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(441,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)],[276,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(442,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ ( kfst @ SX2 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(443,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(444,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( set2prop @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(445,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ( in @ SX1 @ emptyset )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(446,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX0 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(447,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(448,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(449,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)],[330,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(450,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(451,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)],[334,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(452,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(453,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)],[328,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(454,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(455,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)],[264,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(456,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ ( setadjoin @ SX1 @ emptyset ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(457,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)],[313,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(458,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(459,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)],[326,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(460,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setminus @ SX0 @ SX1 )
!= emptyset )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(461,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(462,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)],[279,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(463,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(464,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(465,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ~ ( subset @ SX2 @ SX1 )
| ( subset @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(466,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( powerset @ SX0 ) @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(467,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(468,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ emptyset )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(469,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(470,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)],[272,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(471,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(472,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(473,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX3 )
| ( SX3 = SX2 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3
@ ( dsetconstr @ SX0
@ ^ [SX4: $i] : ( SX1 @ SX4 ) ) )
| ( ( dsetconstr @ SX0
@ ^ [SX4: $i] : ( SX1 @ SX4 ) )
!= ( setadjoin @ SX3 @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,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,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR11,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(474,plain,
! [SV1: $i] :
( ( ! [SY1071: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SY1071 @ emptyset ) ) @ emptyset ) ) )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(475,plain,
! [SV2: $i] :
( ( ( setunion @ ( setadjoin @ SV2 @ emptyset ) )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(476,plain,
! [SV3: $i] :
( ( subset @ SV3 @ ( setunion @ ( setadjoin @ SV3 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(477,plain,
! [SV4: $i] :
( ( subset @ ( setunion @ ( setadjoin @ SV4 @ emptyset ) ) @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(478,plain,
! [SV5: $i] :
( ( ! [SY1072: $i] : ( in @ SY1072 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV5 @ ( setadjoin @ SY1072 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(479,plain,
! [SV6: $i] :
( ( ! [SY1073: $i] : ( in @ SV6 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV6 @ ( setadjoin @ SY1073 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(480,plain,
! [SV7: $i] :
( ( ! [SY1074: $i] : ( in @ SY1074 @ ( setadjoin @ SV7 @ ( setadjoin @ SY1074 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(481,plain,
! [SV8: $i] :
( ( ! [SY1075: $i] : ( subset @ ( setminus @ SV8 @ SY1075 ) @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(482,plain,
! [SV9: $i] :
( ( ! [SY1076: $i,SY1077: $i] :
( ( binintersect @ SV9 @ ( binunion @ SY1076 @ SY1077 ) )
= ( binunion @ ( binintersect @ SV9 @ SY1076 ) @ ( binintersect @ SV9 @ SY1077 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(483,plain,
! [SV10: $i] :
( ( ! [SY1078: $i] : ( subset @ ( binintersect @ SV10 @ SY1078 ) @ SY1078 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(484,plain,
! [SV11: $i] :
( ( ! [SY1079: $i] : ( subset @ ( binintersect @ SV11 @ SY1079 ) @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(485,plain,
! [SV12: $i] :
( ( ! [SY1080: $i] : ( subset @ SY1080 @ ( binunion @ SV12 @ SY1080 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(486,plain,
! [SV13: $i] :
( ( ! [SY1081: $i] : ( subset @ SV13 @ ( binunion @ SV13 @ SY1081 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(487,plain,
! [SV14: $i] :
( ( ! [SY1082: $i] : ( in @ SY1082 @ ( setadjoin @ SV14 @ ( setadjoin @ SY1082 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(488,plain,
! [SV15: $i] :
( ( ! [SY1083: $i > $o] :
( subset
@ ( dsetconstr @ SV15
@ ^ [Xx: $i] : ( SY1083 @ Xx ) )
@ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(489,plain,
! [SV16: $i] :
( ( ! [SY1085: $i > $o] :
( in
@ ( dsetconstr @ SV16
@ ^ [Xx: $i] : ( SY1085 @ Xx ) )
@ ( powerset @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(490,plain,
! [SV17: $i] :
( ( in @ SV17 @ ( powerset @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(491,plain,
! [SV18: $i] :
( ( ! [SY1087: $i] : ( subset @ SY1087 @ ( setadjoin @ SV18 @ SY1087 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(492,plain,
! [SV19: $i] :
( ( subset @ SV19 @ SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(493,plain,
! [SV20: $i] :
( ( subset @ emptyset @ SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(494,plain,
! [SV21: $i] :
( ( ! [SY1088: $i] : ( in @ SY1088 @ ( setadjoin @ SV21 @ ( setadjoin @ SY1088 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(495,plain,
! [SV22: $i] :
( ( ! [SY1089: $i] : ( in @ SV22 @ ( setadjoin @ SV22 @ ( setadjoin @ SY1089 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(496,plain,
! [SV23: $i] :
( ( in @ emptyset @ ( powerset @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(497,plain,
! [SV24: $i] :
( ( in @ emptyset @ ( powerset @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(498,plain,
! [SV25: $i] :
( ( ( dsetconstr @ SV25
@ ^ [Xx: $i] : $true )
= SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(499,plain,
! [SV26: $i] :
( ( ! [SY1091: $i] : ( in @ SV26 @ ( setadjoin @ SV26 @ SY1091 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(500,plain,
! [SV27: $i] :
( ( ~ ( in @ SV27 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(501,plain,
! [SV28: $i] :
( ( ~ ( in @ SV28 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(502,plain,
! [SV29: $i] :
( ( ! [SY1092: $i] :
( ( SV29 != SY1092 )
| ! [SY1093: $i > $o,SY1094: $i > $o] :
( ~ ! [SY1095: $i] :
( ~ ( in @ SY1095 @ SV29 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY1092 )
| ( SY1095 != SX5 )
| ~ ( ~ ( ~ ( SY1093 @ SY1095 )
| ( SY1094 @ SX5 ) )
| ~ ( ~ ( SY1094 @ SX5 )
| ( SY1093 @ SY1095 ) ) ) ) )
| ( ( dsetconstr @ SV29
@ ^ [SX4: $i] : ( SY1093 @ SX4 ) )
= ( dsetconstr @ SY1092
@ ^ [SX4: $i] : ( SY1094 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(503,plain,
! [SV30: $i] :
( ( ~ ~ ! [SY1099: $i] :
~ ~ ( ~ ( in @ SY1099 @ SV30 )
| ( SV30
!= ( setadjoin @ SY1099 @ emptyset ) ) )
| ( in @ ( setunion @ SV30 ) @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(504,plain,
! [SV31: $i] :
( ( ! [SY1100: $i > $o] :
( ~ ~ ! [SY1101: $i] :
~ ~ ( ~ ( in @ SY1101 @ SV31 )
| ~ ( SY1100 @ SY1101 ) )
| ( ( dsetconstr @ SV31
@ ^ [SX2: $i] : ( SY1100 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(505,plain,
! [SV32: $i] :
( ( ! [SY1103: $i,SY1104: $i] :
( ~ ( in @ SY1104 @ ( setadjoin @ SV32 @ ( setadjoin @ SY1103 @ emptyset ) ) )
| ( SY1104 = SV32 )
| ( SY1104 = SY1103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(506,plain,
! [SV33: $i] :
( ( ! [SY1105: $i,SY1106: $i] :
( ~ ( in @ SY1106 @ SV33 )
| ~ ( in @ SY1106 @ SY1105 )
| ( in @ SY1106 @ ( binintersect @ SV33 @ SY1105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(507,plain,
! [SV34: $i] :
( ( ! [SY1107: $i,SY1108: $i] :
( ~ ( in @ SY1108 @ SV34 )
| ( in @ ( setadjoin @ SY1108 @ emptyset ) @ ( powerset @ ( binunion @ SV34 @ SY1107 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(508,plain,
! [SV35: $i] :
( ( ~ ! [SY1109: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1110: $i] :
( ~ ( in @ SY1110 @ SY1109 )
| ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SY1110 )
| ( in @ SY1111 @ SV35 ) ) )
| ~ ! [SY1112: $i,SY1113: $i] :
( ~ ~ ( ~ ( in @ SY1112 @ SV35 )
| ~ ( in @ SY1113 @ SV35 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1109 )
| ~ ( ~ ( ~ ( in @ SY1112 @ SX4 )
| ( in @ SY1113 @ SX4 ) )
| ~ ( ~ ( in @ SY1113 @ SX4 )
| ( in @ SY1112 @ SX4 ) ) ) )
| ( SY1112 = SY1113 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY1109 )
| ~ ( in @ SX3 @ SY1109 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY1119: $i] :
( ~ ~ ( ~ ! [SY1120: $i] :
( ~ ( in @ SY1120 @ SY1119 )
| ( in @ SY1120 @ SV35 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1119 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY1109 )
| ~ ( in @ SX4 @ SY1119 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY1119 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY1109 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(509,plain,
! [SV36: $i] :
( ( ! [SY1127: $i] :
( ~ ( subset @ SV36 @ SY1127 )
| ( in @ SV36 @ ( powerset @ SY1127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(510,plain,
! [SV37: $i > $o] :
( ( ~ ~ ! [SY1128: $i] :
~ ~ ( ~ ( SV37 @ SY1128 )
| ~ ! [SY1129: $i] :
( ~ ( SV37 @ SY1129 )
| ( SY1128 = SY1129 ) ) )
| ! [SY1130: $i,SY1131: $i] :
( ~ ( SV37 @ SY1130 )
| ~ ( SV37 @ SY1131 )
| ( SY1130 = SY1131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(511,plain,
! [SV38: $i] :
( ( ! [SY1132: $i > $o] :
( ~ ~ ! [SY1133: $i] :
~ ~ ( ~ ( in @ SY1133 @ SV38 )
| ~ ~ ( SY1132 @ SY1133 ) )
| ~ ! [SY1134: $i] :
( ~ ( in @ SY1134 @ SV38 )
| ( SY1132 @ SY1134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(512,plain,
! [SV39: $i] :
( ( ! [SY1135: $i > $o,SY1136: $i] :
( ~ ( in @ SY1136 @ SV39 )
| ~ ( SY1135 @ SY1136 )
| ( ( dsetconstr @ SV39
@ ^ [SX3: $i] : ( SY1135 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(513,plain,
! [SV40: $i] :
( ( ! [SY1138: $i,SY1139: $i] :
( ~ ( in @ SY1139 @ SV40 )
| ! [SY1140: $i] :
( ~ ( in @ SY1140 @ SY1138 )
| ( in @ ( setadjoin @ ( setadjoin @ SY1139 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1139 @ ( setadjoin @ SY1140 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SV40 @ SY1138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(514,plain,
! [SV41: $i] :
( ( ! [SY1141: $i] :
( ( SV41 != SY1141 )
| ( subset @ SV41 @ SY1141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(515,plain,
! [SV42: $i] :
( ( ! [SY1142: $i,SY1143: $i,SY1144: $i] :
( ( ( setadjoin @ ( setadjoin @ SV42 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV42 @ ( setadjoin @ SY1142 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1143 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1143 @ ( setadjoin @ SY1144 @ emptyset ) ) @ emptyset ) ) )
| ( SV42 = SY1143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(516,plain,
! [SV43: $i] :
( ( ! [SY1145: $i] :
( ( SV43 != SY1145 )
| ( ( setunion @ SV43 )
= ( setunion @ SY1145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(517,plain,
! [SV44: $i] :
( ( ! [SY1146: $i,SY1147: $i] :
( ~ ( in @ SY1147 @ SV44 )
| ~ ~ ( in @ SY1147 @ SY1146 )
| ~ ( subset @ SV44 @ SY1146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(518,plain,
! [SV45: $i] :
( ( ! [SY1148: $i > $o] :
( ~ ~ ! [SY1149: $i] :
( ~ ( in @ SY1149 @ SV45 )
| ( SY1148 @ SY1149 ) )
| ~ ! [SY1150: $i] :
~ ~ ( ~ ( in @ SY1150 @ SV45 )
| ~ ~ ( SY1148 @ SY1150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(519,plain,
! [SV46: $i] :
( ( ! [SY1151: $i,SY1152: $i] :
( ~ ( in @ SY1151 @ ( powerset @ SV46 ) )
| ~ ( in @ SY1152 @ SY1151 )
| ( in @ SY1152 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(520,plain,
! [SV47: $i] :
( ( ! [SY1153: $i] :
( ~ ( subset @ SY1153 @ SV47 )
| ( ( binintersect @ SV47 @ SY1153 )
= SY1153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(521,plain,
! [SV48: $i] :
( ( ! [SY1154: $i,SY1155: $i] :
( ~ ( in @ SY1155 @ SV48 )
| ! [SY1156: $i] :
( ~ ( in @ SY1156 @ SY1154 )
| ( in @ ( setadjoin @ ( setadjoin @ SY1155 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1155 @ ( setadjoin @ SY1156 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV48 @ SY1154 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(522,plain,
! [SV49: $i] :
( ( ! [SY1157: $i] :
( ( SV49 != SY1157 )
| ( ( powerset @ SV49 )
= ( powerset @ SY1157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(523,plain,
! [SV50: $i > $o] :
( ( ~ ~ ! [SY1158: $i] :
~ ~ ( ~ ( SV50 @ SY1158 )
| ~ ! [SY1159: $i] :
( ~ ( SV50 @ SY1159 )
| ( SY1158 = SY1159 ) ) )
| ~ ! [SY1160: $i] :
~ ~ ( ~ ( SV50 @ SY1160 )
| ~ ! [SY1161: $i] :
( ~ ( SV50 @ SY1161 )
| ( SY1160 = SY1161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(524,plain,
! [SV51: $i] :
( ( ! [SY1162: $i] :
( ~ ! [SY1163: $i] :
( ~ ( in @ SY1163 @ SV51 )
| ( in @ SY1163 @ SY1162 ) )
| ~ ! [SY1164: $i] :
( ~ ( in @ SY1164 @ SY1162 )
| ( in @ SY1164 @ SV51 ) )
| ( SV51 = SY1162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(525,plain,
! [SV52: $i] :
( ( ~ ( ( SV52 != emptyset ) )
| ~ ! [SY1165: $i] :
~ ( in @ SY1165 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(526,plain,
! [SV53: $i] :
( ( ! [SY1166: $i,SY1167: $i] :
( ~ ( in @ SY1167 @ SV53 )
| ~ ~ ( in @ SY1167 @ SY1166 )
| ( in @ SY1167 @ ( setminus @ SV53 @ SY1166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(527,plain,
! [SV54: $i] :
( ( ! [SY1168: $i] :
~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SY1168 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SY1168 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SY1168 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1169 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1169 @ ( setadjoin @ SY1170 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(528,plain,
! [SV55: $i] :
( ( ! [SY1171: $i,SY1172: $i] :
( ~ ~ ( in @ SY1172 @ SV55 )
| ~ ( in @ SY1172 @ ( setminus @ SV55 @ SY1171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(529,plain,
! [SV56: $i] :
( ( ! [SY1173: $i,SY1174: $i] :
( ~ ( in @ SY1173 @ SY1174 )
| ~ ( in @ SY1174 @ SV56 )
| ( in @ SY1173 @ ( setunion @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(530,plain,
! [SV57: $i] :
( ( ! [SY1175: $i,SY1176: $i] :
( ~ ( in @ SY1176 @ ( setadjoin @ SV57 @ ( setadjoin @ SY1175 @ emptyset ) ) )
| ( SY1176 = SV57 )
| ( SY1176 = SY1175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(531,plain,
! [SV58: $i] :
( ( ! [SY1177: $i,SY1178: $i] :
( ~ ( in @ SY1178 @ ( cartprod @ SV58 @ SY1177 ) )
| ~ ! [SY1179: $i] :
~ ~ ( ~ ( in @ SY1179 @ SV58 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SY1177 )
| ( SY1178
!= ( setadjoin @ ( setadjoin @ SY1179 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1179 @ ( setadjoin @ SX4 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(532,plain,
! [SV59: $i] :
( ( ! [SY1181: $i] :
( ~ ! [SY1182: $i] :
~ ( ~ ( ~ ( in @ SY1182 @ SV59 )
| ( in @ SY1182 @ SY1181 ) )
| ~ ( ~ ( in @ SY1182 @ SY1181 )
| ( in @ SY1182 @ SV59 ) ) )
| ( SV59 = SY1181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(533,plain,
! [SV60: $i] :
( ( ! [SY1183: $i,SY1184: $i,SY1185: $o] :
( ~ ( in @ SY1184 @ ( binunion @ SV60 @ SY1183 ) )
| ~ ( ~ ( in @ SY1184 @ SV60 )
| SY1185 )
| ~ ( ~ ( in @ SY1184 @ SY1183 )
| SY1185 )
| SY1185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(534,plain,
! [SV61: $i] :
( ( ! [SY1186: $i] :
~ ! [SY1187: $i] :
~ ~ ( ~ ( in @ SY1187 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SY1186 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1188: $i] :
~ ~ ( ~ ( in @ SY1188 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SY1186 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SY1186 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1187 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1187 @ ( setadjoin @ SY1188 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(535,plain,
! [SV62: $i] :
( ( ! [SY1189: $i > $o] :
( ~ ! [SY1190: $i] :
( ~ ( in @ SY1190 @ SV62 )
| ~ ( SY1189 @ SY1190 ) )
| ~ ~ ! [SY1191: $i] :
~ ~ ( ~ ( in @ SY1191 @ SV62 )
| ~ ( SY1189 @ SY1191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(536,plain,
! [SV63: $i] :
( ( ! [SY1192: $i] :
( ~ ( in @ SY1192 @ SV63 )
| ( subset @ ( setadjoin @ SY1192 @ emptyset ) @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(537,plain,
! [SV64: $i > $i > $o] :
( ( ! [SY1193: $i] :
( ~ ! [SY1194: $i] :
( ~ ( in @ SY1194 @ SY1193 )
| ~ ! [SY1195: $i] :
~ ~ ( ~ ( SV64 @ SY1194 @ SY1195 )
| ~ ! [SY1196: $i] :
( ~ ( SV64 @ SY1194 @ SY1196 )
| ( SY1195 = SY1196 ) ) ) )
| ~ ! [SY1197: $i] :
~ ! [SY1198: $i] :
~ ( ~ ( ~ ( in @ SY1198 @ SY1197 )
| ~ ! [SY1199: $i] :
~ ~ ( ~ ( in @ SY1199 @ SY1193 )
| ~ ( SV64 @ SY1199 @ SY1198 ) ) )
| ~ ( ~ ~ ! [SY1200: $i] :
~ ~ ( ~ ( in @ SY1200 @ SY1193 )
| ~ ( SV64 @ SY1200 @ SY1198 ) )
| ( in @ SY1198 @ SY1197 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(538,plain,
! [SV65: $i] :
( ( ! [SY1201: $i,SY1202: $i] :
( ~ ( in @ ( setadjoin @ SY1202 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV65 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV65 @ ( setadjoin @ SY1201 @ emptyset ) ) @ emptyset ) ) )
| ( SV65 = SY1202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(539,plain,
! [SV66: $i] :
( ( ! [SY1203: $i,SY1204: $i,SY1205: $i] :
( ( ( setadjoin @ ( setadjoin @ SV66 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV66 @ ( setadjoin @ SY1203 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1204 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1204 @ ( setadjoin @ SY1205 @ emptyset ) ) @ emptyset ) ) )
| ( SV66 = SY1204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(540,plain,
! [SV67: $i] :
( ( ! [SY1206: $i,SY1207: $i] :
( ~ ( in @ SY1207 @ SV67 )
| ~ ( in @ SY1207 @ SY1206 )
| ~ ( in @ SY1207 @ ( symdiff @ SV67 @ SY1206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(541,plain,
! [SV68: $i] :
( ( ! [SY1208: $i] :
( ~ ~ ( subset @ SV68 @ SY1208 )
| ( SV68 != SY1208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(542,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ emptyset ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(543,plain,
! [SV69: $i] :
( ( ! [SY1209: $i] :
( ( SV69 != SY1209 )
| ( subset @ SY1209 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(544,plain,
! [SV70: $i] :
( ( ! [SY1210: $i > $o] :
( ~ ! [SY1211: $i] :
( ~ ( in @ SY1211 @ SV70 )
| ! [SY1212: $i] :
( ~ ( in @ SY1212 @ SV70 )
| ~ ( SY1210 @ SY1211 )
| ~ ( SY1210 @ SY1212 )
| ( SY1211 = SY1212 ) ) )
| ~ ~ ! [SY1213: $i] :
~ ~ ( ~ ( in @ SY1213 @ SV70 )
| ~ ( SY1210 @ SY1213 ) )
| ~ ! [SY1214: $i] :
~ ~ ( ~ ( in @ SY1214
@ ( dsetconstr @ SV70
@ ^ [SX3: $i] : ( SY1210 @ SX3 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SX3: $i] : ( SY1210 @ SX3 ) )
!= ( setadjoin @ SY1214 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(545,plain,
! [SV71: $i] :
( ( ! [SY1217: $i > $o,SY1218: $i] :
( ~ ( in @ SY1218 @ SV71 )
| ~ ( SY1217 @ SY1218 )
| ( in @ SY1218
@ ( dsetconstr @ SV71
@ ^ [SX3: $i] : ( SY1217 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(546,plain,
! [SV72: $i] :
( ( ! [SY1220: $i] :
( ~ ( in @ SY1220 @ ( setunion @ SV72 ) )
| ! [SY1221: $o] :
( ~ ! [SY1222: $i] :
( ~ ( in @ SY1220 @ SY1222 )
| ~ ( in @ SY1222 @ SV72 )
| SY1221 )
| SY1221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(547,plain,
! [SV73: $o] :
( ( ~ SV73
| ( in @ emptyset @ ( prop2set @ SV73 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[384]) ).
thf(548,plain,
( ( ~ $true
| ( in @ emptyset @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[384]) ).
thf(550,plain,
! [SV74: $i] :
( ( ! [SY1223: $i] :
( ( SV74 != SY1223 )
| ! [SY1224: $i,SY1225: $i] :
( ( SY1224 != SY1225 )
| ~ ( in @ SY1224 @ SV74 )
| ( in @ SY1225 @ SY1223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(551,plain,
! [SV75: $i] :
( ( ! [SY1226: $i > $o] :
( ~ ~ ! [SY1227: $i] :
~ ~ ( ~ ( in @ SY1227
@ ( dsetconstr @ SV75
@ ^ [SX3: $i] : ( SY1226 @ SX3 ) ) )
| ( ( dsetconstr @ SV75
@ ^ [SX3: $i] : ( SY1226 @ SX3 ) )
!= ( setadjoin @ SY1227 @ emptyset ) ) )
| ~ ! [SY1230: $i] :
~ ~ ( ~ ( in @ SY1230 @ SV75 )
| ~ ( SY1226 @ SY1230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(552,plain,
! [SV76: $i] :
( ( ~ ( in @ SV76 @ emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(553,plain,
! [SV77: $i] :
( ( ! [SY1231: $i,SY1232: $i] :
( ~ ( in @ SY1232 @ SV77 )
| ! [SY1233: $i] :
( ~ ( in @ SY1233 @ SY1231 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY1232 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1232 @ ( setadjoin @ SY1233 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV77 @ SY1231 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(554,plain,
! [SV78: $i] :
( ( ! [SY1234: $i] :
( ~ ( in @ SY1234 @ ( powerset @ SV78 ) )
| ( subset @ SY1234 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(555,plain,
! [SV79: $i] :
( ( ! [SY1235: $i,SY1236: $i] :
( ~ ~ ( in @ SY1236 @ SV79 )
| ~ ( in @ SY1236 @ SY1235 )
| ( in @ SY1236 @ ( symdiff @ SV79 @ SY1235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(556,plain,
! [SV80: $i] :
( ( ! [SY1237: $i] :
( ( SV80 != SY1237 )
| ! [SY1238: $i,SY1239: $i] :
( ( SY1238 != SY1239 )
| ( ( setadjoin @ SV80 @ SY1238 )
= ( setadjoin @ SY1237 @ SY1239 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(557,plain,
! [SV81: $i] :
( ( ! [SY1240: $i] :
( ~ ( subset @ SV81 @ SY1240 )
| ( ( binintersect @ SV81 @ SY1240 )
= SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(558,plain,
! [SV82: $i] :
( ( ! [SY1241: $i] :
( ( SV82 != SY1241 )
| ( ( setadjoin @ SV82 @ ( setadjoin @ SY1241 @ emptyset ) )
= ( setadjoin @ SV82 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(559,plain,
! [SV83: $i] :
( ( ! [SY1242: $i] :
( ( ( binintersect @ SV83 @ SY1242 )
!= SY1242 )
| ( subset @ SY1242 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(560,plain,
! [SV84: $i] :
( ( ~ ( in @ SV84 @ emptyset )
| ! [SX1: $o] : SX1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(561,plain,
! [SV85: $i > $o] :
( ( ! [SY1244: $i > $o] :
( ~ ! [SY1245: $i,SY1246: $i] :
( ( SY1245 != SY1246 )
| ~ ( ~ ( ~ ( SV85 @ SY1245 )
| ( SY1244 @ SY1246 ) )
| ~ ( ~ ( SY1244 @ SY1246 )
| ( SV85 @ SY1245 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SY1244 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY1244 @ SX3 )
| ( SX2 = SX3 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY1244 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY1244 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(562,plain,
! [SV86: $i] :
( ( ! [SY1255: $i] :
( ~ ! [SY1256: $i] :
( ~ ( in @ SY1256 @ SV86 )
| ( in @ SY1256 @ SY1255 ) )
| ( subset @ SV86 @ SY1255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(563,plain,
! [SV87: $i] :
( ( ! [SY1257: $i,SY1258: $i] :
( ~ ( in @ SY1258 @ SV87 )
| ! [SY1259: $i] :
( ~ ( in @ SY1259 @ SY1257 )
| ( in @ ( setadjoin @ ( setadjoin @ SY1258 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1258 @ ( setadjoin @ SY1259 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV87 @ SY1257 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(564,plain,
! [SV88: $i] :
( ( ! [SY1260: $i,SY1261: $i] :
( ~ ( in @ SY1261 @ SY1260 )
| ( in @ SY1261 @ ( setadjoin @ SV88 @ SY1260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(565,plain,
! [SV89: $i] :
( ( ! [SY1262: $i] :
( ~ ~ ~ ! [SY1263: $i] :
~ ~ ( ~ ( in @ SY1263 @ SV89 )
| ~ ( in @ SY1263 @ SY1262 ) )
| ( ( binintersect @ SV89 @ SY1262 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(566,plain,
! [SV90: $i > $o] :
( ( ~ ~ ! [SY1264: $i] :
~ ~ ( ~ ( SV90 @ SY1264 )
| ~ ! [SY1265: $i] :
( ~ ( SV90 @ SY1265 )
| ( SY1264 = SY1265 ) ) )
| ~ ! [SY1266: $i] :
~ ! [SY1267: $i] :
~ ( ~ ( ~ ( SV90 @ SY1267 )
| ( SY1267 = SY1266 ) )
| ~ ( ( SY1267 != SY1266 )
| ( SV90 @ SY1267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(567,plain,
! [SV91: $i] :
( ( ! [SY1268: $i,SY1269: $i] :
( ~ ( in @ SY1269 @ ( setadjoin @ SV91 @ SY1268 ) )
| ! [SY1270: $o] :
( ~ ( ( SY1269 != SV91 )
| SY1270 )
| ~ ( ~ ( in @ SY1269 @ SY1268 )
| SY1270 )
| SY1270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(568,plain,
! [SV92: $i] :
( ( ! [SY1271: $i > $o] :
( ~ ! [SY1272: $i] :
( ~ ( in @ SY1272 @ SV92 )
| ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV92 )
| ~ ( SY1271 @ SY1272 )
| ~ ( SY1271 @ SY1273 )
| ( SY1272 = SY1273 ) ) )
| ~ ~ ! [SY1274: $i] :
~ ~ ( ~ ( in @ SY1274 @ SV92 )
| ~ ( SY1271 @ SY1274 ) )
| ~ ! [SY1275: $i] :
~ ~ ( ~ ( in @ SY1275
@ ( dsetconstr @ SV92
@ ^ [SX3: $i] : ( SY1271 @ SX3 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SX3: $i] : ( SY1271 @ SX3 ) )
!= ( setadjoin @ SY1275 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(569,plain,
! [SV93: $i] :
( ( ! [SY1278: $i > $o,SY1279: $i] :
( ~ ( in @ SY1279
@ ( dsetconstr @ SV93
@ ^ [SX3: $i] : ( SY1278 @ SX3 ) ) )
| ( SY1278 @ SY1279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(570,plain,
! [SV94: $i] :
( ( ! [SY1281: $i,SY1282: $i] :
( ~ ( in @ SY1282 @ SY1281 )
| ~ ( in @ SY1282 @ ( setminus @ SV94 @ SY1281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(571,plain,
! [SV95: $i] :
( ( ! [SY1283: $i,SY1284: $i] :
( ~ ( in @ SY1284 @ SV95 )
| ! [SY1285: $i] :
( ~ ( in @ SY1285 @ SY1283 )
| ( in @ ( setadjoin @ SY1284 @ ( setadjoin @ SY1285 @ emptyset ) ) @ ( powerset @ ( binunion @ SV95 @ SY1283 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(572,plain,
! [SV96: $i] :
( ( ! [SY1286: $i,SY1287: $i] :
~ ( ~ ( ~ ( in @ SY1287 @ ( setadjoin @ SV96 @ SY1286 ) )
| ( SY1287 = SV96 )
| ( in @ SY1287 @ SY1286 ) )
| ~ ( ~ ( ( SY1287 = SV96 )
| ( in @ SY1287 @ SY1286 ) )
| ( in @ SY1287 @ ( setadjoin @ SV96 @ SY1286 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(573,plain,
! [SV97: $i] :
( ( ! [SY1288: $i,SY1289: $i] :
( ~ ~ ( in @ SY1289 @ ( setminus @ SV97 @ SY1288 ) )
| ~ ( in @ SY1289 @ SV97 )
| ( in @ SY1289 @ SY1288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(574,plain,
! [SV98: $i > $o] :
( ( ~ ~ ! [SY1290: $i] :
~ ! [SY1291: $i] :
~ ( ~ ( ~ ( SV98 @ SY1291 )
| ( SY1291 = SY1290 ) )
| ~ ( ( SY1291 != SY1290 )
| ( SV98 @ SY1291 ) ) )
| ~ ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(575,plain,
! [SV99: $i] :
( ( ! [SY1294: $i] :
( ( ( setadjoin @ SV99 @ emptyset )
!= ( setadjoin @ SY1294 @ emptyset ) )
| ( SV99 = SY1294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(576,plain,
! [SV100: $i] :
( ( ! [SY1295: $i,SY1296: $i] :
( ~ ( in @ SY1296 @ ( cartprod @ SV100 @ SY1295 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ ( setunion @ SY1296 ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ ( setunion @ SY1296 ) )
| ( SY1296
!= ( setadjoin @ ( setadjoin @ SX3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX3 @ ( setadjoin @ SX4 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(577,plain,
! [SV101: $i] :
( ( ! [SY1299: $i,SY1300: $i] :
( ~ ( in @ SY1300 @ SV101 )
| ( in @ SY1300 @ ( binunion @ SV101 @ SY1299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(578,plain,
! [SV102: $i] :
( ( ! [SY1301: $i > $o,SY1302: $i] :
( ~ ( in @ SY1302
@ ( dsetconstr @ SV102
@ ^ [SX3: $i] : ( SY1301 @ SX3 ) ) )
| ( in @ SY1302 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(579,plain,
! [SV103: $i] :
( ( ! [SY1304: $i,SY1305: $i] :
( ~ ( in @ SY1305 @ SV103 )
| ~ ~ ( in @ SY1305 @ SY1304 )
| ( SV103 != SY1304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(580,plain,
! [SV104: $i] :
( ( ! [SY1306: $i > $o] :
( ~ ~ ~ ! [SY1307: $i] :
~ ~ ( ~ ( in @ SY1307 @ SV104 )
| ~ ( SY1306 @ SY1307 ) )
| ! [SY1308: $i] :
( ~ ( in @ SY1308 @ SV104 )
| ~ ( SY1306 @ SY1308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(581,plain,
! [SV105: $i] :
( ( ! [SY1309: $i,SY1310: $i] :
( ~ ( in @ SY1310 @ ( binintersect @ SV105 @ SY1309 ) )
| ( in @ SY1310 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(582,plain,
! [SV106: $i] :
( ( ! [SY1311: $i,SY1312: $i] :
( ~ ( in @ SY1312 @ ( setminus @ SV106 @ SY1311 ) )
| ~ ( in @ SY1312 @ SY1311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(583,plain,
! [SV107: $i] :
( ( ! [SY1313: $i] :
( ~ ( ( SV107 != SY1313 ) )
| ~ ( in @ SY1313 @ ( setadjoin @ SV107 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(584,plain,
! [SV108: $i] :
( ( ~ ~ ! [SY1314: $i] :
~ ~ ( ~ ( in @ SY1314 @ ( setunion @ SV108 ) )
| ~ ~ ! [SY1315: $i] :
~ ~ ( ~ ( in @ SY1315 @ ( setunion @ SV108 ) )
| ( SV108
!= ( setadjoin @ ( setadjoin @ SY1314 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1314 @ ( setadjoin @ SY1315 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ! [SY1316: $i] :
~ ~ ( ~ ( in @ SY1316
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ SY1316 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(585,plain,
! [SV109: $i] :
( ( ! [SY1319: $i,SY1320: $i] :
( ~ ( subset @ SV109 @ SY1319 )
| ~ ~ ( in @ SY1320 @ SY1319 )
| ~ ( in @ SY1320 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(586,plain,
! [SV110: $i] :
( ( ~ ! [SY1321: $i] :
~ ( in @ SY1321 @ SV110 )
| ( SV110 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(587,plain,
! [SV111: $i] :
( ( ! [SY1322: $i,SY1323: $i] :
( ~ ( in @ SY1323 @ SV111 )
| ! [SY1324: $i] :
( ~ ( in @ SY1324 @ SY1322 )
| ( subset @ ( setadjoin @ SY1323 @ ( setadjoin @ SY1324 @ emptyset ) ) @ ( binunion @ SV111 @ SY1322 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(588,plain,
! [SV112: $o] :
( ( ! [SY1325: $i] :
( ~ ( in @ SY1325 @ ( prop2set @ SV112 ) )
| SV112 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[423]) ).
thf(590,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $false ) )
| $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[423]) ).
thf(591,plain,
! [SV113: $i] :
( ( ! [SY1326: $i,SY1327: $i] :
( ~ ( in @ SY1327 @ ( symdiff @ SV113 @ SY1326 ) )
| ! [SY1328: $o] :
( ~ ( ~ ( in @ SY1327 @ SV113 )
| ~ ~ ( in @ SY1327 @ SY1326 )
| SY1328 )
| ~ ( ~ ~ ( in @ SY1327 @ SV113 )
| ~ ( in @ SY1327 @ SY1326 )
| SY1328 )
| SY1328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(592,plain,
! [SV114: $i] :
( ( ~ ( in @ SV114 @ omega )
| ( in @ ( setadjoin @ SV114 @ SV114 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(593,plain,
! [SV115: $i] :
( ( ! [SY1329: $i,SY1330: $i] :
( ~ ( subset @ SV115 @ SY1330 )
| ( subset @ SV115 @ ( setadjoin @ SY1329 @ SY1330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(594,plain,
! [SV116: $i] :
( ( ! [SY1331: $i,SY1332: $i] :
( ~ ( subset @ SV116 @ SY1331 )
| ~ ( in @ SY1332 @ SV116 )
| ( in @ SY1332 @ SY1331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(595,plain,
! [SV117: $i] :
( ( ! [SY1333: $i] :
( ~ ( subset @ SY1333 @ SV117 )
| ( in @ SY1333 @ ( powerset @ SV117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(596,plain,
! [SV118: $i] :
( ( ! [SY1334: $i] :
( ( SV118 != SY1334 )
| ! [SY1335: $i,SY1336: $i] :
( ( SY1335 != SY1336 )
| ~ ( ~ ( ~ ( in @ SY1335 @ SV118 )
| ( in @ SY1336 @ SY1334 ) )
| ~ ( ~ ( in @ SY1336 @ SY1334 )
| ( in @ SY1335 @ SV118 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(597,plain,
! [SV119: $i] :
( ( ! [SY1337: $i > $o] :
( ~ ~ ! [SY1338: $i] :
( ~ ( in @ SY1338 @ SV119 )
| ( SY1337 @ SY1338 ) )
| ~ ! [SY1339: $i] :
~ ~ ( ~ ( in @ SY1339 @ SV119 )
| ~ ~ ( SY1337 @ SY1339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(598,plain,
! [SV120: $i] :
( ( ! [SY1340: $i] :
( ~ ! [SY1341: $i] :
( ~ ( in @ SY1341 @ SY1340 )
| ( in @ SY1341 @ SV120 ) )
| ( in @ SY1340 @ ( powerset @ SV120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(599,plain,
! [SV121: $i] :
( ( ! [SY1342: $i,SY1343: $i] :
( ~ ( in @ SY1343 @ SV121 )
| ~ ~ ( in @ SY1343 @ SY1342 )
| ( in @ SY1343 @ ( symdiff @ SV121 @ SY1342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(600,plain,
! [SV122: $i] :
( ( ! [SY1344: $i] :
( ~ ( subset @ SV122 @ SY1344 )
| ( ( setminus @ SV122 @ SY1344 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(601,plain,
! [SV123: $i] :
( ( ! [SY1345: $i] :
( ~ ( in @ SV123 @ ( setadjoin @ SY1345 @ emptyset ) )
| ( in @ SY1345 @ ( setadjoin @ SV123 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(602,plain,
! [SV124: $i > $o] :
( ( ~ ~ ! [SY1346: $i] :
~ ~ ( ~ ( SV124 @ SY1346 )
| ~ ! [SY1347: $i] :
( ~ ( SV124 @ SY1347 )
| ( SY1346 = SY1347 ) ) )
| ~ ! [SY1348: $i] :
~ ~ ( ~ ( SV124 @ SY1348 )
| ~ ! [SY1349: $i] :
( ~ ( SV124 @ SY1349 )
| ( SY1348 = SY1349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(603,plain,
! [SV125: $i] :
( ( ! [SY1350: $i,SY1351: $i] :
( ~ ~ ( in @ SY1351 @ SV125 )
| ~ ~ ( in @ SY1351 @ SY1350 )
| ~ ( in @ SY1351 @ ( symdiff @ SV125 @ SY1350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(604,plain,
! [SV126: $i] :
( ( ! [SY1352: $i] :
~ ( ~ ( ~ ( in @ SY1352 @ ( setunion @ SV126 ) )
| ~ ! [SY1353: $i] :
~ ~ ( ~ ( in @ SY1352 @ SY1353 )
| ~ ( in @ SY1353 @ SV126 ) ) )
| ~ ( ~ ~ ! [SY1354: $i] :
~ ~ ( ~ ( in @ SY1352 @ SY1354 )
| ~ ( in @ SY1354 @ SV126 ) )
| ( in @ SY1352 @ ( setunion @ SV126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(605,plain,
! [SV127: $i] :
( ( ~ ~ ! [SY1355: $i] :
~ ( in @ SY1355 @ SV127 )
| ( SV127 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(606,plain,
! [SV128: $i] :
( ( ! [SY1356: $i] :
( ~ ( in @ SV128 @ ( setadjoin @ SY1356 @ emptyset ) )
| ( SV128 = SY1356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(607,plain,
! [SV129: $i] :
( ( ~ ! [SY1357: $i] :
~ ( in @ SY1357 @ SV129 )
| ( SV129 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(608,plain,
! [SV130: $i > $o] :
( ( ~ ~ ! [SY1358: $i] :
~ ( SV130 @ SY1358 )
| ~ ! [SY1359: $i,SY1360: $i] :
( ~ ( SV130 @ SY1359 )
| ~ ( SV130 @ SY1360 )
| ( SY1359 = SY1360 ) )
| ~ ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(609,plain,
! [SV131: $i] :
( ( ! [SY1363: $i,SY1364: $i] :
( ~ ( in @ SY1364 @ ( cartprod @ SV131 @ SY1363 ) )
| ( in @ ( kfst @ SY1364 ) @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(610,plain,
! [SV132: $i] :
( ( ! [SY1365: $i] :
( ( SV132 != SY1365 )
| ( in @ SV132 @ ( setadjoin @ SY1365 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(611,plain,
! [SV133: $o] :
( ( ~ SV133
| ( set2prop @ ( prop2set @ SV133 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[444]) ).
thf(612,plain,
( ( ~ $true
| ( set2prop @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[444]) ).
thf(614,plain,
! [SV134: $i > $o] :
( ( ! [SY1366: $i] :
( ~ ( in @ SY1366 @ emptyset )
| ( SV134 @ SY1366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(615,plain,
! [SV135: $i] :
( ( ! [SY1367: $i] :
( ( ( binintersect @ SV135 @ SY1367 )
!= SV135 )
| ( subset @ SV135 @ SY1367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(616,plain,
! [SV136: $i] :
( ( ! [SY1368: $i,SY1369: $i] :
( ~ ~ ( in @ SY1369 @ ( setminus @ SV136 @ SY1368 ) )
| ~ ~ ( in @ SY1369 @ SY1368 )
| ~ ( in @ SY1369 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(617,plain,
! [SV137: $i > $o] :
( ( ~ ~ ! [SY1370: $i] :
~ ~ ( ~ ( SV137 @ SY1370 )
| ~ ! [SY1371: $i] :
( ~ ( SV137 @ SY1371 )
| ( SY1370 = SY1371 ) ) )
| ~ ! [SY1372: $i] :
~ ( SV137 @ SY1372 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(618,plain,
! [SV138: $i] :
( ( ~ ~ ( ~ ( in @ emptyset @ SV138 )
| ~ ! [SY1373: $i] :
( ~ ~ ( ~ ( in @ SY1373 @ omega )
| ~ ( in @ SY1373 @ SV138 ) )
| ( in @ ( setadjoin @ SY1373 @ SY1373 ) @ SV138 ) ) )
| ! [SY1374: $i] :
( ~ ( in @ SY1374 @ omega )
| ( in @ SY1374 @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(619,plain,
! [SV139: $i] :
( ( ! [SY1375: $i,SY1376: $i] :
( ~ ( subset @ SV139 @ SY1375 )
| ~ ( subset @ SY1375 @ SY1376 )
| ( subset @ SV139 @ SY1376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(620,plain,
! [SV140: $i] :
( ( ! [SY1377: $i] :
~ ( ~ ( ~ ( in @ SY1377 @ ( powerset @ SV140 ) )
| ! [SY1378: $i] :
( ~ ( in @ SY1378 @ SY1377 )
| ( in @ SY1378 @ SV140 ) ) )
| ~ ( ~ ! [SY1379: $i] :
( ~ ( in @ SY1379 @ SY1377 )
| ( in @ SY1379 @ SV140 ) )
| ( in @ SY1377 @ ( powerset @ SV140 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(621,plain,
! [SV141: $i] :
( ( ! [SY1380: $i] :
( ~ ! [SY1381: $i] :
( ~ ( in @ SY1381 @ SV141 )
| ( in @ SY1381 @ SY1380 ) )
| ( subset @ SV141 @ SY1380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(622,plain,
! [SV142: $i] :
( ( ~ ~ ! [SY1382: $i] :
~ ( in @ SY1382 @ SV142 )
| ~ ! [SY1383: $i] :
~ ~ ( ~ ( in @ SY1383 @ SV142 )
| ~ ~ ~ ! [SY1384: $i] :
~ ~ ( ~ ( in @ SY1384 @ SY1383 )
| ~ ( in @ SY1384 @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(623,plain,
! [SV143: $i] :
( ( ~ ( ( SV143 != emptyset ) )
| ~ ! [SY1385: $i] :
~ ~ ( ~ ( in @ SY1385 @ SV143 )
| ~ $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(624,plain,
! [SV144: $i > $o] :
( ( ! [SY1386: $i > $o] :
( ~ ! [SY1387: $i,SY1388: $i] :
( ( SY1387 != SY1388 )
| ~ ( ~ ( ~ ( SV144 @ SY1387 )
| ( SY1386 @ SY1388 ) )
| ~ ( ~ ( SY1386 @ SY1388 )
| ( SV144 @ SY1387 ) ) ) )
| ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY1386 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY1386 @ SX3 )
| ( SX2 = SX3 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SX2: $i] : ( SY1386 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(625,plain,
! [SV145: $i] :
( ( ! [SY1395: $i] :
( ~ ( in @ SY1395 @ SV145 )
| ( in @ ( setadjoin @ SY1395 @ emptyset ) @ ( powerset @ SV145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(626,plain,
! [SV146: $i] :
( ( ! [SY1396: $i > $o,SY1397: $i] :
( ~ ( in @ SY1397 @ SV146 )
| ~ ( ~ ( ~ ( in @ SY1397
@ ( dsetconstr @ SV146
@ ^ [SX3: $i] : ( SY1396 @ SX3 ) ) )
| ( SY1396 @ SY1397 ) )
| ~ ( ~ ( SY1396 @ SY1397 )
| ( in @ SY1397
@ ( dsetconstr @ SV146
@ ^ [SX3: $i] : ( SY1396 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(627,plain,
! [SV147: $i] :
( ( ! [SY1400: $i,SY1401: $i] :
( ~ ( in @ SY1401 @ ( binintersect @ SV147 @ SY1400 ) )
| ( in @ SY1401 @ SY1400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(628,plain,
! [SV148: $i > $o] :
( ( ~ ~ ! [SY1402: $i] :
~ ~ ( ~ ( SV148 @ SY1402 )
| ~ ! [SY1403: $i] :
( ~ ( SV148 @ SY1403 )
| ( SY1402 = SY1403 ) ) )
| ( SV148
@ ( descr
@ ^ [SY1404: $i] : ( SV148 @ SY1404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(629,plain,
! [SV149: $i] :
( ( ! [SY1405: $i] :
( ( ( setminus @ SV149 @ SY1405 )
!= emptyset )
| ( subset @ SV149 @ SY1405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(630,plain,
! [SV150: $i] :
( ( ! [SY1406: $i] :
( ~ ( in @ SY1406 @ SV150 )
| ( in @ SY1406 @ ( powerset @ ( setunion @ SV150 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(631,plain,
! [SV151: $i] :
( ( ! [SY1407: $i > $o] :
( ~ ~ ~ ! [SY1408: $i] :
~ ~ ( ~ ( in @ SY1408 @ SV151 )
| ~ ( SY1407 @ SY1408 ) )
| ! [SY1409: $i] :
( ~ ( in @ SY1409 @ SV151 )
| ~ ( SY1407 @ SY1409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(632,plain,
! [SV152: $i] :
( ( ! [SY1410: $i] :
( ~ ( subset @ SV152 @ SY1410 )
| ~ ( subset @ SY1410 @ SV152 )
| ( SV152 = SY1410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(633,plain,
! [SV153: $i] :
( ( ! [SY1411: $i,SY1412: $i] :
( ~ ( in @ SY1412 @ SY1411 )
| ( in @ SY1412 @ ( binunion @ SV153 @ SY1411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(634,plain,
! [SV154: $i] :
( ( ! [SY1413: $i,SY1414: $i] :
( ~ ( subset @ SY1414 @ SV154 )
| ~ ( subset @ SY1414 @ SY1413 )
| ( subset @ SY1414 @ ( binintersect @ SV154 @ SY1413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(635,plain,
! [SV155: $i] :
( ( ! [SY1415: $i] :
( ~ ( subset @ SV155 @ SY1415 )
| ( subset @ ( powerset @ SV155 ) @ ( powerset @ SY1415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(636,plain,
! [SV156: $i] :
( ( ! [SY1416: $i,SY1417: $i] :
( ~ ( in @ SY1417 @ ( setadjoin @ SV156 @ SY1416 ) )
| ( SY1417 = SV156 )
| ( in @ SY1417 @ SY1416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(637,plain,
! [SV157: $i] :
( ( ~ ( subset @ SV157 @ emptyset )
| ( SV157 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(638,plain,
! [SV158: $i] :
( ( ! [SY1418: $i,SY1419: $i] :
( ~ ( in @ SY1419 @ ( binunion @ SV158 @ SY1418 ) )
| ( in @ SY1419 @ SV158 )
| ( in @ SY1419 @ SY1418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(639,plain,
! [SV159: $i > $o] :
( ( ~ ~ ! [SY1420: $i] :
~ ~ ( ~ ( SV159 @ SY1420 )
| ~ ! [SY1421: $i] :
( ~ ( SV159 @ SY1421 )
| ( SY1420 = SY1421 ) ) )
| ! [SY1422: $i,SY1423: $i] :
( ~ ( SV159 @ SY1422 )
| ~ ( SV159 @ SY1423 )
| ( SY1422 = SY1423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(640,plain,
! [SV160: $i] :
( ( ! [SY1424: $i,SY1425: $i] :
( ~ ( in @ SY1425 @ ( setminus @ SV160 @ SY1424 ) )
| ( in @ SY1425 @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(641,plain,
! [SV161: $i] :
( ( ! [SY1426: $i] :
( ~ ( in @ SY1426 @ ( setunion @ SV161 ) )
| ~ ! [SY1427: $i] :
~ ~ ( ~ ( in @ SY1427 @ SV161 )
| ~ ( in @ SY1426 @ SY1427 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(642,plain,
! [SV162: $i] :
( ( ! [SY1428: $i > $o,SY1429: $i] :
( ~ ( in @ SY1429 @ SV162 )
| ~ ( SY1428 @ SY1429 )
| ~ ! [SY1430: $i] :
( ~ ( in @ SY1430 @ SV162 )
| ~ ( SY1428 @ SY1430 )
| ( SY1430 = SY1429 ) )
| ~ ! [SY1431: $i] :
~ ~ ( ~ ( in @ SY1431
@ ( dsetconstr @ SV162
@ ^ [SX4: $i] : ( SY1428 @ SX4 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SX4: $i] : ( SY1428 @ SX4 ) )
!= ( setadjoin @ SY1431 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(643,plain,
! [SV163: $i,SV1: $i] :
( ( ( kfst @ ( setadjoin @ ( setadjoin @ SV1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV1 @ ( setadjoin @ SV163 @ emptyset ) ) @ emptyset ) ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(644,plain,
! [SV5: $i,SV164: $i] :
( ( in @ SV164 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV5 @ ( setadjoin @ SV164 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(645,plain,
! [SV165: $i,SV6: $i] :
( ( in @ SV6 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV6 @ ( setadjoin @ SV165 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(646,plain,
! [SV7: $i,SV166: $i] :
( ( in @ SV166 @ ( setadjoin @ SV7 @ ( setadjoin @ SV166 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(647,plain,
! [SV167: $i,SV8: $i] :
( ( subset @ ( setminus @ SV8 @ SV167 ) @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(648,plain,
! [SV168: $i,SV9: $i] :
( ( ! [SY1434: $i] :
( ( binintersect @ SV9 @ ( binunion @ SV168 @ SY1434 ) )
= ( binunion @ ( binintersect @ SV9 @ SV168 ) @ ( binintersect @ SV9 @ SY1434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(649,plain,
! [SV169: $i,SV10: $i] :
( ( subset @ ( binintersect @ SV10 @ SV169 ) @ SV169 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(650,plain,
! [SV170: $i,SV11: $i] :
( ( subset @ ( binintersect @ SV11 @ SV170 ) @ SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(651,plain,
! [SV12: $i,SV171: $i] :
( ( subset @ SV171 @ ( binunion @ SV12 @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(652,plain,
! [SV172: $i,SV13: $i] :
( ( subset @ SV13 @ ( binunion @ SV13 @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(653,plain,
! [SV14: $i,SV173: $i] :
( ( in @ SV173 @ ( setadjoin @ SV14 @ ( setadjoin @ SV173 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(654,plain,
! [SV174: $i > $o,SV15: $i] :
( ( subset
@ ( dsetconstr @ SV15
@ ^ [SY1435: $i] : ( SV174 @ SY1435 ) )
@ SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(655,plain,
! [SV175: $i > $o,SV16: $i] :
( ( in
@ ( dsetconstr @ SV16
@ ^ [SY1436: $i] : ( SV175 @ SY1436 ) )
@ ( powerset @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(656,plain,
! [SV18: $i,SV176: $i] :
( ( subset @ SV176 @ ( setadjoin @ SV18 @ SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(657,plain,
! [SV21: $i,SV177: $i] :
( ( in @ SV177 @ ( setadjoin @ SV21 @ ( setadjoin @ SV177 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(658,plain,
! [SV178: $i,SV22: $i] :
( ( in @ SV22 @ ( setadjoin @ SV22 @ ( setadjoin @ SV178 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(659,plain,
! [SV179: $i,SV26: $i] :
( ( in @ SV26 @ ( setadjoin @ SV26 @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(660,plain,
! [SV27: $i] :
( ( in @ SV27 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(661,plain,
! [SV28: $i] :
( ( in @ SV28 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(662,plain,
! [SV180: $i,SV29: $i] :
( ( ( SV29 != SV180 )
| ! [SY1437: $i > $o,SY1438: $i > $o] :
( ~ ! [SY1439: $i] :
( ~ ( in @ SY1439 @ SV29 )
| ! [SY1440: $i] :
( ~ ( in @ SY1440 @ SV180 )
| ( SY1439 != SY1440 )
| ~ ( ~ ( ~ ( SY1437 @ SY1439 )
| ( SY1438 @ SY1440 ) )
| ~ ( ~ ( SY1438 @ SY1440 )
| ( SY1437 @ SY1439 ) ) ) ) )
| ( ( dsetconstr @ SV29
@ ^ [SX4: $i] : ( SY1437 @ SX4 ) )
= ( dsetconstr @ SV180
@ ^ [SX4: $i] : ( SY1438 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(663,plain,
! [SV30: $i] :
( ( ( ~ ~ ! [SY1099: $i] :
~ ~ ( ~ ( in @ SY1099 @ SV30 )
| ( SV30
!= ( setadjoin @ SY1099 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( setunion @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(664,plain,
! [SV181: $i > $o,SV31: $i] :
( ( ~ ~ ! [SY1443: $i] :
~ ~ ( ~ ( in @ SY1443 @ SV31 )
| ~ ( SV181 @ SY1443 ) )
| ( ( dsetconstr @ SV31
@ ^ [SY1444: $i] : ( SV181 @ SY1444 ) )
!= emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(665,plain,
! [SV182: $i,SV32: $i] :
( ( ! [SY1445: $i] :
( ~ ( in @ SY1445 @ ( setadjoin @ SV32 @ ( setadjoin @ SV182 @ emptyset ) ) )
| ( SY1445 = SV32 )
| ( SY1445 = SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(666,plain,
! [SV183: $i,SV33: $i] :
( ( ! [SY1446: $i] :
( ~ ( in @ SY1446 @ SV33 )
| ~ ( in @ SY1446 @ SV183 )
| ( in @ SY1446 @ ( binintersect @ SV33 @ SV183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(667,plain,
! [SV184: $i,SV34: $i] :
( ( ! [SY1447: $i] :
( ~ ( in @ SY1447 @ SV34 )
| ( in @ ( setadjoin @ SY1447 @ emptyset ) @ ( powerset @ ( binunion @ SV34 @ SV184 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(668,plain,
! [SV35: $i] :
( ( ! [SY1109: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1110: $i] :
( ~ ( in @ SY1110 @ SY1109 )
| ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SY1110 )
| ( in @ SY1111 @ SV35 ) ) )
| ~ ! [SY1112: $i,SY1113: $i] :
( ~ ~ ( ~ ( in @ SY1112 @ SV35 )
| ~ ( in @ SY1113 @ SV35 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1109 )
| ~ ( ~ ( ~ ( in @ SY1112 @ SX4 )
| ( in @ SY1113 @ SX4 ) )
| ~ ( ~ ( in @ SY1113 @ SX4 )
| ( in @ SY1112 @ SX4 ) ) ) )
| ( SY1112 = SY1113 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY1109 )
| ~ ( in @ SX3 @ SY1109 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY1119: $i] :
( ~ ~ ( ~ ! [SY1120: $i] :
( ~ ( in @ SY1120 @ SY1119 )
| ( in @ SY1120 @ SV35 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1119 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY1109 )
| ~ ( in @ SX4 @ SY1119 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY1119 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY1109 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(669,plain,
! [SV185: $i,SV36: $i] :
( ( ~ ( subset @ SV36 @ SV185 )
| ( in @ SV36 @ ( powerset @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(670,plain,
! [SV37: $i > $o] :
( ( ( ~ ~ ! [SY1128: $i] :
~ ~ ( ~ ( SV37 @ SY1128 )
| ~ ! [SY1129: $i] :
( ~ ( SV37 @ SY1129 )
| ( SY1128 = SY1129 ) ) ) )
= $true )
| ( ( ! [SY1130: $i,SY1131: $i] :
( ~ ( SV37 @ SY1130 )
| ~ ( SV37 @ SY1131 )
| ( SY1130 = SY1131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(671,plain,
! [SV186: $i > $o,SV38: $i] :
( ( ~ ~ ! [SY1448: $i] :
~ ~ ( ~ ( in @ SY1448 @ SV38 )
| ~ ~ ( SV186 @ SY1448 ) )
| ~ ! [SY1449: $i] :
( ~ ( in @ SY1449 @ SV38 )
| ( SV186 @ SY1449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(672,plain,
! [SV187: $i > $o,SV39: $i] :
( ( ! [SY1450: $i] :
( ~ ( in @ SY1450 @ SV39 )
| ~ ( SV187 @ SY1450 )
| ( ( dsetconstr @ SV39
@ ^ [SY1451: $i] : ( SV187 @ SY1451 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(673,plain,
! [SV188: $i,SV40: $i] :
( ( ! [SY1452: $i] :
( ~ ( in @ SY1452 @ SV40 )
| ! [SY1453: $i] :
( ~ ( in @ SY1453 @ SV188 )
| ( in @ ( setadjoin @ ( setadjoin @ SY1452 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1452 @ ( setadjoin @ SY1453 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SV40 @ SV188 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(674,plain,
! [SV189: $i,SV41: $i] :
( ( ( SV41 != SV189 )
| ( subset @ SV41 @ SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(675,plain,
! [SV190: $i,SV42: $i] :
( ( ! [SY1454: $i,SY1455: $i] :
( ( ( setadjoin @ ( setadjoin @ SV42 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV42 @ ( setadjoin @ SV190 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1454 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1454 @ ( setadjoin @ SY1455 @ emptyset ) ) @ emptyset ) ) )
| ( SV42 = SY1454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(676,plain,
! [SV191: $i,SV43: $i] :
( ( ( SV43 != SV191 )
| ( ( setunion @ SV43 )
= ( setunion @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(677,plain,
! [SV192: $i,SV44: $i] :
( ( ! [SY1456: $i] :
( ~ ( in @ SY1456 @ SV44 )
| ~ ~ ( in @ SY1456 @ SV192 )
| ~ ( subset @ SV44 @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(678,plain,
! [SV193: $i > $o,SV45: $i] :
( ( ~ ~ ! [SY1457: $i] :
( ~ ( in @ SY1457 @ SV45 )
| ( SV193 @ SY1457 ) )
| ~ ! [SY1458: $i] :
~ ~ ( ~ ( in @ SY1458 @ SV45 )
| ~ ~ ( SV193 @ SY1458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(679,plain,
! [SV46: $i,SV194: $i] :
( ( ! [SY1459: $i] :
( ~ ( in @ SV194 @ ( powerset @ SV46 ) )
| ~ ( in @ SY1459 @ SV194 )
| ( in @ SY1459 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(680,plain,
! [SV47: $i,SV195: $i] :
( ( ~ ( subset @ SV195 @ SV47 )
| ( ( binintersect @ SV47 @ SV195 )
= SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(681,plain,
! [SV196: $i,SV48: $i] :
( ( ! [SY1460: $i] :
( ~ ( in @ SY1460 @ SV48 )
| ! [SY1461: $i] :
( ~ ( in @ SY1461 @ SV196 )
| ( in @ ( setadjoin @ ( setadjoin @ SY1460 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1460 @ ( setadjoin @ SY1461 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV48 @ SV196 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(682,plain,
! [SV197: $i,SV49: $i] :
( ( ( SV49 != SV197 )
| ( ( powerset @ SV49 )
= ( powerset @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(683,plain,
! [SV50: $i > $o] :
( ( ( ~ ~ ! [SY1158: $i] :
~ ~ ( ~ ( SV50 @ SY1158 )
| ~ ! [SY1159: $i] :
( ~ ( SV50 @ SY1159 )
| ( SY1158 = SY1159 ) ) ) )
= $true )
| ( ( ~ ! [SY1160: $i] :
~ ~ ( ~ ( SV50 @ SY1160 )
| ~ ! [SY1161: $i] :
( ~ ( SV50 @ SY1161 )
| ( SY1160 = SY1161 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(684,plain,
! [SV198: $i,SV51: $i] :
( ( ~ ! [SY1462: $i] :
( ~ ( in @ SY1462 @ SV51 )
| ( in @ SY1462 @ SV198 ) )
| ~ ! [SY1463: $i] :
( ~ ( in @ SY1463 @ SV198 )
| ( in @ SY1463 @ SV51 ) )
| ( SV51 = SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(685,plain,
! [SV52: $i] :
( ( ( ~ ( ( SV52 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY1165: $i] :
~ ( in @ SY1165 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(686,plain,
! [SV199: $i,SV53: $i] :
( ( ! [SY1464: $i] :
( ~ ( in @ SY1464 @ SV53 )
| ~ ~ ( in @ SY1464 @ SV199 )
| ( in @ SY1464 @ ( setminus @ SV53 @ SV199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(687,plain,
! [SV200: $i,SV54: $i] :
( ( ~ ! [SY1465: $i] :
~ ~ ( ~ ( in @ SY1465 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1466: $i] :
~ ~ ( ~ ( in @ SY1466 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1465 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1465 @ ( setadjoin @ SY1466 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(688,plain,
! [SV201: $i,SV55: $i] :
( ( ! [SY1467: $i] :
( ~ ~ ( in @ SY1467 @ SV55 )
| ~ ( in @ SY1467 @ ( setminus @ SV55 @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(689,plain,
! [SV56: $i,SV202: $i] :
( ( ! [SY1468: $i] :
( ~ ( in @ SV202 @ SY1468 )
| ~ ( in @ SY1468 @ SV56 )
| ( in @ SV202 @ ( setunion @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(690,plain,
! [SV203: $i,SV57: $i] :
( ( ! [SY1469: $i] :
( ~ ( in @ SY1469 @ ( setadjoin @ SV57 @ ( setadjoin @ SV203 @ emptyset ) ) )
| ( SY1469 = SV57 )
| ( SY1469 = SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(691,plain,
! [SV204: $i,SV58: $i] :
( ( ! [SY1470: $i] :
( ~ ( in @ SY1470 @ ( cartprod @ SV58 @ SV204 ) )
| ~ ! [SY1471: $i] :
~ ~ ( ~ ( in @ SY1471 @ SV58 )
| ~ ~ ! [SY1472: $i] :
~ ~ ( ~ ( in @ SY1472 @ SV204 )
| ( SY1470
!= ( setadjoin @ ( setadjoin @ SY1471 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1471 @ ( setadjoin @ SY1472 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(692,plain,
! [SV205: $i,SV59: $i] :
( ( ~ ! [SY1473: $i] :
~ ( ~ ( ~ ( in @ SY1473 @ SV59 )
| ( in @ SY1473 @ SV205 ) )
| ~ ( ~ ( in @ SY1473 @ SV205 )
| ( in @ SY1473 @ SV59 ) ) )
| ( SV59 = SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(693,plain,
! [SV206: $i,SV60: $i] :
( ( ! [SY1474: $i,SY1475: $o] :
( ~ ( in @ SY1474 @ ( binunion @ SV60 @ SV206 ) )
| ~ ( ~ ( in @ SY1474 @ SV60 )
| SY1475 )
| ~ ( ~ ( in @ SY1474 @ SV206 )
| SY1475 )
| SY1475 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(694,plain,
! [SV207: $i,SV61: $i] :
( ( ~ ! [SY1476: $i] :
~ ~ ( ~ ( in @ SY1476 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1477: $i] :
~ ~ ( ~ ( in @ SY1477 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1476 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1476 @ ( setadjoin @ SY1477 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(695,plain,
! [SV208: $i > $o,SV62: $i] :
( ( ~ ! [SY1478: $i] :
( ~ ( in @ SY1478 @ SV62 )
| ~ ( SV208 @ SY1478 ) )
| ~ ~ ! [SY1479: $i] :
~ ~ ( ~ ( in @ SY1479 @ SV62 )
| ~ ( SV208 @ SY1479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(696,plain,
! [SV63: $i,SV209: $i] :
( ( ~ ( in @ SV209 @ SV63 )
| ( subset @ ( setadjoin @ SV209 @ emptyset ) @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(697,plain,
! [SV64: $i > $i > $o,SV210: $i] :
( ( ~ ! [SY1480: $i] :
( ~ ( in @ SY1480 @ SV210 )
| ~ ! [SY1195: $i] :
~ ~ ( ~ ( SV64 @ SY1480 @ SY1195 )
| ~ ! [SY1196: $i] :
( ~ ( SV64 @ SY1480 @ SY1196 )
| ( SY1195 = SY1196 ) ) ) )
| ~ ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(698,plain,
! [SV211: $i,SV65: $i] :
( ( ! [SY1487: $i] :
( ~ ( in @ ( setadjoin @ SY1487 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV65 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV65 @ ( setadjoin @ SV211 @ emptyset ) ) @ emptyset ) ) )
| ( SV65 = SY1487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(699,plain,
! [SV212: $i,SV66: $i] :
( ( ! [SY1488: $i,SY1489: $i] :
( ( ( setadjoin @ ( setadjoin @ SV66 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV66 @ ( setadjoin @ SV212 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1488 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1488 @ ( setadjoin @ SY1489 @ emptyset ) ) @ emptyset ) ) )
| ( SV66 = SY1488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(700,plain,
! [SV213: $i,SV67: $i] :
( ( ! [SY1490: $i] :
( ~ ( in @ SY1490 @ SV67 )
| ~ ( in @ SY1490 @ SV213 )
| ~ ( in @ SY1490 @ ( symdiff @ SV67 @ SV213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(701,plain,
! [SV214: $i,SV68: $i] :
( ( ~ ~ ( subset @ SV68 @ SV214 )
| ( SV68 != SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(702,plain,
( ( ! [SY1491: $i] :
( ( sK1_SX0 != SY1491 )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ SY1491 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ emptyset ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[542]) ).
thf(703,plain,
! [SV215: $i,SV69: $i] :
( ( ( SV69 != SV215 )
| ( subset @ SV215 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(704,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ~ ! [SY1492: $i] :
( ~ ( in @ SY1492 @ SV70 )
| ! [SY1493: $i] :
( ~ ( in @ SY1493 @ SV70 )
| ~ ( SV216 @ SY1492 )
| ~ ( SV216 @ SY1493 )
| ( SY1492 = SY1493 ) ) )
| ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) )
| ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(705,plain,
! [SV217: $i > $o,SV71: $i] :
( ( ! [SY1498: $i] :
( ~ ( in @ SY1498 @ SV71 )
| ~ ( SV217 @ SY1498 )
| ( in @ SY1498
@ ( dsetconstr @ SV71
@ ^ [SY1499: $i] : ( SV217 @ SY1499 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(706,plain,
! [SV72: $i,SV218: $i] :
( ( ~ ( in @ SV218 @ ( setunion @ SV72 ) )
| ! [SY1500: $o] :
( ~ ! [SY1501: $i] :
( ~ ( in @ SV218 @ SY1501 )
| ~ ( in @ SY1501 @ SV72 )
| SY1500 )
| SY1500 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(707,plain,
! [SV73: $o] :
( ( ( ~ SV73 ) = $true )
| ( ( in @ emptyset @ ( prop2set @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(708,plain,
( ( ( ~ $true ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(710,plain,
! [SV219: $i,SV74: $i] :
( ( ( SV74 != SV219 )
| ! [SY1502: $i,SY1503: $i] :
( ( SY1502 != SY1503 )
| ~ ( in @ SY1502 @ SV74 )
| ( in @ SY1503 @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(711,plain,
! [SV220: $i > $o,SV75: $i] :
( ( ~ ~ ! [SY1504: $i] :
~ ~ ( ~ ( in @ SY1504
@ ( dsetconstr @ SV75
@ ^ [SY1505: $i] : ( SV220 @ SY1505 ) ) )
| ( ( dsetconstr @ SV75
@ ^ [SY1506: $i] : ( SV220 @ SY1506 ) )
!= ( setadjoin @ SY1504 @ emptyset ) ) )
| ~ ! [SY1507: $i] :
~ ~ ( ~ ( in @ SY1507 @ SV75 )
| ~ ( SV220 @ SY1507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(712,plain,
! [SV76: $i] :
( ( ( ~ ( in @ SV76 @ emptyset ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(713,plain,
! [SV221: $i,SV77: $i] :
( ( ! [SY1508: $i] :
( ~ ( in @ SY1508 @ SV77 )
| ! [SY1509: $i] :
( ~ ( in @ SY1509 @ SV221 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY1508 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1508 @ ( setadjoin @ SY1509 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV77 @ SV221 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(714,plain,
! [SV78: $i,SV222: $i] :
( ( ~ ( in @ SV222 @ ( powerset @ SV78 ) )
| ( subset @ SV222 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(715,plain,
! [SV223: $i,SV79: $i] :
( ( ! [SY1510: $i] :
( ~ ~ ( in @ SY1510 @ SV79 )
| ~ ( in @ SY1510 @ SV223 )
| ( in @ SY1510 @ ( symdiff @ SV79 @ SV223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(716,plain,
! [SV224: $i,SV80: $i] :
( ( ( SV80 != SV224 )
| ! [SY1511: $i,SY1512: $i] :
( ( SY1511 != SY1512 )
| ( ( setadjoin @ SV80 @ SY1511 )
= ( setadjoin @ SV224 @ SY1512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(717,plain,
! [SV225: $i,SV81: $i] :
( ( ~ ( subset @ SV81 @ SV225 )
| ( ( binintersect @ SV81 @ SV225 )
= SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(718,plain,
! [SV226: $i,SV82: $i] :
( ( ( SV82 != SV226 )
| ( ( setadjoin @ SV82 @ ( setadjoin @ SV226 @ emptyset ) )
= ( setadjoin @ SV82 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(719,plain,
! [SV227: $i,SV83: $i] :
( ( ( ( binintersect @ SV83 @ SV227 )
!= SV227 )
| ( subset @ SV227 @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(720,plain,
! [SV84: $i] :
( ( ( ~ ( in @ SV84 @ emptyset ) )
= $true )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(721,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ~ ! [SY1513: $i,SY1514: $i] :
( ( SY1513 != SY1514 )
| ~ ( ~ ( ~ ( SV85 @ SY1513 )
| ( SV228 @ SY1514 ) )
| ~ ( ~ ( SV228 @ SY1514 )
| ( SV85 @ SY1513 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(722,plain,
! [SV229: $i,SV86: $i] :
( ( ~ ! [SY1523: $i] :
( ~ ( in @ SY1523 @ SV86 )
| ( in @ SY1523 @ SV229 ) )
| ( subset @ SV86 @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(723,plain,
! [SV230: $i,SV87: $i] :
( ( ! [SY1524: $i] :
( ~ ( in @ SY1524 @ SV87 )
| ! [SY1525: $i] :
( ~ ( in @ SY1525 @ SV230 )
| ( in @ ( setadjoin @ ( setadjoin @ SY1524 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1524 @ ( setadjoin @ SY1525 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV87 @ SV230 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(724,plain,
! [SV88: $i,SV231: $i] :
( ( ! [SY1526: $i] :
( ~ ( in @ SY1526 @ SV231 )
| ( in @ SY1526 @ ( setadjoin @ SV88 @ SV231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(725,plain,
! [SV232: $i,SV89: $i] :
( ( ~ ~ ~ ! [SY1527: $i] :
~ ~ ( ~ ( in @ SY1527 @ SV89 )
| ~ ( in @ SY1527 @ SV232 ) )
| ( ( binintersect @ SV89 @ SV232 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(726,plain,
! [SV90: $i > $o] :
( ( ( ~ ~ ! [SY1264: $i] :
~ ~ ( ~ ( SV90 @ SY1264 )
| ~ ! [SY1265: $i] :
( ~ ( SV90 @ SY1265 )
| ( SY1264 = SY1265 ) ) ) )
= $true )
| ( ( ~ ! [SY1266: $i] :
~ ! [SY1267: $i] :
~ ( ~ ( ~ ( SV90 @ SY1267 )
| ( SY1267 = SY1266 ) )
| ~ ( ( SY1267 != SY1266 )
| ( SV90 @ SY1267 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(727,plain,
! [SV233: $i,SV91: $i] :
( ( ! [SY1528: $i] :
( ~ ( in @ SY1528 @ ( setadjoin @ SV91 @ SV233 ) )
| ! [SY1529: $o] :
( ~ ( ( SY1528 != SV91 )
| SY1529 )
| ~ ( ~ ( in @ SY1528 @ SV233 )
| SY1529 )
| SY1529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(728,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ~ ! [SY1530: $i] :
( ~ ( in @ SY1530 @ SV92 )
| ! [SY1531: $i] :
( ~ ( in @ SY1531 @ SV92 )
| ~ ( SV234 @ SY1530 )
| ~ ( SV234 @ SY1531 )
| ( SY1530 = SY1531 ) ) )
| ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) )
| ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(729,plain,
! [SV235: $i > $o,SV93: $i] :
( ( ! [SY1536: $i] :
( ~ ( in @ SY1536
@ ( dsetconstr @ SV93
@ ^ [SY1537: $i] : ( SV235 @ SY1537 ) ) )
| ( SV235 @ SY1536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(730,plain,
! [SV94: $i,SV236: $i] :
( ( ! [SY1538: $i] :
( ~ ( in @ SY1538 @ SV236 )
| ~ ( in @ SY1538 @ ( setminus @ SV94 @ SV236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(731,plain,
! [SV237: $i,SV95: $i] :
( ( ! [SY1539: $i] :
( ~ ( in @ SY1539 @ SV95 )
| ! [SY1540: $i] :
( ~ ( in @ SY1540 @ SV237 )
| ( in @ ( setadjoin @ SY1539 @ ( setadjoin @ SY1540 @ emptyset ) ) @ ( powerset @ ( binunion @ SV95 @ SV237 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(732,plain,
! [SV238: $i,SV96: $i] :
( ( ! [SY1541: $i] :
~ ( ~ ( ~ ( in @ SY1541 @ ( setadjoin @ SV96 @ SV238 ) )
| ( SY1541 = SV96 )
| ( in @ SY1541 @ SV238 ) )
| ~ ( ~ ( ( SY1541 = SV96 )
| ( in @ SY1541 @ SV238 ) )
| ( in @ SY1541 @ ( setadjoin @ SV96 @ SV238 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(733,plain,
! [SV239: $i,SV97: $i] :
( ( ! [SY1542: $i] :
( ~ ~ ( in @ SY1542 @ ( setminus @ SV97 @ SV239 ) )
| ~ ( in @ SY1542 @ SV97 )
| ( in @ SY1542 @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(734,plain,
! [SV98: $i > $o] :
( ( ( ~ ~ ! [SY1290: $i] :
~ ! [SY1291: $i] :
~ ( ~ ( ~ ( SV98 @ SY1291 )
| ( SY1291 = SY1290 ) )
| ~ ( ( SY1291 != SY1290 )
| ( SV98 @ SY1291 ) ) ) )
= $true )
| ( ( ~ ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(735,plain,
! [SV240: $i,SV99: $i] :
( ( ( ( setadjoin @ SV99 @ emptyset )
!= ( setadjoin @ SV240 @ emptyset ) )
| ( SV99 = SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(736,plain,
! [SV241: $i,SV100: $i] :
( ( ! [SY1543: $i] :
( ~ ( in @ SY1543 @ ( cartprod @ SV100 @ SV241 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ ( setunion @ SY1543 ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ ( setunion @ SY1543 ) )
| ( SY1543
!= ( setadjoin @ ( setadjoin @ SX3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX3 @ ( setadjoin @ SX4 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(737,plain,
! [SV242: $i,SV101: $i] :
( ( ! [SY1546: $i] :
( ~ ( in @ SY1546 @ SV101 )
| ( in @ SY1546 @ ( binunion @ SV101 @ SV242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(738,plain,
! [SV243: $i > $o,SV102: $i] :
( ( ! [SY1547: $i] :
( ~ ( in @ SY1547
@ ( dsetconstr @ SV102
@ ^ [SY1548: $i] : ( SV243 @ SY1548 ) ) )
| ( in @ SY1547 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(739,plain,
! [SV244: $i,SV103: $i] :
( ( ! [SY1549: $i] :
( ~ ( in @ SY1549 @ SV103 )
| ~ ~ ( in @ SY1549 @ SV244 )
| ( SV103 != SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(740,plain,
! [SV245: $i > $o,SV104: $i] :
( ( ~ ~ ~ ! [SY1550: $i] :
~ ~ ( ~ ( in @ SY1550 @ SV104 )
| ~ ( SV245 @ SY1550 ) )
| ! [SY1551: $i] :
( ~ ( in @ SY1551 @ SV104 )
| ~ ( SV245 @ SY1551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(741,plain,
! [SV246: $i,SV105: $i] :
( ( ! [SY1552: $i] :
( ~ ( in @ SY1552 @ ( binintersect @ SV105 @ SV246 ) )
| ( in @ SY1552 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(742,plain,
! [SV247: $i,SV106: $i] :
( ( ! [SY1553: $i] :
( ~ ( in @ SY1553 @ ( setminus @ SV106 @ SV247 ) )
| ~ ( in @ SY1553 @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(743,plain,
! [SV248: $i,SV107: $i] :
( ( ~ ( ( SV107 != SV248 ) )
| ~ ( in @ SV248 @ ( setadjoin @ SV107 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(744,plain,
! [SV108: $i] :
( ( ( ~ ~ ! [SY1314: $i] :
~ ~ ( ~ ( in @ SY1314 @ ( setunion @ SV108 ) )
| ~ ~ ! [SY1315: $i] :
~ ~ ( ~ ( in @ SY1315 @ ( setunion @ SV108 ) )
| ( SV108
!= ( setadjoin @ ( setadjoin @ SY1314 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1314 @ ( setadjoin @ SY1315 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true )
| ( ( ~ ! [SY1316: $i] :
~ ~ ( ~ ( in @ SY1316
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ SY1316 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(745,plain,
! [SV249: $i,SV109: $i] :
( ( ! [SY1554: $i] :
( ~ ( subset @ SV109 @ SV249 )
| ~ ~ ( in @ SY1554 @ SV249 )
| ~ ( in @ SY1554 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(746,plain,
! [SV110: $i] :
( ( ( ~ ! [SY1321: $i] :
~ ( in @ SY1321 @ SV110 ) )
= $true )
| ( ( SV110 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(747,plain,
! [SV250: $i,SV111: $i] :
( ( ! [SY1555: $i] :
( ~ ( in @ SY1555 @ SV111 )
| ! [SY1556: $i] :
( ~ ( in @ SY1556 @ SV250 )
| ( subset @ ( setadjoin @ SY1555 @ ( setadjoin @ SY1556 @ emptyset ) ) @ ( binunion @ SV111 @ SV250 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(748,plain,
! [SV112: $o,SV251: $i] :
( ( ~ ( in @ SV251 @ ( prop2set @ SV112 ) )
| SV112 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(750,plain,
! [SV253: $i] :
( ( ~ ( in @ SV253 @ ( prop2set @ $false ) )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(751,plain,
! [SV254: $i,SV113: $i] :
( ( ! [SY1557: $i] :
( ~ ( in @ SY1557 @ ( symdiff @ SV113 @ SV254 ) )
| ! [SY1558: $o] :
( ~ ( ~ ( in @ SY1557 @ SV113 )
| ~ ~ ( in @ SY1557 @ SV254 )
| SY1558 )
| ~ ( ~ ~ ( in @ SY1557 @ SV113 )
| ~ ( in @ SY1557 @ SV254 )
| SY1558 )
| SY1558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(752,plain,
! [SV114: $i] :
( ( ( ~ ( in @ SV114 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV114 @ SV114 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[592]) ).
thf(753,plain,
! [SV255: $i,SV115: $i] :
( ( ! [SY1559: $i] :
( ~ ( subset @ SV115 @ SY1559 )
| ( subset @ SV115 @ ( setadjoin @ SV255 @ SY1559 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(754,plain,
! [SV256: $i,SV116: $i] :
( ( ! [SY1560: $i] :
( ~ ( subset @ SV116 @ SV256 )
| ~ ( in @ SY1560 @ SV116 )
| ( in @ SY1560 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(755,plain,
! [SV117: $i,SV257: $i] :
( ( ~ ( subset @ SV257 @ SV117 )
| ( in @ SV257 @ ( powerset @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(756,plain,
! [SV258: $i,SV118: $i] :
( ( ( SV118 != SV258 )
| ! [SY1561: $i,SY1562: $i] :
( ( SY1561 != SY1562 )
| ~ ( ~ ( ~ ( in @ SY1561 @ SV118 )
| ( in @ SY1562 @ SV258 ) )
| ~ ( ~ ( in @ SY1562 @ SV258 )
| ( in @ SY1561 @ SV118 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(757,plain,
! [SV259: $i > $o,SV119: $i] :
( ( ~ ~ ! [SY1563: $i] :
( ~ ( in @ SY1563 @ SV119 )
| ( SV259 @ SY1563 ) )
| ~ ! [SY1564: $i] :
~ ~ ( ~ ( in @ SY1564 @ SV119 )
| ~ ~ ( SV259 @ SY1564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(758,plain,
! [SV120: $i,SV260: $i] :
( ( ~ ! [SY1565: $i] :
( ~ ( in @ SY1565 @ SV260 )
| ( in @ SY1565 @ SV120 ) )
| ( in @ SV260 @ ( powerset @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(759,plain,
! [SV261: $i,SV121: $i] :
( ( ! [SY1566: $i] :
( ~ ( in @ SY1566 @ SV121 )
| ~ ~ ( in @ SY1566 @ SV261 )
| ( in @ SY1566 @ ( symdiff @ SV121 @ SV261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(760,plain,
! [SV262: $i,SV122: $i] :
( ( ~ ( subset @ SV122 @ SV262 )
| ( ( setminus @ SV122 @ SV262 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(761,plain,
! [SV263: $i,SV123: $i] :
( ( ~ ( in @ SV123 @ ( setadjoin @ SV263 @ emptyset ) )
| ( in @ SV263 @ ( setadjoin @ SV123 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(762,plain,
! [SV124: $i > $o] :
( ( ( ~ ~ ! [SY1346: $i] :
~ ~ ( ~ ( SV124 @ SY1346 )
| ~ ! [SY1347: $i] :
( ~ ( SV124 @ SY1347 )
| ( SY1346 = SY1347 ) ) ) )
= $true )
| ( ( ~ ! [SY1348: $i] :
~ ~ ( ~ ( SV124 @ SY1348 )
| ~ ! [SY1349: $i] :
( ~ ( SV124 @ SY1349 )
| ( SY1348 = SY1349 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[602]) ).
thf(763,plain,
! [SV264: $i,SV125: $i] :
( ( ! [SY1567: $i] :
( ~ ~ ( in @ SY1567 @ SV125 )
| ~ ~ ( in @ SY1567 @ SV264 )
| ~ ( in @ SY1567 @ ( symdiff @ SV125 @ SV264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(764,plain,
! [SV126: $i,SV265: $i] :
( ( ~ ( ~ ( ~ ( in @ SV265 @ ( setunion @ SV126 ) )
| ~ ! [SY1568: $i] :
~ ~ ( ~ ( in @ SV265 @ SY1568 )
| ~ ( in @ SY1568 @ SV126 ) ) )
| ~ ( ~ ~ ! [SY1569: $i] :
~ ~ ( ~ ( in @ SV265 @ SY1569 )
| ~ ( in @ SY1569 @ SV126 ) )
| ( in @ SV265 @ ( setunion @ SV126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(765,plain,
! [SV127: $i] :
( ( ( ~ ~ ! [SY1355: $i] :
~ ( in @ SY1355 @ SV127 ) )
= $true )
| ( ( SV127 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(766,plain,
! [SV266: $i,SV128: $i] :
( ( ~ ( in @ SV128 @ ( setadjoin @ SV266 @ emptyset ) )
| ( SV128 = SV266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(767,plain,
! [SV129: $i] :
( ( ( ~ ! [SY1357: $i] :
~ ( in @ SY1357 @ SV129 ) )
= $true )
| ( ( SV129 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(768,plain,
! [SV130: $i > $o] :
( ( ( ~ ~ ! [SY1358: $i] :
~ ( SV130 @ SY1358 ) )
= $true )
| ( ( ~ ! [SY1359: $i,SY1360: $i] :
( ~ ( SV130 @ SY1359 )
| ~ ( SV130 @ SY1360 )
| ( SY1359 = SY1360 ) )
| ~ ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(769,plain,
! [SV267: $i,SV131: $i] :
( ( ! [SY1570: $i] :
( ~ ( in @ SY1570 @ ( cartprod @ SV131 @ SV267 ) )
| ( in @ ( kfst @ SY1570 ) @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(770,plain,
! [SV268: $i,SV132: $i] :
( ( ( SV132 != SV268 )
| ( in @ SV132 @ ( setadjoin @ SV268 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(771,plain,
! [SV133: $o] :
( ( ( ~ SV133 ) = $true )
| ( ( set2prop @ ( prop2set @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(772,plain,
( ( ( ~ $true ) = $true )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(774,plain,
! [SV134: $i > $o,SV269: $i] :
( ( ~ ( in @ SV269 @ emptyset )
| ( SV134 @ SV269 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(775,plain,
! [SV270: $i,SV135: $i] :
( ( ( ( binintersect @ SV135 @ SV270 )
!= SV135 )
| ( subset @ SV135 @ SV270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(776,plain,
! [SV271: $i,SV136: $i] :
( ( ! [SY1571: $i] :
( ~ ~ ( in @ SY1571 @ ( setminus @ SV136 @ SV271 ) )
| ~ ~ ( in @ SY1571 @ SV271 )
| ~ ( in @ SY1571 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(777,plain,
! [SV137: $i > $o] :
( ( ( ~ ~ ! [SY1370: $i] :
~ ~ ( ~ ( SV137 @ SY1370 )
| ~ ! [SY1371: $i] :
( ~ ( SV137 @ SY1371 )
| ( SY1370 = SY1371 ) ) ) )
= $true )
| ( ( ~ ! [SY1372: $i] :
~ ( SV137 @ SY1372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(778,plain,
! [SV138: $i] :
( ( ( ~ ~ ( ~ ( in @ emptyset @ SV138 )
| ~ ! [SY1373: $i] :
( ~ ~ ( ~ ( in @ SY1373 @ omega )
| ~ ( in @ SY1373 @ SV138 ) )
| ( in @ ( setadjoin @ SY1373 @ SY1373 ) @ SV138 ) ) ) )
= $true )
| ( ( ! [SY1374: $i] :
( ~ ( in @ SY1374 @ omega )
| ( in @ SY1374 @ SV138 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(779,plain,
! [SV272: $i,SV139: $i] :
( ( ! [SY1572: $i] :
( ~ ( subset @ SV139 @ SV272 )
| ~ ( subset @ SV272 @ SY1572 )
| ( subset @ SV139 @ SY1572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(780,plain,
! [SV140: $i,SV273: $i] :
( ( ~ ( ~ ( ~ ( in @ SV273 @ ( powerset @ SV140 ) )
| ! [SY1573: $i] :
( ~ ( in @ SY1573 @ SV273 )
| ( in @ SY1573 @ SV140 ) ) )
| ~ ( ~ ! [SY1574: $i] :
( ~ ( in @ SY1574 @ SV273 )
| ( in @ SY1574 @ SV140 ) )
| ( in @ SV273 @ ( powerset @ SV140 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(781,plain,
! [SV274: $i,SV141: $i] :
( ( ~ ! [SY1575: $i] :
( ~ ( in @ SY1575 @ SV141 )
| ( in @ SY1575 @ SV274 ) )
| ( subset @ SV141 @ SV274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(782,plain,
! [SV142: $i] :
( ( ( ~ ~ ! [SY1382: $i] :
~ ( in @ SY1382 @ SV142 ) )
= $true )
| ( ( ~ ! [SY1383: $i] :
~ ~ ( ~ ( in @ SY1383 @ SV142 )
| ~ ~ ~ ! [SY1384: $i] :
~ ~ ( ~ ( in @ SY1384 @ SY1383 )
| ~ ( in @ SY1384 @ SV142 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[622]) ).
thf(783,plain,
! [SV143: $i] :
( ( ( ~ ( ( SV143 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY1385: $i] :
~ ~ ( ~ ( in @ SY1385 @ SV143 )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[623]) ).
thf(784,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ~ ! [SY1576: $i,SY1577: $i] :
( ( SY1576 != SY1577 )
| ~ ( ~ ( ~ ( SV144 @ SY1576 )
| ( SV275 @ SY1577 ) )
| ~ ( ~ ( SV275 @ SY1577 )
| ( SV144 @ SY1576 ) ) ) )
| ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(785,plain,
! [SV145: $i,SV276: $i] :
( ( ~ ( in @ SV276 @ SV145 )
| ( in @ ( setadjoin @ SV276 @ emptyset ) @ ( powerset @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(786,plain,
! [SV277: $i > $o,SV146: $i] :
( ( ! [SY1584: $i] :
( ~ ( in @ SY1584 @ SV146 )
| ~ ( ~ ( ~ ( in @ SY1584
@ ( dsetconstr @ SV146
@ ^ [SY1585: $i] : ( SV277 @ SY1585 ) ) )
| ( SV277 @ SY1584 ) )
| ~ ( ~ ( SV277 @ SY1584 )
| ( in @ SY1584
@ ( dsetconstr @ SV146
@ ^ [SY1586: $i] : ( SV277 @ SY1586 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(787,plain,
! [SV278: $i,SV147: $i] :
( ( ! [SY1587: $i] :
( ~ ( in @ SY1587 @ ( binintersect @ SV147 @ SV278 ) )
| ( in @ SY1587 @ SV278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(788,plain,
! [SV148: $i > $o] :
( ( ( ~ ~ ! [SY1402: $i] :
~ ~ ( ~ ( SV148 @ SY1402 )
| ~ ! [SY1403: $i] :
( ~ ( SV148 @ SY1403 )
| ( SY1402 = SY1403 ) ) ) )
= $true )
| ( ( SV148
@ ( descr
@ ^ [SY1404: $i] : ( SV148 @ SY1404 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(789,plain,
! [SV279: $i,SV149: $i] :
( ( ( ( setminus @ SV149 @ SV279 )
!= emptyset )
| ( subset @ SV149 @ SV279 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(790,plain,
! [SV150: $i,SV280: $i] :
( ( ~ ( in @ SV280 @ SV150 )
| ( in @ SV280 @ ( powerset @ ( setunion @ SV150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(791,plain,
! [SV281: $i > $o,SV151: $i] :
( ( ~ ~ ~ ! [SY1588: $i] :
~ ~ ( ~ ( in @ SY1588 @ SV151 )
| ~ ( SV281 @ SY1588 ) )
| ! [SY1589: $i] :
( ~ ( in @ SY1589 @ SV151 )
| ~ ( SV281 @ SY1589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(792,plain,
! [SV282: $i,SV152: $i] :
( ( ~ ( subset @ SV152 @ SV282 )
| ~ ( subset @ SV282 @ SV152 )
| ( SV152 = SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(793,plain,
! [SV153: $i,SV283: $i] :
( ( ! [SY1590: $i] :
( ~ ( in @ SY1590 @ SV283 )
| ( in @ SY1590 @ ( binunion @ SV153 @ SV283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(794,plain,
! [SV284: $i,SV154: $i] :
( ( ! [SY1591: $i] :
( ~ ( subset @ SY1591 @ SV154 )
| ~ ( subset @ SY1591 @ SV284 )
| ( subset @ SY1591 @ ( binintersect @ SV154 @ SV284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(795,plain,
! [SV285: $i,SV155: $i] :
( ( ~ ( subset @ SV155 @ SV285 )
| ( subset @ ( powerset @ SV155 ) @ ( powerset @ SV285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(796,plain,
! [SV286: $i,SV156: $i] :
( ( ! [SY1592: $i] :
( ~ ( in @ SY1592 @ ( setadjoin @ SV156 @ SV286 ) )
| ( SY1592 = SV156 )
| ( in @ SY1592 @ SV286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(797,plain,
! [SV157: $i] :
( ( ( ~ ( subset @ SV157 @ emptyset ) )
= $true )
| ( ( SV157 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(798,plain,
! [SV287: $i,SV158: $i] :
( ( ! [SY1593: $i] :
( ~ ( in @ SY1593 @ ( binunion @ SV158 @ SV287 ) )
| ( in @ SY1593 @ SV158 )
| ( in @ SY1593 @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(799,plain,
! [SV159: $i > $o] :
( ( ( ~ ~ ! [SY1420: $i] :
~ ~ ( ~ ( SV159 @ SY1420 )
| ~ ! [SY1421: $i] :
( ~ ( SV159 @ SY1421 )
| ( SY1420 = SY1421 ) ) ) )
= $true )
| ( ( ! [SY1422: $i,SY1423: $i] :
( ~ ( SV159 @ SY1422 )
| ~ ( SV159 @ SY1423 )
| ( SY1422 = SY1423 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(800,plain,
! [SV288: $i,SV160: $i] :
( ( ! [SY1594: $i] :
( ~ ( in @ SY1594 @ ( setminus @ SV160 @ SV288 ) )
| ( in @ SY1594 @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(801,plain,
! [SV161: $i,SV289: $i] :
( ( ~ ( in @ SV289 @ ( setunion @ SV161 ) )
| ~ ! [SY1595: $i] :
~ ~ ( ~ ( in @ SY1595 @ SV161 )
| ~ ( in @ SV289 @ SY1595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(802,plain,
! [SV290: $i > $o,SV162: $i] :
( ( ! [SY1596: $i] :
( ~ ( in @ SY1596 @ SV162 )
| ~ ( SV290 @ SY1596 )
| ~ ! [SY1597: $i] :
( ~ ( in @ SY1597 @ SV162 )
| ~ ( SV290 @ SY1597 )
| ( SY1597 = SY1596 ) )
| ~ ! [SY1598: $i] :
~ ~ ( ~ ( in @ SY1598
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ SY1598 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(803,plain,
! [SV291: $i,SV168: $i,SV9: $i] :
( ( ( binintersect @ SV9 @ ( binunion @ SV168 @ SV291 ) )
= ( binunion @ ( binintersect @ SV9 @ SV168 ) @ ( binintersect @ SV9 @ SV291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(804,plain,
! [SV180: $i,SV29: $i] :
( ( ( SV29 != SV180 )
= $true )
| ( ( ! [SY1437: $i > $o,SY1438: $i > $o] :
( ~ ! [SY1439: $i] :
( ~ ( in @ SY1439 @ SV29 )
| ! [SY1440: $i] :
( ~ ( in @ SY1440 @ SV180 )
| ( SY1439 != SY1440 )
| ~ ( ~ ( ~ ( SY1437 @ SY1439 )
| ( SY1438 @ SY1440 ) )
| ~ ( ~ ( SY1438 @ SY1440 )
| ( SY1437 @ SY1439 ) ) ) ) )
| ( ( dsetconstr @ SV29
@ ^ [SX4: $i] : ( SY1437 @ SX4 ) )
= ( dsetconstr @ SV180
@ ^ [SX4: $i] : ( SY1438 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(805,plain,
! [SV30: $i] :
( ( ( ~ ! [SY1099: $i] :
~ ~ ( ~ ( in @ SY1099 @ SV30 )
| ( SV30
!= ( setadjoin @ SY1099 @ emptyset ) ) ) )
= $false )
| ( ( in @ ( setunion @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(806,plain,
! [SV181: $i > $o,SV31: $i] :
( ( ( ~ ~ ! [SY1443: $i] :
~ ~ ( ~ ( in @ SY1443 @ SV31 )
| ~ ( SV181 @ SY1443 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV31
@ ^ [SY1444: $i] : ( SV181 @ SY1444 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[664]) ).
thf(807,plain,
! [SV182: $i,SV32: $i,SV292: $i] :
( ( ~ ( in @ SV292 @ ( setadjoin @ SV32 @ ( setadjoin @ SV182 @ emptyset ) ) )
| ( SV292 = SV32 )
| ( SV292 = SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(808,plain,
! [SV183: $i,SV33: $i,SV293: $i] :
( ( ~ ( in @ SV293 @ SV33 )
| ~ ( in @ SV293 @ SV183 )
| ( in @ SV293 @ ( binintersect @ SV33 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(809,plain,
! [SV184: $i,SV34: $i,SV294: $i] :
( ( ~ ( in @ SV294 @ SV34 )
| ( in @ ( setadjoin @ SV294 @ emptyset ) @ ( powerset @ ( binunion @ SV34 @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(810,plain,
! [SV35: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1601: $i] :
( ~ ( in @ SY1601 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SY1601 )
| ( in @ SY1111 @ SV35 ) ) )
| ~ ! [SY1603: $i,SY1604: $i] :
( ~ ~ ( ~ ( in @ SY1603 @ SV35 )
| ~ ( in @ SY1604 @ SV35 ) )
| ~ ! [SY1605: $i] :
( ~ ( in @ SY1605 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SY1603 @ SY1605 )
| ( in @ SY1604 @ SY1605 ) )
| ~ ( ~ ( in @ SY1604 @ SY1605 )
| ( in @ SY1603 @ SY1605 ) ) ) )
| ( SY1603 = SY1604 ) ) )
| ~ ! [SY1606: $i,SY1607: $i] :
( ~ ~ ( ~ ( in @ SY1606 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1607 @ ( sK2_SY1109 @ SV35 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1606 )
| ( in @ SX4 @ SY1607 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1607 )
| ( in @ SX4 @ SY1606 ) ) ) )
| ~ ! [SY1610: $i] :
( ~ ~ ( ~ ! [SY1120: $i] :
( ~ ( in @ SY1120 @ SY1610 )
| ( in @ SY1120 @ SV35 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1610 ) )
| ~ ! [SY1613: $i] :
~ ~ ! [SY1614: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1613 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1614 @ SY1610 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1613 )
| ~ ( in @ SX5 @ SY1610 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1613 ) )
| ( in @ SY1614 @ SY1616 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[668]) ).
thf(811,plain,
! [SV185: $i,SV36: $i] :
( ( ( ~ ( subset @ SV36 @ SV185 ) )
= $true )
| ( ( in @ SV36 @ ( powerset @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(812,plain,
! [SV37: $i > $o] :
( ( ( ~ ! [SY1128: $i] :
~ ~ ( ~ ( SV37 @ SY1128 )
| ~ ! [SY1129: $i] :
( ~ ( SV37 @ SY1129 )
| ( SY1128 = SY1129 ) ) ) )
= $false )
| ( ( ! [SY1130: $i,SY1131: $i] :
( ~ ( SV37 @ SY1130 )
| ~ ( SV37 @ SY1131 )
| ( SY1130 = SY1131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(813,plain,
! [SV186: $i > $o,SV38: $i] :
( ( ( ~ ~ ! [SY1448: $i] :
~ ~ ( ~ ( in @ SY1448 @ SV38 )
| ~ ~ ( SV186 @ SY1448 ) ) )
= $true )
| ( ( ~ ! [SY1449: $i] :
( ~ ( in @ SY1449 @ SV38 )
| ( SV186 @ SY1449 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[671]) ).
thf(814,plain,
! [SV187: $i > $o,SV39: $i,SV295: $i] :
( ( ~ ( in @ SV295 @ SV39 )
| ~ ( SV187 @ SV295 )
| ( ( dsetconstr @ SV39
@ ^ [SY1451: $i] : ( SV187 @ SY1451 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(815,plain,
! [SV188: $i,SV40: $i,SV296: $i] :
( ( ~ ( in @ SV296 @ SV40 )
| ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV188 )
| ( in @ ( setadjoin @ ( setadjoin @ SV296 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV296 @ ( setadjoin @ SY1619 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SV40 @ SV188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(816,plain,
! [SV189: $i,SV41: $i] :
( ( ( SV41 != SV189 )
= $true )
| ( ( subset @ SV41 @ SV189 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(817,plain,
! [SV297: $i,SV190: $i,SV42: $i] :
( ( ! [SY1620: $i] :
( ( ( setadjoin @ ( setadjoin @ SV42 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV42 @ ( setadjoin @ SV190 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV297 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV297 @ ( setadjoin @ SY1620 @ emptyset ) ) @ emptyset ) ) )
| ( SV42 = SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(818,plain,
! [SV191: $i,SV43: $i] :
( ( ( SV43 != SV191 )
= $true )
| ( ( ( setunion @ SV43 )
= ( setunion @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(819,plain,
! [SV192: $i,SV44: $i,SV298: $i] :
( ( ~ ( in @ SV298 @ SV44 )
| ~ ~ ( in @ SV298 @ SV192 )
| ~ ( subset @ SV44 @ SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(820,plain,
! [SV193: $i > $o,SV45: $i] :
( ( ( ~ ~ ! [SY1457: $i] :
( ~ ( in @ SY1457 @ SV45 )
| ( SV193 @ SY1457 ) ) )
= $true )
| ( ( ~ ! [SY1458: $i] :
~ ~ ( ~ ( in @ SY1458 @ SV45 )
| ~ ~ ( SV193 @ SY1458 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(821,plain,
! [SV299: $i,SV46: $i,SV194: $i] :
( ( ~ ( in @ SV194 @ ( powerset @ SV46 ) )
| ~ ( in @ SV299 @ SV194 )
| ( in @ SV299 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(822,plain,
! [SV47: $i,SV195: $i] :
( ( ( ~ ( subset @ SV195 @ SV47 ) )
= $true )
| ( ( ( binintersect @ SV47 @ SV195 )
= SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(823,plain,
! [SV196: $i,SV48: $i,SV300: $i] :
( ( ~ ( in @ SV300 @ SV48 )
| ! [SY1621: $i] :
( ~ ( in @ SY1621 @ SV196 )
| ( in @ ( setadjoin @ ( setadjoin @ SV300 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV300 @ ( setadjoin @ SY1621 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV48 @ SV196 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(824,plain,
! [SV197: $i,SV49: $i] :
( ( ( SV49 != SV197 )
= $true )
| ( ( ( powerset @ SV49 )
= ( powerset @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(825,plain,
! [SV50: $i > $o] :
( ( ( ~ ! [SY1158: $i] :
~ ~ ( ~ ( SV50 @ SY1158 )
| ~ ! [SY1159: $i] :
( ~ ( SV50 @ SY1159 )
| ( SY1158 = SY1159 ) ) ) )
= $false )
| ( ( ~ ! [SY1160: $i] :
~ ~ ( ~ ( SV50 @ SY1160 )
| ~ ! [SY1161: $i] :
( ~ ( SV50 @ SY1161 )
| ( SY1160 = SY1161 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(826,plain,
! [SV198: $i,SV51: $i] :
( ( ( ~ ! [SY1462: $i] :
( ~ ( in @ SY1462 @ SV51 )
| ( in @ SY1462 @ SV198 ) ) )
= $true )
| ( ( ~ ! [SY1463: $i] :
( ~ ( in @ SY1463 @ SV198 )
| ( in @ SY1463 @ SV51 ) )
| ( SV51 = SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[684]) ).
thf(827,plain,
! [SV52: $i] :
( ( ( SV52 != emptyset )
= $false )
| ( ( ~ ! [SY1165: $i] :
~ ( in @ SY1165 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(828,plain,
! [SV199: $i,SV53: $i,SV301: $i] :
( ( ~ ( in @ SV301 @ SV53 )
| ~ ~ ( in @ SV301 @ SV199 )
| ( in @ SV301 @ ( setminus @ SV53 @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(829,plain,
! [SV200: $i,SV54: $i] :
( ( ! [SY1465: $i] :
~ ~ ( ~ ( in @ SY1465 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1466: $i] :
~ ~ ( ~ ( in @ SY1466 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1465 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1465 @ ( setadjoin @ SY1466 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(830,plain,
! [SV201: $i,SV55: $i,SV302: $i] :
( ( ~ ~ ( in @ SV302 @ SV55 )
| ~ ( in @ SV302 @ ( setminus @ SV55 @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(831,plain,
! [SV56: $i,SV303: $i,SV202: $i] :
( ( ~ ( in @ SV202 @ SV303 )
| ~ ( in @ SV303 @ SV56 )
| ( in @ SV202 @ ( setunion @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(832,plain,
! [SV203: $i,SV57: $i,SV304: $i] :
( ( ~ ( in @ SV304 @ ( setadjoin @ SV57 @ ( setadjoin @ SV203 @ emptyset ) ) )
| ( SV304 = SV57 )
| ( SV304 = SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(833,plain,
! [SV204: $i,SV58: $i,SV305: $i] :
( ( ~ ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) )
| ~ ! [SY1622: $i] :
~ ~ ( ~ ( in @ SY1622 @ SV58 )
| ~ ~ ! [SY1623: $i] :
~ ~ ( ~ ( in @ SY1623 @ SV204 )
| ( SV305
!= ( setadjoin @ ( setadjoin @ SY1622 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1622 @ ( setadjoin @ SY1623 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(834,plain,
! [SV205: $i,SV59: $i] :
( ( ( ~ ! [SY1473: $i] :
~ ( ~ ( ~ ( in @ SY1473 @ SV59 )
| ( in @ SY1473 @ SV205 ) )
| ~ ( ~ ( in @ SY1473 @ SV205 )
| ( in @ SY1473 @ SV59 ) ) ) )
= $true )
| ( ( SV59 = SV205 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[692]) ).
thf(835,plain,
! [SV206: $i,SV60: $i,SV306: $i] :
( ( ! [SY1624: $o] :
( ~ ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
| ~ ( ~ ( in @ SV306 @ SV60 )
| SY1624 )
| ~ ( ~ ( in @ SV306 @ SV206 )
| SY1624 )
| SY1624 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(836,plain,
! [SV207: $i,SV61: $i] :
( ( ! [SY1476: $i] :
~ ~ ( ~ ( in @ SY1476 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1477: $i] :
~ ~ ( ~ ( in @ SY1477 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1476 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1476 @ ( setadjoin @ SY1477 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(837,plain,
! [SV208: $i > $o,SV62: $i] :
( ( ( ~ ! [SY1478: $i] :
( ~ ( in @ SY1478 @ SV62 )
| ~ ( SV208 @ SY1478 ) ) )
= $true )
| ( ( ~ ~ ! [SY1479: $i] :
~ ~ ( ~ ( in @ SY1479 @ SV62 )
| ~ ( SV208 @ SY1479 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[695]) ).
thf(838,plain,
! [SV63: $i,SV209: $i] :
( ( ( ~ ( in @ SV209 @ SV63 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV209 @ emptyset ) @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(839,plain,
! [SV64: $i > $i > $o,SV210: $i] :
( ( ( ~ ! [SY1480: $i] :
( ~ ( in @ SY1480 @ SV210 )
| ~ ! [SY1195: $i] :
~ ~ ( ~ ( SV64 @ SY1480 @ SY1195 )
| ~ ! [SY1196: $i] :
( ~ ( SV64 @ SY1480 @ SY1196 )
| ( SY1195 = SY1196 ) ) ) ) )
= $true )
| ( ( ~ ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(840,plain,
! [SV211: $i,SV65: $i,SV307: $i] :
( ( ~ ( in @ ( setadjoin @ SV307 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV65 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV65 @ ( setadjoin @ SV211 @ emptyset ) ) @ emptyset ) ) )
| ( SV65 = SV307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(841,plain,
! [SV308: $i,SV212: $i,SV66: $i] :
( ( ! [SY1625: $i] :
( ( ( setadjoin @ ( setadjoin @ SV66 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV66 @ ( setadjoin @ SV212 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV308 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV308 @ ( setadjoin @ SY1625 @ emptyset ) ) @ emptyset ) ) )
| ( SV66 = SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(842,plain,
! [SV213: $i,SV67: $i,SV309: $i] :
( ( ~ ( in @ SV309 @ SV67 )
| ~ ( in @ SV309 @ SV213 )
| ~ ( in @ SV309 @ ( symdiff @ SV67 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(843,plain,
! [SV214: $i,SV68: $i] :
( ( ( ~ ~ ( subset @ SV68 @ SV214 ) )
= $true )
| ( ( SV68 != SV214 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[701]) ).
thf(844,plain,
( ( ( sK1_SX0 != sK3_SY1491 )
| ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1491 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ emptyset ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[702]) ).
thf(845,plain,
! [SV215: $i,SV69: $i] :
( ( ( SV69 != SV215 )
= $true )
| ( ( subset @ SV215 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[703]) ).
thf(846,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ( ~ ! [SY1492: $i] :
( ~ ( in @ SY1492 @ SV70 )
| ! [SY1493: $i] :
( ~ ( in @ SY1493 @ SV70 )
| ~ ( SV216 @ SY1492 )
| ~ ( SV216 @ SY1493 )
| ( SY1492 = SY1493 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) )
| ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[704]) ).
thf(847,plain,
! [SV217: $i > $o,SV71: $i,SV310: $i] :
( ( ~ ( in @ SV310 @ SV71 )
| ~ ( SV217 @ SV310 )
| ( in @ SV310
@ ( dsetconstr @ SV71
@ ^ [SY1499: $i] : ( SV217 @ SY1499 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(848,plain,
! [SV72: $i,SV218: $i] :
( ( ( ~ ( in @ SV218 @ ( setunion @ SV72 ) ) )
= $true )
| ( ( ! [SY1500: $o] :
( ~ ! [SY1501: $i] :
( ~ ( in @ SV218 @ SY1501 )
| ~ ( in @ SY1501 @ SV72 )
| SY1500 )
| SY1500 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[706]) ).
thf(849,plain,
! [SV73: $o] :
( ( SV73 = $false )
| ( ( in @ emptyset @ ( prop2set @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(850,plain,
( ( $true = $false )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(852,plain,
! [SV219: $i,SV74: $i] :
( ( ( SV74 != SV219 )
= $true )
| ( ( ! [SY1502: $i,SY1503: $i] :
( ( SY1502 != SY1503 )
| ~ ( in @ SY1502 @ SV74 )
| ( in @ SY1503 @ SV219 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[710]) ).
thf(853,plain,
! [SV220: $i > $o,SV75: $i] :
( ( ( ~ ~ ! [SY1504: $i] :
~ ~ ( ~ ( in @ SY1504
@ ( dsetconstr @ SV75
@ ^ [SY1505: $i] : ( SV220 @ SY1505 ) ) )
| ( ( dsetconstr @ SV75
@ ^ [SY1506: $i] : ( SV220 @ SY1506 ) )
!= ( setadjoin @ SY1504 @ emptyset ) ) ) )
= $true )
| ( ( ~ ! [SY1507: $i] :
~ ~ ( ~ ( in @ SY1507 @ SV75 )
| ~ ( SV220 @ SY1507 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[711]) ).
thf(854,plain,
! [SV76: $i] :
( ( ( in @ SV76 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(855,plain,
! [SV221: $i,SV77: $i,SV311: $i] :
( ( ~ ( in @ SV311 @ SV77 )
| ! [SY1627: $i] :
( ~ ( in @ SY1627 @ SV221 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV311 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV311 @ ( setadjoin @ SY1627 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV77 @ SV221 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(856,plain,
! [SV78: $i,SV222: $i] :
( ( ( ~ ( in @ SV222 @ ( powerset @ SV78 ) ) )
= $true )
| ( ( subset @ SV222 @ SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(857,plain,
! [SV223: $i,SV79: $i,SV312: $i] :
( ( ~ ~ ( in @ SV312 @ SV79 )
| ~ ( in @ SV312 @ SV223 )
| ( in @ SV312 @ ( symdiff @ SV79 @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(858,plain,
! [SV224: $i,SV80: $i] :
( ( ( SV80 != SV224 )
= $true )
| ( ( ! [SY1511: $i,SY1512: $i] :
( ( SY1511 != SY1512 )
| ( ( setadjoin @ SV80 @ SY1511 )
= ( setadjoin @ SV224 @ SY1512 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[716]) ).
thf(859,plain,
! [SV225: $i,SV81: $i] :
( ( ( ~ ( subset @ SV81 @ SV225 ) )
= $true )
| ( ( ( binintersect @ SV81 @ SV225 )
= SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[717]) ).
thf(860,plain,
! [SV226: $i,SV82: $i] :
( ( ( SV82 != SV226 )
= $true )
| ( ( ( setadjoin @ SV82 @ ( setadjoin @ SV226 @ emptyset ) )
= ( setadjoin @ SV82 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[718]) ).
thf(861,plain,
! [SV227: $i,SV83: $i] :
( ( ( ( binintersect @ SV83 @ SV227 )
!= SV227 )
= $true )
| ( ( subset @ SV227 @ SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(862,plain,
! [SV84: $i] :
( ( ( in @ SV84 @ emptyset )
= $false )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(863,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ! [SY1513: $i,SY1514: $i] :
( ( SY1513 != SY1514 )
| ~ ( ~ ( ~ ( SV85 @ SY1513 )
| ( SV228 @ SY1514 ) )
| ~ ( ~ ( SV228 @ SY1514 )
| ( SV85 @ SY1513 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(864,plain,
! [SV229: $i,SV86: $i] :
( ( ( ~ ! [SY1523: $i] :
( ~ ( in @ SY1523 @ SV86 )
| ( in @ SY1523 @ SV229 ) ) )
= $true )
| ( ( subset @ SV86 @ SV229 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(865,plain,
! [SV230: $i,SV87: $i,SV313: $i] :
( ( ~ ( in @ SV313 @ SV87 )
| ! [SY1628: $i] :
( ~ ( in @ SY1628 @ SV230 )
| ( in @ ( setadjoin @ ( setadjoin @ SV313 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV313 @ ( setadjoin @ SY1628 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV87 @ SV230 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(866,plain,
! [SV88: $i,SV231: $i,SV314: $i] :
( ( ~ ( in @ SV314 @ SV231 )
| ( in @ SV314 @ ( setadjoin @ SV88 @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(867,plain,
! [SV232: $i,SV89: $i] :
( ( ( ~ ~ ~ ! [SY1527: $i] :
~ ~ ( ~ ( in @ SY1527 @ SV89 )
| ~ ( in @ SY1527 @ SV232 ) ) )
= $true )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[725]) ).
thf(868,plain,
! [SV90: $i > $o] :
( ( ( ~ ! [SY1264: $i] :
~ ~ ( ~ ( SV90 @ SY1264 )
| ~ ! [SY1265: $i] :
( ~ ( SV90 @ SY1265 )
| ( SY1264 = SY1265 ) ) ) )
= $false )
| ( ( ~ ! [SY1266: $i] :
~ ! [SY1267: $i] :
~ ( ~ ( ~ ( SV90 @ SY1267 )
| ( SY1267 = SY1266 ) )
| ~ ( ( SY1267 != SY1266 )
| ( SV90 @ SY1267 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(869,plain,
! [SV233: $i,SV91: $i,SV315: $i] :
( ( ~ ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
| ! [SY1629: $o] :
( ~ ( ( SV315 != SV91 )
| SY1629 )
| ~ ( ~ ( in @ SV315 @ SV233 )
| SY1629 )
| SY1629 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(870,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ( ~ ! [SY1530: $i] :
( ~ ( in @ SY1530 @ SV92 )
| ! [SY1531: $i] :
( ~ ( in @ SY1531 @ SV92 )
| ~ ( SV234 @ SY1530 )
| ~ ( SV234 @ SY1531 )
| ( SY1530 = SY1531 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) )
| ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[728]) ).
thf(871,plain,
! [SV235: $i > $o,SV93: $i,SV316: $i] :
( ( ~ ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SY1537: $i] : ( SV235 @ SY1537 ) ) )
| ( SV235 @ SV316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(872,plain,
! [SV94: $i,SV236: $i,SV317: $i] :
( ( ~ ( in @ SV317 @ SV236 )
| ~ ( in @ SV317 @ ( setminus @ SV94 @ SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(873,plain,
! [SV237: $i,SV95: $i,SV318: $i] :
( ( ~ ( in @ SV318 @ SV95 )
| ! [SY1631: $i] :
( ~ ( in @ SY1631 @ SV237 )
| ( in @ ( setadjoin @ SV318 @ ( setadjoin @ SY1631 @ emptyset ) ) @ ( powerset @ ( binunion @ SV95 @ SV237 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(874,plain,
! [SV238: $i,SV96: $i,SV319: $i] :
( ( ~ ( ~ ( ~ ( in @ SV319 @ ( setadjoin @ SV96 @ SV238 ) )
| ( SV319 = SV96 )
| ( in @ SV319 @ SV238 ) )
| ~ ( ~ ( ( SV319 = SV96 )
| ( in @ SV319 @ SV238 ) )
| ( in @ SV319 @ ( setadjoin @ SV96 @ SV238 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(875,plain,
! [SV239: $i,SV97: $i,SV320: $i] :
( ( ~ ~ ( in @ SV320 @ ( setminus @ SV97 @ SV239 ) )
| ~ ( in @ SV320 @ SV97 )
| ( in @ SV320 @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(876,plain,
! [SV98: $i > $o] :
( ( ( ~ ! [SY1290: $i] :
~ ! [SY1291: $i] :
~ ( ~ ( ~ ( SV98 @ SY1291 )
| ( SY1291 = SY1290 ) )
| ~ ( ( SY1291 != SY1290 )
| ( SV98 @ SY1291 ) ) ) )
= $false )
| ( ( ~ ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(877,plain,
! [SV240: $i,SV99: $i] :
( ( ( ( setadjoin @ SV99 @ emptyset )
!= ( setadjoin @ SV240 @ emptyset ) )
= $true )
| ( ( SV99 = SV240 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(878,plain,
! [SV241: $i,SV100: $i,SV321: $i] :
( ( ~ ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) )
| ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ ( setunion @ SV321 ) )
| ~ ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633 @ ( setunion @ SV321 ) )
| ( SV321
!= ( setadjoin @ ( setadjoin @ SY1632 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1632 @ ( setadjoin @ SY1633 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(879,plain,
! [SV242: $i,SV101: $i,SV322: $i] :
( ( ~ ( in @ SV322 @ SV101 )
| ( in @ SV322 @ ( binunion @ SV101 @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(880,plain,
! [SV243: $i > $o,SV102: $i,SV323: $i] :
( ( ~ ( in @ SV323
@ ( dsetconstr @ SV102
@ ^ [SY1548: $i] : ( SV243 @ SY1548 ) ) )
| ( in @ SV323 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(881,plain,
! [SV244: $i,SV103: $i,SV324: $i] :
( ( ~ ( in @ SV324 @ SV103 )
| ~ ~ ( in @ SV324 @ SV244 )
| ( SV103 != SV244 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(882,plain,
! [SV245: $i > $o,SV104: $i] :
( ( ( ~ ~ ~ ! [SY1550: $i] :
~ ~ ( ~ ( in @ SY1550 @ SV104 )
| ~ ( SV245 @ SY1550 ) ) )
= $true )
| ( ( ! [SY1551: $i] :
( ~ ( in @ SY1551 @ SV104 )
| ~ ( SV245 @ SY1551 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[740]) ).
thf(883,plain,
! [SV246: $i,SV105: $i,SV325: $i] :
( ( ~ ( in @ SV325 @ ( binintersect @ SV105 @ SV246 ) )
| ( in @ SV325 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(884,plain,
! [SV247: $i,SV106: $i,SV326: $i] :
( ( ~ ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) )
| ~ ( in @ SV326 @ SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(885,plain,
! [SV248: $i,SV107: $i] :
( ( ( ~ ( ( SV107 != SV248 ) ) )
= $true )
| ( ( ~ ( in @ SV248 @ ( setadjoin @ SV107 @ emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(886,plain,
! [SV108: $i] :
( ( ( ~ ! [SY1314: $i] :
~ ~ ( ~ ( in @ SY1314 @ ( setunion @ SV108 ) )
| ~ ~ ! [SY1315: $i] :
~ ~ ( ~ ( in @ SY1315 @ ( setunion @ SV108 ) )
| ( SV108
!= ( setadjoin @ ( setadjoin @ SY1314 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1314 @ ( setadjoin @ SY1315 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false )
| ( ( ~ ! [SY1316: $i] :
~ ~ ( ~ ( in @ SY1316
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ SY1316 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(887,plain,
! [SV327: $i,SV249: $i,SV109: $i] :
( ( ~ ( subset @ SV109 @ SV249 )
| ~ ~ ( in @ SV327 @ SV249 )
| ~ ( in @ SV327 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(888,plain,
! [SV110: $i] :
( ( ( ! [SY1321: $i] :
~ ( in @ SY1321 @ SV110 ) )
= $false )
| ( ( SV110 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(889,plain,
! [SV250: $i,SV111: $i,SV328: $i] :
( ( ~ ( in @ SV328 @ SV111 )
| ! [SY1635: $i] :
( ~ ( in @ SY1635 @ SV250 )
| ( subset @ ( setadjoin @ SV328 @ ( setadjoin @ SY1635 @ emptyset ) ) @ ( binunion @ SV111 @ SV250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(890,plain,
! [SV112: $o,SV251: $i] :
( ( ( ~ ( in @ SV251 @ ( prop2set @ SV112 ) ) )
= $true )
| ( SV112 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(892,plain,
! [SV253: $i] :
( ( ( ~ ( in @ SV253 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(893,plain,
! [SV254: $i,SV113: $i,SV329: $i] :
( ( ~ ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
| ! [SY1636: $o] :
( ~ ( ~ ( in @ SV329 @ SV113 )
| ~ ~ ( in @ SV329 @ SV254 )
| SY1636 )
| ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| SY1636 )
| SY1636 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(894,plain,
! [SV114: $i] :
( ( ( in @ SV114 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV114 @ SV114 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(895,plain,
! [SV255: $i,SV330: $i,SV115: $i] :
( ( ~ ( subset @ SV115 @ SV330 )
| ( subset @ SV115 @ ( setadjoin @ SV255 @ SV330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(896,plain,
! [SV331: $i,SV256: $i,SV116: $i] :
( ( ~ ( subset @ SV116 @ SV256 )
| ~ ( in @ SV331 @ SV116 )
| ( in @ SV331 @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(897,plain,
! [SV117: $i,SV257: $i] :
( ( ( ~ ( subset @ SV257 @ SV117 ) )
= $true )
| ( ( in @ SV257 @ ( powerset @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(898,plain,
! [SV258: $i,SV118: $i] :
( ( ( SV118 != SV258 )
= $true )
| ( ( ! [SY1561: $i,SY1562: $i] :
( ( SY1561 != SY1562 )
| ~ ( ~ ( ~ ( in @ SY1561 @ SV118 )
| ( in @ SY1562 @ SV258 ) )
| ~ ( ~ ( in @ SY1562 @ SV258 )
| ( in @ SY1561 @ SV118 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[756]) ).
thf(899,plain,
! [SV259: $i > $o,SV119: $i] :
( ( ( ~ ~ ! [SY1563: $i] :
( ~ ( in @ SY1563 @ SV119 )
| ( SV259 @ SY1563 ) ) )
= $true )
| ( ( ~ ! [SY1564: $i] :
~ ~ ( ~ ( in @ SY1564 @ SV119 )
| ~ ~ ( SV259 @ SY1564 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[757]) ).
thf(900,plain,
! [SV120: $i,SV260: $i] :
( ( ( ~ ! [SY1565: $i] :
( ~ ( in @ SY1565 @ SV260 )
| ( in @ SY1565 @ SV120 ) ) )
= $true )
| ( ( in @ SV260 @ ( powerset @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[758]) ).
thf(901,plain,
! [SV261: $i,SV121: $i,SV332: $i] :
( ( ~ ( in @ SV332 @ SV121 )
| ~ ~ ( in @ SV332 @ SV261 )
| ( in @ SV332 @ ( symdiff @ SV121 @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(902,plain,
! [SV262: $i,SV122: $i] :
( ( ( ~ ( subset @ SV122 @ SV262 ) )
= $true )
| ( ( ( setminus @ SV122 @ SV262 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[760]) ).
thf(903,plain,
! [SV263: $i,SV123: $i] :
( ( ( ~ ( in @ SV123 @ ( setadjoin @ SV263 @ emptyset ) ) )
= $true )
| ( ( in @ SV263 @ ( setadjoin @ SV123 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(904,plain,
! [SV124: $i > $o] :
( ( ( ~ ! [SY1346: $i] :
~ ~ ( ~ ( SV124 @ SY1346 )
| ~ ! [SY1347: $i] :
( ~ ( SV124 @ SY1347 )
| ( SY1346 = SY1347 ) ) ) )
= $false )
| ( ( ~ ! [SY1348: $i] :
~ ~ ( ~ ( SV124 @ SY1348 )
| ~ ! [SY1349: $i] :
( ~ ( SV124 @ SY1349 )
| ( SY1348 = SY1349 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(905,plain,
! [SV264: $i,SV125: $i,SV333: $i] :
( ( ~ ~ ( in @ SV333 @ SV125 )
| ~ ~ ( in @ SV333 @ SV264 )
| ~ ( in @ SV333 @ ( symdiff @ SV125 @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(906,plain,
! [SV126: $i,SV265: $i] :
( ( ~ ( ~ ( in @ SV265 @ ( setunion @ SV126 ) )
| ~ ! [SY1568: $i] :
~ ~ ( ~ ( in @ SV265 @ SY1568 )
| ~ ( in @ SY1568 @ SV126 ) ) )
| ~ ( ~ ~ ! [SY1569: $i] :
~ ~ ( ~ ( in @ SV265 @ SY1569 )
| ~ ( in @ SY1569 @ SV126 ) )
| ( in @ SV265 @ ( setunion @ SV126 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(907,plain,
! [SV127: $i] :
( ( ( ~ ! [SY1355: $i] :
~ ( in @ SY1355 @ SV127 ) )
= $false )
| ( ( SV127 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(908,plain,
! [SV266: $i,SV128: $i] :
( ( ( ~ ( in @ SV128 @ ( setadjoin @ SV266 @ emptyset ) ) )
= $true )
| ( ( SV128 = SV266 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(909,plain,
! [SV129: $i] :
( ( ( ! [SY1357: $i] :
~ ( in @ SY1357 @ SV129 ) )
= $false )
| ( ( SV129 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(910,plain,
! [SV130: $i > $o] :
( ( ( ~ ! [SY1358: $i] :
~ ( SV130 @ SY1358 ) )
= $false )
| ( ( ~ ! [SY1359: $i,SY1360: $i] :
( ~ ( SV130 @ SY1359 )
| ~ ( SV130 @ SY1360 )
| ( SY1359 = SY1360 ) )
| ~ ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(911,plain,
! [SV267: $i,SV131: $i,SV334: $i] :
( ( ~ ( in @ SV334 @ ( cartprod @ SV131 @ SV267 ) )
| ( in @ ( kfst @ SV334 ) @ SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(912,plain,
! [SV268: $i,SV132: $i] :
( ( ( SV132 != SV268 )
= $true )
| ( ( in @ SV132 @ ( setadjoin @ SV268 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(913,plain,
! [SV133: $o] :
( ( SV133 = $false )
| ( ( set2prop @ ( prop2set @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(914,plain,
( ( $true = $false )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(916,plain,
! [SV134: $i > $o,SV269: $i] :
( ( ( ~ ( in @ SV269 @ emptyset ) )
= $true )
| ( ( SV134 @ SV269 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(917,plain,
! [SV270: $i,SV135: $i] :
( ( ( ( binintersect @ SV135 @ SV270 )
!= SV135 )
= $true )
| ( ( subset @ SV135 @ SV270 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[775]) ).
thf(918,plain,
! [SV271: $i,SV136: $i,SV335: $i] :
( ( ~ ~ ( in @ SV335 @ ( setminus @ SV136 @ SV271 ) )
| ~ ~ ( in @ SV335 @ SV271 )
| ~ ( in @ SV335 @ SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(919,plain,
! [SV137: $i > $o] :
( ( ( ~ ! [SY1370: $i] :
~ ~ ( ~ ( SV137 @ SY1370 )
| ~ ! [SY1371: $i] :
( ~ ( SV137 @ SY1371 )
| ( SY1370 = SY1371 ) ) ) )
= $false )
| ( ( ~ ! [SY1372: $i] :
~ ( SV137 @ SY1372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(920,plain,
! [SV138: $i] :
( ( ( ~ ( ~ ( in @ emptyset @ SV138 )
| ~ ! [SY1373: $i] :
( ~ ~ ( ~ ( in @ SY1373 @ omega )
| ~ ( in @ SY1373 @ SV138 ) )
| ( in @ ( setadjoin @ SY1373 @ SY1373 ) @ SV138 ) ) ) )
= $false )
| ( ( ! [SY1374: $i] :
( ~ ( in @ SY1374 @ omega )
| ( in @ SY1374 @ SV138 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[778]) ).
thf(921,plain,
! [SV336: $i,SV272: $i,SV139: $i] :
( ( ~ ( subset @ SV139 @ SV272 )
| ~ ( subset @ SV272 @ SV336 )
| ( subset @ SV139 @ SV336 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(922,plain,
! [SV140: $i,SV273: $i] :
( ( ~ ( ~ ( in @ SV273 @ ( powerset @ SV140 ) )
| ! [SY1573: $i] :
( ~ ( in @ SY1573 @ SV273 )
| ( in @ SY1573 @ SV140 ) ) )
| ~ ( ~ ! [SY1574: $i] :
( ~ ( in @ SY1574 @ SV273 )
| ( in @ SY1574 @ SV140 ) )
| ( in @ SV273 @ ( powerset @ SV140 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(923,plain,
! [SV274: $i,SV141: $i] :
( ( ( ~ ! [SY1575: $i] :
( ~ ( in @ SY1575 @ SV141 )
| ( in @ SY1575 @ SV274 ) ) )
= $true )
| ( ( subset @ SV141 @ SV274 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[781]) ).
thf(924,plain,
! [SV142: $i] :
( ( ( ~ ! [SY1382: $i] :
~ ( in @ SY1382 @ SV142 ) )
= $false )
| ( ( ~ ! [SY1383: $i] :
~ ~ ( ~ ( in @ SY1383 @ SV142 )
| ~ ~ ~ ! [SY1384: $i] :
~ ~ ( ~ ( in @ SY1384 @ SY1383 )
| ~ ( in @ SY1384 @ SV142 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(925,plain,
! [SV143: $i] :
( ( ( SV143 != emptyset )
= $false )
| ( ( ~ ! [SY1385: $i] :
~ ~ ( ~ ( in @ SY1385 @ SV143 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(926,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ( ~ ! [SY1576: $i,SY1577: $i] :
( ( SY1576 != SY1577 )
| ~ ( ~ ( ~ ( SV144 @ SY1576 )
| ( SV275 @ SY1577 ) )
| ~ ( ~ ( SV275 @ SY1577 )
| ( SV144 @ SY1576 ) ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[784]) ).
thf(927,plain,
! [SV145: $i,SV276: $i] :
( ( ( ~ ( in @ SV276 @ SV145 ) )
= $true )
| ( ( in @ ( setadjoin @ SV276 @ emptyset ) @ ( powerset @ SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[785]) ).
thf(928,plain,
! [SV277: $i > $o,SV146: $i,SV337: $i] :
( ( ~ ( in @ SV337 @ SV146 )
| ~ ( ~ ( ~ ( in @ SV337
@ ( dsetconstr @ SV146
@ ^ [SY1585: $i] : ( SV277 @ SY1585 ) ) )
| ( SV277 @ SV337 ) )
| ~ ( ~ ( SV277 @ SV337 )
| ( in @ SV337
@ ( dsetconstr @ SV146
@ ^ [SY1586: $i] : ( SV277 @ SY1586 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(929,plain,
! [SV278: $i,SV147: $i,SV338: $i] :
( ( ~ ( in @ SV338 @ ( binintersect @ SV147 @ SV278 ) )
| ( in @ SV338 @ SV278 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(930,plain,
! [SV148: $i > $o] :
( ( ( ~ ! [SY1402: $i] :
~ ~ ( ~ ( SV148 @ SY1402 )
| ~ ! [SY1403: $i] :
( ~ ( SV148 @ SY1403 )
| ( SY1402 = SY1403 ) ) ) )
= $false )
| ( ( SV148
@ ( descr
@ ^ [SY1404: $i] : ( SV148 @ SY1404 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(931,plain,
! [SV279: $i,SV149: $i] :
( ( ( ( setminus @ SV149 @ SV279 )
!= emptyset )
= $true )
| ( ( subset @ SV149 @ SV279 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(932,plain,
! [SV150: $i,SV280: $i] :
( ( ( ~ ( in @ SV280 @ SV150 ) )
= $true )
| ( ( in @ SV280 @ ( powerset @ ( setunion @ SV150 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[790]) ).
thf(933,plain,
! [SV281: $i > $o,SV151: $i] :
( ( ( ~ ~ ~ ! [SY1588: $i] :
~ ~ ( ~ ( in @ SY1588 @ SV151 )
| ~ ( SV281 @ SY1588 ) ) )
= $true )
| ( ( ! [SY1589: $i] :
( ~ ( in @ SY1589 @ SV151 )
| ~ ( SV281 @ SY1589 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[791]) ).
thf(934,plain,
! [SV282: $i,SV152: $i] :
( ( ( ~ ( subset @ SV152 @ SV282 ) )
= $true )
| ( ( ~ ( subset @ SV282 @ SV152 )
| ( SV152 = SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[792]) ).
thf(935,plain,
! [SV153: $i,SV283: $i,SV339: $i] :
( ( ~ ( in @ SV339 @ SV283 )
| ( in @ SV339 @ ( binunion @ SV153 @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(936,plain,
! [SV284: $i,SV154: $i,SV340: $i] :
( ( ~ ( subset @ SV340 @ SV154 )
| ~ ( subset @ SV340 @ SV284 )
| ( subset @ SV340 @ ( binintersect @ SV154 @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(937,plain,
! [SV285: $i,SV155: $i] :
( ( ( ~ ( subset @ SV155 @ SV285 ) )
= $true )
| ( ( subset @ ( powerset @ SV155 ) @ ( powerset @ SV285 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[795]) ).
thf(938,plain,
! [SV286: $i,SV156: $i,SV341: $i] :
( ( ~ ( in @ SV341 @ ( setadjoin @ SV156 @ SV286 ) )
| ( SV341 = SV156 )
| ( in @ SV341 @ SV286 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(939,plain,
! [SV157: $i] :
( ( ( subset @ SV157 @ emptyset )
= $false )
| ( ( SV157 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[797]) ).
thf(940,plain,
! [SV287: $i,SV158: $i,SV342: $i] :
( ( ~ ( in @ SV342 @ ( binunion @ SV158 @ SV287 ) )
| ( in @ SV342 @ SV158 )
| ( in @ SV342 @ SV287 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(941,plain,
! [SV159: $i > $o] :
( ( ( ~ ! [SY1420: $i] :
~ ~ ( ~ ( SV159 @ SY1420 )
| ~ ! [SY1421: $i] :
( ~ ( SV159 @ SY1421 )
| ( SY1420 = SY1421 ) ) ) )
= $false )
| ( ( ! [SY1422: $i,SY1423: $i] :
( ~ ( SV159 @ SY1422 )
| ~ ( SV159 @ SY1423 )
| ( SY1422 = SY1423 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(942,plain,
! [SV288: $i,SV160: $i,SV343: $i] :
( ( ~ ( in @ SV343 @ ( setminus @ SV160 @ SV288 ) )
| ( in @ SV343 @ SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(943,plain,
! [SV161: $i,SV289: $i] :
( ( ( ~ ( in @ SV289 @ ( setunion @ SV161 ) ) )
= $true )
| ( ( ~ ! [SY1595: $i] :
~ ~ ( ~ ( in @ SY1595 @ SV161 )
| ~ ( in @ SV289 @ SY1595 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[801]) ).
thf(944,plain,
! [SV290: $i > $o,SV162: $i,SV344: $i] :
( ( ~ ( in @ SV344 @ SV162 )
| ~ ( SV290 @ SV344 )
| ~ ! [SY1639: $i] :
( ~ ( in @ SY1639 @ SV162 )
| ~ ( SV290 @ SY1639 )
| ( SY1639 = SV344 ) )
| ~ ! [SY1598: $i] :
~ ~ ( ~ ( in @ SY1598
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ SY1598 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(945,plain,
! [SV180: $i,SV29: $i] :
( ( ( SV29 = SV180 )
= $false )
| ( ( ! [SY1437: $i > $o,SY1438: $i > $o] :
( ~ ! [SY1439: $i] :
( ~ ( in @ SY1439 @ SV29 )
| ! [SY1440: $i] :
( ~ ( in @ SY1440 @ SV180 )
| ( SY1439 != SY1440 )
| ~ ( ~ ( ~ ( SY1437 @ SY1439 )
| ( SY1438 @ SY1440 ) )
| ~ ( ~ ( SY1438 @ SY1440 )
| ( SY1437 @ SY1439 ) ) ) ) )
| ( ( dsetconstr @ SV29
@ ^ [SX4: $i] : ( SY1437 @ SX4 ) )
= ( dsetconstr @ SV180
@ ^ [SX4: $i] : ( SY1438 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(946,plain,
! [SV30: $i] :
( ( ( ! [SY1099: $i] :
~ ~ ( ~ ( in @ SY1099 @ SV30 )
| ( SV30
!= ( setadjoin @ SY1099 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( setunion @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[805]) ).
thf(947,plain,
! [SV181: $i > $o,SV31: $i] :
( ( ( ~ ! [SY1443: $i] :
~ ~ ( ~ ( in @ SY1443 @ SV31 )
| ~ ( SV181 @ SY1443 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV31
@ ^ [SY1444: $i] : ( SV181 @ SY1444 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(948,plain,
! [SV182: $i,SV32: $i,SV292: $i] :
( ( ( ~ ( in @ SV292 @ ( setadjoin @ SV32 @ ( setadjoin @ SV182 @ emptyset ) ) ) )
= $true )
| ( ( ( SV292 = SV32 )
| ( SV292 = SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[807]) ).
thf(949,plain,
! [SV183: $i,SV33: $i,SV293: $i] :
( ( ( ~ ( in @ SV293 @ SV33 ) )
= $true )
| ( ( ~ ( in @ SV293 @ SV183 )
| ( in @ SV293 @ ( binintersect @ SV33 @ SV183 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[808]) ).
thf(950,plain,
! [SV184: $i,SV34: $i,SV294: $i] :
( ( ( ~ ( in @ SV294 @ SV34 ) )
= $true )
| ( ( in @ ( setadjoin @ SV294 @ emptyset ) @ ( powerset @ ( binunion @ SV34 @ SV184 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[809]) ).
thf(951,plain,
! [SV35: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1601: $i] :
( ~ ( in @ SY1601 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SY1601 )
| ( in @ SY1111 @ SV35 ) ) )
| ~ ! [SY1603: $i,SY1604: $i] :
( ~ ~ ( ~ ( in @ SY1603 @ SV35 )
| ~ ( in @ SY1604 @ SV35 ) )
| ~ ! [SY1605: $i] :
( ~ ( in @ SY1605 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SY1603 @ SY1605 )
| ( in @ SY1604 @ SY1605 ) )
| ~ ( ~ ( in @ SY1604 @ SY1605 )
| ( in @ SY1603 @ SY1605 ) ) ) )
| ( SY1603 = SY1604 ) ) )
| ~ ! [SY1606: $i,SY1607: $i] :
( ~ ~ ( ~ ( in @ SY1606 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1607 @ ( sK2_SY1109 @ SV35 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1606 )
| ( in @ SX4 @ SY1607 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1607 )
| ( in @ SX4 @ SY1606 ) ) ) )
| ~ ! [SY1610: $i] :
( ~ ~ ( ~ ! [SY1120: $i] :
( ~ ( in @ SY1120 @ SY1610 )
| ( in @ SY1120 @ SV35 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1610 ) )
| ~ ! [SY1613: $i] :
~ ~ ! [SY1614: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1613 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1614 @ SY1610 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1613 )
| ~ ( in @ SX5 @ SY1610 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1613 ) )
| ( in @ SY1614 @ SY1616 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(952,plain,
! [SV185: $i,SV36: $i] :
( ( ( subset @ SV36 @ SV185 )
= $false )
| ( ( in @ SV36 @ ( powerset @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(953,plain,
! [SV37: $i > $o] :
( ( ( ! [SY1128: $i] :
~ ~ ( ~ ( SV37 @ SY1128 )
| ~ ! [SY1129: $i] :
( ~ ( SV37 @ SY1129 )
| ( SY1128 = SY1129 ) ) ) )
= $true )
| ( ( ! [SY1130: $i,SY1131: $i] :
( ~ ( SV37 @ SY1130 )
| ~ ( SV37 @ SY1131 )
| ( SY1130 = SY1131 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[812]) ).
thf(954,plain,
! [SV186: $i > $o,SV38: $i] :
( ( ( ~ ! [SY1448: $i] :
~ ~ ( ~ ( in @ SY1448 @ SV38 )
| ~ ~ ( SV186 @ SY1448 ) ) )
= $false )
| ( ( ~ ! [SY1449: $i] :
( ~ ( in @ SY1449 @ SV38 )
| ( SV186 @ SY1449 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(955,plain,
! [SV187: $i > $o,SV39: $i,SV295: $i] :
( ( ( ~ ( in @ SV295 @ SV39 ) )
= $true )
| ( ( ~ ( SV187 @ SV295 )
| ( ( dsetconstr @ SV39
@ ^ [SY1451: $i] : ( SV187 @ SY1451 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[814]) ).
thf(956,plain,
! [SV188: $i,SV40: $i,SV296: $i] :
( ( ( ~ ( in @ SV296 @ SV40 ) )
= $true )
| ( ( ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV188 )
| ( in @ ( setadjoin @ ( setadjoin @ SV296 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV296 @ ( setadjoin @ SY1619 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SV40 @ SV188 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[815]) ).
thf(957,plain,
! [SV189: $i,SV41: $i] :
( ( ( SV41 = SV189 )
= $false )
| ( ( subset @ SV41 @ SV189 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(958,plain,
! [SV345: $i,SV297: $i,SV190: $i,SV42: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV42 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV42 @ ( setadjoin @ SV190 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV297 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV297 @ ( setadjoin @ SV345 @ emptyset ) ) @ emptyset ) ) )
| ( SV42 = SV297 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(959,plain,
! [SV191: $i,SV43: $i] :
( ( ( SV43 = SV191 )
= $false )
| ( ( ( setunion @ SV43 )
= ( setunion @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[818]) ).
thf(960,plain,
! [SV192: $i,SV44: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ SV44 ) )
= $true )
| ( ( ~ ~ ( in @ SV298 @ SV192 )
| ~ ( subset @ SV44 @ SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[819]) ).
thf(961,plain,
! [SV193: $i > $o,SV45: $i] :
( ( ( ~ ! [SY1457: $i] :
( ~ ( in @ SY1457 @ SV45 )
| ( SV193 @ SY1457 ) ) )
= $false )
| ( ( ~ ! [SY1458: $i] :
~ ~ ( ~ ( in @ SY1458 @ SV45 )
| ~ ~ ( SV193 @ SY1458 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(962,plain,
! [SV299: $i,SV46: $i,SV194: $i] :
( ( ( ~ ( in @ SV194 @ ( powerset @ SV46 ) ) )
= $true )
| ( ( ~ ( in @ SV299 @ SV194 )
| ( in @ SV299 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(963,plain,
! [SV47: $i,SV195: $i] :
( ( ( subset @ SV195 @ SV47 )
= $false )
| ( ( ( binintersect @ SV47 @ SV195 )
= SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[822]) ).
thf(964,plain,
! [SV196: $i,SV48: $i,SV300: $i] :
( ( ( ~ ( in @ SV300 @ SV48 ) )
= $true )
| ( ( ! [SY1621: $i] :
( ~ ( in @ SY1621 @ SV196 )
| ( in @ ( setadjoin @ ( setadjoin @ SV300 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV300 @ ( setadjoin @ SY1621 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV48 @ SV196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(965,plain,
! [SV197: $i,SV49: $i] :
( ( ( SV49 = SV197 )
= $false )
| ( ( ( powerset @ SV49 )
= ( powerset @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[824]) ).
thf(966,plain,
! [SV50: $i > $o] :
( ( ( ! [SY1158: $i] :
~ ~ ( ~ ( SV50 @ SY1158 )
| ~ ! [SY1159: $i] :
( ~ ( SV50 @ SY1159 )
| ( SY1158 = SY1159 ) ) ) )
= $true )
| ( ( ~ ! [SY1160: $i] :
~ ~ ( ~ ( SV50 @ SY1160 )
| ~ ! [SY1161: $i] :
( ~ ( SV50 @ SY1161 )
| ( SY1160 = SY1161 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(967,plain,
! [SV198: $i,SV51: $i] :
( ( ( ! [SY1462: $i] :
( ~ ( in @ SY1462 @ SV51 )
| ( in @ SY1462 @ SV198 ) ) )
= $false )
| ( ( ~ ! [SY1463: $i] :
( ~ ( in @ SY1463 @ SV198 )
| ( in @ SY1463 @ SV51 ) )
| ( SV51 = SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(968,plain,
! [SV52: $i] :
( ( ( SV52 = emptyset )
= $true )
| ( ( ~ ! [SY1165: $i] :
~ ( in @ SY1165 @ SV52 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[827]) ).
thf(969,plain,
! [SV199: $i,SV53: $i,SV301: $i] :
( ( ( ~ ( in @ SV301 @ SV53 ) )
= $true )
| ( ( ~ ~ ( in @ SV301 @ SV199 )
| ( in @ SV301 @ ( setminus @ SV53 @ SV199 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[828]) ).
thf(970,plain,
! [SV54: $i,SV200: $i] :
( ( ~ ~ ( ~ ( in @ ( sK4_SY1465 @ SV200 @ SV54 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1643: $i] :
~ ~ ( ~ ( in @ SY1643 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ ( setadjoin @ SY1643 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[829]) ).
thf(971,plain,
! [SV201: $i,SV55: $i,SV302: $i] :
( ( ( ~ ~ ( in @ SV302 @ SV55 ) )
= $true )
| ( ( ~ ( in @ SV302 @ ( setminus @ SV55 @ SV201 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[830]) ).
thf(972,plain,
! [SV56: $i,SV303: $i,SV202: $i] :
( ( ( ~ ( in @ SV202 @ SV303 ) )
= $true )
| ( ( ~ ( in @ SV303 @ SV56 )
| ( in @ SV202 @ ( setunion @ SV56 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[831]) ).
thf(973,plain,
! [SV203: $i,SV57: $i,SV304: $i] :
( ( ( ~ ( in @ SV304 @ ( setadjoin @ SV57 @ ( setadjoin @ SV203 @ emptyset ) ) ) )
= $true )
| ( ( ( SV304 = SV57 )
| ( SV304 = SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[832]) ).
thf(974,plain,
! [SV204: $i,SV58: $i,SV305: $i] :
( ( ( ~ ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) ) )
= $true )
| ( ( ~ ! [SY1622: $i] :
~ ~ ( ~ ( in @ SY1622 @ SV58 )
| ~ ~ ! [SY1623: $i] :
~ ~ ( ~ ( in @ SY1623 @ SV204 )
| ( SV305
!= ( setadjoin @ ( setadjoin @ SY1622 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1622 @ ( setadjoin @ SY1623 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[833]) ).
thf(975,plain,
! [SV205: $i,SV59: $i] :
( ( ( ! [SY1473: $i] :
~ ( ~ ( ~ ( in @ SY1473 @ SV59 )
| ( in @ SY1473 @ SV205 ) )
| ~ ( ~ ( in @ SY1473 @ SV205 )
| ( in @ SY1473 @ SV59 ) ) ) )
= $false )
| ( ( SV59 = SV205 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(976,plain,
! [SV346: $o,SV206: $i,SV60: $i,SV306: $i] :
( ( ~ ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
| ~ ( ~ ( in @ SV306 @ SV60 )
| SV346 )
| ~ ( ~ ( in @ SV306 @ SV206 )
| SV346 )
| SV346 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[835]) ).
thf(978,plain,
! [SV206: $i,SV60: $i,SV306: $i] :
( ( ~ ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
| ~ ( ~ ( in @ SV306 @ SV60 )
| $false )
| ~ ( ~ ( in @ SV306 @ SV206 )
| $false )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[835]) ).
thf(979,plain,
! [SV61: $i,SV207: $i] :
( ( ~ ~ ( ~ ( in @ ( sK5_SY1476 @ SV207 @ SV61 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1644: $i] :
~ ~ ( ~ ( in @ SY1644 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ ( setadjoin @ SY1644 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[836]) ).
thf(980,plain,
! [SV208: $i > $o,SV62: $i] :
( ( ( ! [SY1478: $i] :
( ~ ( in @ SY1478 @ SV62 )
| ~ ( SV208 @ SY1478 ) ) )
= $false )
| ( ( ~ ~ ! [SY1479: $i] :
~ ~ ( ~ ( in @ SY1479 @ SV62 )
| ~ ( SV208 @ SY1479 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(981,plain,
! [SV63: $i,SV209: $i] :
( ( ( in @ SV209 @ SV63 )
= $false )
| ( ( subset @ ( setadjoin @ SV209 @ emptyset ) @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(982,plain,
! [SV64: $i > $i > $o,SV210: $i] :
( ( ( ! [SY1480: $i] :
( ~ ( in @ SY1480 @ SV210 )
| ~ ! [SY1195: $i] :
~ ~ ( ~ ( SV64 @ SY1480 @ SY1195 )
| ~ ! [SY1196: $i] :
( ~ ( SV64 @ SY1480 @ SY1196 )
| ( SY1195 = SY1196 ) ) ) ) )
= $false )
| ( ( ~ ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[839]) ).
thf(983,plain,
! [SV211: $i,SV65: $i,SV307: $i] :
( ( ( ~ ( in @ ( setadjoin @ SV307 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV65 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV65 @ ( setadjoin @ SV211 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( SV65 = SV307 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(984,plain,
! [SV347: $i,SV308: $i,SV212: $i,SV66: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV66 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV66 @ ( setadjoin @ SV212 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV308 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV308 @ ( setadjoin @ SV347 @ emptyset ) ) @ emptyset ) ) )
| ( SV66 = SV308 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(985,plain,
! [SV213: $i,SV67: $i,SV309: $i] :
( ( ( ~ ( in @ SV309 @ SV67 ) )
= $true )
| ( ( ~ ( in @ SV309 @ SV213 )
| ~ ( in @ SV309 @ ( symdiff @ SV67 @ SV213 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(986,plain,
! [SV214: $i,SV68: $i] :
( ( ( ~ ( subset @ SV68 @ SV214 ) )
= $false )
| ( ( SV68 != SV214 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(987,plain,
( ( sK1_SX0 != sK3_SY1491 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[844]) ).
thf(988,plain,
( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1491 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ emptyset ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[844]) ).
thf(989,plain,
! [SV215: $i,SV69: $i] :
( ( ( SV69 = SV215 )
= $false )
| ( ( subset @ SV215 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(990,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ( ! [SY1492: $i] :
( ~ ( in @ SY1492 @ SV70 )
| ! [SY1493: $i] :
( ~ ( in @ SY1493 @ SV70 )
| ~ ( SV216 @ SY1492 )
| ~ ( SV216 @ SY1493 )
| ( SY1492 = SY1493 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) )
| ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(991,plain,
! [SV217: $i > $o,SV71: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ SV71 ) )
= $true )
| ( ( ~ ( SV217 @ SV310 )
| ( in @ SV310
@ ( dsetconstr @ SV71
@ ^ [SY1499: $i] : ( SV217 @ SY1499 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(992,plain,
! [SV72: $i,SV218: $i] :
( ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false )
| ( ( ! [SY1500: $o] :
( ~ ! [SY1501: $i] :
( ~ ( in @ SV218 @ SY1501 )
| ~ ( in @ SY1501 @ SV72 )
| SY1500 )
| SY1500 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(993,plain,
! [SV219: $i,SV74: $i] :
( ( ( SV74 = SV219 )
= $false )
| ( ( ! [SY1502: $i,SY1503: $i] :
( ( SY1502 != SY1503 )
| ~ ( in @ SY1502 @ SV74 )
| ( in @ SY1503 @ SV219 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(994,plain,
! [SV220: $i > $o,SV75: $i] :
( ( ( ~ ! [SY1504: $i] :
~ ~ ( ~ ( in @ SY1504
@ ( dsetconstr @ SV75
@ ^ [SY1505: $i] : ( SV220 @ SY1505 ) ) )
| ( ( dsetconstr @ SV75
@ ^ [SY1506: $i] : ( SV220 @ SY1506 ) )
!= ( setadjoin @ SY1504 @ emptyset ) ) ) )
= $false )
| ( ( ~ ! [SY1507: $i] :
~ ~ ( ~ ( in @ SY1507 @ SV75 )
| ~ ( SV220 @ SY1507 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[853]) ).
thf(995,plain,
! [SV221: $i,SV77: $i,SV311: $i] :
( ( ( ~ ( in @ SV311 @ SV77 ) )
= $true )
| ( ( ! [SY1627: $i] :
( ~ ( in @ SY1627 @ SV221 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV311 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV311 @ ( setadjoin @ SY1627 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV77 @ SV221 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[855]) ).
thf(996,plain,
! [SV78: $i,SV222: $i] :
( ( ( in @ SV222 @ ( powerset @ SV78 ) )
= $false )
| ( ( subset @ SV222 @ SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(997,plain,
! [SV223: $i,SV79: $i,SV312: $i] :
( ( ( ~ ~ ( in @ SV312 @ SV79 ) )
= $true )
| ( ( ~ ( in @ SV312 @ SV223 )
| ( in @ SV312 @ ( symdiff @ SV79 @ SV223 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[857]) ).
thf(998,plain,
! [SV224: $i,SV80: $i] :
( ( ( SV80 = SV224 )
= $false )
| ( ( ! [SY1511: $i,SY1512: $i] :
( ( SY1511 != SY1512 )
| ( ( setadjoin @ SV80 @ SY1511 )
= ( setadjoin @ SV224 @ SY1512 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(999,plain,
! [SV225: $i,SV81: $i] :
( ( ( subset @ SV81 @ SV225 )
= $false )
| ( ( ( binintersect @ SV81 @ SV225 )
= SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[859]) ).
thf(1000,plain,
! [SV226: $i,SV82: $i] :
( ( ( SV82 = SV226 )
= $false )
| ( ( ( setadjoin @ SV82 @ ( setadjoin @ SV226 @ emptyset ) )
= ( setadjoin @ SV82 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(1001,plain,
! [SV227: $i,SV83: $i] :
( ( ( ( binintersect @ SV83 @ SV227 )
= SV227 )
= $false )
| ( ( subset @ SV227 @ SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(1002,plain,
! [SV84: $i,SV348: $o] :
( ( SV348 = $true )
| ( ( in @ SV84 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[862]) ).
thf(1004,plain,
! [SV84: $i] :
( ( $false = $true )
| ( ( in @ SV84 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[862]) ).
thf(1005,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ! [SY1513: $i,SY1514: $i] :
( ( SY1513 != SY1514 )
| ~ ( ~ ( ~ ( SV85 @ SY1513 )
| ( SV228 @ SY1514 ) )
| ~ ( ~ ( SV228 @ SY1514 )
| ( SV85 @ SY1513 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(1006,plain,
! [SV229: $i,SV86: $i] :
( ( ( ! [SY1523: $i] :
( ~ ( in @ SY1523 @ SV86 )
| ( in @ SY1523 @ SV229 ) ) )
= $false )
| ( ( subset @ SV86 @ SV229 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(1007,plain,
! [SV230: $i,SV87: $i,SV313: $i] :
( ( ( ~ ( in @ SV313 @ SV87 ) )
= $true )
| ( ( ! [SY1628: $i] :
( ~ ( in @ SY1628 @ SV230 )
| ( in @ ( setadjoin @ ( setadjoin @ SV313 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV313 @ ( setadjoin @ SY1628 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV87 @ SV230 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[865]) ).
thf(1008,plain,
! [SV88: $i,SV231: $i,SV314: $i] :
( ( ( ~ ( in @ SV314 @ SV231 ) )
= $true )
| ( ( in @ SV314 @ ( setadjoin @ SV88 @ SV231 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(1009,plain,
! [SV232: $i,SV89: $i] :
( ( ( ~ ~ ! [SY1527: $i] :
~ ~ ( ~ ( in @ SY1527 @ SV89 )
| ~ ( in @ SY1527 @ SV232 ) ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(1010,plain,
! [SV90: $i > $o] :
( ( ( ! [SY1264: $i] :
~ ~ ( ~ ( SV90 @ SY1264 )
| ~ ! [SY1265: $i] :
( ~ ( SV90 @ SY1265 )
| ( SY1264 = SY1265 ) ) ) )
= $true )
| ( ( ~ ! [SY1266: $i] :
~ ! [SY1267: $i] :
~ ( ~ ( ~ ( SV90 @ SY1267 )
| ( SY1267 = SY1266 ) )
| ~ ( ( SY1267 != SY1266 )
| ( SV90 @ SY1267 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(1011,plain,
! [SV233: $i,SV91: $i,SV315: $i] :
( ( ( ~ ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) ) )
= $true )
| ( ( ! [SY1629: $o] :
( ~ ( ( SV315 != SV91 )
| SY1629 )
| ~ ( ~ ( in @ SV315 @ SV233 )
| SY1629 )
| SY1629 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[869]) ).
thf(1012,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ( ! [SY1530: $i] :
( ~ ( in @ SY1530 @ SV92 )
| ! [SY1531: $i] :
( ~ ( in @ SY1531 @ SV92 )
| ~ ( SV234 @ SY1530 )
| ~ ( SV234 @ SY1531 )
| ( SY1530 = SY1531 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) )
| ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(1013,plain,
! [SV235: $i > $o,SV93: $i,SV316: $i] :
( ( ( ~ ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SY1537: $i] : ( SV235 @ SY1537 ) ) ) )
= $true )
| ( ( SV235 @ SV316 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(1014,plain,
! [SV94: $i,SV236: $i,SV317: $i] :
( ( ( ~ ( in @ SV317 @ SV236 ) )
= $true )
| ( ( ~ ( in @ SV317 @ ( setminus @ SV94 @ SV236 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(1015,plain,
! [SV237: $i,SV95: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV95 ) )
= $true )
| ( ( ! [SY1631: $i] :
( ~ ( in @ SY1631 @ SV237 )
| ( in @ ( setadjoin @ SV318 @ ( setadjoin @ SY1631 @ emptyset ) ) @ ( powerset @ ( binunion @ SV95 @ SV237 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(1016,plain,
! [SV238: $i,SV96: $i,SV319: $i] :
( ( ~ ( ~ ( in @ SV319 @ ( setadjoin @ SV96 @ SV238 ) )
| ( SV319 = SV96 )
| ( in @ SV319 @ SV238 ) )
| ~ ( ~ ( ( SV319 = SV96 )
| ( in @ SV319 @ SV238 ) )
| ( in @ SV319 @ ( setadjoin @ SV96 @ SV238 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(1017,plain,
! [SV239: $i,SV97: $i,SV320: $i] :
( ( ( ~ ~ ( in @ SV320 @ ( setminus @ SV97 @ SV239 ) ) )
= $true )
| ( ( ~ ( in @ SV320 @ SV97 )
| ( in @ SV320 @ SV239 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(1018,plain,
! [SV98: $i > $o] :
( ( ( ! [SY1290: $i] :
~ ! [SY1291: $i] :
~ ( ~ ( ~ ( SV98 @ SY1291 )
| ( SY1291 = SY1290 ) )
| ~ ( ( SY1291 != SY1290 )
| ( SV98 @ SY1291 ) ) ) )
= $true )
| ( ( ~ ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[876]) ).
thf(1019,plain,
! [SV240: $i,SV99: $i] :
( ( ( ( setadjoin @ SV99 @ emptyset )
= ( setadjoin @ SV240 @ emptyset ) )
= $false )
| ( ( SV99 = SV240 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(1020,plain,
! [SV241: $i,SV100: $i,SV321: $i] :
( ( ( ~ ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) ) )
= $true )
| ( ( ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ ( setunion @ SV321 ) )
| ~ ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633 @ ( setunion @ SV321 ) )
| ( SV321
!= ( setadjoin @ ( setadjoin @ SY1632 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1632 @ ( setadjoin @ SY1633 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(1021,plain,
! [SV242: $i,SV101: $i,SV322: $i] :
( ( ( ~ ( in @ SV322 @ SV101 ) )
= $true )
| ( ( in @ SV322 @ ( binunion @ SV101 @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(1022,plain,
! [SV243: $i > $o,SV102: $i,SV323: $i] :
( ( ( ~ ( in @ SV323
@ ( dsetconstr @ SV102
@ ^ [SY1548: $i] : ( SV243 @ SY1548 ) ) ) )
= $true )
| ( ( in @ SV323 @ SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(1023,plain,
! [SV244: $i,SV103: $i,SV324: $i] :
( ( ( ~ ( in @ SV324 @ SV103 ) )
= $true )
| ( ( ~ ~ ( in @ SV324 @ SV244 )
| ( SV103 != SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(1024,plain,
! [SV245: $i > $o,SV104: $i] :
( ( ( ~ ~ ! [SY1550: $i] :
~ ~ ( ~ ( in @ SY1550 @ SV104 )
| ~ ( SV245 @ SY1550 ) ) )
= $false )
| ( ( ! [SY1551: $i] :
( ~ ( in @ SY1551 @ SV104 )
| ~ ( SV245 @ SY1551 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(1025,plain,
! [SV246: $i,SV105: $i,SV325: $i] :
( ( ( ~ ( in @ SV325 @ ( binintersect @ SV105 @ SV246 ) ) )
= $true )
| ( ( in @ SV325 @ SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[883]) ).
thf(1026,plain,
! [SV247: $i,SV106: $i,SV326: $i] :
( ( ( ~ ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) ) )
= $true )
| ( ( ~ ( in @ SV326 @ SV247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(1027,plain,
! [SV248: $i,SV107: $i] :
( ( ( SV107 != SV248 )
= $false )
| ( ( ~ ( in @ SV248 @ ( setadjoin @ SV107 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(1028,plain,
! [SV108: $i] :
( ( ( ! [SY1314: $i] :
~ ~ ( ~ ( in @ SY1314 @ ( setunion @ SV108 ) )
| ~ ~ ! [SY1315: $i] :
~ ~ ( ~ ( in @ SY1315 @ ( setunion @ SV108 ) )
| ( SV108
!= ( setadjoin @ ( setadjoin @ SY1314 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1314 @ ( setadjoin @ SY1315 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true )
| ( ( ~ ! [SY1316: $i] :
~ ~ ( ~ ( in @ SY1316
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ SY1316 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[886]) ).
thf(1029,plain,
! [SV327: $i,SV249: $i,SV109: $i] :
( ( ( ~ ( subset @ SV109 @ SV249 ) )
= $true )
| ( ( ~ ~ ( in @ SV327 @ SV249 )
| ~ ( in @ SV327 @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(1030,plain,
! [SV110: $i] :
( ( ( ~ ( in @ ( sK6_SY1321 @ SV110 ) @ SV110 ) )
= $false )
| ( ( SV110 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[888]) ).
thf(1031,plain,
! [SV250: $i,SV111: $i,SV328: $i] :
( ( ( ~ ( in @ SV328 @ SV111 ) )
= $true )
| ( ( ! [SY1635: $i] :
( ~ ( in @ SY1635 @ SV250 )
| ( subset @ ( setadjoin @ SV328 @ ( setadjoin @ SY1635 @ emptyset ) ) @ ( binunion @ SV111 @ SV250 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(1032,plain,
! [SV112: $o,SV251: $i] :
( ( ( in @ SV251 @ ( prop2set @ SV112 ) )
= $false )
| ( SV112 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(1034,plain,
! [SV253: $i] :
( ( ( in @ SV253 @ ( prop2set @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[892]) ).
thf(1035,plain,
! [SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) ) )
= $true )
| ( ( ! [SY1636: $o] :
( ~ ( ~ ( in @ SV329 @ SV113 )
| ~ ~ ( in @ SV329 @ SV254 )
| SY1636 )
| ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| SY1636 )
| SY1636 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(1036,plain,
! [SV255: $i,SV330: $i,SV115: $i] :
( ( ( ~ ( subset @ SV115 @ SV330 ) )
= $true )
| ( ( subset @ SV115 @ ( setadjoin @ SV255 @ SV330 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[895]) ).
thf(1037,plain,
! [SV331: $i,SV256: $i,SV116: $i] :
( ( ( ~ ( subset @ SV116 @ SV256 ) )
= $true )
| ( ( ~ ( in @ SV331 @ SV116 )
| ( in @ SV331 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[896]) ).
thf(1038,plain,
! [SV117: $i,SV257: $i] :
( ( ( subset @ SV257 @ SV117 )
= $false )
| ( ( in @ SV257 @ ( powerset @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(1039,plain,
! [SV258: $i,SV118: $i] :
( ( ( SV118 = SV258 )
= $false )
| ( ( ! [SY1561: $i,SY1562: $i] :
( ( SY1561 != SY1562 )
| ~ ( ~ ( ~ ( in @ SY1561 @ SV118 )
| ( in @ SY1562 @ SV258 ) )
| ~ ( ~ ( in @ SY1562 @ SV258 )
| ( in @ SY1561 @ SV118 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(1040,plain,
! [SV259: $i > $o,SV119: $i] :
( ( ( ~ ! [SY1563: $i] :
( ~ ( in @ SY1563 @ SV119 )
| ( SV259 @ SY1563 ) ) )
= $false )
| ( ( ~ ! [SY1564: $i] :
~ ~ ( ~ ( in @ SY1564 @ SV119 )
| ~ ~ ( SV259 @ SY1564 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(1041,plain,
! [SV120: $i,SV260: $i] :
( ( ( ! [SY1565: $i] :
( ~ ( in @ SY1565 @ SV260 )
| ( in @ SY1565 @ SV120 ) ) )
= $false )
| ( ( in @ SV260 @ ( powerset @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(1042,plain,
! [SV261: $i,SV121: $i,SV332: $i] :
( ( ( ~ ( in @ SV332 @ SV121 ) )
= $true )
| ( ( ~ ~ ( in @ SV332 @ SV261 )
| ( in @ SV332 @ ( symdiff @ SV121 @ SV261 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[901]) ).
thf(1043,plain,
! [SV262: $i,SV122: $i] :
( ( ( subset @ SV122 @ SV262 )
= $false )
| ( ( ( setminus @ SV122 @ SV262 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(1044,plain,
! [SV263: $i,SV123: $i] :
( ( ( in @ SV123 @ ( setadjoin @ SV263 @ emptyset ) )
= $false )
| ( ( in @ SV263 @ ( setadjoin @ SV123 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(1045,plain,
! [SV124: $i > $o] :
( ( ( ! [SY1346: $i] :
~ ~ ( ~ ( SV124 @ SY1346 )
| ~ ! [SY1347: $i] :
( ~ ( SV124 @ SY1347 )
| ( SY1346 = SY1347 ) ) ) )
= $true )
| ( ( ~ ! [SY1348: $i] :
~ ~ ( ~ ( SV124 @ SY1348 )
| ~ ! [SY1349: $i] :
( ~ ( SV124 @ SY1349 )
| ( SY1348 = SY1349 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[904]) ).
thf(1046,plain,
! [SV264: $i,SV125: $i,SV333: $i] :
( ( ( ~ ~ ( in @ SV333 @ SV125 ) )
= $true )
| ( ( ~ ~ ( in @ SV333 @ SV264 )
| ~ ( in @ SV333 @ ( symdiff @ SV125 @ SV264 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[905]) ).
thf(1047,plain,
! [SV126: $i,SV265: $i] :
( ( ~ ( ~ ( in @ SV265 @ ( setunion @ SV126 ) )
| ~ ! [SY1568: $i] :
~ ~ ( ~ ( in @ SV265 @ SY1568 )
| ~ ( in @ SY1568 @ SV126 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(1048,plain,
! [SV126: $i,SV265: $i] :
( ( ~ ( ~ ~ ! [SY1569: $i] :
~ ~ ( ~ ( in @ SV265 @ SY1569 )
| ~ ( in @ SY1569 @ SV126 ) )
| ( in @ SV265 @ ( setunion @ SV126 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(1049,plain,
! [SV127: $i] :
( ( ( ! [SY1355: $i] :
~ ( in @ SY1355 @ SV127 ) )
= $true )
| ( ( SV127 != emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[907]) ).
thf(1050,plain,
! [SV266: $i,SV128: $i] :
( ( ( in @ SV128 @ ( setadjoin @ SV266 @ emptyset ) )
= $false )
| ( ( SV128 = SV266 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(1051,plain,
! [SV129: $i] :
( ( ( ~ ( in @ ( sK7_SY1357 @ SV129 ) @ SV129 ) )
= $false )
| ( ( SV129 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[909]) ).
thf(1052,plain,
! [SV130: $i > $o] :
( ( ( ! [SY1358: $i] :
~ ( SV130 @ SY1358 ) )
= $true )
| ( ( ~ ! [SY1359: $i,SY1360: $i] :
( ~ ( SV130 @ SY1359 )
| ~ ( SV130 @ SY1360 )
| ( SY1359 = SY1360 ) )
| ~ ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[910]) ).
thf(1053,plain,
! [SV267: $i,SV131: $i,SV334: $i] :
( ( ( ~ ( in @ SV334 @ ( cartprod @ SV131 @ SV267 ) ) )
= $true )
| ( ( in @ ( kfst @ SV334 ) @ SV131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(1054,plain,
! [SV268: $i,SV132: $i] :
( ( ( SV132 = SV268 )
= $false )
| ( ( in @ SV132 @ ( setadjoin @ SV268 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(1055,plain,
! [SV134: $i > $o,SV269: $i] :
( ( ( in @ SV269 @ emptyset )
= $false )
| ( ( SV134 @ SV269 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[916]) ).
thf(1056,plain,
! [SV270: $i,SV135: $i] :
( ( ( ( binintersect @ SV135 @ SV270 )
= SV135 )
= $false )
| ( ( subset @ SV135 @ SV270 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(1057,plain,
! [SV271: $i,SV136: $i,SV335: $i] :
( ( ( ~ ~ ( in @ SV335 @ ( setminus @ SV136 @ SV271 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV335 @ SV271 )
| ~ ( in @ SV335 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(1058,plain,
! [SV137: $i > $o] :
( ( ( ! [SY1370: $i] :
~ ~ ( ~ ( SV137 @ SY1370 )
| ~ ! [SY1371: $i] :
( ~ ( SV137 @ SY1371 )
| ( SY1370 = SY1371 ) ) ) )
= $true )
| ( ( ~ ! [SY1372: $i] :
~ ( SV137 @ SY1372 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[919]) ).
thf(1059,plain,
! [SV138: $i] :
( ( ( ~ ( in @ emptyset @ SV138 )
| ~ ! [SY1373: $i] :
( ~ ~ ( ~ ( in @ SY1373 @ omega )
| ~ ( in @ SY1373 @ SV138 ) )
| ( in @ ( setadjoin @ SY1373 @ SY1373 ) @ SV138 ) ) )
= $true )
| ( ( ! [SY1374: $i] :
( ~ ( in @ SY1374 @ omega )
| ( in @ SY1374 @ SV138 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[920]) ).
thf(1060,plain,
! [SV336: $i,SV272: $i,SV139: $i] :
( ( ( ~ ( subset @ SV139 @ SV272 ) )
= $true )
| ( ( ~ ( subset @ SV272 @ SV336 )
| ( subset @ SV139 @ SV336 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(1061,plain,
! [SV140: $i,SV273: $i] :
( ( ~ ( ~ ( in @ SV273 @ ( powerset @ SV140 ) )
| ! [SY1573: $i] :
( ~ ( in @ SY1573 @ SV273 )
| ( in @ SY1573 @ SV140 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[922]) ).
thf(1062,plain,
! [SV140: $i,SV273: $i] :
( ( ~ ( ~ ! [SY1574: $i] :
( ~ ( in @ SY1574 @ SV273 )
| ( in @ SY1574 @ SV140 ) )
| ( in @ SV273 @ ( powerset @ SV140 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[922]) ).
thf(1063,plain,
! [SV274: $i,SV141: $i] :
( ( ( ! [SY1575: $i] :
( ~ ( in @ SY1575 @ SV141 )
| ( in @ SY1575 @ SV274 ) ) )
= $false )
| ( ( subset @ SV141 @ SV274 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(1064,plain,
! [SV142: $i] :
( ( ( ! [SY1382: $i] :
~ ( in @ SY1382 @ SV142 ) )
= $true )
| ( ( ~ ! [SY1383: $i] :
~ ~ ( ~ ( in @ SY1383 @ SV142 )
| ~ ~ ~ ! [SY1384: $i] :
~ ~ ( ~ ( in @ SY1384 @ SY1383 )
| ~ ( in @ SY1384 @ SV142 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[924]) ).
thf(1065,plain,
! [SV143: $i] :
( ( ( SV143 = emptyset )
= $true )
| ( ( ~ ! [SY1385: $i] :
~ ~ ( ~ ( in @ SY1385 @ SV143 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[925]) ).
thf(1066,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ( ! [SY1576: $i,SY1577: $i] :
( ( SY1576 != SY1577 )
| ~ ( ~ ( ~ ( SV144 @ SY1576 )
| ( SV275 @ SY1577 ) )
| ~ ( ~ ( SV275 @ SY1577 )
| ( SV144 @ SY1576 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(1067,plain,
! [SV145: $i,SV276: $i] :
( ( ( in @ SV276 @ SV145 )
= $false )
| ( ( in @ ( setadjoin @ SV276 @ emptyset ) @ ( powerset @ SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(1068,plain,
! [SV277: $i > $o,SV146: $i,SV337: $i] :
( ( ( ~ ( in @ SV337 @ SV146 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV337
@ ( dsetconstr @ SV146
@ ^ [SY1585: $i] : ( SV277 @ SY1585 ) ) )
| ( SV277 @ SV337 ) )
| ~ ( ~ ( SV277 @ SV337 )
| ( in @ SV337
@ ( dsetconstr @ SV146
@ ^ [SY1586: $i] : ( SV277 @ SY1586 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(1069,plain,
! [SV278: $i,SV147: $i,SV338: $i] :
( ( ( ~ ( in @ SV338 @ ( binintersect @ SV147 @ SV278 ) ) )
= $true )
| ( ( in @ SV338 @ SV278 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(1070,plain,
! [SV148: $i > $o] :
( ( ( ! [SY1402: $i] :
~ ~ ( ~ ( SV148 @ SY1402 )
| ~ ! [SY1403: $i] :
( ~ ( SV148 @ SY1403 )
| ( SY1402 = SY1403 ) ) ) )
= $true )
| ( ( SV148
@ ( descr
@ ^ [SY1404: $i] : ( SV148 @ SY1404 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[930]) ).
thf(1071,plain,
! [SV279: $i,SV149: $i] :
( ( ( ( setminus @ SV149 @ SV279 )
= emptyset )
= $false )
| ( ( subset @ SV149 @ SV279 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(1072,plain,
! [SV150: $i,SV280: $i] :
( ( ( in @ SV280 @ SV150 )
= $false )
| ( ( in @ SV280 @ ( powerset @ ( setunion @ SV150 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(1073,plain,
! [SV281: $i > $o,SV151: $i] :
( ( ( ~ ~ ! [SY1588: $i] :
~ ~ ( ~ ( in @ SY1588 @ SV151 )
| ~ ( SV281 @ SY1588 ) ) )
= $false )
| ( ( ! [SY1589: $i] :
( ~ ( in @ SY1589 @ SV151 )
| ~ ( SV281 @ SY1589 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(1074,plain,
! [SV282: $i,SV152: $i] :
( ( ( subset @ SV152 @ SV282 )
= $false )
| ( ( ~ ( subset @ SV282 @ SV152 )
| ( SV152 = SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(1075,plain,
! [SV153: $i,SV283: $i,SV339: $i] :
( ( ( ~ ( in @ SV339 @ SV283 ) )
= $true )
| ( ( in @ SV339 @ ( binunion @ SV153 @ SV283 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[935]) ).
thf(1076,plain,
! [SV284: $i,SV154: $i,SV340: $i] :
( ( ( ~ ( subset @ SV340 @ SV154 ) )
= $true )
| ( ( ~ ( subset @ SV340 @ SV284 )
| ( subset @ SV340 @ ( binintersect @ SV154 @ SV284 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[936]) ).
thf(1077,plain,
! [SV285: $i,SV155: $i] :
( ( ( subset @ SV155 @ SV285 )
= $false )
| ( ( subset @ ( powerset @ SV155 ) @ ( powerset @ SV285 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(1078,plain,
! [SV286: $i,SV156: $i,SV341: $i] :
( ( ( ~ ( in @ SV341 @ ( setadjoin @ SV156 @ SV286 ) ) )
= $true )
| ( ( ( SV341 = SV156 )
| ( in @ SV341 @ SV286 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(1079,plain,
! [SV287: $i,SV158: $i,SV342: $i] :
( ( ( ~ ( in @ SV342 @ ( binunion @ SV158 @ SV287 ) ) )
= $true )
| ( ( ( in @ SV342 @ SV158 )
| ( in @ SV342 @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(1080,plain,
! [SV159: $i > $o] :
( ( ( ! [SY1420: $i] :
~ ~ ( ~ ( SV159 @ SY1420 )
| ~ ! [SY1421: $i] :
( ~ ( SV159 @ SY1421 )
| ( SY1420 = SY1421 ) ) ) )
= $true )
| ( ( ! [SY1422: $i,SY1423: $i] :
( ~ ( SV159 @ SY1422 )
| ~ ( SV159 @ SY1423 )
| ( SY1422 = SY1423 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[941]) ).
thf(1081,plain,
! [SV288: $i,SV160: $i,SV343: $i] :
( ( ( ~ ( in @ SV343 @ ( setminus @ SV160 @ SV288 ) ) )
= $true )
| ( ( in @ SV343 @ SV160 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(1082,plain,
! [SV161: $i,SV289: $i] :
( ( ( in @ SV289 @ ( setunion @ SV161 ) )
= $false )
| ( ( ~ ! [SY1595: $i] :
~ ~ ( ~ ( in @ SY1595 @ SV161 )
| ~ ( in @ SV289 @ SY1595 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(1083,plain,
! [SV290: $i > $o,SV162: $i,SV344: $i] :
( ( ( ~ ( in @ SV344 @ SV162 ) )
= $true )
| ( ( ~ ( SV290 @ SV344 )
| ~ ! [SY1639: $i] :
( ~ ( in @ SY1639 @ SV162 )
| ~ ( SV290 @ SY1639 )
| ( SY1639 = SV344 ) )
| ~ ! [SY1598: $i] :
~ ~ ( ~ ( in @ SY1598
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ SY1598 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[944]) ).
thf(1084,plain,
! [SV349: $i > $o,SV180: $i,SV29: $i] :
( ( ( ! [SY1645: $i > $o] :
( ~ ! [SY1646: $i] :
( ~ ( in @ SY1646 @ SV29 )
| ! [SY1647: $i] :
( ~ ( in @ SY1647 @ SV180 )
| ( SY1646 != SY1647 )
| ~ ( ~ ( ~ ( SV349 @ SY1646 )
| ( SY1645 @ SY1647 ) )
| ~ ( ~ ( SY1645 @ SY1647 )
| ( SV349 @ SY1646 ) ) ) ) )
| ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SX4: $i] : ( SY1645 @ SX4 ) ) ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1085,plain,
! [SV30: $i,SV350: $i] :
( ( ( ~ ~ ( ~ ( in @ SV350 @ SV30 )
| ( SV30
!= ( setadjoin @ SV350 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( setunion @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1086,plain,
! [SV181: $i > $o,SV31: $i] :
( ( ( ! [SY1443: $i] :
~ ~ ( ~ ( in @ SY1443 @ SV31 )
| ~ ( SV181 @ SY1443 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV31
@ ^ [SY1444: $i] : ( SV181 @ SY1444 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[947]) ).
thf(1087,plain,
! [SV182: $i,SV32: $i,SV292: $i] :
( ( ( in @ SV292 @ ( setadjoin @ SV32 @ ( setadjoin @ SV182 @ emptyset ) ) )
= $false )
| ( ( ( SV292 = SV32 )
| ( SV292 = SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[948]) ).
thf(1088,plain,
! [SV183: $i,SV33: $i,SV293: $i] :
( ( ( in @ SV293 @ SV33 )
= $false )
| ( ( ~ ( in @ SV293 @ SV183 )
| ( in @ SV293 @ ( binintersect @ SV33 @ SV183 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(1089,plain,
! [SV184: $i,SV34: $i,SV294: $i] :
( ( ( in @ SV294 @ SV34 )
= $false )
| ( ( in @ ( setadjoin @ SV294 @ emptyset ) @ ( powerset @ ( binunion @ SV34 @ SV184 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[950]) ).
thf(1090,plain,
! [SV35: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1601: $i] :
( ~ ( in @ SY1601 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SY1601 )
| ( in @ SY1111 @ SV35 ) ) )
| ~ ! [SY1603: $i,SY1604: $i] :
( ~ ~ ( ~ ( in @ SY1603 @ SV35 )
| ~ ( in @ SY1604 @ SV35 ) )
| ~ ! [SY1605: $i] :
( ~ ( in @ SY1605 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SY1603 @ SY1605 )
| ( in @ SY1604 @ SY1605 ) )
| ~ ( ~ ( in @ SY1604 @ SY1605 )
| ( in @ SY1603 @ SY1605 ) ) ) )
| ( SY1603 = SY1604 ) ) )
| ~ ! [SY1606: $i,SY1607: $i] :
( ~ ~ ( ~ ( in @ SY1606 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1607 @ ( sK2_SY1109 @ SV35 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1606 )
| ( in @ SX4 @ SY1607 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1607 )
| ( in @ SX4 @ SY1606 ) ) ) )
| ~ ! [SY1610: $i] :
( ~ ~ ( ~ ! [SY1120: $i] :
( ~ ( in @ SY1120 @ SY1610 )
| ( in @ SY1120 @ SV35 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1610 ) )
| ~ ! [SY1613: $i] :
~ ~ ! [SY1614: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1613 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1614 @ SY1610 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1613 )
| ~ ( in @ SX5 @ SY1610 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1613 ) )
| ( in @ SY1614 @ SY1616 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(1091,plain,
! [SV351: $i,SV37: $i > $o] :
( ( ( ~ ~ ( ~ ( SV37 @ SV351 )
| ~ ! [SY1650: $i] :
( ~ ( SV37 @ SY1650 )
| ( SV351 = SY1650 ) ) ) )
= $true )
| ( ( ! [SY1130: $i,SY1131: $i] :
( ~ ( SV37 @ SY1130 )
| ~ ( SV37 @ SY1131 )
| ( SY1130 = SY1131 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1092,plain,
! [SV186: $i > $o,SV38: $i] :
( ( ( ! [SY1448: $i] :
~ ~ ( ~ ( in @ SY1448 @ SV38 )
| ~ ~ ( SV186 @ SY1448 ) ) )
= $true )
| ( ( ~ ! [SY1449: $i] :
( ~ ( in @ SY1449 @ SV38 )
| ( SV186 @ SY1449 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[954]) ).
thf(1093,plain,
! [SV187: $i > $o,SV39: $i,SV295: $i] :
( ( ( in @ SV295 @ SV39 )
= $false )
| ( ( ~ ( SV187 @ SV295 )
| ( ( dsetconstr @ SV39
@ ^ [SY1451: $i] : ( SV187 @ SY1451 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1094,plain,
! [SV188: $i,SV40: $i,SV296: $i] :
( ( ( in @ SV296 @ SV40 )
= $false )
| ( ( ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV188 )
| ( in @ ( setadjoin @ ( setadjoin @ SV296 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV296 @ ( setadjoin @ SY1619 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SV40 @ SV188 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(1095,plain,
! [SV345: $i,SV297: $i,SV190: $i,SV42: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV42 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV42 @ ( setadjoin @ SV190 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV297 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV297 @ ( setadjoin @ SV345 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV42 = SV297 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[958]) ).
thf(1096,plain,
! [SV192: $i,SV44: $i,SV298: $i] :
( ( ( in @ SV298 @ SV44 )
= $false )
| ( ( ~ ~ ( in @ SV298 @ SV192 )
| ~ ( subset @ SV44 @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1097,plain,
! [SV193: $i > $o,SV45: $i] :
( ( ( ! [SY1457: $i] :
( ~ ( in @ SY1457 @ SV45 )
| ( SV193 @ SY1457 ) ) )
= $true )
| ( ( ~ ! [SY1458: $i] :
~ ~ ( ~ ( in @ SY1458 @ SV45 )
| ~ ~ ( SV193 @ SY1458 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[961]) ).
thf(1098,plain,
! [SV299: $i,SV46: $i,SV194: $i] :
( ( ( in @ SV194 @ ( powerset @ SV46 ) )
= $false )
| ( ( ~ ( in @ SV299 @ SV194 )
| ( in @ SV299 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(1099,plain,
! [SV196: $i,SV48: $i,SV300: $i] :
( ( ( in @ SV300 @ SV48 )
= $false )
| ( ( ! [SY1621: $i] :
( ~ ( in @ SY1621 @ SV196 )
| ( in @ ( setadjoin @ ( setadjoin @ SV300 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV300 @ ( setadjoin @ SY1621 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV48 @ SV196 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1100,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ~ ~ ( ~ ( SV50 @ SV352 )
| ~ ! [SY1651: $i] :
( ~ ( SV50 @ SY1651 )
| ( SV352 = SY1651 ) ) ) )
= $true )
| ( ( ~ ! [SY1160: $i] :
~ ~ ( ~ ( SV50 @ SY1160 )
| ~ ! [SY1161: $i] :
( ~ ( SV50 @ SY1161 )
| ( SY1160 = SY1161 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1101,plain,
! [SV51: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK8_SY1462 @ SV198 @ SV51 ) @ SV51 )
| ( in @ ( sK8_SY1462 @ SV198 @ SV51 ) @ SV198 ) )
= $false )
| ( ( ~ ! [SY1463: $i] :
( ~ ( in @ SY1463 @ SV198 )
| ( in @ SY1463 @ SV51 ) )
| ( SV51 = SV198 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[967]) ).
thf(1102,plain,
! [SV52: $i] :
( ( ( ! [SY1165: $i] :
~ ( in @ SY1165 @ SV52 ) )
= $false )
| ( ( SV52 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(1103,plain,
! [SV199: $i,SV53: $i,SV301: $i] :
( ( ( in @ SV301 @ SV53 )
= $false )
| ( ( ~ ~ ( in @ SV301 @ SV199 )
| ( in @ SV301 @ ( setminus @ SV53 @ SV199 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[969]) ).
thf(1104,plain,
! [SV54: $i,SV200: $i] :
( ( ~ ( ~ ( in @ ( sK4_SY1465 @ SV200 @ SV54 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1643: $i] :
~ ~ ( ~ ( in @ SY1643 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ ( setadjoin @ SY1643 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[970]) ).
thf(1105,plain,
! [SV201: $i,SV55: $i,SV302: $i] :
( ( ( ~ ( in @ SV302 @ SV55 ) )
= $false )
| ( ( ~ ( in @ SV302 @ ( setminus @ SV55 @ SV201 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1106,plain,
! [SV56: $i,SV303: $i,SV202: $i] :
( ( ( in @ SV202 @ SV303 )
= $false )
| ( ( ~ ( in @ SV303 @ SV56 )
| ( in @ SV202 @ ( setunion @ SV56 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1107,plain,
! [SV203: $i,SV57: $i,SV304: $i] :
( ( ( in @ SV304 @ ( setadjoin @ SV57 @ ( setadjoin @ SV203 @ emptyset ) ) )
= $false )
| ( ( ( SV304 = SV57 )
| ( SV304 = SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(1108,plain,
! [SV204: $i,SV58: $i,SV305: $i] :
( ( ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) )
= $false )
| ( ( ~ ! [SY1622: $i] :
~ ~ ( ~ ( in @ SY1622 @ SV58 )
| ~ ~ ! [SY1623: $i] :
~ ~ ( ~ ( in @ SY1623 @ SV204 )
| ( SV305
!= ( setadjoin @ ( setadjoin @ SY1622 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1622 @ ( setadjoin @ SY1623 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1109,plain,
! [SV59: $i,SV205: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 )
| ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV205 ) )
| ~ ( ~ ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV205 )
| ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 ) ) ) )
= $false )
| ( ( SV59 = SV205 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[975]) ).
thf(1110,plain,
! [SV346: $o,SV206: $i,SV60: $i,SV306: $i] :
( ( ( ~ ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV306 @ SV60 )
| SV346 )
| ~ ( ~ ( in @ SV306 @ SV206 )
| SV346 )
| SV346 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(1112,plain,
! [SV206: $i,SV60: $i,SV306: $i] :
( ( ( ~ ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV306 @ SV60 )
| $false )
| ~ ( ~ ( in @ SV306 @ SV206 )
| $false )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1113,plain,
! [SV61: $i,SV207: $i] :
( ( ~ ( ~ ( in @ ( sK5_SY1476 @ SV207 @ SV61 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1644: $i] :
~ ~ ( ~ ( in @ SY1644 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ ( setadjoin @ SY1644 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[979]) ).
thf(1114,plain,
! [SV62: $i,SV208: $i > $o] :
( ( ( ~ ( in @ ( sK10_SY1478 @ SV208 @ SV62 ) @ SV62 )
| ~ ( SV208 @ ( sK10_SY1478 @ SV208 @ SV62 ) ) )
= $false )
| ( ( ~ ~ ! [SY1479: $i] :
~ ~ ( ~ ( in @ SY1479 @ SV62 )
| ~ ( SV208 @ SY1479 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[980]) ).
thf(1115,plain,
! [SV210: $i,SV64: $i > $i > $o] :
( ( ( ~ ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
| ~ ! [SY1652: $i] :
~ ~ ( ~ ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SY1652 )
| ~ ! [SY1653: $i] :
( ~ ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SY1653 )
| ( SY1652 = SY1653 ) ) ) )
= $false )
| ( ( ~ ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[982]) ).
thf(1116,plain,
! [SV211: $i,SV65: $i,SV307: $i] :
( ( ( in @ ( setadjoin @ SV307 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV65 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV65 @ ( setadjoin @ SV211 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV65 = SV307 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1117,plain,
! [SV347: $i,SV308: $i,SV212: $i,SV66: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV66 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV66 @ ( setadjoin @ SV212 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV308 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV308 @ ( setadjoin @ SV347 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV66 = SV308 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[984]) ).
thf(1118,plain,
! [SV213: $i,SV67: $i,SV309: $i] :
( ( ( in @ SV309 @ SV67 )
= $false )
| ( ( ~ ( in @ SV309 @ SV213 )
| ~ ( in @ SV309 @ ( symdiff @ SV67 @ SV213 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1119,plain,
! [SV214: $i,SV68: $i] :
( ( ( subset @ SV68 @ SV214 )
= $true )
| ( ( SV68 != SV214 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[986]) ).
thf(1120,plain,
( ( sK1_SX0 = sK3_SY1491 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[987]) ).
thf(1121,plain,
! [SV70: $i,SV216: $i > $o] :
( ( ( ~ ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
| ! [SY1654: $i] :
( ~ ( in @ SY1654 @ SV70 )
| ~ ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
| ~ ( SV216 @ SY1654 )
| ( ( sK12_SY1492 @ SV216 @ SV70 )
= SY1654 ) ) )
= $false )
| ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) )
| ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[990]) ).
thf(1122,plain,
! [SV217: $i > $o,SV71: $i,SV310: $i] :
( ( ( in @ SV310 @ SV71 )
= $false )
| ( ( ~ ( SV217 @ SV310 )
| ( in @ SV310
@ ( dsetconstr @ SV71
@ ^ [SY1499: $i] : ( SV217 @ SY1499 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1123,plain,
! [SV353: $o,SV72: $i,SV218: $i] :
( ( ( ~ ! [SY1655: $i] :
( ~ ( in @ SV218 @ SY1655 )
| ~ ( in @ SY1655 @ SV72 )
| SV353 )
| SV353 )
= $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[992]) ).
thf(1125,plain,
! [SV72: $i,SV218: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV218 @ SX0 )
| ~ ( in @ SX0 @ SV72 )
| $false )
| $false )
= $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[992]) ).
thf(1126,plain,
! [SV219: $i,SV74: $i,SV354: $i] :
( ( ( ! [SY1656: $i] :
( ( SV354 != SY1656 )
| ~ ( in @ SV354 @ SV74 )
| ( in @ SY1656 @ SV219 ) ) )
= $true )
| ( ( SV74 = SV219 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1127,plain,
! [SV220: $i > $o,SV75: $i] :
( ( ( ! [SY1504: $i] :
~ ~ ( ~ ( in @ SY1504
@ ( dsetconstr @ SV75
@ ^ [SY1505: $i] : ( SV220 @ SY1505 ) ) )
| ( ( dsetconstr @ SV75
@ ^ [SY1506: $i] : ( SV220 @ SY1506 ) )
!= ( setadjoin @ SY1504 @ emptyset ) ) ) )
= $true )
| ( ( ~ ! [SY1507: $i] :
~ ~ ( ~ ( in @ SY1507 @ SV75 )
| ~ ( SV220 @ SY1507 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[994]) ).
thf(1128,plain,
! [SV221: $i,SV77: $i,SV311: $i] :
( ( ( in @ SV311 @ SV77 )
= $false )
| ( ( ! [SY1627: $i] :
( ~ ( in @ SY1627 @ SV221 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV311 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV311 @ ( setadjoin @ SY1627 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV77 @ SV221 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1129,plain,
! [SV223: $i,SV79: $i,SV312: $i] :
( ( ( ~ ( in @ SV312 @ SV79 ) )
= $false )
| ( ( ~ ( in @ SV312 @ SV223 )
| ( in @ SV312 @ ( symdiff @ SV79 @ SV223 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1130,plain,
! [SV224: $i,SV80: $i,SV355: $i] :
( ( ( ! [SY1657: $i] :
( ( SV355 != SY1657 )
| ( ( setadjoin @ SV80 @ SV355 )
= ( setadjoin @ SV224 @ SY1657 ) ) ) )
= $true )
| ( ( SV80 = SV224 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1131,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ! [SY1658: $i] :
( ( ( sK13_SY1513 @ SV228 @ SV85 )
!= SY1658 )
| ~ ( ~ ( ~ ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
| ( SV228 @ SY1658 ) )
| ~ ( ~ ( SV228 @ SY1658 )
| ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1005]) ).
thf(1132,plain,
! [SV86: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK14_SY1523 @ SV229 @ SV86 ) @ SV86 )
| ( in @ ( sK14_SY1523 @ SV229 @ SV86 ) @ SV229 ) )
= $false )
| ( ( subset @ SV86 @ SV229 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1006]) ).
thf(1133,plain,
! [SV230: $i,SV87: $i,SV313: $i] :
( ( ( in @ SV313 @ SV87 )
= $false )
| ( ( ! [SY1628: $i] :
( ~ ( in @ SY1628 @ SV230 )
| ( in @ ( setadjoin @ ( setadjoin @ SV313 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV313 @ ( setadjoin @ SY1628 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV87 @ SV230 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1134,plain,
! [SV88: $i,SV231: $i,SV314: $i] :
( ( ( in @ SV314 @ SV231 )
= $false )
| ( ( in @ SV314 @ ( setadjoin @ SV88 @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1135,plain,
! [SV232: $i,SV89: $i] :
( ( ( ~ ! [SY1527: $i] :
~ ~ ( ~ ( in @ SY1527 @ SV89 )
| ~ ( in @ SY1527 @ SV232 ) ) )
= $true )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1009]) ).
thf(1136,plain,
! [SV356: $i,SV90: $i > $o] :
( ( ( ~ ~ ( ~ ( SV90 @ SV356 )
| ~ ! [SY1659: $i] :
( ~ ( SV90 @ SY1659 )
| ( SV356 = SY1659 ) ) ) )
= $true )
| ( ( ~ ! [SY1266: $i] :
~ ! [SY1267: $i] :
~ ( ~ ( ~ ( SV90 @ SY1267 )
| ( SY1267 = SY1266 ) )
| ~ ( ( SY1267 != SY1266 )
| ( SV90 @ SY1267 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1137,plain,
! [SV233: $i,SV91: $i,SV315: $i] :
( ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false )
| ( ( ! [SY1629: $o] :
( ~ ( ( SV315 != SV91 )
| SY1629 )
| ~ ( ~ ( in @ SV315 @ SV233 )
| SY1629 )
| SY1629 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1138,plain,
! [SV92: $i,SV234: $i > $o] :
( ( ( ~ ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
| ! [SY1660: $i] :
( ~ ( in @ SY1660 @ SV92 )
| ~ ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
| ~ ( SV234 @ SY1660 )
| ( ( sK15_SY1530 @ SV234 @ SV92 )
= SY1660 ) ) )
= $false )
| ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) )
| ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1012]) ).
thf(1139,plain,
! [SV235: $i > $o,SV93: $i,SV316: $i] :
( ( ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SY1537: $i] : ( SV235 @ SY1537 ) ) )
= $false )
| ( ( SV235 @ SV316 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1140,plain,
! [SV94: $i,SV236: $i,SV317: $i] :
( ( ( in @ SV317 @ SV236 )
= $false )
| ( ( ~ ( in @ SV317 @ ( setminus @ SV94 @ SV236 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1141,plain,
! [SV237: $i,SV95: $i,SV318: $i] :
( ( ( in @ SV318 @ SV95 )
= $false )
| ( ( ! [SY1631: $i] :
( ~ ( in @ SY1631 @ SV237 )
| ( in @ ( setadjoin @ SV318 @ ( setadjoin @ SY1631 @ emptyset ) ) @ ( powerset @ ( binunion @ SV95 @ SV237 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1142,plain,
! [SV238: $i,SV96: $i,SV319: $i] :
( ( ~ ( ~ ( in @ SV319 @ ( setadjoin @ SV96 @ SV238 ) )
| ( SV319 = SV96 )
| ( in @ SV319 @ SV238 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1143,plain,
! [SV238: $i,SV96: $i,SV319: $i] :
( ( ~ ( ~ ( ( SV319 = SV96 )
| ( in @ SV319 @ SV238 ) )
| ( in @ SV319 @ ( setadjoin @ SV96 @ SV238 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1144,plain,
! [SV239: $i,SV97: $i,SV320: $i] :
( ( ( ~ ( in @ SV320 @ ( setminus @ SV97 @ SV239 ) ) )
= $false )
| ( ( ~ ( in @ SV320 @ SV97 )
| ( in @ SV320 @ SV239 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1145,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ~ ! [SY1661: $i] :
~ ( ~ ( ~ ( SV98 @ SY1661 )
| ( SY1661 = SV357 ) )
| ~ ( ( SY1661 != SV357 )
| ( SV98 @ SY1661 ) ) ) )
= $true )
| ( ( ~ ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1146,plain,
! [SV241: $i,SV100: $i,SV321: $i] :
( ( ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) )
= $false )
| ( ( ~ ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ ( setunion @ SV321 ) )
| ~ ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633 @ ( setunion @ SV321 ) )
| ( SV321
!= ( setadjoin @ ( setadjoin @ SY1632 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1632 @ ( setadjoin @ SY1633 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1147,plain,
! [SV242: $i,SV101: $i,SV322: $i] :
( ( ( in @ SV322 @ SV101 )
= $false )
| ( ( in @ SV322 @ ( binunion @ SV101 @ SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1148,plain,
! [SV243: $i > $o,SV102: $i,SV323: $i] :
( ( ( in @ SV323
@ ( dsetconstr @ SV102
@ ^ [SY1548: $i] : ( SV243 @ SY1548 ) ) )
= $false )
| ( ( in @ SV323 @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1149,plain,
! [SV244: $i,SV103: $i,SV324: $i] :
( ( ( in @ SV324 @ SV103 )
= $false )
| ( ( ~ ~ ( in @ SV324 @ SV244 )
| ( SV103 != SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1150,plain,
! [SV245: $i > $o,SV104: $i] :
( ( ( ~ ! [SY1550: $i] :
~ ~ ( ~ ( in @ SY1550 @ SV104 )
| ~ ( SV245 @ SY1550 ) ) )
= $true )
| ( ( ! [SY1551: $i] :
( ~ ( in @ SY1551 @ SV104 )
| ~ ( SV245 @ SY1551 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1024]) ).
thf(1151,plain,
! [SV246: $i,SV105: $i,SV325: $i] :
( ( ( in @ SV325 @ ( binintersect @ SV105 @ SV246 ) )
= $false )
| ( ( in @ SV325 @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1152,plain,
! [SV247: $i,SV106: $i,SV326: $i] :
( ( ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) )
= $false )
| ( ( ~ ( in @ SV326 @ SV247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1153,plain,
! [SV248: $i,SV107: $i] :
( ( ( SV107 = SV248 )
= $true )
| ( ( ~ ( in @ SV248 @ ( setadjoin @ SV107 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1027]) ).
thf(1154,plain,
! [SV108: $i,SV358: $i] :
( ( ( ~ ~ ( ~ ( in @ SV358 @ ( setunion @ SV108 ) )
| ~ ~ ! [SY1662: $i] :
~ ~ ( ~ ( in @ SY1662 @ ( setunion @ SV108 ) )
| ( SV108
!= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SY1662 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true )
| ( ( ~ ! [SY1316: $i] :
~ ~ ( ~ ( in @ SY1316
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ SY1316 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1155,plain,
! [SV327: $i,SV249: $i,SV109: $i] :
( ( ( subset @ SV109 @ SV249 )
= $false )
| ( ( ~ ~ ( in @ SV327 @ SV249 )
| ~ ( in @ SV327 @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1156,plain,
! [SV110: $i] :
( ( ( in @ ( sK6_SY1321 @ SV110 ) @ SV110 )
= $true )
| ( ( SV110 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1030]) ).
thf(1157,plain,
! [SV250: $i,SV111: $i,SV328: $i] :
( ( ( in @ SV328 @ SV111 )
= $false )
| ( ( ! [SY1635: $i] :
( ~ ( in @ SY1635 @ SV250 )
| ( subset @ ( setadjoin @ SV328 @ ( setadjoin @ SY1635 @ emptyset ) ) @ ( binunion @ SV111 @ SV250 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1158,plain,
! [SV254: $i,SV113: $i,SV329: $i] :
( ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false )
| ( ( ! [SY1636: $o] :
( ~ ( ~ ( in @ SV329 @ SV113 )
| ~ ~ ( in @ SV329 @ SV254 )
| SY1636 )
| ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| SY1636 )
| SY1636 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1159,plain,
! [SV255: $i,SV330: $i,SV115: $i] :
( ( ( subset @ SV115 @ SV330 )
= $false )
| ( ( subset @ SV115 @ ( setadjoin @ SV255 @ SV330 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1160,plain,
! [SV331: $i,SV256: $i,SV116: $i] :
( ( ( subset @ SV116 @ SV256 )
= $false )
| ( ( ~ ( in @ SV331 @ SV116 )
| ( in @ SV331 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1161,plain,
! [SV258: $i,SV118: $i,SV359: $i] :
( ( ( ! [SY1663: $i] :
( ( SV359 != SY1663 )
| ~ ( ~ ( ~ ( in @ SV359 @ SV118 )
| ( in @ SY1663 @ SV258 ) )
| ~ ( ~ ( in @ SY1663 @ SV258 )
| ( in @ SV359 @ SV118 ) ) ) ) )
= $true )
| ( ( SV118 = SV258 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1162,plain,
! [SV259: $i > $o,SV119: $i] :
( ( ( ! [SY1563: $i] :
( ~ ( in @ SY1563 @ SV119 )
| ( SV259 @ SY1563 ) ) )
= $true )
| ( ( ~ ! [SY1564: $i] :
~ ~ ( ~ ( in @ SY1564 @ SV119 )
| ~ ~ ( SV259 @ SY1564 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1040]) ).
thf(1163,plain,
! [SV260: $i,SV120: $i] :
( ( ( ~ ( in @ ( sK16_SY1565 @ SV120 @ SV260 ) @ SV260 )
| ( in @ ( sK16_SY1565 @ SV120 @ SV260 ) @ SV120 ) )
= $false )
| ( ( in @ SV260 @ ( powerset @ SV120 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1041]) ).
thf(1164,plain,
! [SV261: $i,SV121: $i,SV332: $i] :
( ( ( in @ SV332 @ SV121 )
= $false )
| ( ( ~ ~ ( in @ SV332 @ SV261 )
| ( in @ SV332 @ ( symdiff @ SV121 @ SV261 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1165,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ~ ~ ( ~ ( SV124 @ SV360 )
| ~ ! [SY1664: $i] :
( ~ ( SV124 @ SY1664 )
| ( SV360 = SY1664 ) ) ) )
= $true )
| ( ( ~ ! [SY1348: $i] :
~ ~ ( ~ ( SV124 @ SY1348 )
| ~ ! [SY1349: $i] :
( ~ ( SV124 @ SY1349 )
| ( SY1348 = SY1349 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1166,plain,
! [SV264: $i,SV125: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ SV125 ) )
= $false )
| ( ( ~ ~ ( in @ SV333 @ SV264 )
| ~ ( in @ SV333 @ ( symdiff @ SV125 @ SV264 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1167,plain,
! [SV126: $i,SV265: $i] :
( ( ~ ( in @ SV265 @ ( setunion @ SV126 ) )
| ~ ! [SY1568: $i] :
~ ~ ( ~ ( in @ SV265 @ SY1568 )
| ~ ( in @ SY1568 @ SV126 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1047]) ).
thf(1168,plain,
! [SV126: $i,SV265: $i] :
( ( ~ ~ ! [SY1569: $i] :
~ ~ ( ~ ( in @ SV265 @ SY1569 )
| ~ ( in @ SY1569 @ SV126 ) )
| ( in @ SV265 @ ( setunion @ SV126 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1048]) ).
thf(1169,plain,
! [SV127: $i,SV361: $i] :
( ( ( ~ ( in @ SV361 @ SV127 ) )
= $true )
| ( ( SV127 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1170,plain,
! [SV129: $i] :
( ( ( in @ ( sK7_SY1357 @ SV129 ) @ SV129 )
= $true )
| ( ( SV129 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1051]) ).
thf(1171,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV362 ) )
= $true )
| ( ( ~ ! [SY1359: $i,SY1360: $i] :
( ~ ( SV130 @ SY1359 )
| ~ ( SV130 @ SY1360 )
| ( SY1359 = SY1360 ) )
| ~ ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1172,plain,
! [SV267: $i,SV131: $i,SV334: $i] :
( ( ( in @ SV334 @ ( cartprod @ SV131 @ SV267 ) )
= $false )
| ( ( in @ ( kfst @ SV334 ) @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1173,plain,
! [SV271: $i,SV136: $i,SV335: $i] :
( ( ( ~ ( in @ SV335 @ ( setminus @ SV136 @ SV271 ) ) )
= $false )
| ( ( ~ ~ ( in @ SV335 @ SV271 )
| ~ ( in @ SV335 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1174,plain,
! [SV363: $i,SV137: $i > $o] :
( ( ( ~ ~ ( ~ ( SV137 @ SV363 )
| ~ ! [SY1665: $i] :
( ~ ( SV137 @ SY1665 )
| ( SV363 = SY1665 ) ) ) )
= $true )
| ( ( ~ ! [SY1372: $i] :
~ ( SV137 @ SY1372 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1175,plain,
! [SV138: $i] :
( ( ( ~ ( in @ emptyset @ SV138 ) )
= $true )
| ( ( ~ ! [SY1373: $i] :
( ~ ~ ( ~ ( in @ SY1373 @ omega )
| ~ ( in @ SY1373 @ SV138 ) )
| ( in @ ( setadjoin @ SY1373 @ SY1373 ) @ SV138 ) ) )
= $true )
| ( ( ! [SY1374: $i] :
( ~ ( in @ SY1374 @ omega )
| ( in @ SY1374 @ SV138 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1176,plain,
! [SV336: $i,SV272: $i,SV139: $i] :
( ( ( subset @ SV139 @ SV272 )
= $false )
| ( ( ~ ( subset @ SV272 @ SV336 )
| ( subset @ SV139 @ SV336 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1177,plain,
! [SV140: $i,SV273: $i] :
( ( ~ ( in @ SV273 @ ( powerset @ SV140 ) )
| ! [SY1573: $i] :
( ~ ( in @ SY1573 @ SV273 )
| ( in @ SY1573 @ SV140 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1061]) ).
thf(1178,plain,
! [SV140: $i,SV273: $i] :
( ( ~ ! [SY1574: $i] :
( ~ ( in @ SY1574 @ SV273 )
| ( in @ SY1574 @ SV140 ) )
| ( in @ SV273 @ ( powerset @ SV140 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1062]) ).
thf(1179,plain,
! [SV141: $i,SV274: $i] :
( ( ( ~ ( in @ ( sK17_SY1575 @ SV274 @ SV141 ) @ SV141 )
| ( in @ ( sK17_SY1575 @ SV274 @ SV141 ) @ SV274 ) )
= $false )
| ( ( subset @ SV141 @ SV274 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1063]) ).
thf(1180,plain,
! [SV142: $i,SV364: $i] :
( ( ( ~ ( in @ SV364 @ SV142 ) )
= $true )
| ( ( ~ ! [SY1383: $i] :
~ ~ ( ~ ( in @ SY1383 @ SV142 )
| ~ ~ ~ ! [SY1384: $i] :
~ ~ ( ~ ( in @ SY1384 @ SY1383 )
| ~ ( in @ SY1384 @ SV142 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1181,plain,
! [SV143: $i] :
( ( ( ! [SY1385: $i] :
~ ~ ( ~ ( in @ SY1385 @ SV143 )
| ~ $true ) )
= $false )
| ( ( SV143 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1182,plain,
! [SV144: $i > $o,SV275: $i > $o] :
( ( ( ! [SY1666: $i] :
( ( ( sK18_SY1576 @ SV275 @ SV144 )
!= SY1666 )
| ~ ( ~ ( ~ ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
| ( SV275 @ SY1666 ) )
| ~ ( ~ ( SV275 @ SY1666 )
| ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1066]) ).
thf(1183,plain,
! [SV277: $i > $o,SV146: $i,SV337: $i] :
( ( ( in @ SV337 @ SV146 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV337
@ ( dsetconstr @ SV146
@ ^ [SY1585: $i] : ( SV277 @ SY1585 ) ) )
| ( SV277 @ SV337 ) )
| ~ ( ~ ( SV277 @ SV337 )
| ( in @ SV337
@ ( dsetconstr @ SV146
@ ^ [SY1586: $i] : ( SV277 @ SY1586 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1184,plain,
! [SV278: $i,SV147: $i,SV338: $i] :
( ( ( in @ SV338 @ ( binintersect @ SV147 @ SV278 ) )
= $false )
| ( ( in @ SV338 @ SV278 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1185,plain,
! [SV365: $i,SV148: $i > $o] :
( ( ( ~ ~ ( ~ ( SV148 @ SV365 )
| ~ ! [SY1667: $i] :
( ~ ( SV148 @ SY1667 )
| ( SV365 = SY1667 ) ) ) )
= $true )
| ( ( SV148
@ ( descr
@ ^ [SY1404: $i] : ( SV148 @ SY1404 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1186,plain,
! [SV281: $i > $o,SV151: $i] :
( ( ( ~ ! [SY1588: $i] :
~ ~ ( ~ ( in @ SY1588 @ SV151 )
| ~ ( SV281 @ SY1588 ) ) )
= $true )
| ( ( ! [SY1589: $i] :
( ~ ( in @ SY1589 @ SV151 )
| ~ ( SV281 @ SY1589 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1073]) ).
thf(1187,plain,
! [SV152: $i,SV282: $i] :
( ( ( ~ ( subset @ SV282 @ SV152 ) )
= $true )
| ( ( SV152 = SV282 )
= $true )
| ( ( subset @ SV152 @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1074]) ).
thf(1188,plain,
! [SV153: $i,SV283: $i,SV339: $i] :
( ( ( in @ SV339 @ SV283 )
= $false )
| ( ( in @ SV339 @ ( binunion @ SV153 @ SV283 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1189,plain,
! [SV284: $i,SV154: $i,SV340: $i] :
( ( ( subset @ SV340 @ SV154 )
= $false )
| ( ( ~ ( subset @ SV340 @ SV284 )
| ( subset @ SV340 @ ( binintersect @ SV154 @ SV284 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1190,plain,
! [SV286: $i,SV156: $i,SV341: $i] :
( ( ( in @ SV341 @ ( setadjoin @ SV156 @ SV286 ) )
= $false )
| ( ( ( SV341 = SV156 )
| ( in @ SV341 @ SV286 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1191,plain,
! [SV287: $i,SV158: $i,SV342: $i] :
( ( ( in @ SV342 @ ( binunion @ SV158 @ SV287 ) )
= $false )
| ( ( ( in @ SV342 @ SV158 )
| ( in @ SV342 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1192,plain,
! [SV366: $i,SV159: $i > $o] :
( ( ( ~ ~ ( ~ ( SV159 @ SV366 )
| ~ ! [SY1668: $i] :
( ~ ( SV159 @ SY1668 )
| ( SV366 = SY1668 ) ) ) )
= $true )
| ( ( ! [SY1422: $i,SY1423: $i] :
( ~ ( SV159 @ SY1422 )
| ~ ( SV159 @ SY1423 )
| ( SY1422 = SY1423 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1193,plain,
! [SV288: $i,SV160: $i,SV343: $i] :
( ( ( in @ SV343 @ ( setminus @ SV160 @ SV288 ) )
= $false )
| ( ( in @ SV343 @ SV160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1194,plain,
! [SV289: $i,SV161: $i] :
( ( ( ! [SY1595: $i] :
~ ~ ( ~ ( in @ SY1595 @ SV161 )
| ~ ( in @ SV289 @ SY1595 ) ) )
= $false )
| ( ( in @ SV289 @ ( setunion @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1195,plain,
! [SV290: $i > $o,SV162: $i,SV344: $i] :
( ( ( in @ SV344 @ SV162 )
= $false )
| ( ( ~ ( SV290 @ SV344 )
| ~ ! [SY1639: $i] :
( ~ ( in @ SY1639 @ SV162 )
| ~ ( SV290 @ SY1639 )
| ( SY1639 = SV344 ) )
| ~ ! [SY1598: $i] :
~ ~ ( ~ ( in @ SY1598
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ SY1598 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1196,plain,
! [SV367: $i > $o,SV349: $i > $o,SV180: $i,SV29: $i] :
( ( ( ~ ! [SY1669: $i] :
( ~ ( in @ SY1669 @ SV29 )
| ! [SY1670: $i] :
( ~ ( in @ SY1670 @ SV180 )
| ( SY1669 != SY1670 )
| ~ ( ~ ( ~ ( SV349 @ SY1669 )
| ( SV367 @ SY1670 ) )
| ~ ( ~ ( SV367 @ SY1670 )
| ( SV349 @ SY1669 ) ) ) ) )
| ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1197,plain,
! [SV30: $i,SV350: $i] :
( ( ( ~ ( ~ ( in @ SV350 @ SV30 )
| ( SV30
!= ( setadjoin @ SV350 @ emptyset ) ) ) )
= $false )
| ( ( in @ ( setunion @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1198,plain,
! [SV181: $i > $o,SV31: $i,SV368: $i] :
( ( ( ~ ~ ( ~ ( in @ SV368 @ SV31 )
| ~ ( SV181 @ SV368 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV31
@ ^ [SY1444: $i] : ( SV181 @ SY1444 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1199,plain,
! [SV182: $i,SV32: $i,SV292: $i] :
( ( ( SV292 = SV32 )
= $true )
| ( ( SV292 = SV182 )
= $true )
| ( ( in @ SV292 @ ( setadjoin @ SV32 @ ( setadjoin @ SV182 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1200,plain,
! [SV33: $i,SV183: $i,SV293: $i] :
( ( ( ~ ( in @ SV293 @ SV183 ) )
= $true )
| ( ( in @ SV293 @ ( binintersect @ SV33 @ SV183 ) )
= $true )
| ( ( in @ SV293 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1201,plain,
! [SV35: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1601: $i] :
( ~ ( in @ SY1601 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SY1601 )
| ( in @ SY1111 @ SV35 ) ) )
| ~ ! [SY1603: $i,SY1604: $i] :
( ~ ~ ( ~ ( in @ SY1603 @ SV35 )
| ~ ( in @ SY1604 @ SV35 ) )
| ~ ! [SY1605: $i] :
( ~ ( in @ SY1605 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SY1603 @ SY1605 )
| ( in @ SY1604 @ SY1605 ) )
| ~ ( ~ ( in @ SY1604 @ SY1605 )
| ( in @ SY1603 @ SY1605 ) ) ) )
| ( SY1603 = SY1604 ) ) )
| ~ ! [SY1606: $i,SY1607: $i] :
( ~ ~ ( ~ ( in @ SY1606 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1607 @ ( sK2_SY1109 @ SV35 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1606 )
| ( in @ SX4 @ SY1607 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1607 )
| ( in @ SX4 @ SY1606 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1202,plain,
! [SV35: $i] :
( ( ~ ! [SY1610: $i] :
( ~ ~ ( ~ ! [SY1120: $i] :
( ~ ( in @ SY1120 @ SY1610 )
| ( in @ SY1120 @ SV35 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1610 ) )
| ~ ! [SY1613: $i] :
~ ~ ! [SY1614: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1613 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1614 @ SY1610 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1613 )
| ~ ( in @ SX5 @ SY1610 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1613 ) )
| ( in @ SY1614 @ SY1616 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1203,plain,
! [SV351: $i,SV37: $i > $o] :
( ( ( ~ ( ~ ( SV37 @ SV351 )
| ~ ! [SY1650: $i] :
( ~ ( SV37 @ SY1650 )
| ( SV351 = SY1650 ) ) ) )
= $false )
| ( ( ! [SY1130: $i,SY1131: $i] :
( ~ ( SV37 @ SY1130 )
| ~ ( SV37 @ SY1131 )
| ( SY1130 = SY1131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1204,plain,
! [SV186: $i > $o,SV38: $i,SV369: $i] :
( ( ( ~ ~ ( ~ ( in @ SV369 @ SV38 )
| ~ ~ ( SV186 @ SV369 ) ) )
= $true )
| ( ( ~ ! [SY1449: $i] :
( ~ ( in @ SY1449 @ SV38 )
| ( SV186 @ SY1449 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1205,plain,
! [SV39: $i,SV295: $i,SV187: $i > $o] :
( ( ( ~ ( SV187 @ SV295 ) )
= $true )
| ( ( ( dsetconstr @ SV39
@ ^ [SY1451: $i] : ( SV187 @ SY1451 ) )
!= emptyset )
= $true )
| ( ( in @ SV295 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1093]) ).
thf(1206,plain,
! [SV40: $i,SV296: $i,SV188: $i,SV370: $i] :
( ( ( ~ ( in @ SV370 @ SV188 )
| ( in @ ( setadjoin @ ( setadjoin @ SV296 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV296 @ ( setadjoin @ SV370 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SV40 @ SV188 ) ) )
= $true )
| ( ( in @ SV296 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1207,plain,
! [SV345: $i,SV297: $i,SV190: $i,SV42: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV42 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV42 @ ( setadjoin @ SV190 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV297 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV297 @ ( setadjoin @ SV345 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV42 = SV297 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1208,plain,
! [SV44: $i,SV192: $i,SV298: $i] :
( ( ( ~ ~ ( in @ SV298 @ SV192 ) )
= $true )
| ( ( ~ ( subset @ SV44 @ SV192 ) )
= $true )
| ( ( in @ SV298 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1096]) ).
thf(1209,plain,
! [SV193: $i > $o,SV45: $i,SV371: $i] :
( ( ( ~ ( in @ SV371 @ SV45 )
| ( SV193 @ SV371 ) )
= $true )
| ( ( ~ ! [SY1458: $i] :
~ ~ ( ~ ( in @ SY1458 @ SV45 )
| ~ ~ ( SV193 @ SY1458 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1210,plain,
! [SV46: $i,SV194: $i,SV299: $i] :
( ( ( ~ ( in @ SV299 @ SV194 ) )
= $true )
| ( ( in @ SV299 @ SV46 )
= $true )
| ( ( in @ SV194 @ ( powerset @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1211,plain,
! [SV48: $i,SV300: $i,SV196: $i,SV372: $i] :
( ( ( ~ ( in @ SV372 @ SV196 )
| ( in @ ( setadjoin @ ( setadjoin @ SV300 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV300 @ ( setadjoin @ SV372 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV48 @ SV196 ) ) ) ) )
= $true )
| ( ( in @ SV300 @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1212,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ~ ( ~ ( SV50 @ SV352 )
| ~ ! [SY1651: $i] :
( ~ ( SV50 @ SY1651 )
| ( SV352 = SY1651 ) ) ) )
= $false )
| ( ( ~ ! [SY1160: $i] :
~ ~ ( ~ ( SV50 @ SY1160 )
| ~ ! [SY1161: $i] :
( ~ ( SV50 @ SY1161 )
| ( SY1160 = SY1161 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1213,plain,
! [SV51: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK8_SY1462 @ SV198 @ SV51 ) @ SV51 ) )
= $false )
| ( ( ~ ! [SY1463: $i] :
( ~ ( in @ SY1463 @ SV198 )
| ( in @ SY1463 @ SV51 ) )
| ( SV51 = SV198 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1101]) ).
thf(1214,plain,
! [SV51: $i,SV198: $i] :
( ( ( in @ ( sK8_SY1462 @ SV198 @ SV51 ) @ SV198 )
= $false )
| ( ( ~ ! [SY1463: $i] :
( ~ ( in @ SY1463 @ SV198 )
| ( in @ SY1463 @ SV51 ) )
| ( SV51 = SV198 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1101]) ).
thf(1215,plain,
! [SV52: $i] :
( ( ( ~ ( in @ ( sK19_SY1165 @ SV52 ) @ SV52 ) )
= $false )
| ( ( SV52 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1102]) ).
thf(1216,plain,
! [SV53: $i,SV199: $i,SV301: $i] :
( ( ( ~ ~ ( in @ SV301 @ SV199 ) )
= $true )
| ( ( in @ SV301 @ ( setminus @ SV53 @ SV199 ) )
= $true )
| ( ( in @ SV301 @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1103]) ).
thf(1217,plain,
! [SV54: $i,SV200: $i] :
( ( ~ ( in @ ( sK4_SY1465 @ SV200 @ SV54 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1643: $i] :
~ ~ ( ~ ( in @ SY1643 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ ( setadjoin @ SY1643 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1218,plain,
! [SV201: $i,SV55: $i,SV302: $i] :
( ( ( in @ SV302 @ SV55 )
= $true )
| ( ( ~ ( in @ SV302 @ ( setminus @ SV55 @ SV201 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1105]) ).
thf(1219,plain,
! [SV202: $i,SV56: $i,SV303: $i] :
( ( ( ~ ( in @ SV303 @ SV56 ) )
= $true )
| ( ( in @ SV202 @ ( setunion @ SV56 ) )
= $true )
| ( ( in @ SV202 @ SV303 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1106]) ).
thf(1220,plain,
! [SV203: $i,SV57: $i,SV304: $i] :
( ( ( SV304 = SV57 )
= $true )
| ( ( SV304 = SV203 )
= $true )
| ( ( in @ SV304 @ ( setadjoin @ SV57 @ ( setadjoin @ SV203 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1221,plain,
! [SV305: $i,SV204: $i,SV58: $i] :
( ( ( ! [SY1622: $i] :
~ ~ ( ~ ( in @ SY1622 @ SV58 )
| ~ ~ ! [SY1623: $i] :
~ ~ ( ~ ( in @ SY1623 @ SV204 )
| ( SV305
!= ( setadjoin @ ( setadjoin @ SY1622 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1622 @ ( setadjoin @ SY1623 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false )
| ( ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1222,plain,
! [SV59: $i,SV205: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 )
| ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV205 ) )
| ~ ( ~ ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV205 )
| ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV205 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1109]) ).
thf(1223,plain,
! [SV346: $o,SV206: $i,SV60: $i,SV306: $i] :
( ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV306 @ SV60 )
| SV346 )
| ~ ( ~ ( in @ SV306 @ SV206 )
| SV346 )
| SV346 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1225,plain,
! [SV206: $i,SV60: $i,SV306: $i] :
( ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV306 @ SV60 )
| $false )
| ~ ( ~ ( in @ SV306 @ SV206 )
| $false )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1226,plain,
! [SV61: $i,SV207: $i] :
( ( ~ ( in @ ( sK5_SY1476 @ SV207 @ SV61 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ~ ! [SY1644: $i] :
~ ~ ( ~ ( in @ SY1644 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ ( setadjoin @ SY1644 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1227,plain,
! [SV62: $i,SV208: $i > $o] :
( ( ( ~ ( in @ ( sK10_SY1478 @ SV208 @ SV62 ) @ SV62 ) )
= $false )
| ( ( ~ ~ ! [SY1479: $i] :
~ ~ ( ~ ( in @ SY1479 @ SV62 )
| ~ ( SV208 @ SY1479 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1114]) ).
thf(1228,plain,
! [SV62: $i,SV208: $i > $o] :
( ( ( ~ ( SV208 @ ( sK10_SY1478 @ SV208 @ SV62 ) ) )
= $false )
| ( ( ~ ~ ! [SY1479: $i] :
~ ~ ( ~ ( in @ SY1479 @ SV62 )
| ~ ( SV208 @ SY1479 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1114]) ).
thf(1229,plain,
! [SV210: $i,SV64: $i > $i > $o] :
( ( ( ~ ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 ) )
= $false )
| ( ( ~ ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1115]) ).
thf(1230,plain,
! [SV210: $i,SV64: $i > $i > $o] :
( ( ( ~ ! [SY1652: $i] :
~ ~ ( ~ ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SY1652 )
| ~ ! [SY1653: $i] :
( ~ ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SY1653 )
| ( SY1652 = SY1653 ) ) ) )
= $false )
| ( ( ~ ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1115]) ).
thf(1231,plain,
! [SV347: $i,SV308: $i,SV212: $i,SV66: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV66 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV66 @ ( setadjoin @ SV212 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV308 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV308 @ ( setadjoin @ SV347 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV66 = SV308 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1232,plain,
! [SV67: $i,SV213: $i,SV309: $i] :
( ( ( ~ ( in @ SV309 @ SV213 ) )
= $true )
| ( ( ~ ( in @ SV309 @ ( symdiff @ SV67 @ SV213 ) ) )
= $true )
| ( ( in @ SV309 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1118]) ).
thf(1233,plain,
! [SV214: $i,SV68: $i] :
( ( ( SV68 = SV214 )
= $false )
| ( ( subset @ SV68 @ SV214 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1234,plain,
! [SV70: $i,SV216: $i > $o] :
( ( ( ~ ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 ) )
= $false )
| ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) )
| ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1121]) ).
thf(1235,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ( ! [SY1654: $i] :
( ~ ( in @ SY1654 @ SV70 )
| ~ ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
| ~ ( SV216 @ SY1654 )
| ( ( sK12_SY1492 @ SV216 @ SV70 )
= SY1654 ) ) )
= $false )
| ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) )
| ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1121]) ).
thf(1236,plain,
! [SV71: $i,SV310: $i,SV217: $i > $o] :
( ( ( ~ ( SV217 @ SV310 ) )
= $true )
| ( ( in @ SV310
@ ( dsetconstr @ SV71
@ ^ [SY1499: $i] : ( SV217 @ SY1499 ) ) )
= $true )
| ( ( in @ SV310 @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1122]) ).
thf(1237,plain,
! [SV353: $o,SV72: $i,SV218: $i] :
( ( ( ~ ! [SY1655: $i] :
( ~ ( in @ SV218 @ SY1655 )
| ~ ( in @ SY1655 @ SV72 )
| SV353 ) )
= $true )
| ( SV353 = $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1239,plain,
! [SV72: $i,SV218: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV218 @ SX0 )
| ~ ( in @ SX0 @ SV72 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1125]) ).
thf(1240,plain,
! [SV219: $i,SV74: $i,SV373: $i,SV354: $i] :
( ( ( ( SV354 != SV373 )
| ~ ( in @ SV354 @ SV74 )
| ( in @ SV373 @ SV219 ) )
= $true )
| ( ( SV74 = SV219 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1241,plain,
! [SV220: $i > $o,SV75: $i,SV374: $i] :
( ( ( ~ ~ ( ~ ( in @ SV374
@ ( dsetconstr @ SV75
@ ^ [SY1505: $i] : ( SV220 @ SY1505 ) ) )
| ( ( dsetconstr @ SV75
@ ^ [SY1506: $i] : ( SV220 @ SY1506 ) )
!= ( setadjoin @ SV374 @ emptyset ) ) ) )
= $true )
| ( ( ~ ! [SY1507: $i] :
~ ~ ( ~ ( in @ SY1507 @ SV75 )
| ~ ( SV220 @ SY1507 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1242,plain,
! [SV77: $i,SV311: $i,SV221: $i,SV375: $i] :
( ( ( ~ ( in @ SV375 @ SV221 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV311 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV311 @ ( setadjoin @ SV375 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV77 @ SV221 ) ) ) )
= $true )
| ( ( in @ SV311 @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1243,plain,
! [SV223: $i,SV79: $i,SV312: $i] :
( ( ( in @ SV312 @ SV79 )
= $true )
| ( ( ~ ( in @ SV312 @ SV223 )
| ( in @ SV312 @ ( symdiff @ SV79 @ SV223 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1129]) ).
thf(1244,plain,
! [SV224: $i,SV80: $i,SV376: $i,SV355: $i] :
( ( ( ( SV355 != SV376 )
| ( ( setadjoin @ SV80 @ SV355 )
= ( setadjoin @ SV224 @ SV376 ) ) )
= $true )
| ( ( SV80 = SV224 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1245,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ( ( sK13_SY1513 @ SV228 @ SV85 )
!= ( sK20_SY1658 @ SV85 @ SV228 ) )
| ~ ( ~ ( ~ ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
| ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) ) )
| ~ ( ~ ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
| ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1131]) ).
thf(1246,plain,
! [SV86: $i,SV229: $i] :
( ( ( ~ ( in @ ( sK14_SY1523 @ SV229 @ SV86 ) @ SV86 ) )
= $false )
| ( ( subset @ SV86 @ SV229 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1132]) ).
thf(1247,plain,
! [SV86: $i,SV229: $i] :
( ( ( in @ ( sK14_SY1523 @ SV229 @ SV86 ) @ SV229 )
= $false )
| ( ( subset @ SV86 @ SV229 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1132]) ).
thf(1248,plain,
! [SV87: $i,SV313: $i,SV230: $i,SV377: $i] :
( ( ( ~ ( in @ SV377 @ SV230 )
| ( in @ ( setadjoin @ ( setadjoin @ SV313 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV313 @ ( setadjoin @ SV377 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV87 @ SV230 ) ) ) ) )
= $true )
| ( ( in @ SV313 @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1249,plain,
! [SV232: $i,SV89: $i] :
( ( ( ! [SY1527: $i] :
~ ~ ( ~ ( in @ SY1527 @ SV89 )
| ~ ( in @ SY1527 @ SV232 ) ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1250,plain,
! [SV356: $i,SV90: $i > $o] :
( ( ( ~ ( ~ ( SV90 @ SV356 )
| ~ ! [SY1659: $i] :
( ~ ( SV90 @ SY1659 )
| ( SV356 = SY1659 ) ) ) )
= $false )
| ( ( ~ ! [SY1266: $i] :
~ ! [SY1267: $i] :
~ ( ~ ( ~ ( SV90 @ SY1267 )
| ( SY1267 = SY1266 ) )
| ~ ( ( SY1267 != SY1266 )
| ( SV90 @ SY1267 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1251,plain,
! [SV233: $i,SV378: $o,SV91: $i,SV315: $i] :
( ( ( ~ ( ( SV315 != SV91 )
| SV378 )
| ~ ( ~ ( in @ SV315 @ SV233 )
| SV378 )
| SV378 )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1137]) ).
thf(1253,plain,
! [SV233: $i,SV91: $i,SV315: $i] :
( ( ( ~ ( ( SV315 != SV91 )
| $false )
| ~ ( ~ ( in @ SV315 @ SV233 )
| $false )
| $false )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1137]) ).
thf(1254,plain,
! [SV92: $i,SV234: $i > $o] :
( ( ( ~ ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 ) )
= $false )
| ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) )
| ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1138]) ).
thf(1255,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ( ! [SY1660: $i] :
( ~ ( in @ SY1660 @ SV92 )
| ~ ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
| ~ ( SV234 @ SY1660 )
| ( ( sK15_SY1530 @ SV234 @ SV92 )
= SY1660 ) ) )
= $false )
| ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) )
| ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1138]) ).
thf(1256,plain,
! [SV236: $i,SV94: $i,SV317: $i] :
( ( ( in @ SV317 @ ( setminus @ SV94 @ SV236 ) )
= $false )
| ( ( in @ SV317 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1257,plain,
! [SV95: $i,SV318: $i,SV237: $i,SV379: $i] :
( ( ( ~ ( in @ SV379 @ SV237 )
| ( in @ ( setadjoin @ SV318 @ ( setadjoin @ SV379 @ emptyset ) ) @ ( powerset @ ( binunion @ SV95 @ SV237 ) ) ) )
= $true )
| ( ( in @ SV318 @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1258,plain,
! [SV238: $i,SV96: $i,SV319: $i] :
( ( ~ ( in @ SV319 @ ( setadjoin @ SV96 @ SV238 ) )
| ( SV319 = SV96 )
| ( in @ SV319 @ SV238 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1142]) ).
thf(1259,plain,
! [SV238: $i,SV96: $i,SV319: $i] :
( ( ~ ( ( SV319 = SV96 )
| ( in @ SV319 @ SV238 ) )
| ( in @ SV319 @ ( setadjoin @ SV96 @ SV238 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1143]) ).
thf(1260,plain,
! [SV239: $i,SV97: $i,SV320: $i] :
( ( ( in @ SV320 @ ( setminus @ SV97 @ SV239 ) )
= $true )
| ( ( ~ ( in @ SV320 @ SV97 )
| ( in @ SV320 @ SV239 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1144]) ).
thf(1261,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ! [SY1661: $i] :
~ ( ~ ( ~ ( SV98 @ SY1661 )
| ( SY1661 = SV357 ) )
| ~ ( ( SY1661 != SV357 )
| ( SV98 @ SY1661 ) ) ) )
= $false )
| ( ( ~ ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1262,plain,
! [SV241: $i,SV100: $i,SV321: $i] :
( ( ( ! [SY1632: $i] :
~ ~ ( ~ ( in @ SY1632 @ ( setunion @ SV321 ) )
| ~ ~ ! [SY1633: $i] :
~ ~ ( ~ ( in @ SY1633 @ ( setunion @ SV321 ) )
| ( SV321
!= ( setadjoin @ ( setadjoin @ SY1632 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1632 @ ( setadjoin @ SY1633 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false )
| ( ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1263,plain,
! [SV103: $i,SV244: $i,SV324: $i] :
( ( ( ~ ~ ( in @ SV324 @ SV244 ) )
= $true )
| ( ( SV103 != SV244 )
= $true )
| ( ( in @ SV324 @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1264,plain,
! [SV245: $i > $o,SV104: $i] :
( ( ( ! [SY1550: $i] :
~ ~ ( ~ ( in @ SY1550 @ SV104 )
| ~ ( SV245 @ SY1550 ) ) )
= $false )
| ( ( ! [SY1551: $i] :
( ~ ( in @ SY1551 @ SV104 )
| ~ ( SV245 @ SY1551 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1265,plain,
! [SV106: $i,SV247: $i,SV326: $i] :
( ( ( in @ SV326 @ SV247 )
= $false )
| ( ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1266,plain,
! [SV107: $i,SV248: $i] :
( ( ( in @ SV248 @ ( setadjoin @ SV107 @ emptyset ) )
= $false )
| ( ( SV107 = SV248 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1267,plain,
! [SV108: $i,SV358: $i] :
( ( ( ~ ( ~ ( in @ SV358 @ ( setunion @ SV108 ) )
| ~ ~ ! [SY1662: $i] :
~ ~ ( ~ ( in @ SY1662 @ ( setunion @ SV108 ) )
| ( SV108
!= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SY1662 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false )
| ( ( ~ ! [SY1316: $i] :
~ ~ ( ~ ( in @ SY1316
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ SY1316 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1268,plain,
! [SV109: $i,SV249: $i,SV327: $i] :
( ( ( ~ ~ ( in @ SV327 @ SV249 ) )
= $true )
| ( ( ~ ( in @ SV327 @ SV109 ) )
= $true )
| ( ( subset @ SV109 @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1269,plain,
! [SV111: $i,SV328: $i,SV250: $i,SV380: $i] :
( ( ( ~ ( in @ SV380 @ SV250 )
| ( subset @ ( setadjoin @ SV328 @ ( setadjoin @ SV380 @ emptyset ) ) @ ( binunion @ SV111 @ SV250 ) ) )
= $true )
| ( ( in @ SV328 @ SV111 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1270,plain,
! [SV381: $o,SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ( ~ ( in @ SV329 @ SV113 )
| ~ ~ ( in @ SV329 @ SV254 )
| SV381 )
| ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| SV381 )
| SV381 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1158]) ).
thf(1272,plain,
! [SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ( ~ ( in @ SV329 @ SV113 )
| ~ ~ ( in @ SV329 @ SV254 )
| $false )
| ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| $false )
| $false )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1158]) ).
thf(1273,plain,
! [SV256: $i,SV116: $i,SV331: $i] :
( ( ( ~ ( in @ SV331 @ SV116 ) )
= $true )
| ( ( in @ SV331 @ SV256 )
= $true )
| ( ( subset @ SV116 @ SV256 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1274,plain,
! [SV258: $i,SV118: $i,SV382: $i,SV359: $i] :
( ( ( ( SV359 != SV382 )
| ~ ( ~ ( ~ ( in @ SV359 @ SV118 )
| ( in @ SV382 @ SV258 ) )
| ~ ( ~ ( in @ SV382 @ SV258 )
| ( in @ SV359 @ SV118 ) ) ) )
= $true )
| ( ( SV118 = SV258 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1275,plain,
! [SV259: $i > $o,SV119: $i,SV383: $i] :
( ( ( ~ ( in @ SV383 @ SV119 )
| ( SV259 @ SV383 ) )
= $true )
| ( ( ~ ! [SY1564: $i] :
~ ~ ( ~ ( in @ SY1564 @ SV119 )
| ~ ~ ( SV259 @ SY1564 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1276,plain,
! [SV260: $i,SV120: $i] :
( ( ( ~ ( in @ ( sK16_SY1565 @ SV120 @ SV260 ) @ SV260 ) )
= $false )
| ( ( in @ SV260 @ ( powerset @ SV120 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1163]) ).
thf(1277,plain,
! [SV260: $i,SV120: $i] :
( ( ( in @ ( sK16_SY1565 @ SV120 @ SV260 ) @ SV120 )
= $false )
| ( ( in @ SV260 @ ( powerset @ SV120 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1163]) ).
thf(1278,plain,
! [SV121: $i,SV261: $i,SV332: $i] :
( ( ( ~ ~ ( in @ SV332 @ SV261 ) )
= $true )
| ( ( in @ SV332 @ ( symdiff @ SV121 @ SV261 ) )
= $true )
| ( ( in @ SV332 @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1164]) ).
thf(1279,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ~ ( ~ ( SV124 @ SV360 )
| ~ ! [SY1664: $i] :
( ~ ( SV124 @ SY1664 )
| ( SV360 = SY1664 ) ) ) )
= $false )
| ( ( ~ ! [SY1348: $i] :
~ ~ ( ~ ( SV124 @ SY1348 )
| ~ ! [SY1349: $i] :
( ~ ( SV124 @ SY1349 )
| ( SY1348 = SY1349 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1280,plain,
! [SV264: $i,SV125: $i,SV333: $i] :
( ( ( in @ SV333 @ SV125 )
= $true )
| ( ( ~ ~ ( in @ SV333 @ SV264 )
| ~ ( in @ SV333 @ ( symdiff @ SV125 @ SV264 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1166]) ).
thf(1281,plain,
! [SV126: $i,SV265: $i] :
( ( ( ~ ( in @ SV265 @ ( setunion @ SV126 ) ) )
= $true )
| ( ( ~ ! [SY1568: $i] :
~ ~ ( ~ ( in @ SV265 @ SY1568 )
| ~ ( in @ SY1568 @ SV126 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1282,plain,
! [SV126: $i,SV265: $i] :
( ( ( ~ ~ ! [SY1569: $i] :
~ ~ ( ~ ( in @ SV265 @ SY1569 )
| ~ ( in @ SY1569 @ SV126 ) ) )
= $true )
| ( ( in @ SV265 @ ( setunion @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1168]) ).
thf(1283,plain,
! [SV127: $i,SV361: $i] :
( ( ( in @ SV361 @ SV127 )
= $false )
| ( ( SV127 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1284,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( SV130 @ SV362 )
= $false )
| ( ( ~ ! [SY1359: $i,SY1360: $i] :
( ~ ( SV130 @ SY1359 )
| ~ ( SV130 @ SY1360 )
| ( SY1359 = SY1360 ) )
| ~ ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1285,plain,
! [SV271: $i,SV136: $i,SV335: $i] :
( ( ( in @ SV335 @ ( setminus @ SV136 @ SV271 ) )
= $true )
| ( ( ~ ~ ( in @ SV335 @ SV271 )
| ~ ( in @ SV335 @ SV136 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1173]) ).
thf(1286,plain,
! [SV363: $i,SV137: $i > $o] :
( ( ( ~ ( ~ ( SV137 @ SV363 )
| ~ ! [SY1665: $i] :
( ~ ( SV137 @ SY1665 )
| ( SV363 = SY1665 ) ) ) )
= $false )
| ( ( ~ ! [SY1372: $i] :
~ ( SV137 @ SY1372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1287,plain,
! [SV138: $i] :
( ( ( in @ emptyset @ SV138 )
= $false )
| ( ( ~ ! [SY1373: $i] :
( ~ ~ ( ~ ( in @ SY1373 @ omega )
| ~ ( in @ SY1373 @ SV138 ) )
| ( in @ ( setadjoin @ SY1373 @ SY1373 ) @ SV138 ) ) )
= $true )
| ( ( ! [SY1374: $i] :
( ~ ( in @ SY1374 @ omega )
| ( in @ SY1374 @ SV138 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1288,plain,
! [SV139: $i,SV336: $i,SV272: $i] :
( ( ( ~ ( subset @ SV272 @ SV336 ) )
= $true )
| ( ( subset @ SV139 @ SV336 )
= $true )
| ( ( subset @ SV139 @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1176]) ).
thf(1289,plain,
! [SV140: $i,SV273: $i] :
( ( ( ~ ( in @ SV273 @ ( powerset @ SV140 ) ) )
= $true )
| ( ( ! [SY1573: $i] :
( ~ ( in @ SY1573 @ SV273 )
| ( in @ SY1573 @ SV140 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1177]) ).
thf(1290,plain,
! [SV140: $i,SV273: $i] :
( ( ( ~ ! [SY1574: $i] :
( ~ ( in @ SY1574 @ SV273 )
| ( in @ SY1574 @ SV140 ) ) )
= $true )
| ( ( in @ SV273 @ ( powerset @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1178]) ).
thf(1291,plain,
! [SV141: $i,SV274: $i] :
( ( ( ~ ( in @ ( sK17_SY1575 @ SV274 @ SV141 ) @ SV141 ) )
= $false )
| ( ( subset @ SV141 @ SV274 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1179]) ).
thf(1292,plain,
! [SV141: $i,SV274: $i] :
( ( ( in @ ( sK17_SY1575 @ SV274 @ SV141 ) @ SV274 )
= $false )
| ( ( subset @ SV141 @ SV274 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1179]) ).
thf(1293,plain,
! [SV142: $i,SV364: $i] :
( ( ( in @ SV364 @ SV142 )
= $false )
| ( ( ~ ! [SY1383: $i] :
~ ~ ( ~ ( in @ SY1383 @ SV142 )
| ~ ~ ~ ! [SY1384: $i] :
~ ~ ( ~ ( in @ SY1384 @ SY1383 )
| ~ ( in @ SY1384 @ SV142 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1294,plain,
! [SV143: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_SY1385 @ SV143 ) @ SV143 )
| ~ $true ) )
= $false )
| ( ( SV143 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1181]) ).
thf(1295,plain,
! [SV144: $i > $o,SV275: $i > $o] :
( ( ( ( ( sK18_SY1576 @ SV275 @ SV144 )
!= ( sK22_SY1666 @ SV144 @ SV275 ) )
| ~ ( ~ ( ~ ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
| ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) ) )
| ~ ( ~ ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
| ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1182]) ).
thf(1296,plain,
! [SV277: $i > $o,SV146: $i,SV337: $i] :
( ( ( ~ ( ~ ( in @ SV337
@ ( dsetconstr @ SV146
@ ^ [SY1585: $i] : ( SV277 @ SY1585 ) ) )
| ( SV277 @ SV337 ) )
| ~ ( ~ ( SV277 @ SV337 )
| ( in @ SV337
@ ( dsetconstr @ SV146
@ ^ [SY1586: $i] : ( SV277 @ SY1586 ) ) ) ) )
= $false )
| ( ( in @ SV337 @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1297,plain,
! [SV365: $i,SV148: $i > $o] :
( ( ( ~ ( ~ ( SV148 @ SV365 )
| ~ ! [SY1667: $i] :
( ~ ( SV148 @ SY1667 )
| ( SV365 = SY1667 ) ) ) )
= $false )
| ( ( SV148
@ ( descr
@ ^ [SY1404: $i] : ( SV148 @ SY1404 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1298,plain,
! [SV281: $i > $o,SV151: $i] :
( ( ( ! [SY1588: $i] :
~ ~ ( ~ ( in @ SY1588 @ SV151 )
| ~ ( SV281 @ SY1588 ) ) )
= $false )
| ( ( ! [SY1589: $i] :
( ~ ( in @ SY1589 @ SV151 )
| ~ ( SV281 @ SY1589 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1299,plain,
! [SV152: $i,SV282: $i] :
( ( ( subset @ SV282 @ SV152 )
= $false )
| ( ( SV152 = SV282 )
= $true )
| ( ( subset @ SV152 @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1300,plain,
! [SV154: $i,SV284: $i,SV340: $i] :
( ( ( ~ ( subset @ SV340 @ SV284 ) )
= $true )
| ( ( subset @ SV340 @ ( binintersect @ SV154 @ SV284 ) )
= $true )
| ( ( subset @ SV340 @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1301,plain,
! [SV286: $i,SV156: $i,SV341: $i] :
( ( ( SV341 = SV156 )
= $true )
| ( ( in @ SV341 @ SV286 )
= $true )
| ( ( in @ SV341 @ ( setadjoin @ SV156 @ SV286 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1190]) ).
thf(1302,plain,
! [SV287: $i,SV158: $i,SV342: $i] :
( ( ( in @ SV342 @ SV158 )
= $true )
| ( ( in @ SV342 @ SV287 )
= $true )
| ( ( in @ SV342 @ ( binunion @ SV158 @ SV287 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1303,plain,
! [SV366: $i,SV159: $i > $o] :
( ( ( ~ ( ~ ( SV159 @ SV366 )
| ~ ! [SY1668: $i] :
( ~ ( SV159 @ SY1668 )
| ( SV366 = SY1668 ) ) ) )
= $false )
| ( ( ! [SY1422: $i,SY1423: $i] :
( ~ ( SV159 @ SY1422 )
| ~ ( SV159 @ SY1423 )
| ( SY1422 = SY1423 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1304,plain,
! [SV161: $i,SV289: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK23_SY1595 @ SV289 @ SV161 ) @ SV161 )
| ~ ( in @ SV289 @ ( sK23_SY1595 @ SV289 @ SV161 ) ) ) )
= $false )
| ( ( in @ SV289 @ ( setunion @ SV161 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1194]) ).
thf(1305,plain,
! [SV162: $i,SV344: $i,SV290: $i > $o] :
( ( ( ~ ( SV290 @ SV344 ) )
= $true )
| ( ( ~ ! [SY1639: $i] :
( ~ ( in @ SY1639 @ SV162 )
| ~ ( SV290 @ SY1639 )
| ( SY1639 = SV344 ) )
| ~ ! [SY1598: $i] :
~ ~ ( ~ ( in @ SY1598
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ SY1598 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1195]) ).
thf(1306,plain,
! [SV367: $i > $o,SV349: $i > $o,SV180: $i,SV29: $i] :
( ( ( ~ ! [SY1669: $i] :
( ~ ( in @ SY1669 @ SV29 )
| ! [SY1670: $i] :
( ~ ( in @ SY1670 @ SV180 )
| ( SY1669 != SY1670 )
| ~ ( ~ ( ~ ( SV349 @ SY1669 )
| ( SV367 @ SY1670 ) )
| ~ ( ~ ( SV367 @ SY1670 )
| ( SV349 @ SY1669 ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1307,plain,
! [SV30: $i,SV350: $i] :
( ( ( ~ ( in @ SV350 @ SV30 )
| ( SV30
!= ( setadjoin @ SV350 @ emptyset ) ) )
= $true )
| ( ( in @ ( setunion @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1197]) ).
thf(1308,plain,
! [SV181: $i > $o,SV31: $i,SV368: $i] :
( ( ( ~ ( ~ ( in @ SV368 @ SV31 )
| ~ ( SV181 @ SV368 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV31
@ ^ [SY1444: $i] : ( SV181 @ SY1444 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1309,plain,
! [SV33: $i,SV183: $i,SV293: $i] :
( ( ( in @ SV293 @ SV183 )
= $false )
| ( ( in @ SV293 @ ( binintersect @ SV33 @ SV183 ) )
= $true )
| ( ( in @ SV293 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1310,plain,
! [SV35: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1601: $i] :
( ~ ( in @ SY1601 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SY1601 )
| ( in @ SY1111 @ SV35 ) ) )
| ~ ! [SY1603: $i,SY1604: $i] :
( ~ ~ ( ~ ( in @ SY1603 @ SV35 )
| ~ ( in @ SY1604 @ SV35 ) )
| ~ ! [SY1605: $i] :
( ~ ( in @ SY1605 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SY1603 @ SY1605 )
| ( in @ SY1604 @ SY1605 ) )
| ~ ( ~ ( in @ SY1604 @ SY1605 )
| ( in @ SY1603 @ SY1605 ) ) ) )
| ( SY1603 = SY1604 ) ) )
| ~ ! [SY1606: $i,SY1607: $i] :
( ~ ~ ( ~ ( in @ SY1606 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1607 @ ( sK2_SY1109 @ SV35 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1606 )
| ( in @ SX4 @ SY1607 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1607 )
| ( in @ SX4 @ SY1606 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1201]) ).
thf(1311,plain,
! [SV35: $i] :
( ( ! [SY1610: $i] :
( ~ ~ ( ~ ! [SY1120: $i] :
( ~ ( in @ SY1120 @ SY1610 )
| ( in @ SY1120 @ SV35 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1610 ) )
| ~ ! [SY1613: $i] :
~ ~ ! [SY1614: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1613 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1614 @ SY1610 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1613 )
| ~ ( in @ SX5 @ SY1610 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1613 ) )
| ( in @ SY1614 @ SY1616 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1202]) ).
thf(1312,plain,
! [SV351: $i,SV37: $i > $o] :
( ( ( ~ ( SV37 @ SV351 )
| ~ ! [SY1650: $i] :
( ~ ( SV37 @ SY1650 )
| ( SV351 = SY1650 ) ) )
= $true )
| ( ( ! [SY1130: $i,SY1131: $i] :
( ~ ( SV37 @ SY1130 )
| ~ ( SV37 @ SY1131 )
| ( SY1130 = SY1131 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1203]) ).
thf(1313,plain,
! [SV186: $i > $o,SV38: $i,SV369: $i] :
( ( ( ~ ( ~ ( in @ SV369 @ SV38 )
| ~ ~ ( SV186 @ SV369 ) ) )
= $false )
| ( ( ~ ! [SY1449: $i] :
( ~ ( in @ SY1449 @ SV38 )
| ( SV186 @ SY1449 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1314,plain,
! [SV39: $i,SV295: $i,SV187: $i > $o] :
( ( ( SV187 @ SV295 )
= $false )
| ( ( ( dsetconstr @ SV39
@ ^ [SY1451: $i] : ( SV187 @ SY1451 ) )
!= emptyset )
= $true )
| ( ( in @ SV295 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1315,plain,
! [SV40: $i,SV296: $i,SV188: $i,SV370: $i] :
( ( ( ~ ( in @ SV370 @ SV188 ) )
= $true )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV296 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV296 @ ( setadjoin @ SV370 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SV40 @ SV188 ) )
= $true )
| ( ( in @ SV296 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1206]) ).
thf(1316,plain,
! [SV44: $i,SV192: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ SV192 ) )
= $false )
| ( ( ~ ( subset @ SV44 @ SV192 ) )
= $true )
| ( ( in @ SV298 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1317,plain,
! [SV193: $i > $o,SV45: $i,SV371: $i] :
( ( ( ~ ( in @ SV371 @ SV45 ) )
= $true )
| ( ( SV193 @ SV371 )
= $true )
| ( ( ~ ! [SY1458: $i] :
~ ~ ( ~ ( in @ SY1458 @ SV45 )
| ~ ~ ( SV193 @ SY1458 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1318,plain,
! [SV46: $i,SV194: $i,SV299: $i] :
( ( ( in @ SV299 @ SV194 )
= $false )
| ( ( in @ SV299 @ SV46 )
= $true )
| ( ( in @ SV194 @ ( powerset @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1319,plain,
! [SV48: $i,SV300: $i,SV196: $i,SV372: $i] :
( ( ( ~ ( in @ SV372 @ SV196 ) )
= $true )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV300 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV300 @ ( setadjoin @ SV372 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV48 @ SV196 ) ) ) )
= $true )
| ( ( in @ SV300 @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1320,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ SV352 )
| ~ ! [SY1651: $i] :
( ~ ( SV50 @ SY1651 )
| ( SV352 = SY1651 ) ) )
= $true )
| ( ( ~ ! [SY1160: $i] :
~ ~ ( ~ ( SV50 @ SY1160 )
| ~ ! [SY1161: $i] :
( ~ ( SV50 @ SY1161 )
| ( SY1160 = SY1161 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1212]) ).
thf(1321,plain,
! [SV51: $i,SV198: $i] :
( ( ( in @ ( sK8_SY1462 @ SV198 @ SV51 ) @ SV51 )
= $true )
| ( ( ~ ! [SY1463: $i] :
( ~ ( in @ SY1463 @ SV198 )
| ( in @ SY1463 @ SV51 ) )
| ( SV51 = SV198 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1213]) ).
thf(1322,plain,
! [SV51: $i,SV198: $i] :
( ( ( ~ ! [SY1463: $i] :
( ~ ( in @ SY1463 @ SV198 )
| ( in @ SY1463 @ SV51 ) ) )
= $true )
| ( ( SV51 = SV198 )
= $true )
| ( ( in @ ( sK8_SY1462 @ SV198 @ SV51 ) @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1323,plain,
! [SV52: $i] :
( ( ( in @ ( sK19_SY1165 @ SV52 ) @ SV52 )
= $true )
| ( ( SV52 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1215]) ).
thf(1324,plain,
! [SV53: $i,SV199: $i,SV301: $i] :
( ( ( ~ ( in @ SV301 @ SV199 ) )
= $false )
| ( ( in @ SV301 @ ( setminus @ SV53 @ SV199 ) )
= $true )
| ( ( in @ SV301 @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1325,plain,
! [SV54: $i,SV200: $i] :
( ( ~ ( in @ ( sK4_SY1465 @ SV200 @ SV54 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1217]) ).
thf(1326,plain,
! [SV200: $i,SV54: $i] :
( ( ~ ~ ! [SY1643: $i] :
~ ~ ( ~ ( in @ SY1643 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ ( setadjoin @ SY1643 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1217]) ).
thf(1327,plain,
! [SV201: $i,SV55: $i,SV302: $i] :
( ( ( in @ SV302 @ ( setminus @ SV55 @ SV201 ) )
= $false )
| ( ( in @ SV302 @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1328,plain,
! [SV202: $i,SV56: $i,SV303: $i] :
( ( ( in @ SV303 @ SV56 )
= $false )
| ( ( in @ SV202 @ ( setunion @ SV56 ) )
= $true )
| ( ( in @ SV202 @ SV303 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1329,plain,
! [SV58: $i,SV204: $i,SV305: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ SV58 )
| ~ ~ ! [SY1675: $i] :
~ ~ ( ~ ( in @ SY1675 @ SV204 )
| ( SV305
!= ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ ( setadjoin @ SY1675 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false )
| ( ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1221]) ).
thf(1330,plain,
! [SV59: $i,SV205: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 )
| ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV205 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV205 )
| ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV205 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1331,plain,
! [SV206: $i,SV346: $o,SV60: $i,SV306: $i] :
( ( ( ~ ( ~ ( in @ SV306 @ SV60 )
| SV346 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV306 @ SV206 )
| SV346 )
| SV346 )
= $true )
| ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1333,plain,
! [SV206: $i,SV60: $i,SV306: $i] :
( ( ( ~ ( ~ ( in @ SV306 @ SV60 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV306 @ SV206 )
| $false )
| $false )
= $true )
| ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1225]) ).
thf(1334,plain,
! [SV61: $i,SV207: $i] :
( ( ~ ( in @ ( sK5_SY1476 @ SV207 @ SV61 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1226]) ).
thf(1335,plain,
! [SV207: $i,SV61: $i] :
( ( ~ ~ ! [SY1644: $i] :
~ ~ ( ~ ( in @ SY1644 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ ( setadjoin @ SY1644 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1226]) ).
thf(1336,plain,
! [SV62: $i,SV208: $i > $o] :
( ( ( in @ ( sK10_SY1478 @ SV208 @ SV62 ) @ SV62 )
= $true )
| ( ( ~ ~ ! [SY1479: $i] :
~ ~ ( ~ ( in @ SY1479 @ SV62 )
| ~ ( SV208 @ SY1479 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1227]) ).
thf(1337,plain,
! [SV62: $i,SV208: $i > $o] :
( ( ( SV208 @ ( sK10_SY1478 @ SV208 @ SV62 ) )
= $true )
| ( ( ~ ~ ! [SY1479: $i] :
~ ~ ( ~ ( in @ SY1479 @ SV62 )
| ~ ( SV208 @ SY1479 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1228]) ).
thf(1338,plain,
! [SV210: $i,SV64: $i > $i > $o] :
( ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true )
| ( ( ~ ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1229]) ).
thf(1339,plain,
! [SV210: $i,SV64: $i > $i > $o] :
( ( ( ! [SY1652: $i] :
~ ~ ( ~ ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SY1652 )
| ~ ! [SY1653: $i] :
( ~ ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SY1653 )
| ( SY1652 = SY1653 ) ) ) )
= $true )
| ( ( ~ ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1230]) ).
thf(1340,plain,
! [SV67: $i,SV213: $i,SV309: $i] :
( ( ( in @ SV309 @ SV213 )
= $false )
| ( ( ~ ( in @ SV309 @ ( symdiff @ SV67 @ SV213 ) ) )
= $true )
| ( ( in @ SV309 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1341,plain,
! [SV70: $i,SV216: $i > $o] :
( ( ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
= $true )
| ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) )
| ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1234]) ).
thf(1342,plain,
! [SV70: $i,SV216: $i > $o] :
( ( ( ~ ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
| ~ ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
| ~ ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
| ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) ) )
= $false )
| ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) )
| ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1235]) ).
thf(1343,plain,
! [SV71: $i,SV310: $i,SV217: $i > $o] :
( ( ( SV217 @ SV310 )
= $false )
| ( ( in @ SV310
@ ( dsetconstr @ SV71
@ ^ [SY1499: $i] : ( SV217 @ SY1499 ) ) )
= $true )
| ( ( in @ SV310 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1344,plain,
! [SV353: $o,SV72: $i,SV218: $i] :
( ( ( ! [SY1655: $i] :
( ~ ( in @ SV218 @ SY1655 )
| ~ ( in @ SY1655 @ SV72 )
| SV353 ) )
= $false )
| ( SV353 = $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1346,plain,
! [SV72: $i,SV218: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV218 @ SX0 )
| ~ ( in @ SX0 @ SV72 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1347,plain,
! [SV219: $i,SV74: $i,SV373: $i,SV354: $i] :
( ( ( SV354 != SV373 )
= $true )
| ( ( ~ ( in @ SV354 @ SV74 )
| ( in @ SV373 @ SV219 ) )
= $true )
| ( ( SV74 = SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1348,plain,
! [SV220: $i > $o,SV75: $i,SV374: $i] :
( ( ( ~ ( ~ ( in @ SV374
@ ( dsetconstr @ SV75
@ ^ [SY1505: $i] : ( SV220 @ SY1505 ) ) )
| ( ( dsetconstr @ SV75
@ ^ [SY1506: $i] : ( SV220 @ SY1506 ) )
!= ( setadjoin @ SV374 @ emptyset ) ) ) )
= $false )
| ( ( ~ ! [SY1507: $i] :
~ ~ ( ~ ( in @ SY1507 @ SV75 )
| ~ ( SV220 @ SY1507 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1349,plain,
! [SV77: $i,SV311: $i,SV221: $i,SV375: $i] :
( ( ( ~ ( in @ SV375 @ SV221 ) )
= $true )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV311 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV311 @ ( setadjoin @ SV375 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV77 @ SV221 ) ) )
= $true )
| ( ( in @ SV311 @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1350,plain,
! [SV79: $i,SV223: $i,SV312: $i] :
( ( ( ~ ( in @ SV312 @ SV223 ) )
= $true )
| ( ( in @ SV312 @ ( symdiff @ SV79 @ SV223 ) )
= $true )
| ( ( in @ SV312 @ SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1243]) ).
thf(1351,plain,
! [SV224: $i,SV80: $i,SV376: $i,SV355: $i] :
( ( ( SV355 != SV376 )
= $true )
| ( ( ( setadjoin @ SV80 @ SV355 )
= ( setadjoin @ SV224 @ SV376 ) )
= $true )
| ( ( SV80 = SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1244]) ).
thf(1352,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ( sK13_SY1513 @ SV228 @ SV85 )
!= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1245]) ).
thf(1353,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
| ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) ) )
| ~ ( ~ ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
| ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1245]) ).
thf(1354,plain,
! [SV86: $i,SV229: $i] :
( ( ( in @ ( sK14_SY1523 @ SV229 @ SV86 ) @ SV86 )
= $true )
| ( ( subset @ SV86 @ SV229 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1246]) ).
thf(1355,plain,
! [SV87: $i,SV313: $i,SV230: $i,SV377: $i] :
( ( ( ~ ( in @ SV377 @ SV230 ) )
= $true )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV313 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV313 @ ( setadjoin @ SV377 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV87 @ SV230 ) ) ) )
= $true )
| ( ( in @ SV313 @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1248]) ).
thf(1356,plain,
! [SV89: $i,SV232: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV89 )
| ~ ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV232 ) ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1249]) ).
thf(1357,plain,
! [SV356: $i,SV90: $i > $o] :
( ( ( ~ ( SV90 @ SV356 )
| ~ ! [SY1659: $i] :
( ~ ( SV90 @ SY1659 )
| ( SV356 = SY1659 ) ) )
= $true )
| ( ( ~ ! [SY1266: $i] :
~ ! [SY1267: $i] :
~ ( ~ ( ~ ( SV90 @ SY1267 )
| ( SY1267 = SY1266 ) )
| ~ ( ( SY1267 != SY1266 )
| ( SV90 @ SY1267 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1250]) ).
thf(1358,plain,
! [SV233: $i,SV378: $o,SV91: $i,SV315: $i] :
( ( ( ~ ( ( SV315 != SV91 )
| SV378 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV315 @ SV233 )
| SV378 )
| SV378 )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1251]) ).
thf(1360,plain,
! [SV233: $i,SV91: $i,SV315: $i] :
( ( ( ~ ( ( SV315 != SV91 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV315 @ SV233 )
| $false )
| $false )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1253]) ).
thf(1361,plain,
! [SV92: $i,SV234: $i > $o] :
( ( ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
= $true )
| ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) )
| ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1254]) ).
thf(1362,plain,
! [SV92: $i,SV234: $i > $o] :
( ( ( ~ ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
| ~ ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
| ~ ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
| ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) ) )
= $false )
| ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) )
| ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1255]) ).
thf(1363,plain,
! [SV95: $i,SV318: $i,SV237: $i,SV379: $i] :
( ( ( ~ ( in @ SV379 @ SV237 ) )
= $true )
| ( ( in @ ( setadjoin @ SV318 @ ( setadjoin @ SV379 @ emptyset ) ) @ ( powerset @ ( binunion @ SV95 @ SV237 ) ) )
= $true )
| ( ( in @ SV318 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1364,plain,
! [SV238: $i,SV96: $i,SV319: $i] :
( ( ( ~ ( in @ SV319 @ ( setadjoin @ SV96 @ SV238 ) ) )
= $true )
| ( ( ( SV319 = SV96 )
| ( in @ SV319 @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1258]) ).
thf(1365,plain,
! [SV238: $i,SV96: $i,SV319: $i] :
( ( ( ~ ( ( SV319 = SV96 )
| ( in @ SV319 @ SV238 ) ) )
= $true )
| ( ( in @ SV319 @ ( setadjoin @ SV96 @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1259]) ).
thf(1366,plain,
! [SV239: $i,SV97: $i,SV320: $i] :
( ( ( ~ ( in @ SV320 @ SV97 ) )
= $true )
| ( ( in @ SV320 @ SV239 )
= $true )
| ( ( in @ SV320 @ ( setminus @ SV97 @ SV239 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1260]) ).
thf(1367,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
| ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 ) )
| ~ ( ( ( sK28_SY1661 @ SV357 @ SV98 )
!= SV357 )
| ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) ) ) ) )
= $false )
| ( ( ~ ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1261]) ).
thf(1368,plain,
! [SV321: $i,SV100: $i,SV241: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ ( setunion @ SV321 ) )
| ~ ~ ! [SY1676: $i] :
~ ~ ( ~ ( in @ SY1676 @ ( setunion @ SV321 ) )
| ( SV321
!= ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ ( setadjoin @ SY1676 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false )
| ( ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1262]) ).
thf(1369,plain,
! [SV103: $i,SV244: $i,SV324: $i] :
( ( ( ~ ( in @ SV324 @ SV244 ) )
= $false )
| ( ( SV103 != SV244 )
= $true )
| ( ( in @ SV324 @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1370,plain,
! [SV104: $i,SV245: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK30_SY1550 @ SV245 @ SV104 ) @ SV104 )
| ~ ( SV245 @ ( sK30_SY1550 @ SV245 @ SV104 ) ) ) )
= $false )
| ( ( ! [SY1551: $i] :
( ~ ( in @ SY1551 @ SV104 )
| ~ ( SV245 @ SY1551 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1264]) ).
thf(1371,plain,
! [SV108: $i,SV358: $i] :
( ( ( ~ ( in @ SV358 @ ( setunion @ SV108 ) )
| ~ ~ ! [SY1662: $i] :
~ ~ ( ~ ( in @ SY1662 @ ( setunion @ SV108 ) )
| ( SV108
!= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SY1662 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( ~ ! [SY1316: $i] :
~ ~ ( ~ ( in @ SY1316
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ SY1316 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1267]) ).
thf(1372,plain,
! [SV109: $i,SV249: $i,SV327: $i] :
( ( ( ~ ( in @ SV327 @ SV249 ) )
= $false )
| ( ( ~ ( in @ SV327 @ SV109 ) )
= $true )
| ( ( subset @ SV109 @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1373,plain,
! [SV111: $i,SV328: $i,SV250: $i,SV380: $i] :
( ( ( ~ ( in @ SV380 @ SV250 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV328 @ ( setadjoin @ SV380 @ emptyset ) ) @ ( binunion @ SV111 @ SV250 ) )
= $true )
| ( ( in @ SV328 @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1269]) ).
thf(1374,plain,
! [SV381: $o,SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ( ~ ( in @ SV329 @ SV113 )
| ~ ~ ( in @ SV329 @ SV254 )
| SV381 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| SV381 )
| SV381 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1270]) ).
thf(1376,plain,
! [SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ( ~ ( in @ SV329 @ SV113 )
| ~ ~ ( in @ SV329 @ SV254 )
| $false ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| $false )
| $false )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1272]) ).
thf(1377,plain,
! [SV256: $i,SV116: $i,SV331: $i] :
( ( ( in @ SV331 @ SV116 )
= $false )
| ( ( in @ SV331 @ SV256 )
= $true )
| ( ( subset @ SV116 @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1273]) ).
thf(1378,plain,
! [SV258: $i,SV118: $i,SV382: $i,SV359: $i] :
( ( ( SV359 != SV382 )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV359 @ SV118 )
| ( in @ SV382 @ SV258 ) )
| ~ ( ~ ( in @ SV382 @ SV258 )
| ( in @ SV359 @ SV118 ) ) ) )
= $true )
| ( ( SV118 = SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1274]) ).
thf(1379,plain,
! [SV259: $i > $o,SV119: $i,SV383: $i] :
( ( ( ~ ( in @ SV383 @ SV119 ) )
= $true )
| ( ( SV259 @ SV383 )
= $true )
| ( ( ~ ! [SY1564: $i] :
~ ~ ( ~ ( in @ SY1564 @ SV119 )
| ~ ~ ( SV259 @ SY1564 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1380,plain,
! [SV260: $i,SV120: $i] :
( ( ( in @ ( sK16_SY1565 @ SV120 @ SV260 ) @ SV260 )
= $true )
| ( ( in @ SV260 @ ( powerset @ SV120 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1276]) ).
thf(1381,plain,
! [SV121: $i,SV261: $i,SV332: $i] :
( ( ( ~ ( in @ SV332 @ SV261 ) )
= $false )
| ( ( in @ SV332 @ ( symdiff @ SV121 @ SV261 ) )
= $true )
| ( ( in @ SV332 @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1382,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ~ ( SV124 @ SV360 )
| ~ ! [SY1664: $i] :
( ~ ( SV124 @ SY1664 )
| ( SV360 = SY1664 ) ) )
= $true )
| ( ( ~ ! [SY1348: $i] :
~ ~ ( ~ ( SV124 @ SY1348 )
| ~ ! [SY1349: $i] :
( ~ ( SV124 @ SY1349 )
| ( SY1348 = SY1349 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1279]) ).
thf(1383,plain,
! [SV125: $i,SV264: $i,SV333: $i] :
( ( ( ~ ~ ( in @ SV333 @ SV264 ) )
= $true )
| ( ( ~ ( in @ SV333 @ ( symdiff @ SV125 @ SV264 ) ) )
= $true )
| ( ( in @ SV333 @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1280]) ).
thf(1384,plain,
! [SV126: $i,SV265: $i] :
( ( ( in @ SV265 @ ( setunion @ SV126 ) )
= $false )
| ( ( ~ ! [SY1568: $i] :
~ ~ ( ~ ( in @ SV265 @ SY1568 )
| ~ ( in @ SY1568 @ SV126 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1385,plain,
! [SV126: $i,SV265: $i] :
( ( ( ~ ! [SY1569: $i] :
~ ~ ( ~ ( in @ SV265 @ SY1569 )
| ~ ( in @ SY1569 @ SV126 ) ) )
= $false )
| ( ( in @ SV265 @ ( setunion @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1386,plain,
! [SV361: $i,SV127: $i] :
( ( ( SV127 = emptyset )
= $false )
| ( ( in @ SV361 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1283]) ).
thf(1387,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ! [SY1359: $i,SY1360: $i] :
( ~ ( SV130 @ SY1359 )
| ~ ( SV130 @ SY1360 )
| ( SY1359 = SY1360 ) ) )
= $true )
| ( ( ~ ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1284]) ).
thf(1388,plain,
! [SV136: $i,SV271: $i,SV335: $i] :
( ( ( ~ ~ ( in @ SV335 @ SV271 ) )
= $true )
| ( ( ~ ( in @ SV335 @ SV136 ) )
= $true )
| ( ( in @ SV335 @ ( setminus @ SV136 @ SV271 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1285]) ).
thf(1389,plain,
! [SV363: $i,SV137: $i > $o] :
( ( ( ~ ( SV137 @ SV363 )
| ~ ! [SY1665: $i] :
( ~ ( SV137 @ SY1665 )
| ( SV363 = SY1665 ) ) )
= $true )
| ( ( ~ ! [SY1372: $i] :
~ ( SV137 @ SY1372 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1286]) ).
thf(1390,plain,
! [SV138: $i] :
( ( ( ! [SY1373: $i] :
( ~ ~ ( ~ ( in @ SY1373 @ omega )
| ~ ( in @ SY1373 @ SV138 ) )
| ( in @ ( setadjoin @ SY1373 @ SY1373 ) @ SV138 ) ) )
= $false )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( ! [SY1374: $i] :
( ~ ( in @ SY1374 @ omega )
| ( in @ SY1374 @ SV138 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1391,plain,
! [SV139: $i,SV336: $i,SV272: $i] :
( ( ( subset @ SV272 @ SV336 )
= $false )
| ( ( subset @ SV139 @ SV336 )
= $true )
| ( ( subset @ SV139 @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1392,plain,
! [SV140: $i,SV273: $i] :
( ( ( in @ SV273 @ ( powerset @ SV140 ) )
= $false )
| ( ( ! [SY1573: $i] :
( ~ ( in @ SY1573 @ SV273 )
| ( in @ SY1573 @ SV140 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1393,plain,
! [SV140: $i,SV273: $i] :
( ( ( ! [SY1574: $i] :
( ~ ( in @ SY1574 @ SV273 )
| ( in @ SY1574 @ SV140 ) ) )
= $false )
| ( ( in @ SV273 @ ( powerset @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1290]) ).
thf(1394,plain,
! [SV141: $i,SV274: $i] :
( ( ( in @ ( sK17_SY1575 @ SV274 @ SV141 ) @ SV141 )
= $true )
| ( ( subset @ SV141 @ SV274 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1291]) ).
thf(1395,plain,
! [SV364: $i,SV142: $i] :
( ( ( ! [SY1383: $i] :
~ ~ ( ~ ( in @ SY1383 @ SV142 )
| ~ ~ ~ ! [SY1384: $i] :
~ ~ ( ~ ( in @ SY1384 @ SY1383 )
| ~ ( in @ SY1384 @ SV142 ) ) ) )
= $false )
| ( ( in @ SV364 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1396,plain,
! [SV143: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_SY1385 @ SV143 ) @ SV143 )
| ~ $true ) )
= $true )
| ( ( SV143 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1294]) ).
thf(1397,plain,
! [SV144: $i > $o,SV275: $i > $o] :
( ( ( ( sK18_SY1576 @ SV275 @ SV144 )
!= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1295]) ).
thf(1398,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
| ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) ) )
| ~ ( ~ ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
| ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1295]) ).
thf(1399,plain,
! [SV277: $i > $o,SV146: $i,SV337: $i] :
( ( ( ~ ( ~ ( in @ SV337
@ ( dsetconstr @ SV146
@ ^ [SY1585: $i] : ( SV277 @ SY1585 ) ) )
| ( SV277 @ SV337 ) ) )
= $false )
| ( ( in @ SV337 @ SV146 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1296]) ).
thf(1400,plain,
! [SV146: $i,SV337: $i,SV277: $i > $o] :
( ( ( ~ ( ~ ( SV277 @ SV337 )
| ( in @ SV337
@ ( dsetconstr @ SV146
@ ^ [SY1586: $i] : ( SV277 @ SY1586 ) ) ) ) )
= $false )
| ( ( in @ SV337 @ SV146 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1296]) ).
thf(1401,plain,
! [SV365: $i,SV148: $i > $o] :
( ( ( ~ ( SV148 @ SV365 )
| ~ ! [SY1667: $i] :
( ~ ( SV148 @ SY1667 )
| ( SV365 = SY1667 ) ) )
= $true )
| ( ( SV148
@ ( descr
@ ^ [SY1404: $i] : ( SV148 @ SY1404 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1297]) ).
thf(1402,plain,
! [SV151: $i,SV281: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK31_SY1588 @ SV281 @ SV151 ) @ SV151 )
| ~ ( SV281 @ ( sK31_SY1588 @ SV281 @ SV151 ) ) ) )
= $false )
| ( ( ! [SY1589: $i] :
( ~ ( in @ SY1589 @ SV151 )
| ~ ( SV281 @ SY1589 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1298]) ).
thf(1403,plain,
! [SV154: $i,SV284: $i,SV340: $i] :
( ( ( subset @ SV340 @ SV284 )
= $false )
| ( ( subset @ SV340 @ ( binintersect @ SV154 @ SV284 ) )
= $true )
| ( ( subset @ SV340 @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1404,plain,
! [SV366: $i,SV159: $i > $o] :
( ( ( ~ ( SV159 @ SV366 )
| ~ ! [SY1668: $i] :
( ~ ( SV159 @ SY1668 )
| ( SV366 = SY1668 ) ) )
= $true )
| ( ( ! [SY1422: $i,SY1423: $i] :
( ~ ( SV159 @ SY1422 )
| ~ ( SV159 @ SY1423 )
| ( SY1422 = SY1423 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1303]) ).
thf(1405,plain,
! [SV161: $i,SV289: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_SY1595 @ SV289 @ SV161 ) @ SV161 )
| ~ ( in @ SV289 @ ( sK23_SY1595 @ SV289 @ SV161 ) ) ) )
= $true )
| ( ( in @ SV289 @ ( setunion @ SV161 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1304]) ).
thf(1406,plain,
! [SV162: $i,SV344: $i,SV290: $i > $o] :
( ( ( SV290 @ SV344 )
= $false )
| ( ( ~ ! [SY1639: $i] :
( ~ ( in @ SY1639 @ SV162 )
| ~ ( SV290 @ SY1639 )
| ( SY1639 = SV344 ) )
| ~ ! [SY1598: $i] :
~ ~ ( ~ ( in @ SY1598
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ SY1598 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1407,plain,
! [SV367: $i > $o,SV349: $i > $o,SV180: $i,SV29: $i] :
( ( ( ! [SY1669: $i] :
( ~ ( in @ SY1669 @ SV29 )
| ! [SY1670: $i] :
( ~ ( in @ SY1670 @ SV180 )
| ( SY1669 != SY1670 )
| ~ ( ~ ( ~ ( SV349 @ SY1669 )
| ( SV367 @ SY1670 ) )
| ~ ( ~ ( SV367 @ SY1670 )
| ( SV349 @ SY1669 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1408,plain,
! [SV30: $i,SV350: $i] :
( ( ( ~ ( in @ SV350 @ SV30 ) )
= $true )
| ( ( SV30
!= ( setadjoin @ SV350 @ emptyset ) )
= $true )
| ( ( in @ ( setunion @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1307]) ).
thf(1409,plain,
! [SV181: $i > $o,SV31: $i,SV368: $i] :
( ( ( ~ ( in @ SV368 @ SV31 )
| ~ ( SV181 @ SV368 ) )
= $true )
| ( ( ( ( dsetconstr @ SV31
@ ^ [SY1444: $i] : ( SV181 @ SY1444 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1308]) ).
thf(1410,plain,
! [SV35: $i] :
( ( ~ ~ ( ~ ! [SY1601: $i] :
( ~ ( in @ SY1601 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SY1601 )
| ( in @ SY1111 @ SV35 ) ) )
| ~ ! [SY1603: $i,SY1604: $i] :
( ~ ~ ( ~ ( in @ SY1603 @ SV35 )
| ~ ( in @ SY1604 @ SV35 ) )
| ~ ! [SY1605: $i] :
( ~ ( in @ SY1605 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SY1603 @ SY1605 )
| ( in @ SY1604 @ SY1605 ) )
| ~ ( ~ ( in @ SY1604 @ SY1605 )
| ( in @ SY1603 @ SY1605 ) ) ) )
| ( SY1603 = SY1604 ) ) )
| ~ ! [SY1606: $i,SY1607: $i] :
( ~ ~ ( ~ ( in @ SY1606 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1607 @ ( sK2_SY1109 @ SV35 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1606 )
| ( in @ SX4 @ SY1607 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1607 )
| ( in @ SX4 @ SY1606 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1411,plain,
! [SV35: $i,SV384: $i] :
( ( ~ ~ ( ~ ! [SY1677: $i] :
( ~ ( in @ SY1677 @ SV384 )
| ( in @ SY1677 @ SV35 ) )
| ~ ~ ! [SY1678: $i] :
~ ( in @ SY1678 @ SV384 ) )
| ~ ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1412,plain,
! [SV351: $i,SV37: $i > $o] :
( ( ( ~ ( SV37 @ SV351 ) )
= $true )
| ( ( ~ ! [SY1650: $i] :
( ~ ( SV37 @ SY1650 )
| ( SV351 = SY1650 ) ) )
= $true )
| ( ( ! [SY1130: $i,SY1131: $i] :
( ~ ( SV37 @ SY1130 )
| ~ ( SV37 @ SY1131 )
| ( SY1130 = SY1131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1312]) ).
thf(1413,plain,
! [SV186: $i > $o,SV38: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV38 )
| ~ ~ ( SV186 @ SV369 ) )
= $true )
| ( ( ~ ! [SY1449: $i] :
( ~ ( in @ SY1449 @ SV38 )
| ( SV186 @ SY1449 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1313]) ).
thf(1414,plain,
! [SV295: $i,SV187: $i > $o,SV39: $i] :
( ( ( ( dsetconstr @ SV39
@ ^ [SY1451: $i] : ( SV187 @ SY1451 ) )
= emptyset )
= $false )
| ( ( SV187 @ SV295 )
= $false )
| ( ( in @ SV295 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1314]) ).
thf(1415,plain,
! [SV40: $i,SV296: $i,SV188: $i,SV370: $i] :
( ( ( in @ SV370 @ SV188 )
= $false )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV296 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV296 @ ( setadjoin @ SV370 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SV40 @ SV188 ) )
= $true )
| ( ( in @ SV296 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1315]) ).
thf(1416,plain,
! [SV44: $i,SV192: $i,SV298: $i] :
( ( ( in @ SV298 @ SV192 )
= $true )
| ( ( ~ ( subset @ SV44 @ SV192 ) )
= $true )
| ( ( in @ SV298 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1316]) ).
thf(1417,plain,
! [SV193: $i > $o,SV45: $i,SV371: $i] :
( ( ( in @ SV371 @ SV45 )
= $false )
| ( ( SV193 @ SV371 )
= $true )
| ( ( ~ ! [SY1458: $i] :
~ ~ ( ~ ( in @ SY1458 @ SV45 )
| ~ ~ ( SV193 @ SY1458 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1317]) ).
thf(1418,plain,
! [SV48: $i,SV300: $i,SV196: $i,SV372: $i] :
( ( ( in @ SV372 @ SV196 )
= $false )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV300 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV300 @ ( setadjoin @ SV372 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV48 @ SV196 ) ) ) )
= $true )
| ( ( in @ SV300 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1419,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ SV352 ) )
= $true )
| ( ( ~ ! [SY1651: $i] :
( ~ ( SV50 @ SY1651 )
| ( SV352 = SY1651 ) ) )
= $true )
| ( ( ~ ! [SY1160: $i] :
~ ~ ( ~ ( SV50 @ SY1160 )
| ~ ! [SY1161: $i] :
( ~ ( SV50 @ SY1161 )
| ( SY1160 = SY1161 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1320]) ).
thf(1420,plain,
! [SV51: $i,SV198: $i] :
( ( ( ~ ! [SY1463: $i] :
( ~ ( in @ SY1463 @ SV198 )
| ( in @ SY1463 @ SV51 ) ) )
= $true )
| ( ( SV51 = SV198 )
= $true )
| ( ( in @ ( sK8_SY1462 @ SV198 @ SV51 ) @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1321]) ).
thf(1421,plain,
! [SV51: $i,SV198: $i] :
( ( ( ! [SY1463: $i] :
( ~ ( in @ SY1463 @ SV198 )
| ( in @ SY1463 @ SV51 ) ) )
= $false )
| ( ( SV51 = SV198 )
= $true )
| ( ( in @ ( sK8_SY1462 @ SV198 @ SV51 ) @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1322]) ).
thf(1422,plain,
! [SV53: $i,SV199: $i,SV301: $i] :
( ( ( in @ SV301 @ SV199 )
= $true )
| ( ( in @ SV301 @ ( setminus @ SV53 @ SV199 ) )
= $true )
| ( ( in @ SV301 @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1324]) ).
thf(1423,plain,
! [SV54: $i,SV200: $i] :
( ( in @ ( sK4_SY1465 @ SV200 @ SV54 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1325]) ).
thf(1424,plain,
! [SV200: $i,SV54: $i] :
( ( ~ ! [SY1643: $i] :
~ ~ ( ~ ( in @ SY1643 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ ( setadjoin @ SY1643 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1326]) ).
thf(1425,plain,
! [SV58: $i,SV204: $i,SV305: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ SV58 )
| ~ ~ ! [SY1675: $i] :
~ ~ ( ~ ( in @ SY1675 @ SV204 )
| ( SV305
!= ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ ( setadjoin @ SY1675 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true )
| ( ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1329]) ).
thf(1426,plain,
! [SV59: $i,SV205: $i] :
( ( ( ~ ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 )
| ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV205 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV205 )
| ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV205 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1427,plain,
! [SV206: $i,SV346: $o,SV60: $i,SV306: $i] :
( ( ( ~ ( in @ SV306 @ SV60 )
| SV346 )
= $false )
| ( ( ~ ( ~ ( in @ SV306 @ SV206 )
| SV346 )
| SV346 )
= $true )
| ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1429,plain,
! [SV206: $i,SV60: $i,SV306: $i] :
( ( ( ~ ( in @ SV306 @ SV60 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV306 @ SV206 )
| $false )
| $false )
= $true )
| ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1333]) ).
thf(1430,plain,
! [SV61: $i,SV207: $i] :
( ( in @ ( sK5_SY1476 @ SV207 @ SV61 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1431,plain,
! [SV207: $i,SV61: $i] :
( ( ~ ! [SY1644: $i] :
~ ~ ( ~ ( in @ SY1644 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ ( setadjoin @ SY1644 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1335]) ).
thf(1432,plain,
! [SV208: $i > $o,SV62: $i] :
( ( ( ~ ! [SY1479: $i] :
~ ~ ( ~ ( in @ SY1479 @ SV62 )
| ~ ( SV208 @ SY1479 ) ) )
= $false )
| ( ( in @ ( sK10_SY1478 @ SV208 @ SV62 ) @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1433,plain,
! [SV208: $i > $o,SV62: $i] :
( ( ( ~ ! [SY1479: $i] :
~ ~ ( ~ ( in @ SY1479 @ SV62 )
| ~ ( SV208 @ SY1479 ) ) )
= $false )
| ( ( SV208 @ ( sK10_SY1478 @ SV208 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1434,plain,
! [SV64: $i > $i > $o,SV210: $i] :
( ( ( ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $false )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1435,plain,
! [SV385: $i,SV210: $i,SV64: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
| ~ ! [SY1684: $i] :
( ~ ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SY1684 )
| ( SV385 = SY1684 ) ) ) )
= $true )
| ( ( ~ ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1436,plain,
! [SV213: $i,SV67: $i,SV309: $i] :
( ( ( in @ SV309 @ ( symdiff @ SV67 @ SV213 ) )
= $false )
| ( ( in @ SV309 @ SV213 )
= $false )
| ( ( in @ SV309 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1340]) ).
thf(1437,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1438,plain,
! [SV70: $i,SV216: $i > $o] :
( ( ( ~ ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 ) )
= $false )
| ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) )
| ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1342]) ).
thf(1439,plain,
! [SV70: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
| ~ ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
| ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) ) )
= $false )
| ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) )
| ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1342]) ).
thf(1440,plain,
! [SV72: $i,SV353: $o,SV218: $i] :
( ( ( ~ ( in @ SV218 @ ( sK32_SY1655 @ SV353 @ SV72 @ SV218 ) )
| ~ ( in @ ( sK32_SY1655 @ SV353 @ SV72 @ SV218 ) @ SV72 )
| SV353 )
= $false )
| ( SV353 = $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1344]) ).
thf(1442,plain,
! [SV72: $i,SV218: $i] :
( ( ( ~ ( in @ SV218 @ ( sK34_SX0 @ SV72 @ SV218 ) )
| ~ ( in @ ( sK34_SX0 @ SV72 @ SV218 ) @ SV72 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1346]) ).
thf(1443,plain,
! [SV219: $i,SV74: $i,SV373: $i,SV354: $i] :
( ( ( SV354 = SV373 )
= $false )
| ( ( ~ ( in @ SV354 @ SV74 )
| ( in @ SV373 @ SV219 ) )
= $true )
| ( ( SV74 = SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1347]) ).
thf(1444,plain,
! [SV220: $i > $o,SV75: $i,SV374: $i] :
( ( ( ~ ( in @ SV374
@ ( dsetconstr @ SV75
@ ^ [SY1505: $i] : ( SV220 @ SY1505 ) ) )
| ( ( dsetconstr @ SV75
@ ^ [SY1506: $i] : ( SV220 @ SY1506 ) )
!= ( setadjoin @ SV374 @ emptyset ) ) )
= $true )
| ( ( ~ ! [SY1507: $i] :
~ ~ ( ~ ( in @ SY1507 @ SV75 )
| ~ ( SV220 @ SY1507 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1348]) ).
thf(1445,plain,
! [SV77: $i,SV311: $i,SV221: $i,SV375: $i] :
( ( ( in @ SV375 @ SV221 )
= $false )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV311 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV311 @ ( setadjoin @ SV375 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV77 @ SV221 ) ) )
= $true )
| ( ( in @ SV311 @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1349]) ).
thf(1446,plain,
! [SV79: $i,SV223: $i,SV312: $i] :
( ( ( in @ SV312 @ SV223 )
= $false )
| ( ( in @ SV312 @ ( symdiff @ SV79 @ SV223 ) )
= $true )
| ( ( in @ SV312 @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1447,plain,
! [SV224: $i,SV80: $i,SV376: $i,SV355: $i] :
( ( ( SV355 = SV376 )
= $false )
| ( ( ( setadjoin @ SV80 @ SV355 )
= ( setadjoin @ SV224 @ SV376 ) )
= $true )
| ( ( SV80 = SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1448,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1352]) ).
thf(1449,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ( ~ ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
| ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) ) )
| ~ ( ~ ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
| ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1353]) ).
thf(1450,plain,
! [SV87: $i,SV313: $i,SV230: $i,SV377: $i] :
( ( ( in @ SV377 @ SV230 )
= $false )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV313 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV313 @ ( setadjoin @ SV377 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV87 @ SV230 ) ) ) )
= $true )
| ( ( in @ SV313 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1451,plain,
! [SV89: $i,SV232: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV89 )
| ~ ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV232 ) ) )
= $true )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1356]) ).
thf(1452,plain,
! [SV356: $i,SV90: $i > $o] :
( ( ( ~ ( SV90 @ SV356 ) )
= $true )
| ( ( ~ ! [SY1659: $i] :
( ~ ( SV90 @ SY1659 )
| ( SV356 = SY1659 ) ) )
= $true )
| ( ( ~ ! [SY1266: $i] :
~ ! [SY1267: $i] :
~ ( ~ ( ~ ( SV90 @ SY1267 )
| ( SY1267 = SY1266 ) )
| ~ ( ( SY1267 != SY1266 )
| ( SV90 @ SY1267 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1357]) ).
thf(1453,plain,
! [SV233: $i,SV378: $o,SV91: $i,SV315: $i] :
( ( ( ( SV315 != SV91 )
| SV378 )
= $false )
| ( ( ~ ( ~ ( in @ SV315 @ SV233 )
| SV378 )
| SV378 )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1455,plain,
! [SV233: $i,SV91: $i,SV315: $i] :
( ( ( ( SV315 != SV91 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV315 @ SV233 )
| $false )
| $false )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1456,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1361]) ).
thf(1457,plain,
! [SV92: $i,SV234: $i > $o] :
( ( ( ~ ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 ) )
= $false )
| ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) )
| ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1362]) ).
thf(1458,plain,
! [SV92: $i,SV234: $i > $o] :
( ( ( ~ ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
| ~ ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
| ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) ) )
= $false )
| ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) )
| ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1362]) ).
thf(1459,plain,
! [SV95: $i,SV318: $i,SV237: $i,SV379: $i] :
( ( ( in @ SV379 @ SV237 )
= $false )
| ( ( in @ ( setadjoin @ SV318 @ ( setadjoin @ SV379 @ emptyset ) ) @ ( powerset @ ( binunion @ SV95 @ SV237 ) ) )
= $true )
| ( ( in @ SV318 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1460,plain,
! [SV238: $i,SV96: $i,SV319: $i] :
( ( ( in @ SV319 @ ( setadjoin @ SV96 @ SV238 ) )
= $false )
| ( ( ( SV319 = SV96 )
| ( in @ SV319 @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1461,plain,
! [SV238: $i,SV96: $i,SV319: $i] :
( ( ( ( SV319 = SV96 )
| ( in @ SV319 @ SV238 ) )
= $false )
| ( ( in @ SV319 @ ( setadjoin @ SV96 @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1462,plain,
! [SV239: $i,SV97: $i,SV320: $i] :
( ( ( in @ SV320 @ SV97 )
= $false )
| ( ( in @ SV320 @ SV239 )
= $true )
| ( ( in @ SV320 @ ( setminus @ SV97 @ SV239 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1366]) ).
thf(1463,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ~ ( ~ ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
| ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 ) )
| ~ ( ( ( sK28_SY1661 @ SV357 @ SV98 )
!= SV357 )
| ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) ) ) )
= $true )
| ( ( ~ ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1367]) ).
thf(1464,plain,
! [SV321: $i,SV100: $i,SV241: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ ( setunion @ SV321 ) )
| ~ ~ ! [SY1676: $i] :
~ ~ ( ~ ( in @ SY1676 @ ( setunion @ SV321 ) )
| ( SV321
!= ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ ( setadjoin @ SY1676 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true )
| ( ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1368]) ).
thf(1465,plain,
! [SV103: $i,SV244: $i,SV324: $i] :
( ( ( in @ SV324 @ SV244 )
= $true )
| ( ( SV103 != SV244 )
= $true )
| ( ( in @ SV324 @ SV103 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1369]) ).
thf(1466,plain,
! [SV104: $i,SV245: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK30_SY1550 @ SV245 @ SV104 ) @ SV104 )
| ~ ( SV245 @ ( sK30_SY1550 @ SV245 @ SV104 ) ) ) )
= $true )
| ( ( ! [SY1551: $i] :
( ~ ( in @ SY1551 @ SV104 )
| ~ ( SV245 @ SY1551 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1370]) ).
thf(1467,plain,
! [SV108: $i,SV358: $i] :
( ( ( ~ ( in @ SV358 @ ( setunion @ SV108 ) ) )
= $true )
| ( ( ~ ~ ! [SY1662: $i] :
~ ~ ( ~ ( in @ SY1662 @ ( setunion @ SV108 ) )
| ( SV108
!= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SY1662 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( ~ ! [SY1316: $i] :
~ ~ ( ~ ( in @ SY1316
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ SY1316 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1371]) ).
thf(1468,plain,
! [SV109: $i,SV249: $i,SV327: $i] :
( ( ( in @ SV327 @ SV249 )
= $true )
| ( ( ~ ( in @ SV327 @ SV109 ) )
= $true )
| ( ( subset @ SV109 @ SV249 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1372]) ).
thf(1469,plain,
! [SV111: $i,SV328: $i,SV250: $i,SV380: $i] :
( ( ( in @ SV380 @ SV250 )
= $false )
| ( ( subset @ ( setadjoin @ SV328 @ ( setadjoin @ SV380 @ emptyset ) ) @ ( binunion @ SV111 @ SV250 ) )
= $true )
| ( ( in @ SV328 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1470,plain,
! [SV381: $o,SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ SV113 )
| ~ ~ ( in @ SV329 @ SV254 )
| SV381 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| SV381 )
| SV381 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1472,plain,
! [SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ SV113 )
| ~ ~ ( in @ SV329 @ SV254 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| $false )
| $false )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1473,plain,
! [SV258: $i,SV118: $i,SV382: $i,SV359: $i] :
( ( ( SV359 = SV382 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV359 @ SV118 )
| ( in @ SV382 @ SV258 ) )
| ~ ( ~ ( in @ SV382 @ SV258 )
| ( in @ SV359 @ SV118 ) ) ) )
= $true )
| ( ( SV118 = SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1474,plain,
! [SV259: $i > $o,SV119: $i,SV383: $i] :
( ( ( in @ SV383 @ SV119 )
= $false )
| ( ( SV259 @ SV383 )
= $true )
| ( ( ~ ! [SY1564: $i] :
~ ~ ( ~ ( in @ SY1564 @ SV119 )
| ~ ~ ( SV259 @ SY1564 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1475,plain,
! [SV121: $i,SV261: $i,SV332: $i] :
( ( ( in @ SV332 @ SV261 )
= $true )
| ( ( in @ SV332 @ ( symdiff @ SV121 @ SV261 ) )
= $true )
| ( ( in @ SV332 @ SV121 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1381]) ).
thf(1476,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ~ ( SV124 @ SV360 ) )
= $true )
| ( ( ~ ! [SY1664: $i] :
( ~ ( SV124 @ SY1664 )
| ( SV360 = SY1664 ) ) )
= $true )
| ( ( ~ ! [SY1348: $i] :
~ ~ ( ~ ( SV124 @ SY1348 )
| ~ ! [SY1349: $i] :
( ~ ( SV124 @ SY1349 )
| ( SY1348 = SY1349 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1477,plain,
! [SV125: $i,SV264: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ SV264 ) )
= $false )
| ( ( ~ ( in @ SV333 @ ( symdiff @ SV125 @ SV264 ) ) )
= $true )
| ( ( in @ SV333 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1478,plain,
! [SV126: $i,SV265: $i] :
( ( ( ! [SY1568: $i] :
~ ~ ( ~ ( in @ SV265 @ SY1568 )
| ~ ( in @ SY1568 @ SV126 ) ) )
= $false )
| ( ( in @ SV265 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1479,plain,
! [SV126: $i,SV265: $i] :
( ( ( ! [SY1569: $i] :
~ ~ ( ~ ( in @ SV265 @ SY1569 )
| ~ ( in @ SY1569 @ SV126 ) ) )
= $true )
| ( ( in @ SV265 @ ( setunion @ SV126 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1385]) ).
thf(1480,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ! [SY1359: $i,SY1360: $i] :
( ~ ( SV130 @ SY1359 )
| ~ ( SV130 @ SY1360 )
| ( SY1359 = SY1360 ) ) )
= $false )
| ( ( ~ ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1387]) ).
thf(1481,plain,
! [SV136: $i,SV271: $i,SV335: $i] :
( ( ( ~ ( in @ SV335 @ SV271 ) )
= $false )
| ( ( ~ ( in @ SV335 @ SV136 ) )
= $true )
| ( ( in @ SV335 @ ( setminus @ SV136 @ SV271 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1482,plain,
! [SV363: $i,SV137: $i > $o] :
( ( ( ~ ( SV137 @ SV363 ) )
= $true )
| ( ( ~ ! [SY1665: $i] :
( ~ ( SV137 @ SY1665 )
| ( SV363 = SY1665 ) ) )
= $true )
| ( ( ~ ! [SY1372: $i] :
~ ( SV137 @ SY1372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1483,plain,
! [SV138: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK35_SY1373 @ SV138 ) @ omega )
| ~ ( in @ ( sK35_SY1373 @ SV138 ) @ SV138 ) )
| ( in @ ( setadjoin @ ( sK35_SY1373 @ SV138 ) @ ( sK35_SY1373 @ SV138 ) ) @ SV138 ) )
= $false )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( ! [SY1374: $i] :
( ~ ( in @ SY1374 @ omega )
| ( in @ SY1374 @ SV138 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1390]) ).
thf(1484,plain,
! [SV140: $i,SV273: $i,SV386: $i] :
( ( ( ~ ( in @ SV386 @ SV273 )
| ( in @ SV386 @ SV140 ) )
= $true )
| ( ( in @ SV273 @ ( powerset @ SV140 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1485,plain,
! [SV273: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK36_SY1574 @ SV140 @ SV273 ) @ SV273 )
| ( in @ ( sK36_SY1574 @ SV140 @ SV273 ) @ SV140 ) )
= $false )
| ( ( in @ SV273 @ ( powerset @ SV140 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1393]) ).
thf(1486,plain,
! [SV142: $i,SV364: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK37_SY1383 @ SV364 @ SV142 ) @ SV142 )
| ~ ~ ~ ! [SY1685: $i] :
~ ~ ( ~ ( in @ SY1685 @ ( sK37_SY1383 @ SV364 @ SV142 ) )
| ~ ( in @ SY1685 @ SV142 ) ) ) )
= $false )
| ( ( in @ SV364 @ SV142 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1395]) ).
thf(1487,plain,
! [SV143: $i] :
( ( ( ~ ( in @ ( sK21_SY1385 @ SV143 ) @ SV143 )
| ~ $true )
= $false )
| ( ( SV143 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1488,plain,
! [SV144: $i > $o,SV275: $i > $o] :
( ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true )
| ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1397]) ).
thf(1489,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ( ~ ( ~ ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
| ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) ) )
| ~ ( ~ ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
| ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1398]) ).
thf(1490,plain,
! [SV277: $i > $o,SV146: $i,SV337: $i] :
( ( ( ~ ( in @ SV337
@ ( dsetconstr @ SV146
@ ^ [SY1585: $i] : ( SV277 @ SY1585 ) ) )
| ( SV277 @ SV337 ) )
= $true )
| ( ( in @ SV337 @ SV146 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1399]) ).
thf(1491,plain,
! [SV146: $i,SV337: $i,SV277: $i > $o] :
( ( ( ~ ( SV277 @ SV337 )
| ( in @ SV337
@ ( dsetconstr @ SV146
@ ^ [SY1586: $i] : ( SV277 @ SY1586 ) ) ) )
= $true )
| ( ( in @ SV337 @ SV146 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1400]) ).
thf(1492,plain,
! [SV365: $i,SV148: $i > $o] :
( ( ( ~ ( SV148 @ SV365 ) )
= $true )
| ( ( ~ ! [SY1667: $i] :
( ~ ( SV148 @ SY1667 )
| ( SV365 = SY1667 ) ) )
= $true )
| ( ( SV148
@ ( descr
@ ^ [SY1404: $i] : ( SV148 @ SY1404 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1401]) ).
thf(1493,plain,
! [SV151: $i,SV281: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK31_SY1588 @ SV281 @ SV151 ) @ SV151 )
| ~ ( SV281 @ ( sK31_SY1588 @ SV281 @ SV151 ) ) ) )
= $true )
| ( ( ! [SY1589: $i] :
( ~ ( in @ SY1589 @ SV151 )
| ~ ( SV281 @ SY1589 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1402]) ).
thf(1494,plain,
! [SV366: $i,SV159: $i > $o] :
( ( ( ~ ( SV159 @ SV366 ) )
= $true )
| ( ( ~ ! [SY1668: $i] :
( ~ ( SV159 @ SY1668 )
| ( SV366 = SY1668 ) ) )
= $true )
| ( ( ! [SY1422: $i,SY1423: $i] :
( ~ ( SV159 @ SY1422 )
| ~ ( SV159 @ SY1423 )
| ( SY1422 = SY1423 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1404]) ).
thf(1495,plain,
! [SV161: $i,SV289: $i] :
( ( ( ~ ( in @ ( sK23_SY1595 @ SV289 @ SV161 ) @ SV161 )
| ~ ( in @ SV289 @ ( sK23_SY1595 @ SV289 @ SV161 ) ) )
= $false )
| ( ( in @ SV289 @ ( setunion @ SV161 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1496,plain,
! [SV344: $i,SV290: $i > $o,SV162: $i] :
( ( ( ~ ! [SY1639: $i] :
( ~ ( in @ SY1639 @ SV162 )
| ~ ( SV290 @ SY1639 )
| ( SY1639 = SV344 ) ) )
= $true )
| ( ( ~ ! [SY1598: $i] :
~ ~ ( ~ ( in @ SY1598
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ SY1598 @ emptyset ) ) ) )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1497,plain,
! [SV29: $i,SV180: $i,SV349: $i > $o,SV367: $i > $o] :
( ( ( ~ ( in @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) @ SV29 )
| ! [SY1686: $i] :
( ~ ( in @ SY1686 @ SV180 )
| ( ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 )
!= SY1686 )
| ~ ( ~ ( ~ ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) )
| ( SV367 @ SY1686 ) )
| ~ ( ~ ( SV367 @ SY1686 )
| ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1407]) ).
thf(1498,plain,
! [SV30: $i,SV350: $i] :
( ( ( in @ SV350 @ SV30 )
= $false )
| ( ( SV30
!= ( setadjoin @ SV350 @ emptyset ) )
= $true )
| ( ( in @ ( setunion @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1499,plain,
! [SV181: $i > $o,SV31: $i,SV368: $i] :
( ( ( ~ ( in @ SV368 @ SV31 ) )
= $true )
| ( ( ~ ( SV181 @ SV368 ) )
= $true )
| ( ( ( ( dsetconstr @ SV31
@ ^ [SY1444: $i] : ( SV181 @ SY1444 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1500,plain,
! [SV35: $i] :
( ( ~ ~ ( ~ ! [SY1601: $i] :
( ~ ( in @ SY1601 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SY1601 )
| ( in @ SY1111 @ SV35 ) ) )
| ~ ! [SY1603: $i,SY1604: $i] :
( ~ ~ ( ~ ( in @ SY1603 @ SV35 )
| ~ ( in @ SY1604 @ SV35 ) )
| ~ ! [SY1605: $i] :
( ~ ( in @ SY1605 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SY1603 @ SY1605 )
| ( in @ SY1604 @ SY1605 ) )
| ~ ( ~ ( in @ SY1604 @ SY1605 )
| ( in @ SY1603 @ SY1605 ) ) ) )
| ( SY1603 = SY1604 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1410]) ).
thf(1501,plain,
! [SV35: $i] :
( ( ~ ! [SY1606: $i,SY1607: $i] :
( ~ ~ ( ~ ( in @ SY1606 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1607 @ ( sK2_SY1109 @ SV35 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1606 )
| ( in @ SX4 @ SY1607 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1607 )
| ( in @ SX4 @ SY1606 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1410]) ).
thf(1502,plain,
! [SV35: $i,SV384: $i] :
( ( ( ~ ~ ( ~ ! [SY1677: $i] :
( ~ ( in @ SY1677 @ SV384 )
| ( in @ SY1677 @ SV35 ) )
| ~ ~ ! [SY1678: $i] :
~ ( in @ SY1678 @ SV384 ) ) )
= $true )
| ( ( ~ ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1411]) ).
thf(1503,plain,
! [SV351: $i,SV37: $i > $o] :
( ( ( SV37 @ SV351 )
= $false )
| ( ( ~ ! [SY1650: $i] :
( ~ ( SV37 @ SY1650 )
| ( SV351 = SY1650 ) ) )
= $true )
| ( ( ! [SY1130: $i,SY1131: $i] :
( ~ ( SV37 @ SY1130 )
| ~ ( SV37 @ SY1131 )
| ( SY1130 = SY1131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1412]) ).
thf(1504,plain,
! [SV186: $i > $o,SV38: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV38 ) )
= $true )
| ( ( ~ ~ ( SV186 @ SV369 ) )
= $true )
| ( ( ~ ! [SY1449: $i] :
( ~ ( in @ SY1449 @ SV38 )
| ( SV186 @ SY1449 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1413]) ).
thf(1505,plain,
! [SV298: $i,SV192: $i,SV44: $i] :
( ( ( subset @ SV44 @ SV192 )
= $false )
| ( ( in @ SV298 @ SV192 )
= $true )
| ( ( in @ SV298 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1506,plain,
! [SV371: $i,SV193: $i > $o,SV45: $i] :
( ( ( ! [SY1458: $i] :
~ ~ ( ~ ( in @ SY1458 @ SV45 )
| ~ ~ ( SV193 @ SY1458 ) ) )
= $false )
| ( ( SV193 @ SV371 )
= $true )
| ( ( in @ SV371 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1417]) ).
thf(1507,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( SV50 @ SV352 )
= $false )
| ( ( ~ ! [SY1651: $i] :
( ~ ( SV50 @ SY1651 )
| ( SV352 = SY1651 ) ) )
= $true )
| ( ( ~ ! [SY1160: $i] :
~ ~ ( ~ ( SV50 @ SY1160 )
| ~ ! [SY1161: $i] :
( ~ ( SV50 @ SY1161 )
| ( SY1160 = SY1161 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1508,plain,
! [SV51: $i,SV198: $i] :
( ( ( ! [SY1463: $i] :
( ~ ( in @ SY1463 @ SV198 )
| ( in @ SY1463 @ SV51 ) ) )
= $false )
| ( ( SV51 = SV198 )
= $true )
| ( ( in @ ( sK8_SY1462 @ SV198 @ SV51 ) @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1420]) ).
thf(1509,plain,
! [SV198: $i,SV51: $i] :
( ( ( ~ ( in @ ( sK39_SY1463 @ SV51 @ SV198 ) @ SV198 )
| ( in @ ( sK39_SY1463 @ SV51 @ SV198 ) @ SV51 ) )
= $false )
| ( ( SV51 = SV198 )
= $true )
| ( ( in @ ( sK8_SY1462 @ SV198 @ SV51 ) @ SV198 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1421]) ).
thf(1510,plain,
! [SV200: $i,SV54: $i] :
( ( ! [SY1643: $i] :
~ ~ ( ~ ( in @ SY1643 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ ( setadjoin @ SY1643 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1511,plain,
! [SV58: $i,SV204: $i,SV305: $i] :
( ( ( ~ ( in @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ SV58 )
| ~ ~ ! [SY1675: $i] :
~ ~ ( ~ ( in @ SY1675 @ SV204 )
| ( SV305
!= ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ ( setadjoin @ SY1675 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false )
| ( ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1512,plain,
! [SV59: $i,SV205: $i] :
( ( ( ~ ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV205 )
| ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV205 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1513,plain,
! [SV59: $i,SV205: $i] :
( ( ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV205 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV205 )
| ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV205 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1514,plain,
! [SV346: $o,SV206: $i,SV60: $i,SV306: $i] :
( ( ( ~ ( in @ SV306 @ SV60 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV306 @ SV206 )
| SV346 )
| SV346 )
= $true )
| ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1427]) ).
thf(1518,plain,
! [SV206: $i,SV60: $i,SV306: $i] :
( ( ( ~ ( in @ SV306 @ SV60 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV306 @ SV206 )
| $false )
| $false )
= $true )
| ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1520,plain,
! [SV207: $i,SV61: $i] :
( ( ! [SY1644: $i] :
~ ~ ( ~ ( in @ SY1644 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ ( setadjoin @ SY1644 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1521,plain,
! [SV208: $i > $o,SV62: $i] :
( ( ( ! [SY1479: $i] :
~ ~ ( ~ ( in @ SY1479 @ SV62 )
| ~ ( SV208 @ SY1479 ) ) )
= $true )
| ( ( in @ ( sK10_SY1478 @ SV208 @ SV62 ) @ SV62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1432]) ).
thf(1522,plain,
! [SV208: $i > $o,SV62: $i] :
( ( ( ! [SY1479: $i] :
~ ~ ( ~ ( in @ SY1479 @ SV62 )
| ~ ( SV208 @ SY1479 ) ) )
= $true )
| ( ( SV208 @ ( sK10_SY1478 @ SV208 @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1433]) ).
thf(1523,plain,
! [SV210: $i,SV64: $i > $i > $o] :
( ( ( ~ ! [SY1687: $i] :
~ ( ~ ( ~ ( in @ SY1687 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1687 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1687 ) )
| ( in @ SY1687 @ ( sK40_SY1483 @ SV64 @ SV210 ) ) ) ) )
= $false )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1434]) ).
thf(1524,plain,
! [SV385: $i,SV210: $i,SV64: $i > $i > $o] :
( ( ( ~ ( ~ ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
| ~ ! [SY1684: $i] :
( ~ ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SY1684 )
| ( SV385 = SY1684 ) ) ) )
= $false )
| ( ( ~ ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1435]) ).
thf(1525,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ( ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) ) )
= $false )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1437]) ).
thf(1526,plain,
! [SV70: $i,SV216: $i > $o] :
( ( ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
= $true )
| ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) )
| ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1438]) ).
thf(1527,plain,
! [SV70: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) ) )
= $false )
| ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) )
| ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1528,plain,
! [SV70: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
| ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) ) )
= $false )
| ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) )
| ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1529,plain,
! [SV72: $i,SV353: $o,SV218: $i] :
( ( ( ~ ( in @ SV218 @ ( sK32_SY1655 @ SV353 @ SV72 @ SV218 ) ) )
= $false )
| ( SV353 = $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1530,plain,
! [SV218: $i,SV72: $i,SV353: $o] :
( ( ( ~ ( in @ ( sK32_SY1655 @ SV353 @ SV72 @ SV218 ) @ SV72 )
| SV353 )
= $false )
| ( SV353 = $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1533,plain,
! [SV72: $i,SV218: $i] :
( ( ( ~ ( in @ SV218 @ ( sK34_SX0 @ SV72 @ SV218 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1442]) ).
thf(1534,plain,
! [SV218: $i,SV72: $i] :
( ( ( ~ ( in @ ( sK34_SX0 @ SV72 @ SV218 ) @ SV72 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1442]) ).
thf(1535,plain,
! [SV219: $i,SV373: $i,SV74: $i,SV354: $i] :
( ( ( ~ ( in @ SV354 @ SV74 ) )
= $true )
| ( ( in @ SV373 @ SV219 )
= $true )
| ( ( SV354 = SV373 )
= $false )
| ( ( SV74 = SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1443]) ).
thf(1536,plain,
! [SV220: $i > $o,SV75: $i,SV374: $i] :
( ( ( ~ ( in @ SV374
@ ( dsetconstr @ SV75
@ ^ [SY1505: $i] : ( SV220 @ SY1505 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV75
@ ^ [SY1506: $i] : ( SV220 @ SY1506 ) )
!= ( setadjoin @ SV374 @ emptyset ) )
= $true )
| ( ( ~ ! [SY1507: $i] :
~ ~ ( ~ ( in @ SY1507 @ SV75 )
| ~ ( SV220 @ SY1507 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1444]) ).
thf(1537,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1538,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ( ~ ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
| ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
| ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1539,plain,
! [SV89: $i,SV232: $i] :
( ( ( ~ ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV89 )
| ~ ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV232 ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1540,plain,
! [SV356: $i,SV90: $i > $o] :
( ( ( SV90 @ SV356 )
= $false )
| ( ( ~ ! [SY1659: $i] :
( ~ ( SV90 @ SY1659 )
| ( SV356 = SY1659 ) ) )
= $true )
| ( ( ~ ! [SY1266: $i] :
~ ! [SY1267: $i] :
~ ( ~ ( ~ ( SV90 @ SY1267 )
| ( SY1267 = SY1266 ) )
| ~ ( ( SY1267 != SY1266 )
| ( SV90 @ SY1267 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1452]) ).
thf(1541,plain,
! [SV378: $o,SV233: $i,SV91: $i,SV315: $i] :
( ( ( SV315 != SV91 )
= $false )
| ( ( ~ ( ~ ( in @ SV315 @ SV233 )
| SV378 )
| SV378 )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1453]) ).
thf(1545,plain,
! [SV233: $i,SV91: $i,SV315: $i] :
( ( ( SV315 != SV91 )
= $false )
| ( ( ~ ( ~ ( in @ SV315 @ SV233 )
| $false )
| $false )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1455]) ).
thf(1547,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ( ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) ) )
= $false )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1456]) ).
thf(1548,plain,
! [SV92: $i,SV234: $i > $o] :
( ( ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
= $true )
| ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) )
| ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1457]) ).
thf(1549,plain,
! [SV92: $i,SV234: $i > $o] :
( ( ( ~ ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) ) )
= $false )
| ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) )
| ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1550,plain,
! [SV92: $i,SV234: $i > $o] :
( ( ( ~ ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
| ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) ) )
= $false )
| ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) )
| ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1551,plain,
! [SV238: $i,SV96: $i,SV319: $i] :
( ( ( SV319 = SV96 )
= $true )
| ( ( in @ SV319 @ SV238 )
= $true )
| ( ( in @ SV319 @ ( setadjoin @ SV96 @ SV238 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1460]) ).
thf(1552,plain,
! [SV238: $i,SV96: $i,SV319: $i] :
( ( ( SV319 = SV96 )
= $false )
| ( ( in @ SV319 @ ( setadjoin @ SV96 @ SV238 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1461]) ).
thf(1553,plain,
! [SV96: $i,SV238: $i,SV319: $i] :
( ( ( in @ SV319 @ SV238 )
= $false )
| ( ( in @ SV319 @ ( setadjoin @ SV96 @ SV238 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1461]) ).
thf(1554,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ~ ( ~ ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
| ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 ) ) )
= $true )
| ( ( ~ ( ( ( sK28_SY1661 @ SV357 @ SV98 )
!= SV357 )
| ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) ) ) )
= $true )
| ( ( ~ ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1463]) ).
thf(1555,plain,
! [SV321: $i,SV100: $i,SV241: $i] :
( ( ( ~ ( in @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ ( setunion @ SV321 ) )
| ~ ~ ! [SY1676: $i] :
~ ~ ( ~ ( in @ SY1676 @ ( setunion @ SV321 ) )
| ( SV321
!= ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ ( setadjoin @ SY1676 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false )
| ( ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1464]) ).
thf(1556,plain,
! [SV324: $i,SV244: $i,SV103: $i] :
( ( ( SV103 = SV244 )
= $false )
| ( ( in @ SV324 @ SV244 )
= $true )
| ( ( in @ SV324 @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1557,plain,
! [SV104: $i,SV245: $i > $o] :
( ( ( ~ ( in @ ( sK30_SY1550 @ SV245 @ SV104 ) @ SV104 )
| ~ ( SV245 @ ( sK30_SY1550 @ SV245 @ SV104 ) ) )
= $false )
| ( ( ! [SY1551: $i] :
( ~ ( in @ SY1551 @ SV104 )
| ~ ( SV245 @ SY1551 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1558,plain,
! [SV108: $i,SV358: $i] :
( ( ( in @ SV358 @ ( setunion @ SV108 ) )
= $false )
| ( ( ~ ~ ! [SY1662: $i] :
~ ~ ( ~ ( in @ SY1662 @ ( setunion @ SV108 ) )
| ( SV108
!= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SY1662 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( ~ ! [SY1316: $i] :
~ ~ ( ~ ( in @ SY1316
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ SY1316 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1559,plain,
! [SV249: $i,SV109: $i,SV327: $i] :
( ( ( in @ SV327 @ SV109 )
= $false )
| ( ( in @ SV327 @ SV249 )
= $true )
| ( ( subset @ SV109 @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1468]) ).
thf(1560,plain,
! [SV381: $o,SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ SV113 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| SV381 )
| SV381 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1470]) ).
thf(1561,plain,
! [SV113: $i,SV381: $o,SV254: $i,SV329: $i] :
( ( ( ~ ~ ( in @ SV329 @ SV254 )
| SV381 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| SV381 )
| SV381 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1470]) ).
thf(1564,plain,
! [SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ SV113 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| $false )
| $false )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1565,plain,
! [SV113: $i,SV254: $i,SV329: $i] :
( ( ( ~ ~ ( in @ SV329 @ SV254 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| $false )
| $false )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1566,plain,
! [SV258: $i,SV382: $i,SV118: $i,SV359: $i] :
( ( ( ~ ( ~ ( in @ SV359 @ SV118 )
| ( in @ SV382 @ SV258 ) )
| ~ ( ~ ( in @ SV382 @ SV258 )
| ( in @ SV359 @ SV118 ) ) )
= $false )
| ( ( SV359 = SV382 )
= $false )
| ( ( SV118 = SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1567,plain,
! [SV383: $i,SV259: $i > $o,SV119: $i] :
( ( ( ! [SY1564: $i] :
~ ~ ( ~ ( in @ SY1564 @ SV119 )
| ~ ~ ( SV259 @ SY1564 ) ) )
= $false )
| ( ( SV259 @ SV383 )
= $true )
| ( ( in @ SV383 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1568,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( SV124 @ SV360 )
= $false )
| ( ( ~ ! [SY1664: $i] :
( ~ ( SV124 @ SY1664 )
| ( SV360 = SY1664 ) ) )
= $true )
| ( ( ~ ! [SY1348: $i] :
~ ~ ( ~ ( SV124 @ SY1348 )
| ~ ! [SY1349: $i] :
( ~ ( SV124 @ SY1349 )
| ( SY1348 = SY1349 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1569,plain,
! [SV125: $i,SV264: $i,SV333: $i] :
( ( ( in @ SV333 @ SV264 )
= $true )
| ( ( ~ ( in @ SV333 @ ( symdiff @ SV125 @ SV264 ) ) )
= $true )
| ( ( in @ SV333 @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1477]) ).
thf(1570,plain,
! [SV126: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ( in @ SV265 @ ( sK41_SY1568 @ SV126 @ SV265 ) )
| ~ ( in @ ( sK41_SY1568 @ SV126 @ SV265 ) @ SV126 ) ) )
= $false )
| ( ( in @ SV265 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1478]) ).
thf(1571,plain,
! [SV126: $i,SV387: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ( in @ SV265 @ SV387 )
| ~ ( in @ SV387 @ SV126 ) ) )
= $true )
| ( ( in @ SV265 @ ( setunion @ SV126 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1572,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ! [SY1690: $i] :
( ~ ( SV130 @ ( sK42_SY1359 @ SV362 @ SV130 ) )
| ~ ( SV130 @ SY1690 )
| ( ( sK42_SY1359 @ SV362 @ SV130 )
= SY1690 ) ) )
= $false )
| ( ( ~ ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1480]) ).
thf(1573,plain,
! [SV136: $i,SV271: $i,SV335: $i] :
( ( ( in @ SV335 @ SV271 )
= $true )
| ( ( ~ ( in @ SV335 @ SV136 ) )
= $true )
| ( ( in @ SV335 @ ( setminus @ SV136 @ SV271 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1481]) ).
thf(1574,plain,
! [SV363: $i,SV137: $i > $o] :
( ( ( SV137 @ SV363 )
= $false )
| ( ( ~ ! [SY1665: $i] :
( ~ ( SV137 @ SY1665 )
| ( SV363 = SY1665 ) ) )
= $true )
| ( ( ~ ! [SY1372: $i] :
~ ( SV137 @ SY1372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1575,plain,
! [SV138: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK35_SY1373 @ SV138 ) @ omega )
| ~ ( in @ ( sK35_SY1373 @ SV138 ) @ SV138 ) ) )
= $false )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( ! [SY1374: $i] :
( ~ ( in @ SY1374 @ omega )
| ( in @ SY1374 @ SV138 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1576,plain,
! [SV138: $i] :
( ( ( in @ ( setadjoin @ ( sK35_SY1373 @ SV138 ) @ ( sK35_SY1373 @ SV138 ) ) @ SV138 )
= $false )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( ! [SY1374: $i] :
( ~ ( in @ SY1374 @ omega )
| ( in @ SY1374 @ SV138 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1577,plain,
! [SV140: $i,SV273: $i,SV386: $i] :
( ( ( ~ ( in @ SV386 @ SV273 ) )
= $true )
| ( ( in @ SV386 @ SV140 )
= $true )
| ( ( in @ SV273 @ ( powerset @ SV140 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1484]) ).
thf(1578,plain,
! [SV273: $i,SV140: $i] :
( ( ( ~ ( in @ ( sK36_SY1574 @ SV140 @ SV273 ) @ SV273 ) )
= $false )
| ( ( in @ SV273 @ ( powerset @ SV140 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1579,plain,
! [SV273: $i,SV140: $i] :
( ( ( in @ ( sK36_SY1574 @ SV140 @ SV273 ) @ SV140 )
= $false )
| ( ( in @ SV273 @ ( powerset @ SV140 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1580,plain,
! [SV142: $i,SV364: $i] :
( ( ( ~ ( ~ ( in @ ( sK37_SY1383 @ SV364 @ SV142 ) @ SV142 )
| ~ ~ ~ ! [SY1685: $i] :
~ ~ ( ~ ( in @ SY1685 @ ( sK37_SY1383 @ SV364 @ SV142 ) )
| ~ ( in @ SY1685 @ SV142 ) ) ) )
= $true )
| ( ( in @ SV364 @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1486]) ).
thf(1581,plain,
! [SV143: $i] :
( ( ( ~ ( in @ ( sK21_SY1385 @ SV143 ) @ SV143 ) )
= $false )
| ( ( SV143 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1487]) ).
thf(1583,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1488]) ).
thf(1584,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ( ~ ( ~ ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
| ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
| ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1489]) ).
thf(1585,plain,
! [SV277: $i > $o,SV146: $i,SV337: $i] :
( ( ( ~ ( in @ SV337
@ ( dsetconstr @ SV146
@ ^ [SY1585: $i] : ( SV277 @ SY1585 ) ) ) )
= $true )
| ( ( SV277 @ SV337 )
= $true )
| ( ( in @ SV337 @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1490]) ).
thf(1586,plain,
! [SV146: $i,SV337: $i,SV277: $i > $o] :
( ( ( ~ ( SV277 @ SV337 ) )
= $true )
| ( ( in @ SV337
@ ( dsetconstr @ SV146
@ ^ [SY1586: $i] : ( SV277 @ SY1586 ) ) )
= $true )
| ( ( in @ SV337 @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1491]) ).
thf(1587,plain,
! [SV365: $i,SV148: $i > $o] :
( ( ( SV148 @ SV365 )
= $false )
| ( ( ~ ! [SY1667: $i] :
( ~ ( SV148 @ SY1667 )
| ( SV365 = SY1667 ) ) )
= $true )
| ( ( SV148
@ ( descr
@ ^ [SY1404: $i] : ( SV148 @ SY1404 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1588,plain,
! [SV151: $i,SV281: $i > $o] :
( ( ( ~ ( in @ ( sK31_SY1588 @ SV281 @ SV151 ) @ SV151 )
| ~ ( SV281 @ ( sK31_SY1588 @ SV281 @ SV151 ) ) )
= $false )
| ( ( ! [SY1589: $i] :
( ~ ( in @ SY1589 @ SV151 )
| ~ ( SV281 @ SY1589 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1589,plain,
! [SV366: $i,SV159: $i > $o] :
( ( ( SV159 @ SV366 )
= $false )
| ( ( ~ ! [SY1668: $i] :
( ~ ( SV159 @ SY1668 )
| ( SV366 = SY1668 ) ) )
= $true )
| ( ( ! [SY1422: $i,SY1423: $i] :
( ~ ( SV159 @ SY1422 )
| ~ ( SV159 @ SY1423 )
| ( SY1422 = SY1423 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1494]) ).
thf(1590,plain,
! [SV161: $i,SV289: $i] :
( ( ( ~ ( in @ ( sK23_SY1595 @ SV289 @ SV161 ) @ SV161 ) )
= $false )
| ( ( in @ SV289 @ ( setunion @ SV161 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1495]) ).
thf(1591,plain,
! [SV161: $i,SV289: $i] :
( ( ( ~ ( in @ SV289 @ ( sK23_SY1595 @ SV289 @ SV161 ) ) )
= $false )
| ( ( in @ SV289 @ ( setunion @ SV161 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1495]) ).
thf(1592,plain,
! [SV344: $i,SV290: $i > $o,SV162: $i] :
( ( ( ! [SY1639: $i] :
( ~ ( in @ SY1639 @ SV162 )
| ~ ( SV290 @ SY1639 )
| ( SY1639 = SV344 ) ) )
= $false )
| ( ( ~ ! [SY1598: $i] :
~ ~ ( ~ ( in @ SY1598
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ SY1598 @ emptyset ) ) ) )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1593,plain,
! [SV29: $i,SV180: $i,SV349: $i > $o,SV367: $i > $o] :
( ( ( ~ ( in @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) @ SV29 ) )
= $false )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1497]) ).
thf(1594,plain,
! [SV29: $i,SV349: $i > $o,SV367: $i > $o,SV180: $i] :
( ( ( ! [SY1686: $i] :
( ~ ( in @ SY1686 @ SV180 )
| ( ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 )
!= SY1686 )
| ~ ( ~ ( ~ ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) )
| ( SV367 @ SY1686 ) )
| ~ ( ~ ( SV367 @ SY1686 )
| ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1497]) ).
thf(1595,plain,
! [SV350: $i,SV30: $i] :
( ( ( SV30
= ( setadjoin @ SV350 @ emptyset ) )
= $false )
| ( ( in @ SV350 @ SV30 )
= $false )
| ( ( in @ ( setunion @ SV30 ) @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1498]) ).
thf(1596,plain,
! [SV181: $i > $o,SV31: $i,SV368: $i] :
( ( ( in @ SV368 @ SV31 )
= $false )
| ( ( ~ ( SV181 @ SV368 ) )
= $true )
| ( ( ( ( dsetconstr @ SV31
@ ^ [SY1444: $i] : ( SV181 @ SY1444 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1597,plain,
! [SV35: $i] :
( ( ~ ( ~ ! [SY1601: $i] :
( ~ ( in @ SY1601 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SY1601 )
| ( in @ SY1111 @ SV35 ) ) )
| ~ ! [SY1603: $i,SY1604: $i] :
( ~ ~ ( ~ ( in @ SY1603 @ SV35 )
| ~ ( in @ SY1604 @ SV35 ) )
| ~ ! [SY1605: $i] :
( ~ ( in @ SY1605 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SY1603 @ SY1605 )
| ( in @ SY1604 @ SY1605 ) )
| ~ ( ~ ( in @ SY1604 @ SY1605 )
| ( in @ SY1603 @ SY1605 ) ) ) )
| ( SY1603 = SY1604 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1500]) ).
thf(1598,plain,
! [SV35: $i] :
( ( ! [SY1606: $i,SY1607: $i] :
( ~ ~ ( ~ ( in @ SY1606 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1607 @ ( sK2_SY1109 @ SV35 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1606 )
| ( in @ SX4 @ SY1607 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1607 )
| ( in @ SX4 @ SY1606 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1501]) ).
thf(1599,plain,
! [SV35: $i,SV384: $i] :
( ( ( ~ ( ~ ! [SY1677: $i] :
( ~ ( in @ SY1677 @ SV384 )
| ( in @ SY1677 @ SV35 ) )
| ~ ~ ! [SY1678: $i] :
~ ( in @ SY1678 @ SV384 ) ) )
= $false )
| ( ( ~ ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1502]) ).
thf(1600,plain,
! [SV351: $i,SV37: $i > $o] :
( ( ( ! [SY1650: $i] :
( ~ ( SV37 @ SY1650 )
| ( SV351 = SY1650 ) ) )
= $false )
| ( ( SV37 @ SV351 )
= $false )
| ( ( ! [SY1130: $i,SY1131: $i] :
( ~ ( SV37 @ SY1130 )
| ~ ( SV37 @ SY1131 )
| ( SY1130 = SY1131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1601,plain,
! [SV186: $i > $o,SV38: $i,SV369: $i] :
( ( ( in @ SV369 @ SV38 )
= $false )
| ( ( ~ ~ ( SV186 @ SV369 ) )
= $true )
| ( ( ~ ! [SY1449: $i] :
( ~ ( in @ SY1449 @ SV38 )
| ( SV186 @ SY1449 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1504]) ).
thf(1602,plain,
! [SV45: $i,SV193: $i > $o,SV371: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK43_SY1458 @ SV371 @ SV193 @ SV45 ) @ SV45 )
| ~ ~ ( SV193 @ ( sK43_SY1458 @ SV371 @ SV193 @ SV45 ) ) ) )
= $false )
| ( ( SV193 @ SV371 )
= $true )
| ( ( in @ SV371 @ SV45 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1506]) ).
thf(1603,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ! [SY1651: $i] :
( ~ ( SV50 @ SY1651 )
| ( SV352 = SY1651 ) ) )
= $false )
| ( ( SV50 @ SV352 )
= $false )
| ( ( ~ ! [SY1160: $i] :
~ ~ ( ~ ( SV50 @ SY1160 )
| ~ ! [SY1161: $i] :
( ~ ( SV50 @ SY1161 )
| ( SY1160 = SY1161 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1604,plain,
! [SV198: $i,SV51: $i] :
( ( ( ~ ( in @ ( sK44_SY1463 @ SV51 @ SV198 ) @ SV198 )
| ( in @ ( sK44_SY1463 @ SV51 @ SV198 ) @ SV51 ) )
= $false )
| ( ( SV51 = SV198 )
= $true )
| ( ( in @ ( sK8_SY1462 @ SV198 @ SV51 ) @ SV51 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1508]) ).
thf(1605,plain,
! [SV198: $i,SV51: $i] :
( ( ( ~ ( in @ ( sK39_SY1463 @ SV51 @ SV198 ) @ SV198 ) )
= $false )
| ( ( SV51 = SV198 )
= $true )
| ( ( in @ ( sK8_SY1462 @ SV198 @ SV51 ) @ SV198 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1509]) ).
thf(1606,plain,
! [SV198: $i,SV51: $i] :
( ( ( in @ ( sK39_SY1463 @ SV51 @ SV198 ) @ SV51 )
= $false )
| ( ( SV51 = SV198 )
= $true )
| ( ( in @ ( sK8_SY1462 @ SV198 @ SV51 ) @ SV198 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1509]) ).
thf(1607,plain,
! [SV54: $i,SV200: $i] :
( ( ~ ~ ( ~ ( in @ ( sK45_SY1643 @ SV200 @ SV54 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ ( setadjoin @ ( sK45_SY1643 @ SV200 @ SV54 ) @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1510]) ).
thf(1608,plain,
! [SV58: $i,SV204: $i,SV305: $i] :
( ( ( ~ ( in @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ SV58 ) )
= $false )
| ( ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1511]) ).
thf(1609,plain,
! [SV58: $i,SV305: $i,SV204: $i] :
( ( ( ~ ~ ! [SY1675: $i] :
~ ~ ( ~ ( in @ SY1675 @ SV204 )
| ( SV305
!= ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ ( setadjoin @ SY1675 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false )
| ( ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1511]) ).
thf(1610,plain,
! [SV59: $i,SV205: $i] :
( ( ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV205 )
| ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV205 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1512]) ).
thf(1611,plain,
! [SV59: $i,SV205: $i] :
( ( ( ~ ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV205 )
| ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 ) )
= $false )
| ( ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV205 )
= $false )
| ( ( SV59 = SV205 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1513]) ).
thf(1612,plain,
! [SV346: $o,SV206: $i,SV60: $i,SV306: $i] :
( ( ( in @ SV306 @ SV60 )
= $true )
| ( ( ~ ( ~ ( in @ SV306 @ SV206 )
| SV346 )
| SV346 )
= $true )
| ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1514]) ).
thf(1616,plain,
! [SV206: $i,SV60: $i,SV306: $i] :
( ( ( in @ SV306 @ SV60 )
= $true )
| ( ( ~ ( ~ ( in @ SV306 @ SV206 )
| $false )
| $false )
= $true )
| ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1518]) ).
thf(1618,plain,
! [SV61: $i,SV207: $i] :
( ( ~ ~ ( ~ ( in @ ( sK46_SY1644 @ SV207 @ SV61 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ ( setadjoin @ ( sK46_SY1644 @ SV207 @ SV61 ) @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1520]) ).
thf(1619,plain,
! [SV208: $i > $o,SV62: $i,SV388: $i] :
( ( ( ~ ~ ( ~ ( in @ SV388 @ SV62 )
| ~ ( SV208 @ SV388 ) ) )
= $true )
| ( ( in @ ( sK10_SY1478 @ SV208 @ SV62 ) @ SV62 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1620,plain,
! [SV208: $i > $o,SV62: $i,SV389: $i] :
( ( ( ~ ~ ( ~ ( in @ SV389 @ SV62 )
| ~ ( SV208 @ SV389 ) ) )
= $true )
| ( ( SV208 @ ( sK10_SY1478 @ SV208 @ SV62 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1621,plain,
! [SV210: $i,SV64: $i > $i > $o] :
( ( ( ! [SY1687: $i] :
~ ( ~ ( ~ ( in @ SY1687 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1687 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1687 ) )
| ( in @ SY1687 @ ( sK40_SY1483 @ SV64 @ SV210 ) ) ) ) )
= $true )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1523]) ).
thf(1622,plain,
! [SV385: $i,SV210: $i,SV64: $i > $i > $o] :
( ( ( ~ ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
| ~ ! [SY1684: $i] :
( ~ ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SY1684 )
| ( SV385 = SY1684 ) ) )
= $true )
| ( ( ~ ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1524]) ).
thf(1623,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ( ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1525]) ).
thf(1624,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1526]) ).
thf(1625,plain,
! [SV70: $i,SV216: $i > $o] :
( ( ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
= $true )
| ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) )
| ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1527]) ).
thf(1626,plain,
! [SV70: $i,SV216: $i > $o] :
( ( ( ~ ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) ) )
= $false )
| ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) )
| ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1528]) ).
thf(1627,plain,
! [SV70: $i,SV216: $i > $o] :
( ( ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) )
= $false )
| ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) )
| ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1528]) ).
thf(1628,plain,
! [SV72: $i,SV353: $o,SV218: $i] :
( ( ( in @ SV218 @ ( sK32_SY1655 @ SV353 @ SV72 @ SV218 ) )
= $true )
| ( SV353 = $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1529]) ).
thf(1629,plain,
! [SV218: $i,SV72: $i,SV353: $o] :
( ( ( ~ ( in @ ( sK32_SY1655 @ SV353 @ SV72 @ SV218 ) @ SV72 ) )
= $false )
| ( SV353 = $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1530]) ).
thf(1634,plain,
! [SV72: $i,SV218: $i] :
( ( ( in @ SV218 @ ( sK34_SX0 @ SV72 @ SV218 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1533]) ).
thf(1635,plain,
! [SV218: $i,SV72: $i] :
( ( ( ~ ( in @ ( sK34_SX0 @ SV72 @ SV218 ) @ SV72 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1534]) ).
thf(1637,plain,
! [SV219: $i,SV373: $i,SV74: $i,SV354: $i] :
( ( ( in @ SV354 @ SV74 )
= $false )
| ( ( in @ SV373 @ SV219 )
= $true )
| ( ( SV354 = SV373 )
= $false )
| ( ( SV74 = SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1535]) ).
thf(1638,plain,
! [SV220: $i > $o,SV75: $i,SV374: $i] :
( ( ( in @ SV374
@ ( dsetconstr @ SV75
@ ^ [SY1505: $i] : ( SV220 @ SY1505 ) ) )
= $false )
| ( ( ( dsetconstr @ SV75
@ ^ [SY1506: $i] : ( SV220 @ SY1506 ) )
!= ( setadjoin @ SV374 @ emptyset ) )
= $true )
| ( ( ~ ! [SY1507: $i] :
~ ~ ( ~ ( in @ SY1507 @ SV75 )
| ~ ( SV220 @ SY1507 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1639,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1537]) ).
thf(1640,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1537]) ).
thf(1641,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
| ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) ) )
= $false )
| ( ( ~ ( ~ ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
| ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1642,plain,
! [SV89: $i,SV232: $i] :
( ( ( ~ ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV89 ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1539]) ).
thf(1643,plain,
! [SV89: $i,SV232: $i] :
( ( ( ~ ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV232 ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1539]) ).
thf(1644,plain,
! [SV356: $i,SV90: $i > $o] :
( ( ( ! [SY1659: $i] :
( ~ ( SV90 @ SY1659 )
| ( SV356 = SY1659 ) ) )
= $false )
| ( ( SV90 @ SV356 )
= $false )
| ( ( ~ ! [SY1266: $i] :
~ ! [SY1267: $i] :
~ ( ~ ( ~ ( SV90 @ SY1267 )
| ( SY1267 = SY1266 ) )
| ~ ( ( SY1267 != SY1266 )
| ( SV90 @ SY1267 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1645,plain,
! [SV378: $o,SV233: $i,SV91: $i,SV315: $i] :
( ( ( SV315 = SV91 )
= $true )
| ( ( ~ ( ~ ( in @ SV315 @ SV233 )
| SV378 )
| SV378 )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1541]) ).
thf(1649,plain,
! [SV233: $i,SV91: $i,SV315: $i] :
( ( ( SV315 = SV91 )
= $true )
| ( ( ~ ( ~ ( in @ SV315 @ SV233 )
| $false )
| $false )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1545]) ).
thf(1651,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ( ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1547]) ).
thf(1652,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1548]) ).
thf(1653,plain,
! [SV92: $i,SV234: $i > $o] :
( ( ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
= $true )
| ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) )
| ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1549]) ).
thf(1654,plain,
! [SV92: $i,SV234: $i > $o] :
( ( ( ~ ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) ) )
= $false )
| ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) )
| ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1550]) ).
thf(1655,plain,
! [SV92: $i,SV234: $i > $o] :
( ( ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) )
= $false )
| ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) )
| ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1550]) ).
thf(1656,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
| ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 ) )
= $false )
| ( ( ~ ( ( ( sK28_SY1661 @ SV357 @ SV98 )
!= SV357 )
| ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) ) ) )
= $true )
| ( ( ~ ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1657,plain,
! [SV321: $i,SV100: $i,SV241: $i] :
( ( ( ~ ( in @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ ( setunion @ SV321 ) ) )
= $false )
| ( ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1555]) ).
thf(1658,plain,
! [SV100: $i,SV241: $i,SV321: $i] :
( ( ( ~ ~ ! [SY1676: $i] :
~ ~ ( ~ ( in @ SY1676 @ ( setunion @ SV321 ) )
| ( SV321
!= ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ ( setadjoin @ SY1676 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false )
| ( ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1555]) ).
thf(1659,plain,
! [SV104: $i,SV245: $i > $o] :
( ( ( ~ ( in @ ( sK30_SY1550 @ SV245 @ SV104 ) @ SV104 ) )
= $false )
| ( ( ! [SY1551: $i] :
( ~ ( in @ SY1551 @ SV104 )
| ~ ( SV245 @ SY1551 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1660,plain,
! [SV104: $i,SV245: $i > $o] :
( ( ( ~ ( SV245 @ ( sK30_SY1550 @ SV245 @ SV104 ) ) )
= $false )
| ( ( ! [SY1551: $i] :
( ~ ( in @ SY1551 @ SV104 )
| ~ ( SV245 @ SY1551 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1661,plain,
! [SV358: $i,SV108: $i] :
( ( ( ~ ! [SY1662: $i] :
~ ~ ( ~ ( in @ SY1662 @ ( setunion @ SV108 ) )
| ( SV108
!= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SY1662 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false )
| ( ( in @ SV358 @ ( setunion @ SV108 ) )
= $false )
| ( ( ~ ! [SY1316: $i] :
~ ~ ( ~ ( in @ SY1316
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ SY1316 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1558]) ).
thf(1662,plain,
! [SV381: $o,SV254: $i,SV113: $i,SV329: $i] :
( ( ( in @ SV329 @ SV113 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| SV381 )
| SV381 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1560]) ).
thf(1663,plain,
! [SV381: $o,SV113: $i,SV254: $i,SV329: $i] :
( ( ( ~ ~ ( in @ SV329 @ SV254 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| SV381 )
| SV381 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1561]) ).
thf(1668,plain,
! [SV254: $i,SV113: $i,SV329: $i] :
( ( ( in @ SV329 @ SV113 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| $false )
| $false )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1564]) ).
thf(1669,plain,
! [SV113: $i,SV254: $i,SV329: $i] :
( ( ( ~ ~ ( in @ SV329 @ SV254 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| $false )
| $false )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1565]) ).
thf(1671,plain,
! [SV258: $i,SV382: $i,SV118: $i,SV359: $i] :
( ( ( ~ ( ~ ( in @ SV359 @ SV118 )
| ( in @ SV382 @ SV258 ) ) )
= $false )
| ( ( SV359 = SV382 )
= $false )
| ( ( SV118 = SV258 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1566]) ).
thf(1672,plain,
! [SV118: $i,SV359: $i,SV258: $i,SV382: $i] :
( ( ( ~ ( ~ ( in @ SV382 @ SV258 )
| ( in @ SV359 @ SV118 ) ) )
= $false )
| ( ( SV359 = SV382 )
= $false )
| ( ( SV118 = SV258 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1566]) ).
thf(1673,plain,
! [SV119: $i,SV259: $i > $o,SV383: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK47_SY1564 @ SV383 @ SV259 @ SV119 ) @ SV119 )
| ~ ~ ( SV259 @ ( sK47_SY1564 @ SV383 @ SV259 @ SV119 ) ) ) )
= $false )
| ( ( SV259 @ SV383 )
= $true )
| ( ( in @ SV383 @ SV119 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1567]) ).
thf(1674,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ! [SY1664: $i] :
( ~ ( SV124 @ SY1664 )
| ( SV360 = SY1664 ) ) )
= $false )
| ( ( SV124 @ SV360 )
= $false )
| ( ( ~ ! [SY1348: $i] :
~ ~ ( ~ ( SV124 @ SY1348 )
| ~ ! [SY1349: $i] :
( ~ ( SV124 @ SY1349 )
| ( SY1348 = SY1349 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1568]) ).
thf(1675,plain,
! [SV264: $i,SV125: $i,SV333: $i] :
( ( ( in @ SV333 @ ( symdiff @ SV125 @ SV264 ) )
= $false )
| ( ( in @ SV333 @ SV264 )
= $true )
| ( ( in @ SV333 @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1676,plain,
! [SV126: $i,SV265: $i] :
( ( ( ~ ( ~ ( in @ SV265 @ ( sK41_SY1568 @ SV126 @ SV265 ) )
| ~ ( in @ ( sK41_SY1568 @ SV126 @ SV265 ) @ SV126 ) ) )
= $true )
| ( ( in @ SV265 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1570]) ).
thf(1677,plain,
! [SV126: $i,SV387: $i,SV265: $i] :
( ( ( ~ ( ~ ( in @ SV265 @ SV387 )
| ~ ( in @ SV387 @ SV126 ) ) )
= $false )
| ( ( in @ SV265 @ ( setunion @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1678,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK42_SY1359 @ SV362 @ SV130 ) )
| ~ ( SV130 @ ( sK48_SY1690 @ SV362 @ SV130 ) )
| ( ( sK42_SY1359 @ SV362 @ SV130 )
= ( sK48_SY1690 @ SV362 @ SV130 ) ) )
= $false )
| ( ( ~ ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1572]) ).
thf(1679,plain,
! [SV271: $i,SV136: $i,SV335: $i] :
( ( ( in @ SV335 @ SV136 )
= $false )
| ( ( in @ SV335 @ SV271 )
= $true )
| ( ( in @ SV335 @ ( setminus @ SV136 @ SV271 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1573]) ).
thf(1680,plain,
! [SV363: $i,SV137: $i > $o] :
( ( ( ! [SY1665: $i] :
( ~ ( SV137 @ SY1665 )
| ( SV363 = SY1665 ) ) )
= $false )
| ( ( SV137 @ SV363 )
= $false )
| ( ( ~ ! [SY1372: $i] :
~ ( SV137 @ SY1372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1681,plain,
! [SV138: $i] :
( ( ( ~ ( ~ ( in @ ( sK35_SY1373 @ SV138 ) @ omega )
| ~ ( in @ ( sK35_SY1373 @ SV138 ) @ SV138 ) ) )
= $true )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( ! [SY1374: $i] :
( ~ ( in @ SY1374 @ omega )
| ( in @ SY1374 @ SV138 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1575]) ).
thf(1682,plain,
! [SV138: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ omega )
| ( in @ SV390 @ SV138 ) )
= $true )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( in @ ( setadjoin @ ( sK35_SY1373 @ SV138 ) @ ( sK35_SY1373 @ SV138 ) ) @ SV138 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1683,plain,
! [SV140: $i,SV273: $i,SV386: $i] :
( ( ( in @ SV386 @ SV273 )
= $false )
| ( ( in @ SV386 @ SV140 )
= $true )
| ( ( in @ SV273 @ ( powerset @ SV140 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1577]) ).
thf(1684,plain,
! [SV273: $i,SV140: $i] :
( ( ( in @ ( sK36_SY1574 @ SV140 @ SV273 ) @ SV273 )
= $true )
| ( ( in @ SV273 @ ( powerset @ SV140 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1578]) ).
thf(1685,plain,
! [SV142: $i,SV364: $i] :
( ( ( ~ ( in @ ( sK37_SY1383 @ SV364 @ SV142 ) @ SV142 )
| ~ ~ ~ ! [SY1685: $i] :
~ ~ ( ~ ( in @ SY1685 @ ( sK37_SY1383 @ SV364 @ SV142 ) )
| ~ ( in @ SY1685 @ SV142 ) ) )
= $false )
| ( ( in @ SV364 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1686,plain,
! [SV143: $i] :
( ( ( in @ ( sK21_SY1385 @ SV143 ) @ SV143 )
= $true )
| ( ( SV143 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1581]) ).
thf(1688,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ( ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1583]) ).
thf(1689,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ( ~ ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
| ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) ) )
= $false )
| ( ( ~ ( ~ ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
| ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1584]) ).
thf(1690,plain,
! [SV277: $i > $o,SV146: $i,SV337: $i] :
( ( ( in @ SV337
@ ( dsetconstr @ SV146
@ ^ [SY1585: $i] : ( SV277 @ SY1585 ) ) )
= $false )
| ( ( SV277 @ SV337 )
= $true )
| ( ( in @ SV337 @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1691,plain,
! [SV146: $i,SV337: $i,SV277: $i > $o] :
( ( ( SV277 @ SV337 )
= $false )
| ( ( in @ SV337
@ ( dsetconstr @ SV146
@ ^ [SY1586: $i] : ( SV277 @ SY1586 ) ) )
= $true )
| ( ( in @ SV337 @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1586]) ).
thf(1692,plain,
! [SV365: $i,SV148: $i > $o] :
( ( ( ! [SY1667: $i] :
( ~ ( SV148 @ SY1667 )
| ( SV365 = SY1667 ) ) )
= $false )
| ( ( SV148 @ SV365 )
= $false )
| ( ( SV148
@ ( descr
@ ^ [SY1404: $i] : ( SV148 @ SY1404 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1587]) ).
thf(1693,plain,
! [SV151: $i,SV281: $i > $o] :
( ( ( ~ ( in @ ( sK31_SY1588 @ SV281 @ SV151 ) @ SV151 ) )
= $false )
| ( ( ! [SY1589: $i] :
( ~ ( in @ SY1589 @ SV151 )
| ~ ( SV281 @ SY1589 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1694,plain,
! [SV151: $i,SV281: $i > $o] :
( ( ( ~ ( SV281 @ ( sK31_SY1588 @ SV281 @ SV151 ) ) )
= $false )
| ( ( ! [SY1589: $i] :
( ~ ( in @ SY1589 @ SV151 )
| ~ ( SV281 @ SY1589 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1695,plain,
! [SV366: $i,SV159: $i > $o] :
( ( ( ! [SY1668: $i] :
( ~ ( SV159 @ SY1668 )
| ( SV366 = SY1668 ) ) )
= $false )
| ( ( SV159 @ SV366 )
= $false )
| ( ( ! [SY1422: $i,SY1423: $i] :
( ~ ( SV159 @ SY1422 )
| ~ ( SV159 @ SY1423 )
| ( SY1422 = SY1423 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1696,plain,
! [SV161: $i,SV289: $i] :
( ( ( in @ ( sK23_SY1595 @ SV289 @ SV161 ) @ SV161 )
= $true )
| ( ( in @ SV289 @ ( setunion @ SV161 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1590]) ).
thf(1697,plain,
! [SV161: $i,SV289: $i] :
( ( ( in @ SV289 @ ( sK23_SY1595 @ SV289 @ SV161 ) )
= $true )
| ( ( in @ SV289 @ ( setunion @ SV161 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1591]) ).
thf(1698,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( ~ ( in @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) @ SV162 )
| ~ ( SV290 @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) )
| ( ( sK49_SY1639 @ SV344 @ SV290 @ SV162 )
= SV344 ) )
= $false )
| ( ( ~ ! [SY1598: $i] :
~ ~ ( ~ ( in @ SY1598
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ SY1598 @ emptyset ) ) ) )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1592]) ).
thf(1699,plain,
! [SV29: $i,SV180: $i,SV349: $i > $o,SV367: $i > $o] :
( ( ( in @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) @ SV29 )
= $true )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1593]) ).
thf(1700,plain,
! [SV180: $i,SV367: $i > $o,SV349: $i > $o,SV29: $i] :
( ( ( ~ ( in @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) @ SV180 )
| ( ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 )
!= ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
| ~ ( ~ ( ~ ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) )
| ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) ) )
| ~ ( ~ ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
| ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1594]) ).
thf(1701,plain,
! [SV31: $i,SV368: $i,SV181: $i > $o] :
( ( ( SV181 @ SV368 )
= $false )
| ( ( in @ SV368 @ SV31 )
= $false )
| ( ( ( ( dsetconstr @ SV31
@ ^ [SY1444: $i] : ( SV181 @ SY1444 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1596]) ).
thf(1702,plain,
! [SV35: $i] :
( ( ~ ! [SY1601: $i] :
( ~ ( in @ SY1601 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SY1601 )
| ( in @ SY1111 @ SV35 ) ) )
| ~ ! [SY1603: $i,SY1604: $i] :
( ~ ~ ( ~ ( in @ SY1603 @ SV35 )
| ~ ( in @ SY1604 @ SV35 ) )
| ~ ! [SY1605: $i] :
( ~ ( in @ SY1605 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SY1603 @ SY1605 )
| ( in @ SY1604 @ SY1605 ) )
| ~ ( ~ ( in @ SY1604 @ SY1605 )
| ( in @ SY1603 @ SY1605 ) ) ) )
| ( SY1603 = SY1604 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1703,plain,
! [SV35: $i,SV391: $i] :
( ( ! [SY1691: $i] :
( ~ ~ ( ~ ( in @ SV391 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1691 @ ( sK2_SY1109 @ SV35 ) ) )
| ! [SY1692: $i] :
( ~ ( in @ SY1692 @ SV391 )
| ( in @ SY1692 @ SY1691 ) )
| ! [SY1693: $i] :
( ~ ( in @ SY1693 @ SY1691 )
| ( in @ SY1693 @ SV391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(1704,plain,
! [SV35: $i,SV384: $i] :
( ( ( ~ ! [SY1677: $i] :
( ~ ( in @ SY1677 @ SV384 )
| ( in @ SY1677 @ SV35 ) )
| ~ ~ ! [SY1678: $i] :
~ ( in @ SY1678 @ SV384 ) )
= $true )
| ( ( ~ ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1599]) ).
thf(1705,plain,
! [SV351: $i,SV37: $i > $o] :
( ( ( ~ ( SV37 @ ( sK51_SY1650 @ SV351 @ SV37 ) )
| ( SV351
= ( sK51_SY1650 @ SV351 @ SV37 ) ) )
= $false )
| ( ( SV37 @ SV351 )
= $false )
| ( ( ! [SY1130: $i,SY1131: $i] :
( ~ ( SV37 @ SY1130 )
| ~ ( SV37 @ SY1131 )
| ( SY1130 = SY1131 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1600]) ).
thf(1706,plain,
! [SV38: $i,SV369: $i,SV186: $i > $o] :
( ( ( ~ ( SV186 @ SV369 ) )
= $false )
| ( ( in @ SV369 @ SV38 )
= $false )
| ( ( ~ ! [SY1449: $i] :
( ~ ( in @ SY1449 @ SV38 )
| ( SV186 @ SY1449 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1707,plain,
! [SV45: $i,SV193: $i > $o,SV371: $i] :
( ( ( ~ ( ~ ( in @ ( sK43_SY1458 @ SV371 @ SV193 @ SV45 ) @ SV45 )
| ~ ~ ( SV193 @ ( sK43_SY1458 @ SV371 @ SV193 @ SV45 ) ) ) )
= $true )
| ( ( SV193 @ SV371 )
= $true )
| ( ( in @ SV371 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1602]) ).
thf(1708,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ ( sK52_SY1651 @ SV352 @ SV50 ) )
| ( SV352
= ( sK52_SY1651 @ SV352 @ SV50 ) ) )
= $false )
| ( ( SV50 @ SV352 )
= $false )
| ( ( ~ ! [SY1160: $i] :
~ ~ ( ~ ( SV50 @ SY1160 )
| ~ ! [SY1161: $i] :
( ~ ( SV50 @ SY1161 )
| ( SY1160 = SY1161 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1603]) ).
thf(1709,plain,
! [SV198: $i,SV51: $i] :
( ( ( ~ ( in @ ( sK44_SY1463 @ SV51 @ SV198 ) @ SV198 ) )
= $false )
| ( ( SV51 = SV198 )
= $true )
| ( ( in @ ( sK8_SY1462 @ SV198 @ SV51 ) @ SV51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1604]) ).
thf(1710,plain,
! [SV198: $i,SV51: $i] :
( ( ( in @ ( sK44_SY1463 @ SV51 @ SV198 ) @ SV51 )
= $false )
| ( ( SV51 = SV198 )
= $true )
| ( ( in @ ( sK8_SY1462 @ SV198 @ SV51 ) @ SV51 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1604]) ).
thf(1711,plain,
! [SV198: $i,SV51: $i] :
( ( ( in @ ( sK39_SY1463 @ SV51 @ SV198 ) @ SV198 )
= $true )
| ( ( SV51 = SV198 )
= $true )
| ( ( in @ ( sK8_SY1462 @ SV198 @ SV51 ) @ SV198 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1605]) ).
thf(1712,plain,
! [SV54: $i,SV200: $i] :
( ( ~ ( ~ ( in @ ( sK45_SY1643 @ SV200 @ SV54 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ ( setadjoin @ ( sK45_SY1643 @ SV200 @ SV54 ) @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1607]) ).
thf(1713,plain,
! [SV58: $i,SV204: $i,SV305: $i] :
( ( ( in @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ SV58 )
= $true )
| ( ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1608]) ).
thf(1714,plain,
! [SV58: $i,SV305: $i,SV204: $i] :
( ( ( ~ ! [SY1675: $i] :
~ ~ ( ~ ( in @ SY1675 @ SV204 )
| ( SV305
!= ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ ( setadjoin @ SY1675 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1609]) ).
thf(1715,plain,
! [SV59: $i,SV205: $i] :
( ( ( ~ ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV205 )
| ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 ) )
= $false )
| ( ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 )
= $true )
| ( ( SV59 = SV205 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1717,plain,
! [SV59: $i,SV205: $i] :
( ( ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 )
= $false )
| ( ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV205 )
= $false )
| ( ( SV59 = SV205 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1611]) ).
thf(1718,plain,
! [SV60: $i,SV346: $o,SV206: $i,SV306: $i] :
( ( ( ~ ( ~ ( in @ SV306 @ SV206 )
| SV346 ) )
= $true )
| ( SV346 = $true )
| ( ( in @ SV306 @ SV60 )
= $true )
| ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1612]) ).
thf(1722,plain,
! [SV60: $i,SV206: $i,SV306: $i] :
( ( ( ~ ( ~ ( in @ SV306 @ SV206 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV306 @ SV60 )
= $true )
| ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1616]) ).
thf(1724,plain,
! [SV61: $i,SV207: $i] :
( ( ~ ( ~ ( in @ ( sK46_SY1644 @ SV207 @ SV61 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ ( setadjoin @ ( sK46_SY1644 @ SV207 @ SV61 ) @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1618]) ).
thf(1725,plain,
! [SV208: $i > $o,SV62: $i,SV388: $i] :
( ( ( ~ ( ~ ( in @ SV388 @ SV62 )
| ~ ( SV208 @ SV388 ) ) )
= $false )
| ( ( in @ ( sK10_SY1478 @ SV208 @ SV62 ) @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1619]) ).
thf(1726,plain,
! [SV208: $i > $o,SV62: $i,SV389: $i] :
( ( ( ~ ( ~ ( in @ SV389 @ SV62 )
| ~ ( SV208 @ SV389 ) ) )
= $false )
| ( ( SV208 @ ( sK10_SY1478 @ SV208 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1620]) ).
thf(1727,plain,
! [SV210: $i,SV64: $i > $i > $o,SV392: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV210 )
| ~ ( SV64 @ SY1694 @ SV392 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV210 )
| ~ ( SV64 @ SY1695 @ SV392 ) )
| ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) ) ) ) )
= $true )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1728,plain,
! [SV385: $i,SV210: $i,SV64: $i > $i > $o] :
( ( ( ~ ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 ) )
= $true )
| ( ( ~ ! [SY1684: $i] :
( ~ ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SY1684 )
| ( SV385 = SY1684 ) ) )
= $true )
| ( ( ~ ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1622]) ).
thf(1729,plain,
! [SV216: $i > $o,SV70: $i,SV393: $i] :
( ( ( ~ ~ ( ~ ( in @ SV393 @ SV70 )
| ~ ( SV216 @ SV393 ) ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(1730,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ( ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) ) )
= $false )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1731,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1625]) ).
thf(1732,plain,
! [SV70: $i,SV216: $i > $o] :
( ( ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
= $true )
| ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) )
| ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1626]) ).
thf(1733,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1734,plain,
! [SV218: $i,SV72: $i,SV353: $o] :
( ( ( in @ ( sK32_SY1655 @ SV353 @ SV72 @ SV218 ) @ SV72 )
= $true )
| ( SV353 = $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1629]) ).
thf(1736,plain,
! [SV218: $i,SV72: $i] :
( ( ( in @ ( sK34_SX0 @ SV72 @ SV218 ) @ SV72 )
= $true )
| ( $false = $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1635]) ).
thf(1737,plain,
! [SV374: $i,SV220: $i > $o,SV75: $i] :
( ( ( ( dsetconstr @ SV75
@ ^ [SY1506: $i] : ( SV220 @ SY1506 ) )
= ( setadjoin @ SV374 @ emptyset ) )
= $false )
| ( ( in @ SV374
@ ( dsetconstr @ SV75
@ ^ [SY1505: $i] : ( SV220 @ SY1505 ) ) )
= $false )
| ( ( ~ ! [SY1507: $i] :
~ ~ ( ~ ( in @ SY1507 @ SV75 )
| ~ ( SV220 @ SY1507 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1738,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1639]) ).
thf(1739,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1640]) ).
thf(1740,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) ) )
= $false )
| ( ( ~ ( ~ ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
| ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1641]) ).
thf(1741,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( ~ ( ~ ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
| ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1641]) ).
thf(1742,plain,
! [SV89: $i,SV232: $i] :
( ( ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV89 )
= $true )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1642]) ).
thf(1743,plain,
! [SV89: $i,SV232: $i] :
( ( ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV232 )
= $true )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1643]) ).
thf(1744,plain,
! [SV356: $i,SV90: $i > $o] :
( ( ( ~ ( SV90 @ ( sK53_SY1659 @ SV356 @ SV90 ) )
| ( SV356
= ( sK53_SY1659 @ SV356 @ SV90 ) ) )
= $false )
| ( ( SV90 @ SV356 )
= $false )
| ( ( ~ ! [SY1266: $i] :
~ ! [SY1267: $i] :
~ ( ~ ( ~ ( SV90 @ SY1267 )
| ( SY1267 = SY1266 ) )
| ~ ( ( SY1267 != SY1266 )
| ( SV90 @ SY1267 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1644]) ).
thf(1745,plain,
! [SV91: $i,SV378: $o,SV233: $i,SV315: $i] :
( ( ( ~ ( ~ ( in @ SV315 @ SV233 )
| SV378 ) )
= $true )
| ( SV378 = $true )
| ( ( SV315 = SV91 )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1645]) ).
thf(1749,plain,
! [SV91: $i,SV233: $i,SV315: $i] :
( ( ( ~ ( ~ ( in @ SV315 @ SV233 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( SV315 = SV91 )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1649]) ).
thf(1751,plain,
! [SV234: $i > $o,SV92: $i,SV394: $i] :
( ( ( ~ ~ ( ~ ( in @ SV394 @ SV92 )
| ~ ( SV234 @ SV394 ) ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(1752,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ( ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) ) )
= $false )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1753,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1653]) ).
thf(1754,plain,
! [SV92: $i,SV234: $i > $o] :
( ( ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
= $true )
| ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) )
| ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1654]) ).
thf(1755,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1655]) ).
thf(1756,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) ) )
= $false )
| ( ( ~ ( ( ( sK28_SY1661 @ SV357 @ SV98 )
!= SV357 )
| ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) ) ) )
= $true )
| ( ( ~ ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1656]) ).
thf(1757,plain,
! [SV98: $i > $o,SV357: $i] :
( ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $false )
| ( ( ~ ( ( ( sK28_SY1661 @ SV357 @ SV98 )
!= SV357 )
| ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) ) ) )
= $true )
| ( ( ~ ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1656]) ).
thf(1758,plain,
! [SV321: $i,SV100: $i,SV241: $i] :
( ( ( in @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ ( setunion @ SV321 ) )
= $true )
| ( ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1657]) ).
thf(1759,plain,
! [SV100: $i,SV241: $i,SV321: $i] :
( ( ( ~ ! [SY1676: $i] :
~ ~ ( ~ ( in @ SY1676 @ ( setunion @ SV321 ) )
| ( SV321
!= ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ ( setadjoin @ SY1676 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1658]) ).
thf(1760,plain,
! [SV104: $i,SV245: $i > $o] :
( ( ( in @ ( sK30_SY1550 @ SV245 @ SV104 ) @ SV104 )
= $true )
| ( ( ! [SY1551: $i] :
( ~ ( in @ SY1551 @ SV104 )
| ~ ( SV245 @ SY1551 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1659]) ).
thf(1761,plain,
! [SV104: $i,SV245: $i > $o] :
( ( ( SV245 @ ( sK30_SY1550 @ SV245 @ SV104 ) )
= $true )
| ( ( ! [SY1551: $i] :
( ~ ( in @ SY1551 @ SV104 )
| ~ ( SV245 @ SY1551 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1660]) ).
thf(1762,plain,
! [SV358: $i,SV108: $i] :
( ( ( ! [SY1662: $i] :
~ ~ ( ~ ( in @ SY1662 @ ( setunion @ SV108 ) )
| ( SV108
!= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SY1662 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( in @ SV358 @ ( setunion @ SV108 ) )
= $false )
| ( ( ~ ! [SY1316: $i] :
~ ~ ( ~ ( in @ SY1316
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ SY1316 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1661]) ).
thf(1763,plain,
! [SV381: $o,SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| SV381 ) )
= $true )
| ( SV381 = $true )
| ( ( in @ SV329 @ SV113 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1662]) ).
thf(1764,plain,
! [SV381: $o,SV113: $i,SV254: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ SV254 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| SV381 )
| SV381 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1663]) ).
thf(1769,plain,
! [SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV329 @ SV113 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1668]) ).
thf(1770,plain,
! [SV113: $i,SV254: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ SV254 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| $false )
| $false )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1669]) ).
thf(1772,plain,
! [SV258: $i,SV382: $i,SV118: $i,SV359: $i] :
( ( ( ~ ( in @ SV359 @ SV118 )
| ( in @ SV382 @ SV258 ) )
= $true )
| ( ( SV359 = SV382 )
= $false )
| ( ( SV118 = SV258 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1671]) ).
thf(1773,plain,
! [SV118: $i,SV359: $i,SV258: $i,SV382: $i] :
( ( ( ~ ( in @ SV382 @ SV258 )
| ( in @ SV359 @ SV118 ) )
= $true )
| ( ( SV359 = SV382 )
= $false )
| ( ( SV118 = SV258 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1672]) ).
thf(1774,plain,
! [SV119: $i,SV259: $i > $o,SV383: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_SY1564 @ SV383 @ SV259 @ SV119 ) @ SV119 )
| ~ ~ ( SV259 @ ( sK47_SY1564 @ SV383 @ SV259 @ SV119 ) ) ) )
= $true )
| ( ( SV259 @ SV383 )
= $true )
| ( ( in @ SV383 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1673]) ).
thf(1775,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ~ ( SV124 @ ( sK54_SY1664 @ SV360 @ SV124 ) )
| ( SV360
= ( sK54_SY1664 @ SV360 @ SV124 ) ) )
= $false )
| ( ( SV124 @ SV360 )
= $false )
| ( ( ~ ! [SY1348: $i] :
~ ~ ( ~ ( SV124 @ SY1348 )
| ~ ! [SY1349: $i] :
( ~ ( SV124 @ SY1349 )
| ( SY1348 = SY1349 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1674]) ).
thf(1776,plain,
! [SV126: $i,SV265: $i] :
( ( ( ~ ( in @ SV265 @ ( sK41_SY1568 @ SV126 @ SV265 ) )
| ~ ( in @ ( sK41_SY1568 @ SV126 @ SV265 ) @ SV126 ) )
= $false )
| ( ( in @ SV265 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1676]) ).
thf(1777,plain,
! [SV126: $i,SV387: $i,SV265: $i] :
( ( ( ~ ( in @ SV265 @ SV387 )
| ~ ( in @ SV387 @ SV126 ) )
= $true )
| ( ( in @ SV265 @ ( setunion @ SV126 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1677]) ).
thf(1778,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK42_SY1359 @ SV362 @ SV130 ) ) )
= $false )
| ( ( ~ ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1678]) ).
thf(1779,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK48_SY1690 @ SV362 @ SV130 ) )
| ( ( sK42_SY1359 @ SV362 @ SV130 )
= ( sK48_SY1690 @ SV362 @ SV130 ) ) )
= $false )
| ( ( ~ ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1678]) ).
thf(1780,plain,
! [SV363: $i,SV137: $i > $o] :
( ( ( ~ ( SV137 @ ( sK55_SY1665 @ SV363 @ SV137 ) )
| ( SV363
= ( sK55_SY1665 @ SV363 @ SV137 ) ) )
= $false )
| ( ( SV137 @ SV363 )
= $false )
| ( ( ~ ! [SY1372: $i] :
~ ( SV137 @ SY1372 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1680]) ).
thf(1781,plain,
! [SV138: $i] :
( ( ( ~ ( in @ ( sK35_SY1373 @ SV138 ) @ omega )
| ~ ( in @ ( sK35_SY1373 @ SV138 ) @ SV138 ) )
= $false )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( ! [SY1374: $i] :
( ~ ( in @ SY1374 @ omega )
| ( in @ SY1374 @ SV138 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1681]) ).
thf(1782,plain,
! [SV138: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ omega ) )
= $true )
| ( ( in @ SV390 @ SV138 )
= $true )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( in @ ( setadjoin @ ( sK35_SY1373 @ SV138 ) @ ( sK35_SY1373 @ SV138 ) ) @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1682]) ).
thf(1783,plain,
! [SV142: $i,SV364: $i] :
( ( ( ~ ( in @ ( sK37_SY1383 @ SV364 @ SV142 ) @ SV142 ) )
= $false )
| ( ( in @ SV364 @ SV142 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1685]) ).
thf(1784,plain,
! [SV142: $i,SV364: $i] :
( ( ( ~ ~ ~ ! [SY1685: $i] :
~ ~ ( ~ ( in @ SY1685 @ ( sK37_SY1383 @ SV364 @ SV142 ) )
| ~ ( in @ SY1685 @ SV142 ) ) )
= $false )
| ( ( in @ SV364 @ SV142 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1685]) ).
thf(1785,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ( ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1688]) ).
thf(1786,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ( ~ ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) ) )
= $false )
| ( ( ~ ( ~ ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
| ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1689]) ).
thf(1787,plain,
! [SV144: $i > $o,SV275: $i > $o] :
( ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( ~ ( ~ ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
| ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1689]) ).
thf(1788,plain,
! [SV365: $i,SV148: $i > $o] :
( ( ( ~ ( SV148 @ ( sK56_SY1667 @ SV365 @ SV148 ) )
| ( SV365
= ( sK56_SY1667 @ SV365 @ SV148 ) ) )
= $false )
| ( ( SV148 @ SV365 )
= $false )
| ( ( SV148
@ ( descr
@ ^ [SY1404: $i] : ( SV148 @ SY1404 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1692]) ).
thf(1789,plain,
! [SV151: $i,SV281: $i > $o] :
( ( ( in @ ( sK31_SY1588 @ SV281 @ SV151 ) @ SV151 )
= $true )
| ( ( ! [SY1589: $i] :
( ~ ( in @ SY1589 @ SV151 )
| ~ ( SV281 @ SY1589 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1693]) ).
thf(1790,plain,
! [SV151: $i,SV281: $i > $o] :
( ( ( SV281 @ ( sK31_SY1588 @ SV281 @ SV151 ) )
= $true )
| ( ( ! [SY1589: $i] :
( ~ ( in @ SY1589 @ SV151 )
| ~ ( SV281 @ SY1589 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1694]) ).
thf(1791,plain,
! [SV366: $i,SV159: $i > $o] :
( ( ( ~ ( SV159 @ ( sK57_SY1668 @ SV366 @ SV159 ) )
| ( SV366
= ( sK57_SY1668 @ SV366 @ SV159 ) ) )
= $false )
| ( ( SV159 @ SV366 )
= $false )
| ( ( ! [SY1422: $i,SY1423: $i] :
( ~ ( SV159 @ SY1422 )
| ~ ( SV159 @ SY1423 )
| ( SY1422 = SY1423 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1695]) ).
thf(1792,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( ~ ( in @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) @ SV162 ) )
= $false )
| ( ( ~ ! [SY1598: $i] :
~ ~ ( ~ ( in @ SY1598
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ SY1598 @ emptyset ) ) ) )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1698]) ).
thf(1793,plain,
! [SV162: $i,SV344: $i,SV290: $i > $o] :
( ( ( ~ ( SV290 @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) )
| ( ( sK49_SY1639 @ SV344 @ SV290 @ SV162 )
= SV344 ) )
= $false )
| ( ( ~ ! [SY1598: $i] :
~ ~ ( ~ ( in @ SY1598
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ SY1598 @ emptyset ) ) ) )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1698]) ).
thf(1794,plain,
! [SV180: $i,SV367: $i > $o,SV349: $i > $o,SV29: $i] :
( ( ( ~ ( in @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) @ SV180 ) )
= $false )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1700]) ).
thf(1795,plain,
! [SV29: $i,SV180: $i,SV349: $i > $o,SV367: $i > $o] :
( ( ( ( ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 )
!= ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
| ~ ( ~ ( ~ ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) )
| ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) ) )
| ~ ( ~ ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
| ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1700]) ).
thf(1796,plain,
! [SV368: $i,SV181: $i > $o,SV31: $i] :
( ( ( ( dsetconstr @ SV31
@ ^ [SY1444: $i] : ( SV181 @ SY1444 ) )
!= emptyset )
= $true )
| ( $false = $true )
| ( ( in @ SV368 @ SV31 )
= $false )
| ( ( SV181 @ SV368 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1701]) ).
thf(1797,plain,
! [SV35: $i] :
( ( ~ ! [SY1601: $i] :
( ~ ( in @ SY1601 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SY1601 )
| ( in @ SY1111 @ SV35 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1702]) ).
thf(1798,plain,
! [SV35: $i] :
( ( ~ ! [SY1603: $i,SY1604: $i] :
( ~ ~ ( ~ ( in @ SY1603 @ SV35 )
| ~ ( in @ SY1604 @ SV35 ) )
| ~ ! [SY1605: $i] :
( ~ ( in @ SY1605 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SY1603 @ SY1605 )
| ( in @ SY1604 @ SY1605 ) )
| ~ ( ~ ( in @ SY1604 @ SY1605 )
| ( in @ SY1603 @ SY1605 ) ) ) )
| ( SY1603 = SY1604 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1702]) ).
thf(1799,plain,
! [SV395: $i,SV35: $i,SV391: $i] :
( ( ~ ~ ( ~ ( in @ SV391 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SV395 @ ( sK2_SY1109 @ SV35 ) ) )
| ! [SY1696: $i] :
( ~ ( in @ SY1696 @ SV391 )
| ( in @ SY1696 @ SV395 ) )
| ! [SY1697: $i] :
( ~ ( in @ SY1697 @ SV395 )
| ( in @ SY1697 @ SV391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(1800,plain,
! [SV35: $i,SV384: $i] :
( ( ( ~ ! [SY1677: $i] :
( ~ ( in @ SY1677 @ SV384 )
| ( in @ SY1677 @ SV35 ) ) )
= $true )
| ( ( ~ ~ ! [SY1678: $i] :
~ ( in @ SY1678 @ SV384 ) )
= $true )
| ( ( ~ ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(1801,plain,
! [SV351: $i,SV37: $i > $o] :
( ( ( ~ ( SV37 @ ( sK51_SY1650 @ SV351 @ SV37 ) ) )
= $false )
| ( ( SV37 @ SV351 )
= $false )
| ( ( ! [SY1130: $i,SY1131: $i] :
( ~ ( SV37 @ SY1130 )
| ~ ( SV37 @ SY1131 )
| ( SY1130 = SY1131 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1705]) ).
thf(1802,plain,
! [SV37: $i > $o,SV351: $i] :
( ( ( SV351
= ( sK51_SY1650 @ SV351 @ SV37 ) )
= $false )
| ( ( SV37 @ SV351 )
= $false )
| ( ( ! [SY1130: $i,SY1131: $i] :
( ~ ( SV37 @ SY1130 )
| ~ ( SV37 @ SY1131 )
| ( SY1130 = SY1131 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1705]) ).
thf(1803,plain,
! [SV38: $i,SV369: $i,SV186: $i > $o] :
( ( ( SV186 @ SV369 )
= $true )
| ( ( in @ SV369 @ SV38 )
= $false )
| ( ( ~ ! [SY1449: $i] :
( ~ ( in @ SY1449 @ SV38 )
| ( SV186 @ SY1449 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1706]) ).
thf(1804,plain,
! [SV45: $i,SV193: $i > $o,SV371: $i] :
( ( ( ~ ( in @ ( sK43_SY1458 @ SV371 @ SV193 @ SV45 ) @ SV45 )
| ~ ~ ( SV193 @ ( sK43_SY1458 @ SV371 @ SV193 @ SV45 ) ) )
= $false )
| ( ( SV193 @ SV371 )
= $true )
| ( ( in @ SV371 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1707]) ).
thf(1805,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ ( sK52_SY1651 @ SV352 @ SV50 ) ) )
= $false )
| ( ( SV50 @ SV352 )
= $false )
| ( ( ~ ! [SY1160: $i] :
~ ~ ( ~ ( SV50 @ SY1160 )
| ~ ! [SY1161: $i] :
( ~ ( SV50 @ SY1161 )
| ( SY1160 = SY1161 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1708]) ).
thf(1806,plain,
! [SV50: $i > $o,SV352: $i] :
( ( ( SV352
= ( sK52_SY1651 @ SV352 @ SV50 ) )
= $false )
| ( ( SV50 @ SV352 )
= $false )
| ( ( ~ ! [SY1160: $i] :
~ ~ ( ~ ( SV50 @ SY1160 )
| ~ ! [SY1161: $i] :
( ~ ( SV50 @ SY1161 )
| ( SY1160 = SY1161 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1708]) ).
thf(1807,plain,
! [SV198: $i,SV51: $i] :
( ( ( in @ ( sK44_SY1463 @ SV51 @ SV198 ) @ SV198 )
= $true )
| ( ( SV51 = SV198 )
= $true )
| ( ( in @ ( sK8_SY1462 @ SV198 @ SV51 ) @ SV51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1709]) ).
thf(1808,plain,
! [SV54: $i,SV200: $i] :
( ( ~ ( in @ ( sK45_SY1643 @ SV200 @ SV54 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ ( setadjoin @ ( sK45_SY1643 @ SV200 @ SV54 ) @ emptyset ) ) @ emptyset ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1809,plain,
! [SV58: $i,SV305: $i,SV204: $i] :
( ( ( ! [SY1675: $i] :
~ ~ ( ~ ( in @ SY1675 @ SV204 )
| ( SV305
!= ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ ( setadjoin @ SY1675 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false )
| ( ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1714]) ).
thf(1810,plain,
! [SV59: $i,SV205: $i] :
( ( ( ~ ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV205 ) )
= $false )
| ( ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 )
= $true )
| ( ( SV59 = SV205 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1715]) ).
thf(1813,plain,
! [SV60: $i,SV346: $o,SV206: $i,SV306: $i] :
( ( ( ~ ( in @ SV306 @ SV206 )
| SV346 )
= $false )
| ( SV346 = $true )
| ( ( in @ SV306 @ SV60 )
= $true )
| ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1718]) ).
thf(1819,plain,
! [SV60: $i,SV206: $i,SV306: $i] :
( ( ( ~ ( in @ SV306 @ SV206 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV306 @ SV60 )
= $true )
| ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1822,plain,
! [SV61: $i,SV207: $i] :
( ( ~ ( in @ ( sK46_SY1644 @ SV207 @ SV61 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ ( setadjoin @ ( sK46_SY1644 @ SV207 @ SV61 ) @ emptyset ) ) @ emptyset ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(1823,plain,
! [SV208: $i > $o,SV62: $i,SV388: $i] :
( ( ( ~ ( in @ SV388 @ SV62 )
| ~ ( SV208 @ SV388 ) )
= $true )
| ( ( in @ ( sK10_SY1478 @ SV208 @ SV62 ) @ SV62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1725]) ).
thf(1824,plain,
! [SV208: $i > $o,SV62: $i,SV389: $i] :
( ( ( ~ ( in @ SV389 @ SV62 )
| ~ ( SV208 @ SV389 ) )
= $true )
| ( ( SV208 @ ( sK10_SY1478 @ SV208 @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1726]) ).
thf(1825,plain,
! [SV210: $i,SV64: $i > $i > $o,SV392: $i] :
( ( ( ~ ( ~ ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV210 )
| ~ ( SV64 @ SY1694 @ SV392 ) ) )
| ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV210 )
| ~ ( SV64 @ SY1695 @ SV392 ) )
| ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) ) ) )
= $false )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1727]) ).
thf(1826,plain,
! [SV385: $i,SV210: $i,SV64: $i > $i > $o] :
( ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( ~ ! [SY1684: $i] :
( ~ ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SY1684 )
| ( SV385 = SY1684 ) ) )
= $true )
| ( ( ~ ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1728]) ).
thf(1827,plain,
! [SV216: $i > $o,SV70: $i,SV393: $i] :
( ( ( ~ ( ~ ( in @ SV393 @ SV70 )
| ~ ( SV216 @ SV393 ) ) )
= $false )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1828,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ( ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1730]) ).
thf(1829,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ( ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) ) )
= $false )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1731]) ).
thf(1830,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ( ~ ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1732]) ).
thf(1831,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ( ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) ) )
= $false )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(1832,plain,
! [SV374: $i,SV220: $i > $o,SV75: $i] :
( ( ( ! [SY1507: $i] :
~ ~ ( ~ ( in @ SY1507 @ SV75 )
| ~ ( SV220 @ SY1507 ) ) )
= $false )
| ( ( in @ SV374
@ ( dsetconstr @ SV75
@ ^ [SY1505: $i] : ( SV220 @ SY1505 ) ) )
= $false )
| ( ( ( dsetconstr @ SV75
@ ^ [SY1506: $i] : ( SV220 @ SY1506 ) )
= ( setadjoin @ SV374 @ emptyset ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1833,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) ) )
= $true )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1738]) ).
thf(1834,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1739]) ).
thf(1835,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( ~ ( ~ ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
| ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1740]) ).
thf(1836,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
| ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1837,plain,
! [SV356: $i,SV90: $i > $o] :
( ( ( ~ ( SV90 @ ( sK53_SY1659 @ SV356 @ SV90 ) ) )
= $false )
| ( ( SV90 @ SV356 )
= $false )
| ( ( ~ ! [SY1266: $i] :
~ ! [SY1267: $i] :
~ ( ~ ( ~ ( SV90 @ SY1267 )
| ( SY1267 = SY1266 ) )
| ~ ( ( SY1267 != SY1266 )
| ( SV90 @ SY1267 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1744]) ).
thf(1838,plain,
! [SV90: $i > $o,SV356: $i] :
( ( ( SV356
= ( sK53_SY1659 @ SV356 @ SV90 ) )
= $false )
| ( ( SV90 @ SV356 )
= $false )
| ( ( ~ ! [SY1266: $i] :
~ ! [SY1267: $i] :
~ ( ~ ( ~ ( SV90 @ SY1267 )
| ( SY1267 = SY1266 ) )
| ~ ( ( SY1267 != SY1266 )
| ( SV90 @ SY1267 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1744]) ).
thf(1839,plain,
! [SV91: $i,SV378: $o,SV233: $i,SV315: $i] :
( ( ( ~ ( in @ SV315 @ SV233 )
| SV378 )
= $false )
| ( SV378 = $true )
| ( ( SV315 = SV91 )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1745]) ).
thf(1845,plain,
! [SV91: $i,SV233: $i,SV315: $i] :
( ( ( ~ ( in @ SV315 @ SV233 )
| $false )
= $false )
| ( $false = $true )
| ( ( SV315 = SV91 )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1848,plain,
! [SV234: $i > $o,SV92: $i,SV394: $i] :
( ( ( ~ ( ~ ( in @ SV394 @ SV92 )
| ~ ( SV234 @ SV394 ) ) )
= $false )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1751]) ).
thf(1849,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ( ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1752]) ).
thf(1850,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ( ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) ) )
= $false )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(1851,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ( ~ ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1754]) ).
thf(1852,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ( ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) ) )
= $false )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(1853,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $true )
| ( ( ~ ( ( ( sK28_SY1661 @ SV357 @ SV98 )
!= SV357 )
| ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) ) ) )
= $true )
| ( ( ~ ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1756]) ).
thf(1854,plain,
! [SV98: $i > $o,SV357: $i] :
( ( ( ( ( sK28_SY1661 @ SV357 @ SV98 )
!= SV357 )
| ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) ) )
= $false )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $false )
| ( ( ~ ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1855,plain,
! [SV100: $i,SV241: $i,SV321: $i] :
( ( ( ! [SY1676: $i] :
~ ~ ( ~ ( in @ SY1676 @ ( setunion @ SV321 ) )
| ( SV321
!= ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ ( setadjoin @ SY1676 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false )
| ( ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1759]) ).
thf(1856,plain,
! [SV245: $i > $o,SV104: $i,SV396: $i] :
( ( ( ~ ( in @ SV396 @ SV104 )
| ~ ( SV245 @ SV396 ) )
= $true )
| ( ( in @ ( sK30_SY1550 @ SV245 @ SV104 ) @ SV104 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(1857,plain,
! [SV245: $i > $o,SV104: $i,SV397: $i] :
( ( ( ~ ( in @ SV397 @ SV104 )
| ~ ( SV245 @ SV397 ) )
= $true )
| ( ( SV245 @ ( sK30_SY1550 @ SV245 @ SV104 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(1858,plain,
! [SV358: $i,SV108: $i,SV398: $i] :
( ( ( ~ ~ ( ~ ( in @ SV398 @ ( setunion @ SV108 ) )
| ( SV108
!= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( in @ SV358 @ ( setunion @ SV108 ) )
= $false )
| ( ( ~ ! [SY1316: $i] :
~ ~ ( ~ ( in @ SY1316
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ SY1316 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(1859,plain,
! [SV381: $o,SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| SV381 )
= $false )
| ( SV381 = $true )
| ( ( in @ SV329 @ SV113 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1860,plain,
! [SV381: $o,SV113: $i,SV254: $i,SV329: $i] :
( ( ( in @ SV329 @ SV254 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| SV381 )
| SV381 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1764]) ).
thf(1865,plain,
! [SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV329 @ SV113 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1866,plain,
! [SV113: $i,SV254: $i,SV329: $i] :
( ( ( in @ SV329 @ SV254 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| $false )
| $false )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1868,plain,
! [SV258: $i,SV382: $i,SV118: $i,SV359: $i] :
( ( ( ~ ( in @ SV359 @ SV118 ) )
= $true )
| ( ( in @ SV382 @ SV258 )
= $true )
| ( ( SV359 = SV382 )
= $false )
| ( ( SV118 = SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1772]) ).
thf(1869,plain,
! [SV118: $i,SV359: $i,SV258: $i,SV382: $i] :
( ( ( ~ ( in @ SV382 @ SV258 ) )
= $true )
| ( ( in @ SV359 @ SV118 )
= $true )
| ( ( SV359 = SV382 )
= $false )
| ( ( SV118 = SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1773]) ).
thf(1870,plain,
! [SV119: $i,SV259: $i > $o,SV383: $i] :
( ( ( ~ ( in @ ( sK47_SY1564 @ SV383 @ SV259 @ SV119 ) @ SV119 )
| ~ ~ ( SV259 @ ( sK47_SY1564 @ SV383 @ SV259 @ SV119 ) ) )
= $false )
| ( ( SV259 @ SV383 )
= $true )
| ( ( in @ SV383 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1774]) ).
thf(1871,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ~ ( SV124 @ ( sK54_SY1664 @ SV360 @ SV124 ) ) )
= $false )
| ( ( SV124 @ SV360 )
= $false )
| ( ( ~ ! [SY1348: $i] :
~ ~ ( ~ ( SV124 @ SY1348 )
| ~ ! [SY1349: $i] :
( ~ ( SV124 @ SY1349 )
| ( SY1348 = SY1349 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1775]) ).
thf(1872,plain,
! [SV124: $i > $o,SV360: $i] :
( ( ( SV360
= ( sK54_SY1664 @ SV360 @ SV124 ) )
= $false )
| ( ( SV124 @ SV360 )
= $false )
| ( ( ~ ! [SY1348: $i] :
~ ~ ( ~ ( SV124 @ SY1348 )
| ~ ! [SY1349: $i] :
( ~ ( SV124 @ SY1349 )
| ( SY1348 = SY1349 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1775]) ).
thf(1873,plain,
! [SV126: $i,SV265: $i] :
( ( ( ~ ( in @ SV265 @ ( sK41_SY1568 @ SV126 @ SV265 ) ) )
= $false )
| ( ( in @ SV265 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1776]) ).
thf(1874,plain,
! [SV265: $i,SV126: $i] :
( ( ( ~ ( in @ ( sK41_SY1568 @ SV126 @ SV265 ) @ SV126 ) )
= $false )
| ( ( in @ SV265 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1776]) ).
thf(1875,plain,
! [SV126: $i,SV387: $i,SV265: $i] :
( ( ( ~ ( in @ SV265 @ SV387 ) )
= $true )
| ( ( ~ ( in @ SV387 @ SV126 ) )
= $true )
| ( ( in @ SV265 @ ( setunion @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(1876,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( SV130 @ ( sK42_SY1359 @ SV362 @ SV130 ) )
= $true )
| ( ( ~ ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1778]) ).
thf(1877,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK48_SY1690 @ SV362 @ SV130 ) ) )
= $false )
| ( ( ~ ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1779]) ).
thf(1878,plain,
! [SV130: $i > $o,SV362: $i] :
( ( ( ( sK42_SY1359 @ SV362 @ SV130 )
= ( sK48_SY1690 @ SV362 @ SV130 ) )
= $false )
| ( ( ~ ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1779]) ).
thf(1879,plain,
! [SV363: $i,SV137: $i > $o] :
( ( ( ~ ( SV137 @ ( sK55_SY1665 @ SV363 @ SV137 ) ) )
= $false )
| ( ( SV137 @ SV363 )
= $false )
| ( ( ~ ! [SY1372: $i] :
~ ( SV137 @ SY1372 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1780]) ).
thf(1880,plain,
! [SV137: $i > $o,SV363: $i] :
( ( ( SV363
= ( sK55_SY1665 @ SV363 @ SV137 ) )
= $false )
| ( ( SV137 @ SV363 )
= $false )
| ( ( ~ ! [SY1372: $i] :
~ ( SV137 @ SY1372 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1780]) ).
thf(1881,plain,
! [SV138: $i] :
( ( ( ~ ( in @ ( sK35_SY1373 @ SV138 ) @ omega ) )
= $false )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( ! [SY1374: $i] :
( ~ ( in @ SY1374 @ omega )
| ( in @ SY1374 @ SV138 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1781]) ).
thf(1882,plain,
! [SV138: $i] :
( ( ( ~ ( in @ ( sK35_SY1373 @ SV138 ) @ SV138 ) )
= $false )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( ! [SY1374: $i] :
( ~ ( in @ SY1374 @ omega )
| ( in @ SY1374 @ SV138 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1781]) ).
thf(1883,plain,
! [SV138: $i,SV390: $i] :
( ( ( in @ SV390 @ omega )
= $false )
| ( ( in @ SV390 @ SV138 )
= $true )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( in @ ( setadjoin @ ( sK35_SY1373 @ SV138 ) @ ( sK35_SY1373 @ SV138 ) ) @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(1884,plain,
! [SV142: $i,SV364: $i] :
( ( ( in @ ( sK37_SY1383 @ SV364 @ SV142 ) @ SV142 )
= $true )
| ( ( in @ SV364 @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1783]) ).
thf(1885,plain,
! [SV142: $i,SV364: $i] :
( ( ( ~ ~ ! [SY1685: $i] :
~ ~ ( ~ ( in @ SY1685 @ ( sK37_SY1383 @ SV364 @ SV142 ) )
| ~ ( in @ SY1685 @ SV142 ) ) )
= $true )
| ( ( in @ SV364 @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1784]) ).
thf(1886,plain,
! [SV275: $i > $o,SV399: $i,SV144: $i > $o] :
( ( ( ~ ~ ( ~ ( SV144 @ SV399 )
| ~ ! [SY1698: $i] :
( ~ ( SV144 @ SY1698 )
| ( SV399 = SY1698 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(1887,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( ~ ( ~ ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
| ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1786]) ).
thf(1888,plain,
! [SV144: $i > $o,SV275: $i > $o] :
( ( ( ~ ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
| ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) ) )
= $false )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1889,plain,
! [SV365: $i,SV148: $i > $o] :
( ( ( ~ ( SV148 @ ( sK56_SY1667 @ SV365 @ SV148 ) ) )
= $false )
| ( ( SV148 @ SV365 )
= $false )
| ( ( SV148
@ ( descr
@ ^ [SY1404: $i] : ( SV148 @ SY1404 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1788]) ).
thf(1890,plain,
! [SV148: $i > $o,SV365: $i] :
( ( ( SV365
= ( sK56_SY1667 @ SV365 @ SV148 ) )
= $false )
| ( ( SV148 @ SV365 )
= $false )
| ( ( SV148
@ ( descr
@ ^ [SY1404: $i] : ( SV148 @ SY1404 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1788]) ).
thf(1891,plain,
! [SV281: $i > $o,SV151: $i,SV400: $i] :
( ( ( ~ ( in @ SV400 @ SV151 )
| ~ ( SV281 @ SV400 ) )
= $true )
| ( ( in @ ( sK31_SY1588 @ SV281 @ SV151 ) @ SV151 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(1892,plain,
! [SV281: $i > $o,SV151: $i,SV401: $i] :
( ( ( ~ ( in @ SV401 @ SV151 )
| ~ ( SV281 @ SV401 ) )
= $true )
| ( ( SV281 @ ( sK31_SY1588 @ SV281 @ SV151 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(1893,plain,
! [SV366: $i,SV159: $i > $o] :
( ( ( ~ ( SV159 @ ( sK57_SY1668 @ SV366 @ SV159 ) ) )
= $false )
| ( ( SV159 @ SV366 )
= $false )
| ( ( ! [SY1422: $i,SY1423: $i] :
( ~ ( SV159 @ SY1422 )
| ~ ( SV159 @ SY1423 )
| ( SY1422 = SY1423 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1791]) ).
thf(1894,plain,
! [SV159: $i > $o,SV366: $i] :
( ( ( SV366
= ( sK57_SY1668 @ SV366 @ SV159 ) )
= $false )
| ( ( SV159 @ SV366 )
= $false )
| ( ( ! [SY1422: $i,SY1423: $i] :
( ~ ( SV159 @ SY1422 )
| ~ ( SV159 @ SY1423 )
| ( SY1422 = SY1423 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1791]) ).
thf(1895,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( in @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) @ SV162 )
= $true )
| ( ( ~ ! [SY1598: $i] :
~ ~ ( ~ ( in @ SY1598
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ SY1598 @ emptyset ) ) ) )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1792]) ).
thf(1896,plain,
! [SV162: $i,SV344: $i,SV290: $i > $o] :
( ( ( ~ ( SV290 @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) ) )
= $false )
| ( ( ~ ! [SY1598: $i] :
~ ~ ( ~ ( in @ SY1598
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ SY1598 @ emptyset ) ) ) )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1793]) ).
thf(1897,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( ( sK49_SY1639 @ SV344 @ SV290 @ SV162 )
= SV344 )
= $false )
| ( ( ~ ! [SY1598: $i] :
~ ~ ( ~ ( in @ SY1598
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ SY1598 @ emptyset ) ) ) )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1793]) ).
thf(1898,plain,
! [SV180: $i,SV367: $i > $o,SV349: $i > $o,SV29: $i] :
( ( ( in @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) @ SV180 )
= $true )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1794]) ).
thf(1899,plain,
! [SV29: $i,SV180: $i,SV349: $i > $o,SV367: $i > $o] :
( ( ( ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 )
!= ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
= $false )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1795]) ).
thf(1900,plain,
! [SV29: $i,SV180: $i,SV367: $i > $o,SV349: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) )
| ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) ) )
| ~ ( ~ ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
| ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1795]) ).
thf(1901,plain,
! [SV368: $i,SV181: $i > $o,SV31: $i] :
( ( ( ( dsetconstr @ SV31
@ ^ [SY1444: $i] : ( SV181 @ SY1444 ) )
= emptyset )
= $false )
| ( $false = $true )
| ( ( in @ SV368 @ SV31 )
= $false )
| ( ( SV181 @ SV368 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(1902,plain,
! [SV35: $i] :
( ( ! [SY1601: $i] :
( ~ ( in @ SY1601 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1111: $i] :
( ~ ( in @ SY1111 @ SY1601 )
| ( in @ SY1111 @ SV35 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1797]) ).
thf(1903,plain,
! [SV35: $i] :
( ( ! [SY1603: $i,SY1604: $i] :
( ~ ~ ( ~ ( in @ SY1603 @ SV35 )
| ~ ( in @ SY1604 @ SV35 ) )
| ~ ! [SY1605: $i] :
( ~ ( in @ SY1605 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SY1603 @ SY1605 )
| ( in @ SY1604 @ SY1605 ) )
| ~ ( ~ ( in @ SY1604 @ SY1605 )
| ( in @ SY1603 @ SY1605 ) ) ) )
| ( SY1603 = SY1604 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1798]) ).
thf(1904,plain,
! [SV395: $i,SV35: $i,SV391: $i] :
( ( ( ~ ~ ( ~ ( in @ SV391 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SV395 @ ( sK2_SY1109 @ SV35 ) ) ) )
= $true )
| ( ( ! [SY1696: $i] :
( ~ ( in @ SY1696 @ SV391 )
| ( in @ SY1696 @ SV395 ) )
| ! [SY1697: $i] :
( ~ ( in @ SY1697 @ SV395 )
| ( in @ SY1697 @ SV391 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(1905,plain,
! [SV35: $i,SV384: $i] :
( ( ( ! [SY1677: $i] :
( ~ ( in @ SY1677 @ SV384 )
| ( in @ SY1677 @ SV35 ) ) )
= $false )
| ( ( ~ ~ ! [SY1678: $i] :
~ ( in @ SY1678 @ SV384 ) )
= $true )
| ( ( ~ ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(1906,plain,
! [SV351: $i,SV37: $i > $o] :
( ( ( SV37 @ ( sK51_SY1650 @ SV351 @ SV37 ) )
= $true )
| ( ( SV37 @ SV351 )
= $false )
| ( ( ! [SY1130: $i,SY1131: $i] :
( ~ ( SV37 @ SY1130 )
| ~ ( SV37 @ SY1131 )
| ( SY1130 = SY1131 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1801]) ).
thf(1907,plain,
! [SV351: $i,SV402: $i,SV37: $i > $o] :
( ( ( ! [SY1699: $i] :
( ~ ( SV37 @ SV402 )
| ~ ( SV37 @ SY1699 )
| ( SV402 = SY1699 ) ) )
= $true )
| ( ( SV37 @ SV351 )
= $false )
| ( ( SV351
= ( sK51_SY1650 @ SV351 @ SV37 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(1908,plain,
! [SV369: $i,SV186: $i > $o,SV38: $i] :
( ( ( ! [SY1449: $i] :
( ~ ( in @ SY1449 @ SV38 )
| ( SV186 @ SY1449 ) ) )
= $false )
| ( ( in @ SV369 @ SV38 )
= $false )
| ( ( SV186 @ SV369 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(1909,plain,
! [SV45: $i,SV193: $i > $o,SV371: $i] :
( ( ( ~ ( in @ ( sK43_SY1458 @ SV371 @ SV193 @ SV45 ) @ SV45 ) )
= $false )
| ( ( SV193 @ SV371 )
= $true )
| ( ( in @ SV371 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1804]) ).
thf(1910,plain,
! [SV45: $i,SV371: $i,SV193: $i > $o] :
( ( ( ~ ~ ( SV193 @ ( sK43_SY1458 @ SV371 @ SV193 @ SV45 ) ) )
= $false )
| ( ( SV193 @ SV371 )
= $true )
| ( ( in @ SV371 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1804]) ).
thf(1911,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( SV50 @ ( sK52_SY1651 @ SV352 @ SV50 ) )
= $true )
| ( ( SV50 @ SV352 )
= $false )
| ( ( ~ ! [SY1160: $i] :
~ ~ ( ~ ( SV50 @ SY1160 )
| ~ ! [SY1161: $i] :
( ~ ( SV50 @ SY1161 )
| ( SY1160 = SY1161 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1805]) ).
thf(1912,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ! [SY1160: $i] :
~ ~ ( ~ ( SV50 @ SY1160 )
| ~ ! [SY1161: $i] :
( ~ ( SV50 @ SY1161 )
| ( SY1160 = SY1161 ) ) ) )
= $false )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV352
= ( sK52_SY1651 @ SV352 @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(1913,plain,
! [SV54: $i,SV200: $i] :
( ( ~ ( in @ ( sK45_SY1643 @ SV200 @ SV54 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1808]) ).
thf(1914,plain,
! [SV200: $i,SV54: $i] :
( ( ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ ( setadjoin @ ( sK45_SY1643 @ SV200 @ SV54 ) @ emptyset ) ) @ emptyset ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1808]) ).
thf(1915,plain,
! [SV204: $i,SV305: $i,SV58: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK58_SY1675 @ SV58 @ SV305 @ SV204 ) @ SV204 )
| ( SV305
!= ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ ( setadjoin @ ( sK58_SY1675 @ SV58 @ SV305 @ SV204 ) @ emptyset ) ) @ emptyset ) ) ) ) )
= $false )
| ( ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1809]) ).
thf(1916,plain,
! [SV59: $i,SV205: $i] :
( ( ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV205 )
= $true )
| ( ( in @ ( sK9_SY1473 @ SV205 @ SV59 ) @ SV59 )
= $true )
| ( ( SV59 = SV205 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1810]) ).
thf(1917,plain,
! [SV60: $i,SV346: $o,SV206: $i,SV306: $i] :
( ( ( ~ ( in @ SV306 @ SV206 ) )
= $false )
| ( SV346 = $true )
| ( ( in @ SV306 @ SV60 )
= $true )
| ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1813]) ).
thf(1923,plain,
! [SV60: $i,SV206: $i,SV306: $i] :
( ( ( ~ ( in @ SV306 @ SV206 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV306 @ SV60 )
= $true )
| ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1819]) ).
thf(1926,plain,
! [SV61: $i,SV207: $i] :
( ( ~ ( in @ ( sK46_SY1644 @ SV207 @ SV61 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1822]) ).
thf(1927,plain,
! [SV207: $i,SV61: $i] :
( ( ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ ( setadjoin @ ( sK46_SY1644 @ SV207 @ SV61 ) @ emptyset ) ) @ emptyset ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1822]) ).
thf(1928,plain,
! [SV208: $i > $o,SV62: $i,SV388: $i] :
( ( ( ~ ( in @ SV388 @ SV62 ) )
= $true )
| ( ( ~ ( SV208 @ SV388 ) )
= $true )
| ( ( in @ ( sK10_SY1478 @ SV208 @ SV62 ) @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1823]) ).
thf(1929,plain,
! [SV208: $i > $o,SV62: $i,SV389: $i] :
( ( ( ~ ( in @ SV389 @ SV62 ) )
= $true )
| ( ( ~ ( SV208 @ SV389 ) )
= $true )
| ( ( SV208 @ ( sK10_SY1478 @ SV208 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1824]) ).
thf(1930,plain,
! [SV210: $i,SV64: $i > $i > $o,SV392: $i] :
( ( ( ~ ( ~ ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV210 )
| ~ ( SV64 @ SY1694 @ SV392 ) ) ) )
= $false )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1825]) ).
thf(1931,plain,
! [SV392: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ~ ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV210 )
| ~ ( SV64 @ SY1695 @ SV392 ) )
| ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) ) ) )
= $false )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1825]) ).
thf(1932,plain,
! [SV385: $i,SV210: $i,SV64: $i > $i > $o] :
( ( ( ! [SY1684: $i] :
( ~ ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SY1684 )
| ( SV385 = SY1684 ) ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( ~ ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1826]) ).
thf(1933,plain,
! [SV216: $i > $o,SV70: $i,SV393: $i] :
( ( ( ~ ( in @ SV393 @ SV70 )
| ~ ( SV216 @ SV393 ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1827]) ).
thf(1934,plain,
! [SV216: $i > $o,SV70: $i,SV403: $i] :
( ( ( ~ ~ ( ~ ( in @ SV403 @ SV70 )
| ~ ( SV216 @ SV403 ) ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(1935,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ( ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1829]) ).
thf(1936,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ( ~ ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) ) )
= $false )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1830]) ).
thf(1937,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ( ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1831]) ).
thf(1938,plain,
! [SV75: $i,SV220: $i > $o,SV374: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK59_SY1507 @ SV374 @ SV220 @ SV75 ) @ SV75 )
| ~ ( SV220 @ ( sK59_SY1507 @ SV374 @ SV220 @ SV75 ) ) ) )
= $false )
| ( ( in @ SV374
@ ( dsetconstr @ SV75
@ ^ [SY1505: $i] : ( SV220 @ SY1505 ) ) )
= $false )
| ( ( ( dsetconstr @ SV75
@ ^ [SY1506: $i] : ( SV220 @ SY1506 ) )
= ( setadjoin @ SV374 @ emptyset ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1832]) ).
thf(1939,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) ) )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1833]) ).
thf(1940,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) ) )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(1941,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
| ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1835]) ).
thf(1943,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1836]) ).
thf(1944,plain,
! [SV356: $i,SV90: $i > $o] :
( ( ( SV90 @ ( sK53_SY1659 @ SV356 @ SV90 ) )
= $true )
| ( ( SV90 @ SV356 )
= $false )
| ( ( ~ ! [SY1266: $i] :
~ ! [SY1267: $i] :
~ ( ~ ( ~ ( SV90 @ SY1267 )
| ( SY1267 = SY1266 ) )
| ~ ( ( SY1267 != SY1266 )
| ( SV90 @ SY1267 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1837]) ).
thf(1945,plain,
! [SV356: $i,SV90: $i > $o] :
( ( ( ! [SY1266: $i] :
~ ! [SY1267: $i] :
~ ( ~ ( ~ ( SV90 @ SY1267 )
| ( SY1267 = SY1266 ) )
| ~ ( ( SY1267 != SY1266 )
| ( SV90 @ SY1267 ) ) ) )
= $false )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV356
= ( sK53_SY1659 @ SV356 @ SV90 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(1946,plain,
! [SV91: $i,SV378: $o,SV233: $i,SV315: $i] :
( ( ( ~ ( in @ SV315 @ SV233 ) )
= $false )
| ( SV378 = $true )
| ( ( SV315 = SV91 )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1839]) ).
thf(1952,plain,
! [SV91: $i,SV233: $i,SV315: $i] :
( ( ( ~ ( in @ SV315 @ SV233 ) )
= $false )
| ( $false = $true )
| ( ( SV315 = SV91 )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1845]) ).
thf(1955,plain,
! [SV234: $i > $o,SV92: $i,SV394: $i] :
( ( ( ~ ( in @ SV394 @ SV92 )
| ~ ( SV234 @ SV394 ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1848]) ).
thf(1956,plain,
! [SV234: $i > $o,SV92: $i,SV404: $i] :
( ( ( ~ ~ ( ~ ( in @ SV404 @ SV92 )
| ~ ( SV234 @ SV404 ) ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(1957,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ( ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1850]) ).
thf(1958,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ( ~ ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) ) )
= $false )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(1959,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ( ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1852]) ).
thf(1960,plain,
! [SV98: $i > $o,SV357: $i] :
( ( ( ( ( sK28_SY1661 @ SV357 @ SV98 )
!= SV357 )
| ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) ) )
= $false )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $true )
| ( ( ~ ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1853]) ).
thf(1962,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $false )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $false )
| ( ( ~ ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1854]) ).
thf(1963,plain,
! [SV321: $i,SV241: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK60_SY1676 @ SV100 @ SV241 @ SV321 ) @ ( setunion @ SV321 ) )
| ( SV321
!= ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ ( setadjoin @ ( sK60_SY1676 @ SV100 @ SV241 @ SV321 ) @ emptyset ) ) @ emptyset ) ) ) ) )
= $false )
| ( ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1855]) ).
thf(1964,plain,
! [SV245: $i > $o,SV104: $i,SV396: $i] :
( ( ( ~ ( in @ SV396 @ SV104 ) )
= $true )
| ( ( ~ ( SV245 @ SV396 ) )
= $true )
| ( ( in @ ( sK30_SY1550 @ SV245 @ SV104 ) @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1856]) ).
thf(1965,plain,
! [SV245: $i > $o,SV104: $i,SV397: $i] :
( ( ( ~ ( in @ SV397 @ SV104 ) )
= $true )
| ( ( ~ ( SV245 @ SV397 ) )
= $true )
| ( ( SV245 @ ( sK30_SY1550 @ SV245 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1857]) ).
thf(1966,plain,
! [SV358: $i,SV108: $i,SV398: $i] :
( ( ( ~ ( ~ ( in @ SV398 @ ( setunion @ SV108 ) )
| ( SV108
!= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false )
| ( ( in @ SV358 @ ( setunion @ SV108 ) )
= $false )
| ( ( ~ ! [SY1316: $i] :
~ ~ ( ~ ( in @ SY1316
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ SY1316 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(1968,plain,
! [SV113: $i,SV381: $o,SV254: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ SV254 )
| SV381 )
= $false )
| ( SV381 = $true )
| ( ( in @ SV329 @ SV113 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1859]) ).
thf(1969,plain,
! [SV381: $o,SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| SV381 ) )
= $true )
| ( SV381 = $true )
| ( ( in @ SV329 @ SV254 )
= $false )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1860]) ).
thf(1978,plain,
! [SV113: $i,SV254: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ SV254 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV329 @ SV113 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1865]) ).
thf(1979,plain,
! [SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV329 @ SV254 )
= $false )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1866]) ).
thf(1982,plain,
! [SV258: $i,SV382: $i,SV118: $i,SV359: $i] :
( ( ( in @ SV359 @ SV118 )
= $false )
| ( ( in @ SV382 @ SV258 )
= $true )
| ( ( SV359 = SV382 )
= $false )
| ( ( SV118 = SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(1983,plain,
! [SV118: $i,SV359: $i,SV258: $i,SV382: $i] :
( ( ( in @ SV382 @ SV258 )
= $false )
| ( ( in @ SV359 @ SV118 )
= $true )
| ( ( SV359 = SV382 )
= $false )
| ( ( SV118 = SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1984,plain,
! [SV119: $i,SV259: $i > $o,SV383: $i] :
( ( ( ~ ( in @ ( sK47_SY1564 @ SV383 @ SV259 @ SV119 ) @ SV119 ) )
= $false )
| ( ( SV259 @ SV383 )
= $true )
| ( ( in @ SV383 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1870]) ).
thf(1985,plain,
! [SV119: $i,SV383: $i,SV259: $i > $o] :
( ( ( ~ ~ ( SV259 @ ( sK47_SY1564 @ SV383 @ SV259 @ SV119 ) ) )
= $false )
| ( ( SV259 @ SV383 )
= $true )
| ( ( in @ SV383 @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1870]) ).
thf(1986,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( SV124 @ ( sK54_SY1664 @ SV360 @ SV124 ) )
= $true )
| ( ( SV124 @ SV360 )
= $false )
| ( ( ~ ! [SY1348: $i] :
~ ~ ( ~ ( SV124 @ SY1348 )
| ~ ! [SY1349: $i] :
( ~ ( SV124 @ SY1349 )
| ( SY1348 = SY1349 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1871]) ).
thf(1987,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ! [SY1348: $i] :
~ ~ ( ~ ( SV124 @ SY1348 )
| ~ ! [SY1349: $i] :
( ~ ( SV124 @ SY1349 )
| ( SY1348 = SY1349 ) ) ) )
= $false )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV360
= ( sK54_SY1664 @ SV360 @ SV124 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1872]) ).
thf(1988,plain,
! [SV126: $i,SV265: $i] :
( ( ( in @ SV265 @ ( sK41_SY1568 @ SV126 @ SV265 ) )
= $true )
| ( ( in @ SV265 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1873]) ).
thf(1989,plain,
! [SV265: $i,SV126: $i] :
( ( ( in @ ( sK41_SY1568 @ SV126 @ SV265 ) @ SV126 )
= $true )
| ( ( in @ SV265 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1874]) ).
thf(1990,plain,
! [SV126: $i,SV387: $i,SV265: $i] :
( ( ( in @ SV265 @ SV387 )
= $false )
| ( ( ~ ( in @ SV387 @ SV126 ) )
= $true )
| ( ( in @ SV265 @ ( setunion @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1875]) ).
thf(1991,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $false )
| ( ( SV130 @ ( sK42_SY1359 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(1992,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( SV130 @ ( sK48_SY1690 @ SV362 @ SV130 ) )
= $true )
| ( ( ~ ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1877]) ).
thf(1993,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $false )
| ( ( ( sK42_SY1359 @ SV362 @ SV130 )
= ( sK48_SY1690 @ SV362 @ SV130 ) )
= $false )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(1994,plain,
! [SV363: $i,SV137: $i > $o] :
( ( ( SV137 @ ( sK55_SY1665 @ SV363 @ SV137 ) )
= $true )
| ( ( SV137 @ SV363 )
= $false )
| ( ( ~ ! [SY1372: $i] :
~ ( SV137 @ SY1372 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1879]) ).
thf(1995,plain,
! [SV363: $i,SV137: $i > $o] :
( ( ( ! [SY1372: $i] :
~ ( SV137 @ SY1372 ) )
= $false )
| ( ( SV137 @ SV363 )
= $false )
| ( ( SV363
= ( sK55_SY1665 @ SV363 @ SV137 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1880]) ).
thf(1996,plain,
! [SV138: $i] :
( ( ( in @ ( sK35_SY1373 @ SV138 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( ! [SY1374: $i] :
( ~ ( in @ SY1374 @ omega )
| ( in @ SY1374 @ SV138 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1881]) ).
thf(1997,plain,
! [SV138: $i] :
( ( ( in @ ( sK35_SY1373 @ SV138 ) @ SV138 )
= $true )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( ! [SY1374: $i] :
( ~ ( in @ SY1374 @ omega )
| ( in @ SY1374 @ SV138 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1882]) ).
thf(1998,plain,
! [SV142: $i,SV364: $i] :
( ( ( ~ ! [SY1685: $i] :
~ ~ ( ~ ( in @ SY1685 @ ( sK37_SY1383 @ SV364 @ SV142 ) )
| ~ ( in @ SY1685 @ SV142 ) ) )
= $false )
| ( ( in @ SV364 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(1999,plain,
! [SV275: $i > $o,SV399: $i,SV144: $i > $o] :
( ( ( ~ ( ~ ( SV144 @ SV399 )
| ~ ! [SY1698: $i] :
( ~ ( SV144 @ SY1698 )
| ( SV399 = SY1698 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(2000,plain,
! [SV144: $i > $o,SV275: $i > $o] :
( ( ( ~ ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
| ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(2002,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1888]) ).
thf(2003,plain,
! [SV365: $i,SV148: $i > $o] :
( ( ( SV148 @ ( sK56_SY1667 @ SV365 @ SV148 ) )
= $true )
| ( ( SV148 @ SV365 )
= $false )
| ( ( SV148
@ ( descr
@ ^ [SY1404: $i] : ( SV148 @ SY1404 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1889]) ).
thf(2004,plain,
! [SV281: $i > $o,SV151: $i,SV400: $i] :
( ( ( ~ ( in @ SV400 @ SV151 ) )
= $true )
| ( ( ~ ( SV281 @ SV400 ) )
= $true )
| ( ( in @ ( sK31_SY1588 @ SV281 @ SV151 ) @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1891]) ).
thf(2005,plain,
! [SV281: $i > $o,SV151: $i,SV401: $i] :
( ( ( ~ ( in @ SV401 @ SV151 ) )
= $true )
| ( ( ~ ( SV281 @ SV401 ) )
= $true )
| ( ( SV281 @ ( sK31_SY1588 @ SV281 @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(2006,plain,
! [SV366: $i,SV159: $i > $o] :
( ( ( SV159 @ ( sK57_SY1668 @ SV366 @ SV159 ) )
= $true )
| ( ( SV159 @ SV366 )
= $false )
| ( ( ! [SY1422: $i,SY1423: $i] :
( ~ ( SV159 @ SY1422 )
| ~ ( SV159 @ SY1423 )
| ( SY1422 = SY1423 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1893]) ).
thf(2007,plain,
! [SV366: $i,SV405: $i,SV159: $i > $o] :
( ( ( ! [SY1700: $i] :
( ~ ( SV159 @ SV405 )
| ~ ( SV159 @ SY1700 )
| ( SV405 = SY1700 ) ) )
= $true )
| ( ( SV159 @ SV366 )
= $false )
| ( ( SV366
= ( sK57_SY1668 @ SV366 @ SV159 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2008,plain,
! [SV344: $i,SV290: $i > $o,SV162: $i] :
( ( ( ! [SY1598: $i] :
~ ~ ( ~ ( in @ SY1598
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ SY1598 @ emptyset ) ) ) )
= $false )
| ( ( in @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) @ SV162 )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(2009,plain,
! [SV162: $i,SV344: $i,SV290: $i > $o] :
( ( ( SV290 @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) )
= $true )
| ( ( ~ ! [SY1598: $i] :
~ ~ ( ~ ( in @ SY1598
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ SY1598 @ emptyset ) ) ) )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1896]) ).
thf(2010,plain,
! [SV344: $i,SV290: $i > $o,SV162: $i] :
( ( ( ! [SY1598: $i] :
~ ~ ( ~ ( in @ SY1598
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ SY1598 @ emptyset ) ) ) )
= $false )
| ( ( ( sK49_SY1639 @ SV344 @ SV290 @ SV162 )
= SV344 )
= $false )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1897]) ).
thf(2011,plain,
! [SV29: $i,SV180: $i,SV349: $i > $o,SV367: $i > $o] :
( ( ( ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 )
= ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
= $true )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1899]) ).
thf(2012,plain,
! [SV29: $i,SV180: $i,SV367: $i > $o,SV349: $i > $o] :
( ( ( ~ ( ~ ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) )
| ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) ) )
| ~ ( ~ ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
| ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1900]) ).
thf(2013,plain,
! [SV35: $i,SV406: $i] :
( ( ~ ( in @ SV406 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1701: $i] :
( ~ ( in @ SY1701 @ SV406 )
| ( in @ SY1701 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2014,plain,
! [SV35: $i,SV407: $i] :
( ( ! [SY1702: $i] :
( ~ ~ ( ~ ( in @ SV407 @ SV35 )
| ~ ( in @ SY1702 @ SV35 ) )
| ~ ! [SY1703: $i] :
( ~ ( in @ SY1703 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SV407 @ SY1703 )
| ( in @ SY1702 @ SY1703 ) )
| ~ ( ~ ( in @ SY1702 @ SY1703 )
| ( in @ SV407 @ SY1703 ) ) ) )
| ( SV407 = SY1702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2015,plain,
! [SV395: $i,SV35: $i,SV391: $i] :
( ( ( ~ ( ~ ( in @ SV391 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SV395 @ ( sK2_SY1109 @ SV35 ) ) ) )
= $false )
| ( ( ! [SY1696: $i] :
( ~ ( in @ SY1696 @ SV391 )
| ( in @ SY1696 @ SV395 ) )
| ! [SY1697: $i] :
( ~ ( in @ SY1697 @ SV395 )
| ( in @ SY1697 @ SV391 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1904]) ).
thf(2016,plain,
! [SV384: $i,SV35: $i] :
( ( ( ~ ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
| ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 ) )
= $false )
| ( ( ~ ~ ! [SY1678: $i] :
~ ( in @ SY1678 @ SV384 ) )
= $true )
| ( ( ~ ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1905]) ).
thf(2017,plain,
! [SV351: $i,SV408: $i,SV37: $i > $o] :
( ( ( ! [SY1704: $i] :
( ~ ( SV37 @ SV408 )
| ~ ( SV37 @ SY1704 )
| ( SV408 = SY1704 ) ) )
= $true )
| ( ( SV37 @ SV351 )
= $false )
| ( ( SV37 @ ( sK51_SY1650 @ SV351 @ SV37 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2018,plain,
! [SV351: $i,SV409: $i,SV402: $i,SV37: $i > $o] :
( ( ( ~ ( SV37 @ SV402 )
| ~ ( SV37 @ SV409 )
| ( SV402 = SV409 ) )
= $true )
| ( ( SV37 @ SV351 )
= $false )
| ( ( SV351
= ( sK51_SY1650 @ SV351 @ SV37 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2019,plain,
! [SV38: $i,SV186: $i > $o,SV369: $i] :
( ( ( ~ ( in @ ( sK62_SY1449 @ SV369 @ SV186 @ SV38 ) @ SV38 )
| ( SV186 @ ( sK62_SY1449 @ SV369 @ SV186 @ SV38 ) ) )
= $false )
| ( ( in @ SV369 @ SV38 )
= $false )
| ( ( SV186 @ SV369 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1908]) ).
thf(2020,plain,
! [SV45: $i,SV193: $i > $o,SV371: $i] :
( ( ( in @ ( sK43_SY1458 @ SV371 @ SV193 @ SV45 ) @ SV45 )
= $true )
| ( ( SV193 @ SV371 )
= $true )
| ( ( in @ SV371 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1909]) ).
thf(2021,plain,
! [SV45: $i,SV371: $i,SV193: $i > $o] :
( ( ( ~ ( SV193 @ ( sK43_SY1458 @ SV371 @ SV193 @ SV45 ) ) )
= $true )
| ( ( SV193 @ SV371 )
= $true )
| ( ( in @ SV371 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1910]) ).
thf(2022,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ! [SY1160: $i] :
~ ~ ( ~ ( SV50 @ SY1160 )
| ~ ! [SY1161: $i] :
( ~ ( SV50 @ SY1161 )
| ( SY1160 = SY1161 ) ) ) )
= $false )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV50 @ ( sK52_SY1651 @ SV352 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1911]) ).
thf(2023,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ~ ~ ( ~ ( SV50 @ ( sK63_SY1160 @ SV352 @ SV50 ) )
| ~ ! [SY1705: $i] :
( ~ ( SV50 @ SY1705 )
| ( ( sK63_SY1160 @ SV352 @ SV50 )
= SY1705 ) ) ) )
= $false )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV352
= ( sK52_SY1651 @ SV352 @ SV50 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1912]) ).
thf(2024,plain,
! [SV54: $i,SV200: $i] :
( ( in @ ( sK45_SY1643 @ SV200 @ SV54 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1913]) ).
thf(2025,plain,
! [SV200: $i,SV54: $i] :
( ( ( setadjoin @ ( setadjoin @ SV54 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV54 @ ( setadjoin @ SV200 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK4_SY1465 @ SV200 @ SV54 ) @ ( setadjoin @ ( sK45_SY1643 @ SV200 @ SV54 ) @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1914]) ).
thf(2026,plain,
! [SV204: $i,SV305: $i,SV58: $i] :
( ( ( ~ ( ~ ( in @ ( sK58_SY1675 @ SV58 @ SV305 @ SV204 ) @ SV204 )
| ( SV305
!= ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ ( setadjoin @ ( sK58_SY1675 @ SV58 @ SV305 @ SV204 ) @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1915]) ).
thf(2027,plain,
! [SV60: $i,SV346: $o,SV206: $i,SV306: $i] :
( ( ( in @ SV306 @ SV206 )
= $true )
| ( SV346 = $true )
| ( ( in @ SV306 @ SV60 )
= $true )
| ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1917]) ).
thf(2029,plain,
! [SV60: $i,SV206: $i,SV306: $i] :
( ( ( in @ SV306 @ SV206 )
= $true )
| ( $false = $true )
| ( ( in @ SV306 @ SV60 )
= $true )
| ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1923]) ).
thf(2030,plain,
! [SV61: $i,SV207: $i] :
( ( in @ ( sK46_SY1644 @ SV207 @ SV61 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1926]) ).
thf(2031,plain,
! [SV207: $i,SV61: $i] :
( ( ( setadjoin @ ( setadjoin @ SV61 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV61 @ ( setadjoin @ SV207 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK5_SY1476 @ SV207 @ SV61 ) @ ( setadjoin @ ( sK46_SY1644 @ SV207 @ SV61 ) @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1927]) ).
thf(2032,plain,
! [SV208: $i > $o,SV62: $i,SV388: $i] :
( ( ( in @ SV388 @ SV62 )
= $false )
| ( ( ~ ( SV208 @ SV388 ) )
= $true )
| ( ( in @ ( sK10_SY1478 @ SV208 @ SV62 ) @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1928]) ).
thf(2033,plain,
! [SV208: $i > $o,SV62: $i,SV389: $i] :
( ( ( in @ SV389 @ SV62 )
= $false )
| ( ( ~ ( SV208 @ SV389 ) )
= $true )
| ( ( SV208 @ ( sK10_SY1478 @ SV208 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1929]) ).
thf(2034,plain,
! [SV210: $i,SV64: $i > $i > $o,SV392: $i] :
( ( ( ~ ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
| ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV210 )
| ~ ( SV64 @ SY1694 @ SV392 ) ) )
= $true )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1930]) ).
thf(2035,plain,
! [SV392: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV210 )
| ~ ( SV64 @ SY1695 @ SV392 ) )
| ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) ) )
= $true )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1931]) ).
thf(2036,plain,
! [SV385: $i,SV210: $i,SV64: $i > $i > $o] :
( ( ( ~ ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
| ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( ~ ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1932]) ).
thf(2037,plain,
! [SV216: $i > $o,SV70: $i,SV393: $i] :
( ( ( ~ ( in @ SV393 @ SV70 ) )
= $true )
| ( ( ~ ( SV216 @ SV393 ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1933]) ).
thf(2038,plain,
! [SV216: $i > $o,SV70: $i,SV403: $i] :
( ( ( ~ ( ~ ( in @ SV403 @ SV70 )
| ~ ( SV216 @ SV403 ) ) )
= $false )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(2039,plain,
! [SV216: $i > $o,SV70: $i,SV410: $i] :
( ( ( ~ ~ ( ~ ( in @ SV410 @ SV70 )
| ~ ( SV216 @ SV410 ) ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2040,plain,
! [SV216: $i > $o,SV70: $i] :
( ( ( ! [SY1494: $i] :
~ ~ ( ~ ( in @ SY1494 @ SV70 )
| ~ ( SV216 @ SY1494 ) ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1936]) ).
thf(2041,plain,
! [SV216: $i > $o,SV70: $i,SV411: $i] :
( ( ( ~ ~ ( ~ ( in @ SV411 @ SV70 )
| ~ ( SV216 @ SV411 ) ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2042,plain,
! [SV75: $i,SV220: $i > $o,SV374: $i] :
( ( ( ~ ( ~ ( in @ ( sK59_SY1507 @ SV374 @ SV220 @ SV75 ) @ SV75 )
| ~ ( SV220 @ ( sK59_SY1507 @ SV374 @ SV220 @ SV75 ) ) ) )
= $true )
| ( ( in @ SV374
@ ( dsetconstr @ SV75
@ ^ [SY1505: $i] : ( SV220 @ SY1505 ) ) )
= $false )
| ( ( ( dsetconstr @ SV75
@ ^ [SY1506: $i] : ( SV220 @ SY1506 ) )
= ( setadjoin @ SV374 @ emptyset ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1938]) ).
thf(2043,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) ) )
= $true )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1939]) ).
thf(2044,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1940]) ).
thf(2045,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1941]) ).
thf(2048,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1943]) ).
thf(2049,plain,
! [SV356: $i,SV90: $i > $o] :
( ( ( ! [SY1266: $i] :
~ ! [SY1267: $i] :
~ ( ~ ( ~ ( SV90 @ SY1267 )
| ( SY1267 = SY1266 ) )
| ~ ( ( SY1267 != SY1266 )
| ( SV90 @ SY1267 ) ) ) )
= $false )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV90 @ ( sK53_SY1659 @ SV356 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1944]) ).
thf(2050,plain,
! [SV356: $i,SV90: $i > $o] :
( ( ( ~ ! [SY1706: $i] :
~ ( ~ ( ~ ( SV90 @ SY1706 )
| ( SY1706
= ( sK65_SY1266 @ SV356 @ SV90 ) ) )
| ~ ( ( SY1706
!= ( sK65_SY1266 @ SV356 @ SV90 ) )
| ( SV90 @ SY1706 ) ) ) )
= $false )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV356
= ( sK53_SY1659 @ SV356 @ SV90 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1945]) ).
thf(2051,plain,
! [SV91: $i,SV378: $o,SV233: $i,SV315: $i] :
( ( ( in @ SV315 @ SV233 )
= $true )
| ( SV378 = $true )
| ( ( SV315 = SV91 )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1946]) ).
thf(2053,plain,
! [SV91: $i,SV233: $i,SV315: $i] :
( ( ( in @ SV315 @ SV233 )
= $true )
| ( $false = $true )
| ( ( SV315 = SV91 )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1952]) ).
thf(2054,plain,
! [SV234: $i > $o,SV92: $i,SV394: $i] :
( ( ( ~ ( in @ SV394 @ SV92 ) )
= $true )
| ( ( ~ ( SV234 @ SV394 ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1955]) ).
thf(2055,plain,
! [SV234: $i > $o,SV92: $i,SV404: $i] :
( ( ( ~ ( ~ ( in @ SV404 @ SV92 )
| ~ ( SV234 @ SV404 ) ) )
= $false )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1956]) ).
thf(2056,plain,
! [SV234: $i > $o,SV92: $i,SV412: $i] :
( ( ( ~ ~ ( ~ ( in @ SV412 @ SV92 )
| ~ ( SV234 @ SV412 ) ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2057,plain,
! [SV234: $i > $o,SV92: $i] :
( ( ( ! [SY1532: $i] :
~ ~ ( ~ ( in @ SY1532 @ SV92 )
| ~ ( SV234 @ SY1532 ) ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1958]) ).
thf(2058,plain,
! [SV234: $i > $o,SV92: $i,SV413: $i] :
( ( ( ~ ~ ( ~ ( in @ SV413 @ SV92 )
| ~ ( SV234 @ SV413 ) ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2059,plain,
! [SV98: $i > $o,SV357: $i] :
( ( ( ( sK28_SY1661 @ SV357 @ SV98 )
!= SV357 )
= $false )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $true )
| ( ( ~ ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1960]) ).
thf(2062,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $false )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $false )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1962]) ).
thf(2063,plain,
! [SV321: $i,SV241: $i,SV100: $i] :
( ( ( ~ ( ~ ( in @ ( sK60_SY1676 @ SV100 @ SV241 @ SV321 ) @ ( setunion @ SV321 ) )
| ( SV321
!= ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ ( setadjoin @ ( sK60_SY1676 @ SV100 @ SV241 @ SV321 ) @ emptyset ) ) @ emptyset ) ) ) ) )
= $true )
| ( ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1963]) ).
thf(2064,plain,
! [SV245: $i > $o,SV104: $i,SV396: $i] :
( ( ( in @ SV396 @ SV104 )
= $false )
| ( ( ~ ( SV245 @ SV396 ) )
= $true )
| ( ( in @ ( sK30_SY1550 @ SV245 @ SV104 ) @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2065,plain,
! [SV245: $i > $o,SV104: $i,SV397: $i] :
( ( ( in @ SV397 @ SV104 )
= $false )
| ( ( ~ ( SV245 @ SV397 ) )
= $true )
| ( ( SV245 @ ( sK30_SY1550 @ SV245 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1965]) ).
thf(2066,plain,
! [SV358: $i,SV108: $i,SV398: $i] :
( ( ( ~ ( in @ SV398 @ ( setunion @ SV108 ) )
| ( SV108
!= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV358 @ ( setunion @ SV108 ) )
= $false )
| ( ( ~ ! [SY1316: $i] :
~ ~ ( ~ ( in @ SY1316
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ SY1316 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1966]) ).
thf(2068,plain,
! [SV113: $i,SV381: $o,SV254: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ SV254 ) )
= $false )
| ( SV381 = $true )
| ( ( in @ SV329 @ SV113 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1968]) ).
thf(2070,plain,
! [SV381: $o,SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| SV381 )
= $false )
| ( SV381 = $true )
| ( ( in @ SV329 @ SV254 )
= $false )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1969]) ).
thf(2082,plain,
! [SV113: $i,SV254: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ SV254 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV329 @ SV113 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1978]) ).
thf(2084,plain,
! [SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ~ ( in @ SV329 @ SV113 )
| ~ ( in @ SV329 @ SV254 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV329 @ SV254 )
= $false )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1979]) ).
thf(2088,plain,
! [SV119: $i,SV259: $i > $o,SV383: $i] :
( ( ( in @ ( sK47_SY1564 @ SV383 @ SV259 @ SV119 ) @ SV119 )
= $true )
| ( ( SV259 @ SV383 )
= $true )
| ( ( in @ SV383 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1984]) ).
thf(2089,plain,
! [SV119: $i,SV383: $i,SV259: $i > $o] :
( ( ( ~ ( SV259 @ ( sK47_SY1564 @ SV383 @ SV259 @ SV119 ) ) )
= $true )
| ( ( SV259 @ SV383 )
= $true )
| ( ( in @ SV383 @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1985]) ).
thf(2090,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ! [SY1348: $i] :
~ ~ ( ~ ( SV124 @ SY1348 )
| ~ ! [SY1349: $i] :
( ~ ( SV124 @ SY1349 )
| ( SY1348 = SY1349 ) ) ) )
= $false )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV124 @ ( sK54_SY1664 @ SV360 @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1986]) ).
thf(2091,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ~ ~ ( ~ ( SV124 @ ( sK66_SY1348 @ SV360 @ SV124 ) )
| ~ ! [SY1707: $i] :
( ~ ( SV124 @ SY1707 )
| ( ( sK66_SY1348 @ SV360 @ SV124 )
= SY1707 ) ) ) )
= $false )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV360
= ( sK54_SY1664 @ SV360 @ SV124 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1987]) ).
thf(2092,plain,
! [SV265: $i,SV126: $i,SV387: $i] :
( ( ( in @ SV387 @ SV126 )
= $false )
| ( ( in @ SV265 @ SV387 )
= $false )
| ( ( in @ SV265 @ ( setunion @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1990]) ).
thf(2093,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ~ ( ~ ( SV130 @ ( sK67_SY1361 @ SV362 @ SV130 ) )
| ~ ! [SY1708: $i] :
( ~ ( SV130 @ SY1708 )
| ( ( sK67_SY1361 @ SV362 @ SV130 )
= SY1708 ) ) ) )
= $false )
| ( ( SV130 @ ( sK42_SY1359 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1991]) ).
thf(2094,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ! [SY1361: $i] :
~ ~ ( ~ ( SV130 @ SY1361 )
| ~ ! [SY1362: $i] :
( ~ ( SV130 @ SY1362 )
| ( SY1361 = SY1362 ) ) ) )
= $false )
| ( ( SV130 @ ( sK48_SY1690 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1992]) ).
thf(2095,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ~ ( ~ ( SV130 @ ( sK68_SY1361 @ SV362 @ SV130 ) )
| ~ ! [SY1709: $i] :
( ~ ( SV130 @ SY1709 )
| ( ( sK68_SY1361 @ SV362 @ SV130 )
= SY1709 ) ) ) )
= $false )
| ( ( ( sK42_SY1359 @ SV362 @ SV130 )
= ( sK48_SY1690 @ SV362 @ SV130 ) )
= $false )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1993]) ).
thf(2096,plain,
! [SV363: $i,SV137: $i > $o] :
( ( ( ! [SY1372: $i] :
~ ( SV137 @ SY1372 ) )
= $false )
| ( ( SV137 @ SV363 )
= $false )
| ( ( SV137 @ ( sK55_SY1665 @ SV363 @ SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1994]) ).
thf(2097,plain,
! [SV363: $i,SV137: $i > $o] :
( ( ( ~ ( SV137 @ ( sK69_SY1372 @ SV363 @ SV137 ) ) )
= $false )
| ( ( SV137 @ SV363 )
= $false )
| ( ( SV363
= ( sK55_SY1665 @ SV363 @ SV137 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1995]) ).
thf(2098,plain,
! [SV138: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ omega )
| ( in @ SV414 @ SV138 ) )
= $true )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( in @ ( sK35_SY1373 @ SV138 ) @ omega )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2099,plain,
! [SV138: $i,SV415: $i] :
( ( ( ~ ( in @ SV415 @ omega )
| ( in @ SV415 @ SV138 ) )
= $true )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( in @ ( sK35_SY1373 @ SV138 ) @ SV138 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2100,plain,
! [SV142: $i,SV364: $i] :
( ( ( ! [SY1685: $i] :
~ ~ ( ~ ( in @ SY1685 @ ( sK37_SY1383 @ SV364 @ SV142 ) )
| ~ ( in @ SY1685 @ SV142 ) ) )
= $true )
| ( ( in @ SV364 @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1998]) ).
thf(2101,plain,
! [SV275: $i > $o,SV399: $i,SV144: $i > $o] :
( ( ( ~ ( SV144 @ SV399 )
| ~ ! [SY1698: $i] :
( ~ ( SV144 @ SY1698 )
| ( SV399 = SY1698 ) ) )
= $true )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1999]) ).
thf(2102,plain,
! [SV144: $i > $o,SV275: $i > $o] :
( ( ( ~ ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2000]) ).
thf(2105,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2002]) ).
thf(2106,plain,
! [SV281: $i > $o,SV151: $i,SV400: $i] :
( ( ( in @ SV400 @ SV151 )
= $false )
| ( ( ~ ( SV281 @ SV400 ) )
= $true )
| ( ( in @ ( sK31_SY1588 @ SV281 @ SV151 ) @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2107,plain,
! [SV281: $i > $o,SV151: $i,SV401: $i] :
( ( ( in @ SV401 @ SV151 )
= $false )
| ( ( ~ ( SV281 @ SV401 ) )
= $true )
| ( ( SV281 @ ( sK31_SY1588 @ SV281 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2005]) ).
thf(2108,plain,
! [SV366: $i,SV416: $i,SV159: $i > $o] :
( ( ( ! [SY1710: $i] :
( ~ ( SV159 @ SV416 )
| ~ ( SV159 @ SY1710 )
| ( SV416 = SY1710 ) ) )
= $true )
| ( ( SV159 @ SV366 )
= $false )
| ( ( SV159 @ ( sK57_SY1668 @ SV366 @ SV159 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2109,plain,
! [SV366: $i,SV417: $i,SV405: $i,SV159: $i > $o] :
( ( ( ~ ( SV159 @ SV405 )
| ~ ( SV159 @ SV417 )
| ( SV405 = SV417 ) )
= $true )
| ( ( SV159 @ SV366 )
= $false )
| ( ( SV366
= ( sK57_SY1668 @ SV366 @ SV159 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2110,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK70_SY1598 @ SV344 @ SV290 @ SV162 )
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ ( sK70_SY1598 @ SV344 @ SV290 @ SV162 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) @ SV162 )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2008]) ).
thf(2111,plain,
! [SV344: $i,SV290: $i > $o,SV162: $i] :
( ( ( ! [SY1598: $i] :
~ ~ ( ~ ( in @ SY1598
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ SY1598 @ emptyset ) ) ) )
= $false )
| ( ( SV290 @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2112,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK71_SY1598 @ SV344 @ SV290 @ SV162 )
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ ( sK71_SY1598 @ SV344 @ SV290 @ SV162 ) @ emptyset ) ) ) )
= $false )
| ( ( ( sK49_SY1639 @ SV344 @ SV290 @ SV162 )
= SV344 )
= $false )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2010]) ).
thf(2113,plain,
! [SV29: $i,SV180: $i,SV367: $i > $o,SV349: $i > $o] :
( ( ( ~ ( ~ ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) )
| ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
| ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2012]) ).
thf(2114,plain,
! [SV35: $i,SV406: $i] :
( ( ( ~ ( in @ SV406 @ ( sK2_SY1109 @ SV35 ) ) )
= $true )
| ( ( ! [SY1701: $i] :
( ~ ( in @ SY1701 @ SV406 )
| ( in @ SY1701 @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2013]) ).
thf(2115,plain,
! [SV418: $i,SV35: $i,SV407: $i] :
( ( ~ ~ ( ~ ( in @ SV407 @ SV35 )
| ~ ( in @ SV418 @ SV35 ) )
| ~ ! [SY1715: $i] :
( ~ ( in @ SY1715 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SV407 @ SY1715 )
| ( in @ SV418 @ SY1715 ) )
| ~ ( ~ ( in @ SV418 @ SY1715 )
| ( in @ SV407 @ SY1715 ) ) ) )
| ( SV407 = SV418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2116,plain,
! [SV395: $i,SV35: $i,SV391: $i] :
( ( ( ~ ( in @ SV391 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SV395 @ ( sK2_SY1109 @ SV35 ) ) )
= $true )
| ( ( ! [SY1696: $i] :
( ~ ( in @ SY1696 @ SV391 )
| ( in @ SY1696 @ SV395 ) )
| ! [SY1697: $i] :
( ~ ( in @ SY1697 @ SV395 )
| ( in @ SY1697 @ SV391 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2015]) ).
thf(2117,plain,
! [SV384: $i,SV35: $i] :
( ( ( ~ ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 ) )
= $false )
| ( ( ~ ~ ! [SY1678: $i] :
~ ( in @ SY1678 @ SV384 ) )
= $true )
| ( ( ~ ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2016]) ).
thf(2118,plain,
! [SV384: $i,SV35: $i] :
( ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( ~ ~ ! [SY1678: $i] :
~ ( in @ SY1678 @ SV384 ) )
= $true )
| ( ( ~ ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2016]) ).
thf(2119,plain,
! [SV351: $i,SV419: $i,SV408: $i,SV37: $i > $o] :
( ( ( ~ ( SV37 @ SV408 )
| ~ ( SV37 @ SV419 )
| ( SV408 = SV419 ) )
= $true )
| ( ( SV37 @ SV351 )
= $false )
| ( ( SV37 @ ( sK51_SY1650 @ SV351 @ SV37 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2120,plain,
! [SV351: $i,SV409: $i,SV402: $i,SV37: $i > $o] :
( ( ( ~ ( SV37 @ SV402 ) )
= $true )
| ( ( ~ ( SV37 @ SV409 )
| ( SV402 = SV409 ) )
= $true )
| ( ( SV37 @ SV351 )
= $false )
| ( ( SV351
= ( sK51_SY1650 @ SV351 @ SV37 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2018]) ).
thf(2121,plain,
! [SV38: $i,SV186: $i > $o,SV369: $i] :
( ( ( ~ ( in @ ( sK62_SY1449 @ SV369 @ SV186 @ SV38 ) @ SV38 ) )
= $false )
| ( ( in @ SV369 @ SV38 )
= $false )
| ( ( SV186 @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2019]) ).
thf(2122,plain,
! [SV38: $i,SV369: $i,SV186: $i > $o] :
( ( ( SV186 @ ( sK62_SY1449 @ SV369 @ SV186 @ SV38 ) )
= $false )
| ( ( in @ SV369 @ SV38 )
= $false )
| ( ( SV186 @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2019]) ).
thf(2123,plain,
! [SV45: $i,SV371: $i,SV193: $i > $o] :
( ( ( SV193 @ ( sK43_SY1458 @ SV371 @ SV193 @ SV45 ) )
= $false )
| ( ( SV193 @ SV371 )
= $true )
| ( ( in @ SV371 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2021]) ).
thf(2124,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ~ ~ ( ~ ( SV50 @ ( sK72_SY1160 @ SV352 @ SV50 ) )
| ~ ! [SY1716: $i] :
( ~ ( SV50 @ SY1716 )
| ( ( sK72_SY1160 @ SV352 @ SV50 )
= SY1716 ) ) ) )
= $false )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV50 @ ( sK52_SY1651 @ SV352 @ SV50 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2022]) ).
thf(2125,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ~ ( ~ ( SV50 @ ( sK63_SY1160 @ SV352 @ SV50 ) )
| ~ ! [SY1705: $i] :
( ~ ( SV50 @ SY1705 )
| ( ( sK63_SY1160 @ SV352 @ SV50 )
= SY1705 ) ) ) )
= $true )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV352
= ( sK52_SY1651 @ SV352 @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2023]) ).
thf(2126,plain,
! [SV204: $i,SV305: $i,SV58: $i] :
( ( ( ~ ( in @ ( sK58_SY1675 @ SV58 @ SV305 @ SV204 ) @ SV204 )
| ( SV305
!= ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ ( setadjoin @ ( sK58_SY1675 @ SV58 @ SV305 @ SV204 ) @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2026]) ).
thf(2127,plain,
! [SV62: $i,SV388: $i,SV208: $i > $o] :
( ( ( SV208 @ SV388 )
= $false )
| ( ( in @ SV388 @ SV62 )
= $false )
| ( ( in @ ( sK10_SY1478 @ SV208 @ SV62 ) @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2032]) ).
thf(2128,plain,
! [SV62: $i,SV389: $i,SV208: $i > $o] :
( ( ( SV208 @ SV389 )
= $false )
| ( ( in @ SV389 @ SV62 )
= $false )
| ( ( SV208 @ ( sK10_SY1478 @ SV208 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2129,plain,
! [SV210: $i,SV64: $i > $i > $o,SV392: $i] :
( ( ( ~ ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) ) )
= $true )
| ( ( ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV210 )
| ~ ( SV64 @ SY1694 @ SV392 ) ) )
= $true )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2034]) ).
thf(2130,plain,
! [SV392: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ~ ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV210 )
| ~ ( SV64 @ SY1695 @ SV392 ) ) )
= $true )
| ( ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
= $true )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2035]) ).
thf(2131,plain,
! [SV385: $i,SV210: $i,SV64: $i > $i > $o] :
( ( ( ~ ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( ~ ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2036]) ).
thf(2132,plain,
! [SV64: $i > $i > $o,SV210: $i,SV385: $i] :
( ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( ~ ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2036]) ).
thf(2133,plain,
! [SV216: $i > $o,SV70: $i,SV393: $i] :
( ( ( in @ SV393 @ SV70 )
= $false )
| ( ( ~ ( SV216 @ SV393 ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2037]) ).
thf(2134,plain,
! [SV216: $i > $o,SV70: $i,SV403: $i] :
( ( ( ~ ( in @ SV403 @ SV70 )
| ~ ( SV216 @ SV403 ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2038]) ).
thf(2135,plain,
! [SV216: $i > $o,SV70: $i,SV410: $i] :
( ( ( ~ ( ~ ( in @ SV410 @ SV70 )
| ~ ( SV216 @ SV410 ) ) )
= $false )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2039]) ).
thf(2136,plain,
! [SV216: $i > $o,SV70: $i,SV420: $i] :
( ( ( ~ ~ ( ~ ( in @ SV420 @ SV70 )
| ~ ( SV216 @ SV420 ) ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2137,plain,
! [SV216: $i > $o,SV70: $i,SV411: $i] :
( ( ( ~ ( ~ ( in @ SV411 @ SV70 )
| ~ ( SV216 @ SV411 ) ) )
= $false )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2041]) ).
thf(2138,plain,
! [SV75: $i,SV220: $i > $o,SV374: $i] :
( ( ( ~ ( in @ ( sK59_SY1507 @ SV374 @ SV220 @ SV75 ) @ SV75 )
| ~ ( SV220 @ ( sK59_SY1507 @ SV374 @ SV220 @ SV75 ) ) )
= $false )
| ( ( in @ SV374
@ ( dsetconstr @ SV75
@ ^ [SY1505: $i] : ( SV220 @ SY1505 ) ) )
= $false )
| ( ( ( dsetconstr @ SV75
@ ^ [SY1506: $i] : ( SV220 @ SY1506 ) )
= ( setadjoin @ SV374 @ emptyset ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2042]) ).
thf(2139,plain,
! [SV228: $i > $o,SV421: $i,SV85: $i > $o] :
( ( ( ~ ~ ( ~ ( SV85 @ SV421 )
| ~ ! [SY1717: $i] :
( ~ ( SV85 @ SY1717 )
| ( SV421 = SY1717 ) ) ) )
= $true )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2140,plain,
! [SV85: $i > $o,SV422: $i,SV228: $i > $o] :
( ( ( ~ ~ ( ~ ( SV228 @ SV422 )
| ~ ! [SY1718: $i] :
( ~ ( SV228 @ SY1718 )
| ( SV422 = SY1718 ) ) ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2141,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2045]) ).
thf(2144,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2048]) ).
thf(2145,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2048]) ).
thf(2146,plain,
! [SV356: $i,SV90: $i > $o] :
( ( ( ~ ! [SY1719: $i] :
~ ( ~ ( ~ ( SV90 @ SY1719 )
| ( SY1719
= ( sK73_SY1266 @ SV356 @ SV90 ) ) )
| ~ ( ( SY1719
!= ( sK73_SY1266 @ SV356 @ SV90 ) )
| ( SV90 @ SY1719 ) ) ) )
= $false )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV90 @ ( sK53_SY1659 @ SV356 @ SV90 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2049]) ).
thf(2147,plain,
! [SV356: $i,SV90: $i > $o] :
( ( ( ! [SY1706: $i] :
~ ( ~ ( ~ ( SV90 @ SY1706 )
| ( SY1706
= ( sK65_SY1266 @ SV356 @ SV90 ) ) )
| ~ ( ( SY1706
!= ( sK65_SY1266 @ SV356 @ SV90 ) )
| ( SV90 @ SY1706 ) ) ) )
= $true )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV356
= ( sK53_SY1659 @ SV356 @ SV90 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2050]) ).
thf(2148,plain,
! [SV234: $i > $o,SV92: $i,SV394: $i] :
( ( ( in @ SV394 @ SV92 )
= $false )
| ( ( ~ ( SV234 @ SV394 ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2054]) ).
thf(2149,plain,
! [SV234: $i > $o,SV92: $i,SV404: $i] :
( ( ( ~ ( in @ SV404 @ SV92 )
| ~ ( SV234 @ SV404 ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2055]) ).
thf(2150,plain,
! [SV234: $i > $o,SV92: $i,SV412: $i] :
( ( ( ~ ( ~ ( in @ SV412 @ SV92 )
| ~ ( SV234 @ SV412 ) ) )
= $false )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2151,plain,
! [SV234: $i > $o,SV92: $i,SV423: $i] :
( ( ( ~ ~ ( ~ ( in @ SV423 @ SV92 )
| ~ ( SV234 @ SV423 ) ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2152,plain,
! [SV234: $i > $o,SV92: $i,SV413: $i] :
( ( ( ~ ( ~ ( in @ SV413 @ SV92 )
| ~ ( SV234 @ SV413 ) ) )
= $false )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2058]) ).
thf(2153,plain,
! [SV98: $i > $o,SV357: $i] :
( ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $true )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $true )
| ( ( ~ ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2059]) ).
thf(2156,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ~ ~ ( ~ ( SV98 @ ( sK74_SY1292 @ SV357 @ SV98 ) )
| ~ ! [SY1720: $i] :
( ~ ( SV98 @ SY1720 )
| ( ( sK74_SY1292 @ SV357 @ SV98 )
= SY1720 ) ) ) )
= $false )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $false )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2062]) ).
thf(2157,plain,
! [SV321: $i,SV241: $i,SV100: $i] :
( ( ( ~ ( in @ ( sK60_SY1676 @ SV100 @ SV241 @ SV321 ) @ ( setunion @ SV321 ) )
| ( SV321
!= ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ ( setadjoin @ ( sK60_SY1676 @ SV100 @ SV241 @ SV321 ) @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2158,plain,
! [SV104: $i,SV396: $i,SV245: $i > $o] :
( ( ( SV245 @ SV396 )
= $false )
| ( ( in @ SV396 @ SV104 )
= $false )
| ( ( in @ ( sK30_SY1550 @ SV245 @ SV104 ) @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2064]) ).
thf(2159,plain,
! [SV104: $i,SV397: $i,SV245: $i > $o] :
( ( ( SV245 @ SV397 )
= $false )
| ( ( in @ SV397 @ SV104 )
= $false )
| ( ( SV245 @ ( sK30_SY1550 @ SV245 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2065]) ).
thf(2160,plain,
! [SV358: $i,SV108: $i,SV398: $i] :
( ( ( ~ ( in @ SV398 @ ( setunion @ SV108 ) ) )
= $true )
| ( ( SV108
!= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( in @ SV358 @ ( setunion @ SV108 ) )
= $false )
| ( ( ~ ! [SY1316: $i] :
~ ~ ( ~ ( in @ SY1316
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ SY1316 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2066]) ).
thf(2162,plain,
! [SV113: $i,SV381: $o,SV254: $i,SV329: $i] :
( ( ( in @ SV329 @ SV254 )
= $true )
| ( SV381 = $true )
| ( ( in @ SV329 @ SV113 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2068]) ).
thf(2163,plain,
! [SV254: $i,SV381: $o,SV113: $i,SV329: $i] :
( ( ( ~ ~ ( in @ SV329 @ SV113 ) )
= $false )
| ( SV381 = $true )
| ( ( in @ SV329 @ SV254 )
= $false )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2070]) ).
thf(2174,plain,
! [SV113: $i,SV254: $i,SV329: $i] :
( ( ( in @ SV329 @ SV254 )
= $true )
| ( $false = $true )
| ( ( in @ SV329 @ SV113 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2082]) ).
thf(2175,plain,
! [SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ~ ( in @ SV329 @ SV113 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV329 @ SV254 )
= $false )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2084]) ).
thf(2179,plain,
! [SV119: $i,SV383: $i,SV259: $i > $o] :
( ( ( SV259 @ ( sK47_SY1564 @ SV383 @ SV259 @ SV119 ) )
= $false )
| ( ( SV259 @ SV383 )
= $true )
| ( ( in @ SV383 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2089]) ).
thf(2180,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ~ ~ ( ~ ( SV124 @ ( sK75_SY1348 @ SV360 @ SV124 ) )
| ~ ! [SY1721: $i] :
( ~ ( SV124 @ SY1721 )
| ( ( sK75_SY1348 @ SV360 @ SV124 )
= SY1721 ) ) ) )
= $false )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV124 @ ( sK54_SY1664 @ SV360 @ SV124 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2090]) ).
thf(2181,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ~ ( ~ ( SV124 @ ( sK66_SY1348 @ SV360 @ SV124 ) )
| ~ ! [SY1707: $i] :
( ~ ( SV124 @ SY1707 )
| ( ( sK66_SY1348 @ SV360 @ SV124 )
= SY1707 ) ) ) )
= $true )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV360
= ( sK54_SY1664 @ SV360 @ SV124 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2091]) ).
thf(2182,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ( ~ ( SV130 @ ( sK67_SY1361 @ SV362 @ SV130 ) )
| ~ ! [SY1708: $i] :
( ~ ( SV130 @ SY1708 )
| ( ( sK67_SY1361 @ SV362 @ SV130 )
= SY1708 ) ) ) )
= $true )
| ( ( SV130 @ ( sK42_SY1359 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2093]) ).
thf(2183,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ~ ( ~ ( SV130 @ ( sK76_SY1361 @ SV362 @ SV130 ) )
| ~ ! [SY1722: $i] :
( ~ ( SV130 @ SY1722 )
| ( ( sK76_SY1361 @ SV362 @ SV130 )
= SY1722 ) ) ) )
= $false )
| ( ( SV130 @ ( sK48_SY1690 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2094]) ).
thf(2184,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ( ~ ( SV130 @ ( sK68_SY1361 @ SV362 @ SV130 ) )
| ~ ! [SY1709: $i] :
( ~ ( SV130 @ SY1709 )
| ( ( sK68_SY1361 @ SV362 @ SV130 )
= SY1709 ) ) ) )
= $true )
| ( ( ( sK42_SY1359 @ SV362 @ SV130 )
= ( sK48_SY1690 @ SV362 @ SV130 ) )
= $false )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2095]) ).
thf(2185,plain,
! [SV363: $i,SV137: $i > $o] :
( ( ( ~ ( SV137 @ ( sK77_SY1372 @ SV363 @ SV137 ) ) )
= $false )
| ( ( SV137 @ SV363 )
= $false )
| ( ( SV137 @ ( sK55_SY1665 @ SV363 @ SV137 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2096]) ).
thf(2186,plain,
! [SV363: $i,SV137: $i > $o] :
( ( ( SV137 @ ( sK69_SY1372 @ SV363 @ SV137 ) )
= $true )
| ( ( SV137 @ SV363 )
= $false )
| ( ( SV363
= ( sK55_SY1665 @ SV363 @ SV137 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2097]) ).
thf(2187,plain,
! [SV138: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ omega ) )
= $true )
| ( ( in @ SV414 @ SV138 )
= $true )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( in @ ( sK35_SY1373 @ SV138 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2098]) ).
thf(2188,plain,
! [SV138: $i,SV415: $i] :
( ( ( ~ ( in @ SV415 @ omega ) )
= $true )
| ( ( in @ SV415 @ SV138 )
= $true )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( in @ ( sK35_SY1373 @ SV138 ) @ SV138 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2099]) ).
thf(2189,plain,
! [SV142: $i,SV364: $i,SV424: $i] :
( ( ( ~ ~ ( ~ ( in @ SV424 @ ( sK37_SY1383 @ SV364 @ SV142 ) )
| ~ ( in @ SV424 @ SV142 ) ) )
= $true )
| ( ( in @ SV364 @ SV142 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2190,plain,
! [SV275: $i > $o,SV399: $i,SV144: $i > $o] :
( ( ( ~ ( SV144 @ SV399 ) )
= $true )
| ( ( ~ ! [SY1698: $i] :
( ~ ( SV144 @ SY1698 )
| ( SV399 = SY1698 ) ) )
= $true )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2101]) ).
thf(2191,plain,
! [SV144: $i > $o,SV275: $i > $o] :
( ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) )
| ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2102]) ).
thf(2194,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ( ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2105]) ).
thf(2195,plain,
! [SV151: $i,SV400: $i,SV281: $i > $o] :
( ( ( SV281 @ SV400 )
= $false )
| ( ( in @ SV400 @ SV151 )
= $false )
| ( ( in @ ( sK31_SY1588 @ SV281 @ SV151 ) @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2106]) ).
thf(2196,plain,
! [SV151: $i,SV401: $i,SV281: $i > $o] :
( ( ( SV281 @ SV401 )
= $false )
| ( ( in @ SV401 @ SV151 )
= $false )
| ( ( SV281 @ ( sK31_SY1588 @ SV281 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2197,plain,
! [SV366: $i,SV425: $i,SV416: $i,SV159: $i > $o] :
( ( ( ~ ( SV159 @ SV416 )
| ~ ( SV159 @ SV425 )
| ( SV416 = SV425 ) )
= $true )
| ( ( SV159 @ SV366 )
= $false )
| ( ( SV159 @ ( sK57_SY1668 @ SV366 @ SV159 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2108]) ).
thf(2198,plain,
! [SV366: $i,SV417: $i,SV405: $i,SV159: $i > $o] :
( ( ( ~ ( SV159 @ SV405 ) )
= $true )
| ( ( ~ ( SV159 @ SV417 )
| ( SV405 = SV417 ) )
= $true )
| ( ( SV159 @ SV366 )
= $false )
| ( ( SV366
= ( sK57_SY1668 @ SV366 @ SV159 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2109]) ).
thf(2199,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( ~ ( ~ ( in @ ( sK70_SY1598 @ SV344 @ SV290 @ SV162 )
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ ( sK70_SY1598 @ SV344 @ SV290 @ SV162 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) @ SV162 )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2110]) ).
thf(2200,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK78_SY1598 @ SV344 @ SV290 @ SV162 )
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ ( sK78_SY1598 @ SV344 @ SV290 @ SV162 ) @ emptyset ) ) ) )
= $false )
| ( ( SV290 @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2111]) ).
thf(2201,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( ~ ( ~ ( in @ ( sK71_SY1598 @ SV344 @ SV290 @ SV162 )
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ ( sK71_SY1598 @ SV344 @ SV290 @ SV162 ) @ emptyset ) ) ) )
= $true )
| ( ( ( sK49_SY1639 @ SV344 @ SV290 @ SV162 )
= SV344 )
= $false )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2112]) ).
thf(2202,plain,
! [SV29: $i,SV180: $i,SV367: $i > $o,SV349: $i > $o] :
( ( ( ~ ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) )
| ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) ) )
= $false )
| ( ( ~ ( ~ ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
| ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2113]) ).
thf(2203,plain,
! [SV35: $i,SV406: $i] :
( ( ( in @ SV406 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( ! [SY1701: $i] :
( ~ ( in @ SY1701 @ SV406 )
| ( in @ SY1701 @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2204,plain,
! [SV418: $i,SV35: $i,SV407: $i] :
( ( ( ~ ~ ( ~ ( in @ SV407 @ SV35 )
| ~ ( in @ SV418 @ SV35 ) ) )
= $true )
| ( ( ~ ! [SY1715: $i] :
( ~ ( in @ SY1715 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SV407 @ SY1715 )
| ( in @ SV418 @ SY1715 ) )
| ~ ( ~ ( in @ SV418 @ SY1715 )
| ( in @ SV407 @ SY1715 ) ) ) )
| ( SV407 = SV418 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2115]) ).
thf(2205,plain,
! [SV395: $i,SV35: $i,SV391: $i] :
( ( ( ~ ( in @ SV391 @ ( sK2_SY1109 @ SV35 ) ) )
= $true )
| ( ( ~ ( in @ SV395 @ ( sK2_SY1109 @ SV35 ) ) )
= $true )
| ( ( ! [SY1696: $i] :
( ~ ( in @ SY1696 @ SV391 )
| ( in @ SY1696 @ SV395 ) )
| ! [SY1697: $i] :
( ~ ( in @ SY1697 @ SV395 )
| ( in @ SY1697 @ SV391 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2116]) ).
thf(2206,plain,
! [SV384: $i,SV35: $i] :
( ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( ~ ~ ! [SY1678: $i] :
~ ( in @ SY1678 @ SV384 ) )
= $true )
| ( ( ~ ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2117]) ).
thf(2207,plain,
! [SV35: $i,SV384: $i] :
( ( ( ~ ! [SY1678: $i] :
~ ( in @ SY1678 @ SV384 ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( ~ ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2208,plain,
! [SV351: $i,SV419: $i,SV408: $i,SV37: $i > $o] :
( ( ( ~ ( SV37 @ SV408 ) )
= $true )
| ( ( ~ ( SV37 @ SV419 )
| ( SV408 = SV419 ) )
= $true )
| ( ( SV37 @ SV351 )
= $false )
| ( ( SV37 @ ( sK51_SY1650 @ SV351 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2119]) ).
thf(2209,plain,
! [SV351: $i,SV409: $i,SV402: $i,SV37: $i > $o] :
( ( ( SV37 @ SV402 )
= $false )
| ( ( ~ ( SV37 @ SV409 )
| ( SV402 = SV409 ) )
= $true )
| ( ( SV37 @ SV351 )
= $false )
| ( ( SV351
= ( sK51_SY1650 @ SV351 @ SV37 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2210,plain,
! [SV38: $i,SV186: $i > $o,SV369: $i] :
( ( ( in @ ( sK62_SY1449 @ SV369 @ SV186 @ SV38 ) @ SV38 )
= $true )
| ( ( in @ SV369 @ SV38 )
= $false )
| ( ( SV186 @ SV369 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2121]) ).
thf(2211,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ~ ( ~ ( SV50 @ ( sK72_SY1160 @ SV352 @ SV50 ) )
| ~ ! [SY1716: $i] :
( ~ ( SV50 @ SY1716 )
| ( ( sK72_SY1160 @ SV352 @ SV50 )
= SY1716 ) ) ) )
= $true )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV50 @ ( sK52_SY1651 @ SV352 @ SV50 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2124]) ).
thf(2212,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ ( sK63_SY1160 @ SV352 @ SV50 ) )
| ~ ! [SY1705: $i] :
( ~ ( SV50 @ SY1705 )
| ( ( sK63_SY1160 @ SV352 @ SV50 )
= SY1705 ) ) )
= $false )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV352
= ( sK52_SY1651 @ SV352 @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2213,plain,
! [SV204: $i,SV305: $i,SV58: $i] :
( ( ( ~ ( in @ ( sK58_SY1675 @ SV58 @ SV305 @ SV204 ) @ SV204 ) )
= $false )
| ( ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2126]) ).
thf(2214,plain,
! [SV58: $i,SV204: $i,SV305: $i] :
( ( ( SV305
!= ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ ( setadjoin @ ( sK58_SY1675 @ SV58 @ SV305 @ SV204 ) @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2126]) ).
thf(2215,plain,
! [SV210: $i,SV64: $i > $i > $o,SV392: $i] :
( ( ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
= $false )
| ( ( ~ ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV210 )
| ~ ( SV64 @ SY1694 @ SV392 ) ) )
= $true )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2216,plain,
! [SV392: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ~ ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV210 )
| ~ ( SV64 @ SY1695 @ SV392 ) ) )
= $false )
| ( ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
= $true )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2217,plain,
! [SV385: $i,SV210: $i,SV64: $i > $i > $o] :
( ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( ~ ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2131]) ).
thf(2218,plain,
! [SV385: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2219,plain,
! [SV70: $i,SV393: $i,SV216: $i > $o] :
( ( ( SV216 @ SV393 )
= $false )
| ( ( in @ SV393 @ SV70 )
= $false )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2220,plain,
! [SV216: $i > $o,SV70: $i,SV403: $i] :
( ( ( ~ ( in @ SV403 @ SV70 ) )
= $true )
| ( ( ~ ( SV216 @ SV403 ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2134]) ).
thf(2221,plain,
! [SV216: $i > $o,SV70: $i,SV410: $i] :
( ( ( ~ ( in @ SV410 @ SV70 )
| ~ ( SV216 @ SV410 ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2135]) ).
thf(2222,plain,
! [SV216: $i > $o,SV70: $i,SV420: $i] :
( ( ( ~ ( ~ ( in @ SV420 @ SV70 )
| ~ ( SV216 @ SV420 ) ) )
= $false )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2136]) ).
thf(2223,plain,
! [SV216: $i > $o,SV70: $i,SV411: $i] :
( ( ( ~ ( in @ SV411 @ SV70 )
| ~ ( SV216 @ SV411 ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2137]) ).
thf(2224,plain,
! [SV75: $i,SV220: $i > $o,SV374: $i] :
( ( ( ~ ( in @ ( sK59_SY1507 @ SV374 @ SV220 @ SV75 ) @ SV75 ) )
= $false )
| ( ( in @ SV374
@ ( dsetconstr @ SV75
@ ^ [SY1505: $i] : ( SV220 @ SY1505 ) ) )
= $false )
| ( ( ( dsetconstr @ SV75
@ ^ [SY1506: $i] : ( SV220 @ SY1506 ) )
= ( setadjoin @ SV374 @ emptyset ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2138]) ).
thf(2225,plain,
! [SV75: $i,SV374: $i,SV220: $i > $o] :
( ( ( ~ ( SV220 @ ( sK59_SY1507 @ SV374 @ SV220 @ SV75 ) ) )
= $false )
| ( ( in @ SV374
@ ( dsetconstr @ SV75
@ ^ [SY1505: $i] : ( SV220 @ SY1505 ) ) )
= $false )
| ( ( ( dsetconstr @ SV75
@ ^ [SY1506: $i] : ( SV220 @ SY1506 ) )
= ( setadjoin @ SV374 @ emptyset ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2138]) ).
thf(2226,plain,
! [SV228: $i > $o,SV421: $i,SV85: $i > $o] :
( ( ( ~ ( ~ ( SV85 @ SV421 )
| ~ ! [SY1717: $i] :
( ~ ( SV85 @ SY1717 )
| ( SV421 = SY1717 ) ) ) )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2227,plain,
! [SV85: $i > $o,SV422: $i,SV228: $i > $o] :
( ( ( ~ ( ~ ( SV228 @ SV422 )
| ~ ! [SY1718: $i] :
( ~ ( SV228 @ SY1718 )
| ( SV422 = SY1718 ) ) ) )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2228,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
| ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2233,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2144]) ).
thf(2234,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2145]) ).
thf(2235,plain,
! [SV356: $i,SV90: $i > $o] :
( ( ( ! [SY1719: $i] :
~ ( ~ ( ~ ( SV90 @ SY1719 )
| ( SY1719
= ( sK73_SY1266 @ SV356 @ SV90 ) ) )
| ~ ( ( SY1719
!= ( sK73_SY1266 @ SV356 @ SV90 ) )
| ( SV90 @ SY1719 ) ) ) )
= $true )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV90 @ ( sK53_SY1659 @ SV356 @ SV90 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2146]) ).
thf(2236,plain,
! [SV356: $i,SV426: $i,SV90: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV90 @ SV426 )
| ( SV426
= ( sK65_SY1266 @ SV356 @ SV90 ) ) )
| ~ ( ( SV426
!= ( sK65_SY1266 @ SV356 @ SV90 ) )
| ( SV90 @ SV426 ) ) ) )
= $true )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV356
= ( sK53_SY1659 @ SV356 @ SV90 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2237,plain,
! [SV92: $i,SV394: $i,SV234: $i > $o] :
( ( ( SV234 @ SV394 )
= $false )
| ( ( in @ SV394 @ SV92 )
= $false )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2148]) ).
thf(2238,plain,
! [SV234: $i > $o,SV92: $i,SV404: $i] :
( ( ( ~ ( in @ SV404 @ SV92 ) )
= $true )
| ( ( ~ ( SV234 @ SV404 ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2149]) ).
thf(2239,plain,
! [SV234: $i > $o,SV92: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV92 )
| ~ ( SV234 @ SV412 ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2150]) ).
thf(2240,plain,
! [SV234: $i > $o,SV92: $i,SV423: $i] :
( ( ( ~ ( ~ ( in @ SV423 @ SV92 )
| ~ ( SV234 @ SV423 ) ) )
= $false )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2151]) ).
thf(2241,plain,
! [SV234: $i > $o,SV92: $i,SV413: $i] :
( ( ( ~ ( in @ SV413 @ SV92 )
| ~ ( SV234 @ SV413 ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2152]) ).
thf(2242,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ! [SY1292: $i] :
~ ~ ( ~ ( SV98 @ SY1292 )
| ~ ! [SY1293: $i] :
( ~ ( SV98 @ SY1293 )
| ( SY1292 = SY1293 ) ) ) )
= $false )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $true )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2153]) ).
thf(2245,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ~ ( ~ ( SV98 @ ( sK74_SY1292 @ SV357 @ SV98 ) )
| ~ ! [SY1720: $i] :
( ~ ( SV98 @ SY1720 )
| ( ( sK74_SY1292 @ SV357 @ SV98 )
= SY1720 ) ) ) )
= $true )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $false )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2156]) ).
thf(2246,plain,
! [SV321: $i,SV241: $i,SV100: $i] :
( ( ( ~ ( in @ ( sK60_SY1676 @ SV100 @ SV241 @ SV321 ) @ ( setunion @ SV321 ) ) )
= $false )
| ( ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2157]) ).
thf(2247,plain,
! [SV100: $i,SV241: $i,SV321: $i] :
( ( ( SV321
!= ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ ( setadjoin @ ( sK60_SY1676 @ SV100 @ SV241 @ SV321 ) @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2157]) ).
thf(2248,plain,
! [SV358: $i,SV108: $i,SV398: $i] :
( ( ( in @ SV398 @ ( setunion @ SV108 ) )
= $false )
| ( ( SV108
!= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( in @ SV358 @ ( setunion @ SV108 ) )
= $false )
| ( ( ~ ! [SY1316: $i] :
~ ~ ( ~ ( in @ SY1316
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ SY1316 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2160]) ).
thf(2249,plain,
! [SV254: $i,SV381: $o,SV113: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ SV113 ) )
= $true )
| ( SV381 = $true )
| ( ( in @ SV329 @ SV254 )
= $false )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2163]) ).
thf(2255,plain,
! [SV254: $i,SV113: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ SV113 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV329 @ SV254 )
= $false )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2175]) ).
thf(2258,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ~ ( ~ ( SV124 @ ( sK75_SY1348 @ SV360 @ SV124 ) )
| ~ ! [SY1721: $i] :
( ~ ( SV124 @ SY1721 )
| ( ( sK75_SY1348 @ SV360 @ SV124 )
= SY1721 ) ) ) )
= $true )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV124 @ ( sK54_SY1664 @ SV360 @ SV124 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2180]) ).
thf(2259,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ~ ( SV124 @ ( sK66_SY1348 @ SV360 @ SV124 ) )
| ~ ! [SY1707: $i] :
( ~ ( SV124 @ SY1707 )
| ( ( sK66_SY1348 @ SV360 @ SV124 )
= SY1707 ) ) )
= $false )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV360
= ( sK54_SY1664 @ SV360 @ SV124 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2181]) ).
thf(2260,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK67_SY1361 @ SV362 @ SV130 ) )
| ~ ! [SY1708: $i] :
( ~ ( SV130 @ SY1708 )
| ( ( sK67_SY1361 @ SV362 @ SV130 )
= SY1708 ) ) )
= $false )
| ( ( SV130 @ ( sK42_SY1359 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2182]) ).
thf(2261,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ( ~ ( SV130 @ ( sK76_SY1361 @ SV362 @ SV130 ) )
| ~ ! [SY1722: $i] :
( ~ ( SV130 @ SY1722 )
| ( ( sK76_SY1361 @ SV362 @ SV130 )
= SY1722 ) ) ) )
= $true )
| ( ( SV130 @ ( sK48_SY1690 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2183]) ).
thf(2262,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK68_SY1361 @ SV362 @ SV130 ) )
| ~ ! [SY1709: $i] :
( ~ ( SV130 @ SY1709 )
| ( ( sK68_SY1361 @ SV362 @ SV130 )
= SY1709 ) ) )
= $false )
| ( ( ( sK42_SY1359 @ SV362 @ SV130 )
= ( sK48_SY1690 @ SV362 @ SV130 ) )
= $false )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2184]) ).
thf(2263,plain,
! [SV363: $i,SV137: $i > $o] :
( ( ( SV137 @ ( sK77_SY1372 @ SV363 @ SV137 ) )
= $true )
| ( ( SV137 @ SV363 )
= $false )
| ( ( SV137 @ ( sK55_SY1665 @ SV363 @ SV137 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2185]) ).
thf(2264,plain,
! [SV138: $i,SV414: $i] :
( ( ( in @ SV414 @ omega )
= $false )
| ( ( in @ SV414 @ SV138 )
= $true )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( in @ ( sK35_SY1373 @ SV138 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2265,plain,
! [SV138: $i,SV415: $i] :
( ( ( in @ SV415 @ omega )
= $false )
| ( ( in @ SV415 @ SV138 )
= $true )
| ( ( in @ emptyset @ SV138 )
= $false )
| ( ( in @ ( sK35_SY1373 @ SV138 ) @ SV138 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2188]) ).
thf(2266,plain,
! [SV142: $i,SV364: $i,SV424: $i] :
( ( ( ~ ( ~ ( in @ SV424 @ ( sK37_SY1383 @ SV364 @ SV142 ) )
| ~ ( in @ SV424 @ SV142 ) ) )
= $false )
| ( ( in @ SV364 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2189]) ).
thf(2267,plain,
! [SV275: $i > $o,SV399: $i,SV144: $i > $o] :
( ( ( SV144 @ SV399 )
= $false )
| ( ( ~ ! [SY1698: $i] :
( ~ ( SV144 @ SY1698 )
| ( SV399 = SY1698 ) ) )
= $true )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2268,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ( ~ ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2191]) ).
thf(2271,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ( ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2194]) ).
thf(2272,plain,
! [SV366: $i,SV425: $i,SV416: $i,SV159: $i > $o] :
( ( ( ~ ( SV159 @ SV416 ) )
= $true )
| ( ( ~ ( SV159 @ SV425 )
| ( SV416 = SV425 ) )
= $true )
| ( ( SV159 @ SV366 )
= $false )
| ( ( SV159 @ ( sK57_SY1668 @ SV366 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2197]) ).
thf(2273,plain,
! [SV366: $i,SV417: $i,SV405: $i,SV159: $i > $o] :
( ( ( SV159 @ SV405 )
= $false )
| ( ( ~ ( SV159 @ SV417 )
| ( SV405 = SV417 ) )
= $true )
| ( ( SV159 @ SV366 )
= $false )
| ( ( SV366
= ( sK57_SY1668 @ SV366 @ SV159 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2198]) ).
thf(2274,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( ~ ( in @ ( sK70_SY1598 @ SV344 @ SV290 @ SV162 )
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ ( sK70_SY1598 @ SV344 @ SV290 @ SV162 ) @ emptyset ) ) )
= $false )
| ( ( in @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) @ SV162 )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2199]) ).
thf(2275,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( ~ ( ~ ( in @ ( sK78_SY1598 @ SV344 @ SV290 @ SV162 )
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ ( sK78_SY1598 @ SV344 @ SV290 @ SV162 ) @ emptyset ) ) ) )
= $true )
| ( ( SV290 @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2200]) ).
thf(2276,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( ~ ( in @ ( sK71_SY1598 @ SV344 @ SV290 @ SV162 )
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ ( sK71_SY1598 @ SV344 @ SV290 @ SV162 ) @ emptyset ) ) )
= $false )
| ( ( ( sK49_SY1639 @ SV344 @ SV290 @ SV162 )
= SV344 )
= $false )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2201]) ).
thf(2277,plain,
! [SV29: $i,SV180: $i,SV367: $i > $o,SV349: $i > $o] :
( ( ( ~ ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) ) )
= $false )
| ( ( ~ ( ~ ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
| ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2202]) ).
thf(2278,plain,
! [SV180: $i,SV349: $i > $o,SV29: $i,SV367: $i > $o] :
( ( ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
= $false )
| ( ( ~ ( ~ ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
| ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2202]) ).
thf(2279,plain,
! [SV35: $i,SV406: $i,SV427: $i] :
( ( ( ~ ( in @ SV427 @ SV406 )
| ( in @ SV427 @ SV35 ) )
= $true )
| ( ( in @ SV406 @ ( sK2_SY1109 @ SV35 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2203]) ).
thf(2280,plain,
! [SV418: $i,SV35: $i,SV407: $i] :
( ( ( ~ ( ~ ( in @ SV407 @ SV35 )
| ~ ( in @ SV418 @ SV35 ) ) )
= $false )
| ( ( ~ ! [SY1715: $i] :
( ~ ( in @ SY1715 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SV407 @ SY1715 )
| ( in @ SV418 @ SY1715 ) )
| ~ ( ~ ( in @ SV418 @ SY1715 )
| ( in @ SV407 @ SY1715 ) ) ) )
| ( SV407 = SV418 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2204]) ).
thf(2281,plain,
! [SV395: $i,SV35: $i,SV391: $i] :
( ( ( in @ SV391 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( ~ ( in @ SV395 @ ( sK2_SY1109 @ SV35 ) ) )
= $true )
| ( ( ! [SY1696: $i] :
( ~ ( in @ SY1696 @ SV391 )
| ( in @ SY1696 @ SV395 ) )
| ! [SY1697: $i] :
( ~ ( in @ SY1697 @ SV395 )
| ( in @ SY1697 @ SV391 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2205]) ).
thf(2282,plain,
! [SV35: $i,SV384: $i] :
( ( ( ~ ! [SY1678: $i] :
~ ( in @ SY1678 @ SV384 ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( ~ ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2206]) ).
thf(2283,plain,
! [SV35: $i,SV384: $i] :
( ( ( ! [SY1678: $i] :
~ ( in @ SY1678 @ SV384 ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( ~ ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2207]) ).
thf(2284,plain,
! [SV351: $i,SV419: $i,SV408: $i,SV37: $i > $o] :
( ( ( SV37 @ SV408 )
= $false )
| ( ( ~ ( SV37 @ SV419 )
| ( SV408 = SV419 ) )
= $true )
| ( ( SV37 @ SV351 )
= $false )
| ( ( SV37 @ ( sK51_SY1650 @ SV351 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2208]) ).
thf(2285,plain,
! [SV351: $i,SV402: $i,SV409: $i,SV37: $i > $o] :
( ( ( ~ ( SV37 @ SV409 ) )
= $true )
| ( ( SV402 = SV409 )
= $true )
| ( ( SV37 @ SV402 )
= $false )
| ( ( SV37 @ SV351 )
= $false )
| ( ( SV351
= ( sK51_SY1650 @ SV351 @ SV37 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2209]) ).
thf(2286,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ ( sK72_SY1160 @ SV352 @ SV50 ) )
| ~ ! [SY1716: $i] :
( ~ ( SV50 @ SY1716 )
| ( ( sK72_SY1160 @ SV352 @ SV50 )
= SY1716 ) ) )
= $false )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV50 @ ( sK52_SY1651 @ SV352 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2211]) ).
thf(2287,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ ( sK63_SY1160 @ SV352 @ SV50 ) ) )
= $false )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV352
= ( sK52_SY1651 @ SV352 @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2212]) ).
thf(2288,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ~ ! [SY1705: $i] :
( ~ ( SV50 @ SY1705 )
| ( ( sK63_SY1160 @ SV352 @ SV50 )
= SY1705 ) ) )
= $false )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV352
= ( sK52_SY1651 @ SV352 @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2212]) ).
thf(2289,plain,
! [SV204: $i,SV305: $i,SV58: $i] :
( ( ( in @ ( sK58_SY1675 @ SV58 @ SV305 @ SV204 ) @ SV204 )
= $true )
| ( ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2213]) ).
thf(2290,plain,
! [SV58: $i,SV204: $i,SV305: $i] :
( ( ( SV305
= ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK24_SY1622 @ SV305 @ SV204 @ SV58 ) @ ( setadjoin @ ( sK58_SY1675 @ SV58 @ SV305 @ SV204 ) @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( in @ SV305 @ ( cartprod @ SV58 @ SV204 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2214]) ).
thf(2291,plain,
! [SV392: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ! [SY1694: $i] :
~ ~ ( ~ ( in @ SY1694 @ SV210 )
| ~ ( SV64 @ SY1694 @ SV392 ) ) )
= $false )
| ( ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
= $false )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2215]) ).
thf(2292,plain,
! [SV392: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ! [SY1695: $i] :
~ ~ ( ~ ( in @ SY1695 @ SV210 )
| ~ ( SV64 @ SY1695 @ SV392 ) ) )
= $true )
| ( ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
= $true )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2216]) ).
thf(2293,plain,
! [SV385: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ! [SY1483: $i] :
~ ! [SY1484: $i] :
~ ( ~ ( ~ ( in @ SY1484 @ SY1483 )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1484 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1484 ) )
| ( in @ SY1484 @ SY1483 ) ) ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2217]) ).
thf(2294,plain,
! [SV210: $i,SV64: $i > $i > $o,SV385: $i] :
( ( ( ~ ! [SY1727: $i] :
~ ( ~ ( ~ ( in @ SY1727 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1727 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1727 ) )
| ( in @ SY1727 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) ) ) ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2218]) ).
thf(2295,plain,
! [SV393: $i,SV216: $i > $o,SV70: $i] :
( ( ( ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV393 @ SV70 )
= $false )
| ( ( SV216 @ SV393 )
= $false )
| ( ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2219]) ).
thf(2296,plain,
! [SV216: $i > $o,SV70: $i,SV403: $i] :
( ( ( in @ SV403 @ SV70 )
= $false )
| ( ( ~ ( SV216 @ SV403 ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2220]) ).
thf(2297,plain,
! [SV216: $i > $o,SV70: $i,SV410: $i] :
( ( ( ~ ( in @ SV410 @ SV70 ) )
= $true )
| ( ( ~ ( SV216 @ SV410 ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2221]) ).
thf(2298,plain,
! [SV216: $i > $o,SV70: $i,SV420: $i] :
( ( ( ~ ( in @ SV420 @ SV70 )
| ~ ( SV216 @ SV420 ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2222]) ).
thf(2299,plain,
! [SV216: $i > $o,SV70: $i,SV411: $i] :
( ( ( ~ ( in @ SV411 @ SV70 ) )
= $true )
| ( ( ~ ( SV216 @ SV411 ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2223]) ).
thf(2300,plain,
! [SV75: $i,SV220: $i > $o,SV374: $i] :
( ( ( in @ ( sK59_SY1507 @ SV374 @ SV220 @ SV75 ) @ SV75 )
= $true )
| ( ( in @ SV374
@ ( dsetconstr @ SV75
@ ^ [SY1505: $i] : ( SV220 @ SY1505 ) ) )
= $false )
| ( ( ( dsetconstr @ SV75
@ ^ [SY1506: $i] : ( SV220 @ SY1506 ) )
= ( setadjoin @ SV374 @ emptyset ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2224]) ).
thf(2301,plain,
! [SV75: $i,SV374: $i,SV220: $i > $o] :
( ( ( SV220 @ ( sK59_SY1507 @ SV374 @ SV220 @ SV75 ) )
= $true )
| ( ( in @ SV374
@ ( dsetconstr @ SV75
@ ^ [SY1505: $i] : ( SV220 @ SY1505 ) ) )
= $false )
| ( ( ( dsetconstr @ SV75
@ ^ [SY1506: $i] : ( SV220 @ SY1506 ) )
= ( setadjoin @ SV374 @ emptyset ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2225]) ).
thf(2302,plain,
! [SV228: $i > $o,SV421: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ SV421 )
| ~ ! [SY1717: $i] :
( ~ ( SV85 @ SY1717 )
| ( SV421 = SY1717 ) ) )
= $true )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2226]) ).
thf(2303,plain,
! [SV85: $i > $o,SV422: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ SV422 )
| ~ ! [SY1718: $i] :
( ~ ( SV228 @ SY1718 )
| ( SV422 = SY1718 ) ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2227]) ).
thf(2304,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2228]) ).
thf(2305,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2228]) ).
thf(2310,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) ) )
= $true )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2233]) ).
thf(2311,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2234]) ).
thf(2312,plain,
! [SV356: $i,SV428: $i,SV90: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV90 @ SV428 )
| ( SV428
= ( sK73_SY1266 @ SV356 @ SV90 ) ) )
| ~ ( ( SV428
!= ( sK73_SY1266 @ SV356 @ SV90 ) )
| ( SV90 @ SV428 ) ) ) )
= $true )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV90 @ ( sK53_SY1659 @ SV356 @ SV90 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2313,plain,
! [SV356: $i,SV426: $i,SV90: $i > $o] :
( ( ( ~ ( ~ ( SV90 @ SV426 )
| ( SV426
= ( sK65_SY1266 @ SV356 @ SV90 ) ) )
| ~ ( ( SV426
!= ( sK65_SY1266 @ SV356 @ SV90 ) )
| ( SV90 @ SV426 ) ) )
= $false )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV356
= ( sK53_SY1659 @ SV356 @ SV90 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2236]) ).
thf(2314,plain,
! [SV394: $i,SV234: $i > $o,SV92: $i] :
( ( ( ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV394 @ SV92 )
= $false )
| ( ( SV234 @ SV394 )
= $false )
| ( ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2237]) ).
thf(2315,plain,
! [SV234: $i > $o,SV92: $i,SV404: $i] :
( ( ( in @ SV404 @ SV92 )
= $false )
| ( ( ~ ( SV234 @ SV404 ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2238]) ).
thf(2316,plain,
! [SV234: $i > $o,SV92: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV92 ) )
= $true )
| ( ( ~ ( SV234 @ SV412 ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2239]) ).
thf(2317,plain,
! [SV234: $i > $o,SV92: $i,SV423: $i] :
( ( ( ~ ( in @ SV423 @ SV92 )
| ~ ( SV234 @ SV423 ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2240]) ).
thf(2318,plain,
! [SV234: $i > $o,SV92: $i,SV413: $i] :
( ( ( ~ ( in @ SV413 @ SV92 ) )
= $true )
| ( ( ~ ( SV234 @ SV413 ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2241]) ).
thf(2319,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ~ ~ ( ~ ( SV98 @ ( sK82_SY1292 @ SV357 @ SV98 ) )
| ~ ! [SY1730: $i] :
( ~ ( SV98 @ SY1730 )
| ( ( sK82_SY1292 @ SV357 @ SV98 )
= SY1730 ) ) ) )
= $false )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $true )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2242]) ).
thf(2322,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ ( sK74_SY1292 @ SV357 @ SV98 ) )
| ~ ! [SY1720: $i] :
( ~ ( SV98 @ SY1720 )
| ( ( sK74_SY1292 @ SV357 @ SV98 )
= SY1720 ) ) )
= $false )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $false )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2245]) ).
thf(2323,plain,
! [SV321: $i,SV241: $i,SV100: $i] :
( ( ( in @ ( sK60_SY1676 @ SV100 @ SV241 @ SV321 ) @ ( setunion @ SV321 ) )
= $true )
| ( ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2246]) ).
thf(2324,plain,
! [SV100: $i,SV241: $i,SV321: $i] :
( ( ( SV321
= ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK29_SY1632 @ SV241 @ SV100 @ SV321 ) @ ( setadjoin @ ( sK60_SY1676 @ SV100 @ SV241 @ SV321 ) @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( in @ SV321 @ ( cartprod @ SV100 @ SV241 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2247]) ).
thf(2325,plain,
! [SV398: $i,SV358: $i,SV108: $i] :
( ( ( SV108
= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ SV398 @ ( setunion @ SV108 ) )
= $false )
| ( ( in @ SV358 @ ( setunion @ SV108 ) )
= $false )
| ( ( ~ ! [SY1316: $i] :
~ ~ ( ~ ( in @ SY1316
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ SY1316 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2248]) ).
thf(2326,plain,
! [SV254: $i,SV381: $o,SV113: $i,SV329: $i] :
( ( ( in @ SV329 @ SV113 )
= $false )
| ( SV381 = $true )
| ( ( in @ SV329 @ SV254 )
= $false )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2330,plain,
! [SV254: $i,SV113: $i,SV329: $i] :
( ( ( in @ SV329 @ SV113 )
= $false )
| ( $false = $true )
| ( ( in @ SV329 @ SV254 )
= $false )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2255]) ).
thf(2332,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ~ ( SV124 @ ( sK75_SY1348 @ SV360 @ SV124 ) )
| ~ ! [SY1721: $i] :
( ~ ( SV124 @ SY1721 )
| ( ( sK75_SY1348 @ SV360 @ SV124 )
= SY1721 ) ) )
= $false )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV124 @ ( sK54_SY1664 @ SV360 @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2258]) ).
thf(2333,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ~ ( SV124 @ ( sK66_SY1348 @ SV360 @ SV124 ) ) )
= $false )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV360
= ( sK54_SY1664 @ SV360 @ SV124 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2259]) ).
thf(2334,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ~ ! [SY1707: $i] :
( ~ ( SV124 @ SY1707 )
| ( ( sK66_SY1348 @ SV360 @ SV124 )
= SY1707 ) ) )
= $false )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV360
= ( sK54_SY1664 @ SV360 @ SV124 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2259]) ).
thf(2335,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK67_SY1361 @ SV362 @ SV130 ) ) )
= $false )
| ( ( SV130 @ ( sK42_SY1359 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2260]) ).
thf(2336,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ! [SY1708: $i] :
( ~ ( SV130 @ SY1708 )
| ( ( sK67_SY1361 @ SV362 @ SV130 )
= SY1708 ) ) )
= $false )
| ( ( SV130 @ ( sK42_SY1359 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2260]) ).
thf(2337,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK76_SY1361 @ SV362 @ SV130 ) )
| ~ ! [SY1722: $i] :
( ~ ( SV130 @ SY1722 )
| ( ( sK76_SY1361 @ SV362 @ SV130 )
= SY1722 ) ) )
= $false )
| ( ( SV130 @ ( sK48_SY1690 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2261]) ).
thf(2338,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK68_SY1361 @ SV362 @ SV130 ) ) )
= $false )
| ( ( ( sK42_SY1359 @ SV362 @ SV130 )
= ( sK48_SY1690 @ SV362 @ SV130 ) )
= $false )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2262]) ).
thf(2339,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ! [SY1709: $i] :
( ~ ( SV130 @ SY1709 )
| ( ( sK68_SY1361 @ SV362 @ SV130 )
= SY1709 ) ) )
= $false )
| ( ( ( sK42_SY1359 @ SV362 @ SV130 )
= ( sK48_SY1690 @ SV362 @ SV130 ) )
= $false )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2262]) ).
thf(2340,plain,
! [SV142: $i,SV364: $i,SV424: $i] :
( ( ( ~ ( in @ SV424 @ ( sK37_SY1383 @ SV364 @ SV142 ) )
| ~ ( in @ SV424 @ SV142 ) )
= $true )
| ( ( in @ SV364 @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2266]) ).
thf(2341,plain,
! [SV275: $i > $o,SV399: $i,SV144: $i > $o] :
( ( ( ! [SY1698: $i] :
( ~ ( SV144 @ SY1698 )
| ( SV399 = SY1698 ) ) )
= $false )
| ( ( SV144 @ SV399 )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2267]) ).
thf(2342,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ( ~ ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2268]) ).
thf(2345,plain,
! [SV275: $i > $o,SV429: $i,SV144: $i > $o] :
( ( ( ~ ~ ( ~ ( SV144 @ SV429 )
| ~ ! [SY1731: $i] :
( ~ ( SV144 @ SY1731 )
| ( SV429 = SY1731 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2271]) ).
thf(2346,plain,
! [SV366: $i,SV425: $i,SV416: $i,SV159: $i > $o] :
( ( ( SV159 @ SV416 )
= $false )
| ( ( ~ ( SV159 @ SV425 )
| ( SV416 = SV425 ) )
= $true )
| ( ( SV159 @ SV366 )
= $false )
| ( ( SV159 @ ( sK57_SY1668 @ SV366 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2272]) ).
thf(2347,plain,
! [SV366: $i,SV405: $i,SV417: $i,SV159: $i > $o] :
( ( ( ~ ( SV159 @ SV417 ) )
= $true )
| ( ( SV405 = SV417 )
= $true )
| ( ( SV159 @ SV405 )
= $false )
| ( ( SV159 @ SV366 )
= $false )
| ( ( SV366
= ( sK57_SY1668 @ SV366 @ SV159 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2273]) ).
thf(2348,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( ~ ( in @ ( sK70_SY1598 @ SV344 @ SV290 @ SV162 )
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) ) )
= $false )
| ( ( in @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) @ SV162 )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2274]) ).
thf(2349,plain,
! [SV344: $i,SV290: $i > $o,SV162: $i] :
( ( ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ ( sK70_SY1598 @ SV344 @ SV290 @ SV162 ) @ emptyset ) )
= $false )
| ( ( in @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) @ SV162 )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2274]) ).
thf(2350,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( ~ ( in @ ( sK78_SY1598 @ SV344 @ SV290 @ SV162 )
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
| ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ ( sK78_SY1598 @ SV344 @ SV290 @ SV162 ) @ emptyset ) ) )
= $false )
| ( ( SV290 @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2351,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( ~ ( in @ ( sK71_SY1598 @ SV344 @ SV290 @ SV162 )
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) ) )
= $false )
| ( ( ( sK49_SY1639 @ SV344 @ SV290 @ SV162 )
= SV344 )
= $false )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2276]) ).
thf(2352,plain,
! [SV344: $i,SV290: $i > $o,SV162: $i] :
( ( ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ ( sK71_SY1598 @ SV344 @ SV290 @ SV162 ) @ emptyset ) )
= $false )
| ( ( ( sK49_SY1639 @ SV344 @ SV290 @ SV162 )
= SV344 )
= $false )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2276]) ).
thf(2353,plain,
! [SV29: $i,SV180: $i,SV367: $i > $o,SV349: $i > $o] :
( ( ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) )
= $true )
| ( ( ~ ( ~ ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
| ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2277]) ).
thf(2354,plain,
! [SV180: $i,SV349: $i > $o,SV29: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
| ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) ) )
= $false )
| ( ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
= $false )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2278]) ).
thf(2355,plain,
! [SV35: $i,SV406: $i,SV427: $i] :
( ( ( ~ ( in @ SV427 @ SV406 ) )
= $true )
| ( ( in @ SV427 @ SV35 )
= $true )
| ( ( in @ SV406 @ ( sK2_SY1109 @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2279]) ).
thf(2356,plain,
! [SV418: $i,SV35: $i,SV407: $i] :
( ( ( ~ ( in @ SV407 @ SV35 )
| ~ ( in @ SV418 @ SV35 ) )
= $true )
| ( ( ~ ! [SY1715: $i] :
( ~ ( in @ SY1715 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SV407 @ SY1715 )
| ( in @ SV418 @ SY1715 ) )
| ~ ( ~ ( in @ SV418 @ SY1715 )
| ( in @ SV407 @ SY1715 ) ) ) )
| ( SV407 = SV418 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2280]) ).
thf(2357,plain,
! [SV391: $i,SV35: $i,SV395: $i] :
( ( ( in @ SV395 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( in @ SV391 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( ! [SY1696: $i] :
( ~ ( in @ SY1696 @ SV391 )
| ( in @ SY1696 @ SV395 ) )
| ! [SY1697: $i] :
( ~ ( in @ SY1697 @ SV395 )
| ( in @ SY1697 @ SV391 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2281]) ).
thf(2358,plain,
! [SV35: $i,SV384: $i] :
( ( ( ! [SY1678: $i] :
~ ( in @ SY1678 @ SV384 ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( ~ ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2282]) ).
thf(2359,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( ~ ( in @ SV430 @ SV384 ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( ~ ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2360,plain,
! [SV351: $i,SV408: $i,SV419: $i,SV37: $i > $o] :
( ( ( ~ ( SV37 @ SV419 ) )
= $true )
| ( ( SV408 = SV419 )
= $true )
| ( ( SV37 @ SV408 )
= $false )
| ( ( SV37 @ SV351 )
= $false )
| ( ( SV37 @ ( sK51_SY1650 @ SV351 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2284]) ).
thf(2361,plain,
! [SV351: $i,SV402: $i,SV409: $i,SV37: $i > $o] :
( ( ( SV37 @ SV409 )
= $false )
| ( ( SV402 = SV409 )
= $true )
| ( ( SV37 @ SV402 )
= $false )
| ( ( SV37 @ SV351 )
= $false )
| ( ( SV351
= ( sK51_SY1650 @ SV351 @ SV37 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2285]) ).
thf(2362,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ ( sK72_SY1160 @ SV352 @ SV50 ) ) )
= $false )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV50 @ ( sK52_SY1651 @ SV352 @ SV50 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2286]) ).
thf(2363,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ~ ! [SY1716: $i] :
( ~ ( SV50 @ SY1716 )
| ( ( sK72_SY1160 @ SV352 @ SV50 )
= SY1716 ) ) )
= $false )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV50 @ ( sK52_SY1651 @ SV352 @ SV50 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2286]) ).
thf(2364,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( SV50 @ ( sK63_SY1160 @ SV352 @ SV50 ) )
= $true )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV352
= ( sK52_SY1651 @ SV352 @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2287]) ).
thf(2365,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ! [SY1705: $i] :
( ~ ( SV50 @ SY1705 )
| ( ( sK63_SY1160 @ SV352 @ SV50 )
= SY1705 ) ) )
= $true )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV352
= ( sK52_SY1651 @ SV352 @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2288]) ).
thf(2366,plain,
! [SV210: $i,SV64: $i > $i > $o,SV392: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK83_SY1694 @ SV392 @ SV64 @ SV210 ) @ SV210 )
| ~ ( SV64 @ ( sK83_SY1694 @ SV392 @ SV64 @ SV210 ) @ SV392 ) ) )
= $false )
| ( ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
= $false )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2291]) ).
thf(2367,plain,
! [SV392: $i,SV64: $i > $i > $o,SV210: $i,SV431: $i] :
( ( ( ~ ~ ( ~ ( in @ SV431 @ SV210 )
| ~ ( SV64 @ SV431 @ SV392 ) ) )
= $true )
| ( ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
= $true )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2368,plain,
! [SV210: $i,SV64: $i > $i > $o,SV385: $i] :
( ( ( ~ ! [SY1732: $i] :
~ ( ~ ( ~ ( in @ SY1732 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1732 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1732 ) )
| ( in @ SY1732 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) ) ) ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2293]) ).
thf(2369,plain,
! [SV210: $i,SV64: $i > $i > $o,SV385: $i] :
( ( ( ! [SY1727: $i] :
~ ( ~ ( ~ ( in @ SY1727 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1727 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1727 ) )
| ( in @ SY1727 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) ) ) ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2294]) ).
thf(2370,plain,
! [SV70: $i,SV216: $i > $o,SV393: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK85_SY1495 @ SV393 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK85_SY1495 @ SV393 @ SV216 @ SV70 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV393 @ SV70 )
= $false )
| ( ( SV216 @ SV393 )
= $false )
| ( ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2295]) ).
thf(2371,plain,
! [SV70: $i,SV403: $i,SV216: $i > $o] :
( ( ( SV216 @ SV403 )
= $false )
| ( ( in @ SV403 @ SV70 )
= $false )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2296]) ).
thf(2372,plain,
! [SV216: $i > $o,SV70: $i,SV410: $i] :
( ( ( in @ SV410 @ SV70 )
= $false )
| ( ( ~ ( SV216 @ SV410 ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2297]) ).
thf(2373,plain,
! [SV216: $i > $o,SV70: $i,SV420: $i] :
( ( ( ~ ( in @ SV420 @ SV70 ) )
= $true )
| ( ( ~ ( SV216 @ SV420 ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2298]) ).
thf(2374,plain,
! [SV216: $i > $o,SV70: $i,SV411: $i] :
( ( ( in @ SV411 @ SV70 )
= $false )
| ( ( ~ ( SV216 @ SV411 ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2299]) ).
thf(2375,plain,
! [SV228: $i > $o,SV421: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ SV421 ) )
= $true )
| ( ( ~ ! [SY1717: $i] :
( ~ ( SV85 @ SY1717 )
| ( SV421 = SY1717 ) ) )
= $true )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2302]) ).
thf(2376,plain,
! [SV85: $i > $o,SV422: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ SV422 ) )
= $true )
| ( ( ~ ! [SY1718: $i] :
( ~ ( SV228 @ SY1718 )
| ( SV422 = SY1718 ) ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2303]) ).
thf(2377,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) )
| ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2304]) ).
thf(2378,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) )
| ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2305]) ).
thf(2383,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) ) )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2310]) ).
thf(2384,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) ) )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2311]) ).
thf(2385,plain,
! [SV356: $i,SV428: $i,SV90: $i > $o] :
( ( ( ~ ( ~ ( SV90 @ SV428 )
| ( SV428
= ( sK73_SY1266 @ SV356 @ SV90 ) ) )
| ~ ( ( SV428
!= ( sK73_SY1266 @ SV356 @ SV90 ) )
| ( SV90 @ SV428 ) ) )
= $false )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV90 @ ( sK53_SY1659 @ SV356 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2386,plain,
! [SV356: $i,SV426: $i,SV90: $i > $o] :
( ( ( ~ ( ~ ( SV90 @ SV426 )
| ( SV426
= ( sK65_SY1266 @ SV356 @ SV90 ) ) ) )
= $false )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV356
= ( sK53_SY1659 @ SV356 @ SV90 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2313]) ).
thf(2387,plain,
! [SV90: $i > $o,SV356: $i,SV426: $i] :
( ( ( ~ ( ( SV426
!= ( sK65_SY1266 @ SV356 @ SV90 ) )
| ( SV90 @ SV426 ) ) )
= $false )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV356
= ( sK53_SY1659 @ SV356 @ SV90 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2313]) ).
thf(2388,plain,
! [SV92: $i,SV234: $i > $o,SV394: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK86_SY1533 @ SV394 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK86_SY1533 @ SV394 @ SV234 @ SV92 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV394 @ SV92 )
= $false )
| ( ( SV234 @ SV394 )
= $false )
| ( ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2314]) ).
thf(2389,plain,
! [SV92: $i,SV404: $i,SV234: $i > $o] :
( ( ( SV234 @ SV404 )
= $false )
| ( ( in @ SV404 @ SV92 )
= $false )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2315]) ).
thf(2390,plain,
! [SV234: $i > $o,SV92: $i,SV412: $i] :
( ( ( in @ SV412 @ SV92 )
= $false )
| ( ( ~ ( SV234 @ SV412 ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2391,plain,
! [SV234: $i > $o,SV92: $i,SV423: $i] :
( ( ( ~ ( in @ SV423 @ SV92 ) )
= $true )
| ( ( ~ ( SV234 @ SV423 ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2317]) ).
thf(2392,plain,
! [SV234: $i > $o,SV92: $i,SV413: $i] :
( ( ( in @ SV413 @ SV92 )
= $false )
| ( ( ~ ( SV234 @ SV413 ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2318]) ).
thf(2393,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ~ ( ~ ( SV98 @ ( sK82_SY1292 @ SV357 @ SV98 ) )
| ~ ! [SY1730: $i] :
( ~ ( SV98 @ SY1730 )
| ( ( sK82_SY1292 @ SV357 @ SV98 )
= SY1730 ) ) ) )
= $true )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $true )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2319]) ).
thf(2396,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ ( sK74_SY1292 @ SV357 @ SV98 ) ) )
= $false )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $false )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2322]) ).
thf(2397,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ~ ! [SY1720: $i] :
( ~ ( SV98 @ SY1720 )
| ( ( sK74_SY1292 @ SV357 @ SV98 )
= SY1720 ) ) )
= $false )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $false )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2322]) ).
thf(2398,plain,
! [SV398: $i,SV358: $i,SV108: $i] :
( ( ( ! [SY1316: $i] :
~ ~ ( ~ ( in @ SY1316
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ SY1316 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV358 @ ( setunion @ SV108 ) )
= $false )
| ( ( in @ SV398 @ ( setunion @ SV108 ) )
= $false )
| ( ( SV108
= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2399,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ~ ( SV124 @ ( sK75_SY1348 @ SV360 @ SV124 ) ) )
= $false )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV124 @ ( sK54_SY1664 @ SV360 @ SV124 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2332]) ).
thf(2400,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ~ ! [SY1721: $i] :
( ~ ( SV124 @ SY1721 )
| ( ( sK75_SY1348 @ SV360 @ SV124 )
= SY1721 ) ) )
= $false )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV124 @ ( sK54_SY1664 @ SV360 @ SV124 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2332]) ).
thf(2401,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( SV124 @ ( sK66_SY1348 @ SV360 @ SV124 ) )
= $true )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV360
= ( sK54_SY1664 @ SV360 @ SV124 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2333]) ).
thf(2402,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ! [SY1707: $i] :
( ~ ( SV124 @ SY1707 )
| ( ( sK66_SY1348 @ SV360 @ SV124 )
= SY1707 ) ) )
= $true )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV360
= ( sK54_SY1664 @ SV360 @ SV124 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2334]) ).
thf(2403,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( SV130 @ ( sK67_SY1361 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK42_SY1359 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2335]) ).
thf(2404,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ! [SY1708: $i] :
( ~ ( SV130 @ SY1708 )
| ( ( sK67_SY1361 @ SV362 @ SV130 )
= SY1708 ) ) )
= $true )
| ( ( SV130 @ ( sK42_SY1359 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2336]) ).
thf(2405,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK76_SY1361 @ SV362 @ SV130 ) ) )
= $false )
| ( ( SV130 @ ( sK48_SY1690 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2337]) ).
thf(2406,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ~ ! [SY1722: $i] :
( ~ ( SV130 @ SY1722 )
| ( ( sK76_SY1361 @ SV362 @ SV130 )
= SY1722 ) ) )
= $false )
| ( ( SV130 @ ( sK48_SY1690 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2337]) ).
thf(2407,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( SV130 @ ( sK68_SY1361 @ SV362 @ SV130 ) )
= $true )
| ( ( ( sK42_SY1359 @ SV362 @ SV130 )
= ( sK48_SY1690 @ SV362 @ SV130 ) )
= $false )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2338]) ).
thf(2408,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ! [SY1709: $i] :
( ~ ( SV130 @ SY1709 )
| ( ( sK68_SY1361 @ SV362 @ SV130 )
= SY1709 ) ) )
= $true )
| ( ( ( sK42_SY1359 @ SV362 @ SV130 )
= ( sK48_SY1690 @ SV362 @ SV130 ) )
= $false )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2339]) ).
thf(2409,plain,
! [SV142: $i,SV364: $i,SV424: $i] :
( ( ( ~ ( in @ SV424 @ ( sK37_SY1383 @ SV364 @ SV142 ) ) )
= $true )
| ( ( ~ ( in @ SV424 @ SV142 ) )
= $true )
| ( ( in @ SV364 @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2340]) ).
thf(2410,plain,
! [SV399: $i,SV275: $i > $o,SV144: $i > $o] :
( ( ( ~ ( SV144 @ ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
| ( SV399
= ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) ) )
= $false )
| ( ( SV144 @ SV399 )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2341]) ).
thf(2411,plain,
! [SV275: $i > $o,SV144: $i > $o] :
( ( ( ! [SY1389: $i] :
~ ~ ( ~ ( SV144 @ SY1389 )
| ~ ! [SY1390: $i] :
( ~ ( SV144 @ SY1390 )
| ( SY1389 = SY1390 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2342]) ).
thf(2414,plain,
! [SV275: $i > $o,SV429: $i,SV144: $i > $o] :
( ( ( ~ ( ~ ( SV144 @ SV429 )
| ~ ! [SY1731: $i] :
( ~ ( SV144 @ SY1731 )
| ( SV429 = SY1731 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2345]) ).
thf(2415,plain,
! [SV366: $i,SV416: $i,SV425: $i,SV159: $i > $o] :
( ( ( ~ ( SV159 @ SV425 ) )
= $true )
| ( ( SV416 = SV425 )
= $true )
| ( ( SV159 @ SV416 )
= $false )
| ( ( SV159 @ SV366 )
= $false )
| ( ( SV159 @ ( sK57_SY1668 @ SV366 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2346]) ).
thf(2416,plain,
! [SV366: $i,SV405: $i,SV417: $i,SV159: $i > $o] :
( ( ( SV159 @ SV417 )
= $false )
| ( ( SV405 = SV417 )
= $true )
| ( ( SV159 @ SV405 )
= $false )
| ( ( SV159 @ SV366 )
= $false )
| ( ( SV366
= ( sK57_SY1668 @ SV366 @ SV159 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2347]) ).
thf(2417,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( in @ ( sK70_SY1598 @ SV344 @ SV290 @ SV162 )
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
= $true )
| ( ( in @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) @ SV162 )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2348]) ).
thf(2418,plain,
! [SV344: $i,SV290: $i > $o,SV162: $i] :
( ( ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
= ( setadjoin @ ( sK70_SY1598 @ SV344 @ SV290 @ SV162 ) @ emptyset ) )
= $true )
| ( ( in @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) @ SV162 )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2349]) ).
thf(2419,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( ~ ( in @ ( sK78_SY1598 @ SV344 @ SV290 @ SV162 )
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) ) )
= $false )
| ( ( SV290 @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2350]) ).
thf(2420,plain,
! [SV344: $i,SV290: $i > $o,SV162: $i] :
( ( ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
!= ( setadjoin @ ( sK78_SY1598 @ SV344 @ SV290 @ SV162 ) @ emptyset ) )
= $false )
| ( ( SV290 @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2350]) ).
thf(2421,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( in @ ( sK71_SY1598 @ SV344 @ SV290 @ SV162 )
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
= $true )
| ( ( ( sK49_SY1639 @ SV344 @ SV290 @ SV162 )
= SV344 )
= $false )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2351]) ).
thf(2422,plain,
! [SV344: $i,SV290: $i > $o,SV162: $i] :
( ( ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
= ( setadjoin @ ( sK71_SY1598 @ SV344 @ SV290 @ SV162 ) @ emptyset ) )
= $true )
| ( ( ( sK49_SY1639 @ SV344 @ SV290 @ SV162 )
= SV344 )
= $false )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2352]) ).
thf(2423,plain,
! [SV180: $i,SV349: $i > $o,SV29: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
| ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) ) )
= $false )
| ( ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) )
= $true )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2425,plain,
! [SV29: $i,SV180: $i,SV367: $i > $o,SV349: $i > $o] :
( ( ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) )
= $false )
| ( ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
= $false )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2354]) ).
thf(2426,plain,
! [SV35: $i,SV406: $i,SV427: $i] :
( ( ( in @ SV427 @ SV406 )
= $false )
| ( ( in @ SV427 @ SV35 )
= $true )
| ( ( in @ SV406 @ ( sK2_SY1109 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2427,plain,
! [SV418: $i,SV35: $i,SV407: $i] :
( ( ( ~ ( in @ SV407 @ SV35 ) )
= $true )
| ( ( ~ ( in @ SV418 @ SV35 ) )
= $true )
| ( ( ~ ! [SY1715: $i] :
( ~ ( in @ SY1715 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SV407 @ SY1715 )
| ( in @ SV418 @ SY1715 ) )
| ~ ( ~ ( in @ SV418 @ SY1715 )
| ( in @ SV407 @ SY1715 ) ) ) )
| ( SV407 = SV418 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2356]) ).
thf(2428,plain,
! [SV35: $i,SV395: $i,SV391: $i] :
( ( ( ! [SY1696: $i] :
( ~ ( in @ SY1696 @ SV391 )
| ( in @ SY1696 @ SV395 ) ) )
= $true )
| ( ( ! [SY1697: $i] :
( ~ ( in @ SY1697 @ SV395 )
| ( in @ SY1697 @ SV391 ) ) )
= $true )
| ( ( in @ SV391 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( in @ SV395 @ ( sK2_SY1109 @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2357]) ).
thf(2429,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( ~ ( in @ SV434 @ SV384 ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( ~ ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(2430,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( in @ SV430 @ SV384 )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( ~ ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2359]) ).
thf(2431,plain,
! [SV351: $i,SV408: $i,SV419: $i,SV37: $i > $o] :
( ( ( SV37 @ SV419 )
= $false )
| ( ( SV408 = SV419 )
= $true )
| ( ( SV37 @ SV408 )
= $false )
| ( ( SV37 @ SV351 )
= $false )
| ( ( SV37 @ ( sK51_SY1650 @ SV351 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2360]) ).
thf(2432,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( SV50 @ ( sK72_SY1160 @ SV352 @ SV50 ) )
= $true )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV50 @ ( sK52_SY1651 @ SV352 @ SV50 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2362]) ).
thf(2433,plain,
! [SV352: $i,SV50: $i > $o] :
( ( ( ! [SY1716: $i] :
( ~ ( SV50 @ SY1716 )
| ( ( sK72_SY1160 @ SV352 @ SV50 )
= SY1716 ) ) )
= $true )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV50 @ ( sK52_SY1651 @ SV352 @ SV50 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2363]) ).
thf(2434,plain,
! [SV352: $i,SV435: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ SV435 )
| ( ( sK63_SY1160 @ SV352 @ SV50 )
= SV435 ) )
= $true )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV352
= ( sK52_SY1651 @ SV352 @ SV50 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(2435,plain,
! [SV210: $i,SV64: $i > $i > $o,SV392: $i] :
( ( ( ~ ( ~ ( in @ ( sK83_SY1694 @ SV392 @ SV64 @ SV210 ) @ SV210 )
| ~ ( SV64 @ ( sK83_SY1694 @ SV392 @ SV64 @ SV210 ) @ SV392 ) ) )
= $true )
| ( ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
= $false )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2366]) ).
thf(2436,plain,
! [SV392: $i,SV64: $i > $i > $o,SV210: $i,SV431: $i] :
( ( ( ~ ( ~ ( in @ SV431 @ SV210 )
| ~ ( SV64 @ SV431 @ SV392 ) ) )
= $false )
| ( ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
= $true )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2367]) ).
thf(2437,plain,
! [SV210: $i,SV64: $i > $i > $o,SV385: $i] :
( ( ( ! [SY1732: $i] :
~ ( ~ ( ~ ( in @ SY1732 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
| ~ ! [SY1485: $i] :
~ ~ ( ~ ( in @ SY1485 @ SV210 )
| ~ ( SV64 @ SY1485 @ SY1732 ) ) )
| ~ ( ~ ~ ! [SY1486: $i] :
~ ~ ( ~ ( in @ SY1486 @ SV210 )
| ~ ( SV64 @ SY1486 @ SY1732 ) )
| ( in @ SY1732 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) ) ) ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2368]) ).
thf(2438,plain,
! [SV210: $i,SV64: $i > $i > $o,SV385: $i,SV436: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
| ~ ! [SY1741: $i] :
~ ~ ( ~ ( in @ SY1741 @ SV210 )
| ~ ( SV64 @ SY1741 @ SV436 ) ) )
| ~ ( ~ ~ ! [SY1742: $i] :
~ ~ ( ~ ( in @ SY1742 @ SV210 )
| ~ ( SV64 @ SY1742 @ SV436 ) )
| ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) ) ) ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2369]) ).
thf(2439,plain,
! [SV70: $i,SV216: $i > $o,SV393: $i] :
( ( ( ~ ( ~ ( in @ ( sK85_SY1495 @ SV393 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK85_SY1495 @ SV393 @ SV216 @ SV70 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV393 @ SV70 )
= $false )
| ( ( SV216 @ SV393 )
= $false )
| ( ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2370]) ).
thf(2440,plain,
! [SV403: $i,SV216: $i > $o,SV70: $i] :
( ( ( ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV403 @ SV70 )
= $false )
| ( ( SV216 @ SV403 )
= $false )
| ( ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2371]) ).
thf(2441,plain,
! [SV70: $i,SV410: $i,SV216: $i > $o] :
( ( ( SV216 @ SV410 )
= $false )
| ( ( in @ SV410 @ SV70 )
= $false )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2372]) ).
thf(2442,plain,
! [SV216: $i > $o,SV70: $i,SV420: $i] :
( ( ( in @ SV420 @ SV70 )
= $false )
| ( ( ~ ( SV216 @ SV420 ) )
= $true )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2443,plain,
! [SV70: $i,SV411: $i,SV216: $i > $o] :
( ( ( SV216 @ SV411 )
= $false )
| ( ( in @ SV411 @ SV70 )
= $false )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2444,plain,
! [SV228: $i > $o,SV421: $i,SV85: $i > $o] :
( ( ( SV85 @ SV421 )
= $false )
| ( ( ~ ! [SY1717: $i] :
( ~ ( SV85 @ SY1717 )
| ( SV421 = SY1717 ) ) )
= $true )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2375]) ).
thf(2445,plain,
! [SV85: $i > $o,SV422: $i,SV228: $i > $o] :
( ( ( SV228 @ SV422 )
= $false )
| ( ( ~ ! [SY1718: $i] :
( ~ ( SV228 @ SY1718 )
| ( SV422 = SY1718 ) ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2376]) ).
thf(2446,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) ) )
= $true )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2377]) ).
thf(2447,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2378]) ).
thf(2452,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) ) )
= $true )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2383]) ).
thf(2453,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2384]) ).
thf(2454,plain,
! [SV356: $i,SV428: $i,SV90: $i > $o] :
( ( ( ~ ( ~ ( SV90 @ SV428 )
| ( SV428
= ( sK73_SY1266 @ SV356 @ SV90 ) ) ) )
= $false )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV90 @ ( sK53_SY1659 @ SV356 @ SV90 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2385]) ).
thf(2455,plain,
! [SV90: $i > $o,SV356: $i,SV428: $i] :
( ( ( ~ ( ( SV428
!= ( sK73_SY1266 @ SV356 @ SV90 ) )
| ( SV90 @ SV428 ) ) )
= $false )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV90 @ ( sK53_SY1659 @ SV356 @ SV90 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2385]) ).
thf(2456,plain,
! [SV356: $i,SV426: $i,SV90: $i > $o] :
( ( ( ~ ( SV90 @ SV426 )
| ( SV426
= ( sK65_SY1266 @ SV356 @ SV90 ) ) )
= $true )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV356
= ( sK53_SY1659 @ SV356 @ SV90 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2386]) ).
thf(2457,plain,
! [SV90: $i > $o,SV356: $i,SV426: $i] :
( ( ( ( SV426
!= ( sK65_SY1266 @ SV356 @ SV90 ) )
| ( SV90 @ SV426 ) )
= $true )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV356
= ( sK53_SY1659 @ SV356 @ SV90 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2387]) ).
thf(2458,plain,
! [SV92: $i,SV234: $i > $o,SV394: $i] :
( ( ( ~ ( ~ ( in @ ( sK86_SY1533 @ SV394 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK86_SY1533 @ SV394 @ SV234 @ SV92 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV394 @ SV92 )
= $false )
| ( ( SV234 @ SV394 )
= $false )
| ( ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2388]) ).
thf(2459,plain,
! [SV404: $i,SV234: $i > $o,SV92: $i] :
( ( ( ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV404 @ SV92 )
= $false )
| ( ( SV234 @ SV404 )
= $false )
| ( ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2389]) ).
thf(2460,plain,
! [SV92: $i,SV412: $i,SV234: $i > $o] :
( ( ( SV234 @ SV412 )
= $false )
| ( ( in @ SV412 @ SV92 )
= $false )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2461,plain,
! [SV234: $i > $o,SV92: $i,SV423: $i] :
( ( ( in @ SV423 @ SV92 )
= $false )
| ( ( ~ ( SV234 @ SV423 ) )
= $true )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2462,plain,
! [SV92: $i,SV413: $i,SV234: $i > $o] :
( ( ( SV234 @ SV413 )
= $false )
| ( ( in @ SV413 @ SV92 )
= $false )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2392]) ).
thf(2463,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ ( sK82_SY1292 @ SV357 @ SV98 ) )
| ~ ! [SY1730: $i] :
( ~ ( SV98 @ SY1730 )
| ( ( sK82_SY1292 @ SV357 @ SV98 )
= SY1730 ) ) )
= $false )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $true )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2393]) ).
thf(2468,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( SV98 @ ( sK74_SY1292 @ SV357 @ SV98 ) )
= $true )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $false )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2396]) ).
thf(2469,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ! [SY1720: $i] :
( ~ ( SV98 @ SY1720 )
| ( ( sK74_SY1292 @ SV357 @ SV98 )
= SY1720 ) ) )
= $true )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $false )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2397]) ).
thf(2470,plain,
! [SV108: $i,SV358: $i,SV398: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK88_SY1316 @ SV398 @ SV358 @ SV108 )
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ ( sK88_SY1316 @ SV398 @ SV358 @ SV108 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV358 @ ( setunion @ SV108 ) )
= $false )
| ( ( in @ SV398 @ ( setunion @ SV108 ) )
= $false )
| ( ( SV108
= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2398]) ).
thf(2471,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( SV124 @ ( sK75_SY1348 @ SV360 @ SV124 ) )
= $true )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV124 @ ( sK54_SY1664 @ SV360 @ SV124 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2399]) ).
thf(2472,plain,
! [SV360: $i,SV124: $i > $o] :
( ( ( ! [SY1721: $i] :
( ~ ( SV124 @ SY1721 )
| ( ( sK75_SY1348 @ SV360 @ SV124 )
= SY1721 ) ) )
= $true )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV124 @ ( sK54_SY1664 @ SV360 @ SV124 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2400]) ).
thf(2473,plain,
! [SV360: $i,SV437: $i,SV124: $i > $o] :
( ( ( ~ ( SV124 @ SV437 )
| ( ( sK66_SY1348 @ SV360 @ SV124 )
= SV437 ) )
= $true )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV360
= ( sK54_SY1664 @ SV360 @ SV124 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2402]) ).
thf(2474,plain,
! [SV362: $i,SV438: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV438 )
| ( ( sK67_SY1361 @ SV362 @ SV130 )
= SV438 ) )
= $true )
| ( ( SV130 @ ( sK42_SY1359 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(2475,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( SV130 @ ( sK76_SY1361 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK48_SY1690 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2405]) ).
thf(2476,plain,
! [SV362: $i,SV130: $i > $o] :
( ( ( ! [SY1722: $i] :
( ~ ( SV130 @ SY1722 )
| ( ( sK76_SY1361 @ SV362 @ SV130 )
= SY1722 ) ) )
= $true )
| ( ( SV130 @ ( sK48_SY1690 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2406]) ).
thf(2477,plain,
! [SV362: $i,SV439: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV439 )
| ( ( sK68_SY1361 @ SV362 @ SV130 )
= SV439 ) )
= $true )
| ( ( ( sK42_SY1359 @ SV362 @ SV130 )
= ( sK48_SY1690 @ SV362 @ SV130 ) )
= $false )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(2478,plain,
! [SV142: $i,SV364: $i,SV424: $i] :
( ( ( in @ SV424 @ ( sK37_SY1383 @ SV364 @ SV142 ) )
= $false )
| ( ( ~ ( in @ SV424 @ SV142 ) )
= $true )
| ( ( in @ SV364 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2409]) ).
thf(2479,plain,
! [SV399: $i,SV275: $i > $o,SV144: $i > $o] :
( ( ( ~ ( SV144 @ ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) ) )
= $false )
| ( ( SV144 @ SV399 )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2410]) ).
thf(2480,plain,
! [SV144: $i > $o,SV275: $i > $o,SV399: $i] :
( ( ( SV399
= ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $false )
| ( ( SV144 @ SV399 )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2410]) ).
thf(2481,plain,
! [SV275: $i > $o,SV440: $i,SV144: $i > $o] :
( ( ( ~ ~ ( ~ ( SV144 @ SV440 )
| ~ ! [SY1745: $i] :
( ~ ( SV144 @ SY1745 )
| ( SV440 = SY1745 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2411]) ).
thf(2484,plain,
! [SV275: $i > $o,SV429: $i,SV144: $i > $o] :
( ( ( ~ ( SV144 @ SV429 )
| ~ ! [SY1731: $i] :
( ~ ( SV144 @ SY1731 )
| ( SV429 = SY1731 ) ) )
= $true )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2414]) ).
thf(2485,plain,
! [SV366: $i,SV416: $i,SV425: $i,SV159: $i > $o] :
( ( ( SV159 @ SV425 )
= $false )
| ( ( SV416 = SV425 )
= $true )
| ( ( SV159 @ SV416 )
= $false )
| ( ( SV159 @ SV366 )
= $false )
| ( ( SV159 @ ( sK57_SY1668 @ SV366 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2415]) ).
thf(2486,plain,
! [SV162: $i,SV290: $i > $o,SV344: $i] :
( ( ( in @ ( sK78_SY1598 @ SV344 @ SV290 @ SV162 )
@ ( dsetconstr @ SV162
@ ^ [SY1599: $i] : ( SV290 @ SY1599 ) ) )
= $true )
| ( ( SV290 @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2419]) ).
thf(2487,plain,
! [SV344: $i,SV290: $i > $o,SV162: $i] :
( ( ( ( dsetconstr @ SV162
@ ^ [SY1600: $i] : ( SV290 @ SY1600 ) )
= ( setadjoin @ ( sK78_SY1598 @ SV344 @ SV290 @ SV162 ) @ emptyset ) )
= $true )
| ( ( SV290 @ ( sK49_SY1639 @ SV344 @ SV290 @ SV162 ) )
= $true )
| ( ( SV290 @ SV344 )
= $false )
| ( ( in @ SV344 @ SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2420]) ).
thf(2488,plain,
! [SV180: $i,SV349: $i > $o,SV29: $i,SV367: $i > $o] :
( ( ( ~ ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) ) )
= $false )
| ( ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) )
= $true )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2423]) ).
thf(2491,plain,
! [SV418: $i,SV35: $i,SV407: $i] :
( ( ( in @ SV407 @ SV35 )
= $false )
| ( ( ~ ( in @ SV418 @ SV35 ) )
= $true )
| ( ( ~ ! [SY1715: $i] :
( ~ ( in @ SY1715 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SV407 @ SY1715 )
| ( in @ SV418 @ SY1715 ) )
| ~ ( ~ ( in @ SV418 @ SY1715 )
| ( in @ SV407 @ SY1715 ) ) ) )
| ( SV407 = SV418 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2427]) ).
thf(2492,plain,
! [SV35: $i,SV395: $i,SV391: $i,SV441: $i] :
( ( ( ~ ( in @ SV441 @ SV391 )
| ( in @ SV441 @ SV395 ) )
= $true )
| ( ( ! [SY1697: $i] :
( ~ ( in @ SY1697 @ SV395 )
| ( in @ SY1697 @ SV391 ) ) )
= $true )
| ( ( in @ SV391 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( in @ SV395 @ ( sK2_SY1109 @ SV35 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(2493,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( in @ SV434 @ SV384 )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( ~ ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2429]) ).
thf(2494,plain,
! [SV430: $i,SV384: $i,SV35: $i] :
( ( ( ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2430]) ).
thf(2495,plain,
! [SV352: $i,SV442: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ SV442 )
| ( ( sK72_SY1160 @ SV352 @ SV50 )
= SV442 ) )
= $true )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV50 @ ( sK52_SY1651 @ SV352 @ SV50 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(2496,plain,
! [SV352: $i,SV435: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ SV435 ) )
= $true )
| ( ( ( sK63_SY1160 @ SV352 @ SV50 )
= SV435 )
= $true )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV352
= ( sK52_SY1651 @ SV352 @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2434]) ).
thf(2497,plain,
! [SV210: $i,SV64: $i > $i > $o,SV392: $i] :
( ( ( ~ ( in @ ( sK83_SY1694 @ SV392 @ SV64 @ SV210 ) @ SV210 )
| ~ ( SV64 @ ( sK83_SY1694 @ SV392 @ SV64 @ SV210 ) @ SV392 ) )
= $false )
| ( ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
= $false )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2498,plain,
! [SV392: $i,SV64: $i > $i > $o,SV210: $i,SV431: $i] :
( ( ( ~ ( in @ SV431 @ SV210 )
| ~ ( SV64 @ SV431 @ SV392 ) )
= $true )
| ( ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
= $true )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2436]) ).
thf(2499,plain,
! [SV210: $i,SV64: $i > $i > $o,SV385: $i,SV443: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
| ~ ! [SY1746: $i] :
~ ~ ( ~ ( in @ SY1746 @ SV210 )
| ~ ( SV64 @ SY1746 @ SV443 ) ) )
| ~ ( ~ ~ ! [SY1747: $i] :
~ ~ ( ~ ( in @ SY1747 @ SV210 )
| ~ ( SV64 @ SY1747 @ SV443 ) )
| ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) ) ) ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2437]) ).
thf(2500,plain,
! [SV210: $i,SV64: $i > $i > $o,SV385: $i,SV436: $i] :
( ( ( ~ ( ~ ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
| ~ ! [SY1741: $i] :
~ ~ ( ~ ( in @ SY1741 @ SV210 )
| ~ ( SV64 @ SY1741 @ SV436 ) ) )
| ~ ( ~ ~ ! [SY1742: $i] :
~ ~ ( ~ ( in @ SY1742 @ SV210 )
| ~ ( SV64 @ SY1742 @ SV436 ) )
| ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) ) ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2501,plain,
! [SV70: $i,SV216: $i > $o,SV393: $i] :
( ( ( ~ ( in @ ( sK85_SY1495 @ SV393 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK85_SY1495 @ SV393 @ SV216 @ SV70 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV393 @ SV70 )
= $false )
| ( ( SV216 @ SV393 )
= $false )
| ( ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(2502,plain,
! [SV70: $i,SV216: $i > $o,SV403: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK89_SY1495 @ SV403 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK89_SY1495 @ SV403 @ SV216 @ SV70 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV403 @ SV70 )
= $false )
| ( ( SV216 @ SV403 )
= $false )
| ( ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2440]) ).
thf(2503,plain,
! [SV410: $i,SV216: $i > $o,SV70: $i] :
( ( ( ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV410 @ SV70 )
= $false )
| ( ( SV216 @ SV410 )
= $false )
| ( ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2441]) ).
thf(2504,plain,
! [SV70: $i,SV420: $i,SV216: $i > $o] :
( ( ( SV216 @ SV420 )
= $false )
| ( ( in @ SV420 @ SV70 )
= $false )
| ( ( ~ ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $true )
| ( ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2442]) ).
thf(2505,plain,
! [SV411: $i,SV216: $i > $o,SV70: $i] :
( ( ( ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV411 @ SV70 )
= $false )
| ( ( SV216 @ SV411 )
= $false )
| ( ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2443]) ).
thf(2506,plain,
! [SV228: $i > $o,SV421: $i,SV85: $i > $o] :
( ( ( ! [SY1717: $i] :
( ~ ( SV85 @ SY1717 )
| ( SV421 = SY1717 ) ) )
= $false )
| ( ( SV85 @ SV421 )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2444]) ).
thf(2507,plain,
! [SV85: $i > $o,SV422: $i,SV228: $i > $o] :
( ( ( ! [SY1718: $i] :
( ~ ( SV228 @ SY1718 )
| ( SV422 = SY1718 ) ) )
= $false )
| ( ( SV228 @ SV422 )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2445]) ).
thf(2508,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) ) )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2446]) ).
thf(2509,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) ) )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2447]) ).
thf(2514,plain,
! [SV228: $i > $o,SV444: $i,SV85: $i > $o] :
( ( ( ~ ~ ( ~ ( SV85 @ SV444 )
| ~ ! [SY1750: $i] :
( ~ ( SV85 @ SY1750 )
| ( SV444 = SY1750 ) ) ) )
= $true )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(2515,plain,
! [SV85: $i > $o,SV445: $i,SV228: $i > $o] :
( ( ( ~ ~ ( ~ ( SV228 @ SV445 )
| ~ ! [SY1751: $i] :
( ~ ( SV228 @ SY1751 )
| ( SV445 = SY1751 ) ) ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2453]) ).
thf(2516,plain,
! [SV356: $i,SV428: $i,SV90: $i > $o] :
( ( ( ~ ( SV90 @ SV428 )
| ( SV428
= ( sK73_SY1266 @ SV356 @ SV90 ) ) )
= $true )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV90 @ ( sK53_SY1659 @ SV356 @ SV90 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2454]) ).
thf(2517,plain,
! [SV90: $i > $o,SV356: $i,SV428: $i] :
( ( ( ( SV428
!= ( sK73_SY1266 @ SV356 @ SV90 ) )
| ( SV90 @ SV428 ) )
= $true )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV90 @ ( sK53_SY1659 @ SV356 @ SV90 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2455]) ).
thf(2518,plain,
! [SV356: $i,SV426: $i,SV90: $i > $o] :
( ( ( ~ ( SV90 @ SV426 ) )
= $true )
| ( ( SV426
= ( sK65_SY1266 @ SV356 @ SV90 ) )
= $true )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV356
= ( sK53_SY1659 @ SV356 @ SV90 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2456]) ).
thf(2519,plain,
! [SV90: $i > $o,SV356: $i,SV426: $i] :
( ( ( SV426
!= ( sK65_SY1266 @ SV356 @ SV90 ) )
= $true )
| ( ( SV90 @ SV426 )
= $true )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV356
= ( sK53_SY1659 @ SV356 @ SV90 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2457]) ).
thf(2520,plain,
! [SV92: $i,SV234: $i > $o,SV394: $i] :
( ( ( ~ ( in @ ( sK86_SY1533 @ SV394 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK86_SY1533 @ SV394 @ SV234 @ SV92 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV394 @ SV92 )
= $false )
| ( ( SV234 @ SV394 )
= $false )
| ( ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2458]) ).
thf(2521,plain,
! [SV92: $i,SV234: $i > $o,SV404: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK90_SY1533 @ SV404 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK90_SY1533 @ SV404 @ SV234 @ SV92 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV404 @ SV92 )
= $false )
| ( ( SV234 @ SV404 )
= $false )
| ( ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2459]) ).
thf(2522,plain,
! [SV412: $i,SV234: $i > $o,SV92: $i] :
( ( ( ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV412 @ SV92 )
= $false )
| ( ( SV234 @ SV412 )
= $false )
| ( ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2460]) ).
thf(2523,plain,
! [SV92: $i,SV423: $i,SV234: $i > $o] :
( ( ( SV234 @ SV423 )
= $false )
| ( ( in @ SV423 @ SV92 )
= $false )
| ( ( ~ ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $true )
| ( ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2461]) ).
thf(2524,plain,
! [SV413: $i,SV234: $i > $o,SV92: $i] :
( ( ( ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV413 @ SV92 )
= $false )
| ( ( SV234 @ SV413 )
= $false )
| ( ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2462]) ).
thf(2525,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ ( sK82_SY1292 @ SV357 @ SV98 ) ) )
= $false )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $true )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2463]) ).
thf(2526,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ~ ! [SY1730: $i] :
( ~ ( SV98 @ SY1730 )
| ( ( sK82_SY1292 @ SV357 @ SV98 )
= SY1730 ) ) )
= $false )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $true )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2463]) ).
thf(2531,plain,
! [SV357: $i,SV446: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ SV446 )
| ( ( sK74_SY1292 @ SV357 @ SV98 )
= SV446 ) )
= $true )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $false )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(2532,plain,
! [SV108: $i,SV358: $i,SV398: $i] :
( ( ( ~ ( ~ ( in @ ( sK88_SY1316 @ SV398 @ SV358 @ SV108 )
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ ( sK88_SY1316 @ SV398 @ SV358 @ SV108 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV358 @ ( setunion @ SV108 ) )
= $false )
| ( ( in @ SV398 @ ( setunion @ SV108 ) )
= $false )
| ( ( SV108
= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2470]) ).
thf(2533,plain,
! [SV360: $i,SV447: $i,SV124: $i > $o] :
( ( ( ~ ( SV124 @ SV447 )
| ( ( sK75_SY1348 @ SV360 @ SV124 )
= SV447 ) )
= $true )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV124 @ ( sK54_SY1664 @ SV360 @ SV124 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(2534,plain,
! [SV360: $i,SV437: $i,SV124: $i > $o] :
( ( ( ~ ( SV124 @ SV437 ) )
= $true )
| ( ( ( sK66_SY1348 @ SV360 @ SV124 )
= SV437 )
= $true )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV360
= ( sK54_SY1664 @ SV360 @ SV124 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2535,plain,
! [SV362: $i,SV438: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV438 ) )
= $true )
| ( ( ( sK67_SY1361 @ SV362 @ SV130 )
= SV438 )
= $true )
| ( ( SV130 @ ( sK42_SY1359 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2474]) ).
thf(2536,plain,
! [SV362: $i,SV448: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV448 )
| ( ( sK76_SY1361 @ SV362 @ SV130 )
= SV448 ) )
= $true )
| ( ( SV130 @ ( sK48_SY1690 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2476]) ).
thf(2537,plain,
! [SV362: $i,SV439: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV439 ) )
= $true )
| ( ( ( sK68_SY1361 @ SV362 @ SV130 )
= SV439 )
= $true )
| ( ( ( sK42_SY1359 @ SV362 @ SV130 )
= ( sK48_SY1690 @ SV362 @ SV130 ) )
= $false )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2477]) ).
thf(2538,plain,
! [SV364: $i,SV142: $i,SV424: $i] :
( ( ( in @ SV424 @ SV142 )
= $false )
| ( ( in @ SV424 @ ( sK37_SY1383 @ SV364 @ SV142 ) )
= $false )
| ( ( in @ SV364 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2478]) ).
thf(2539,plain,
! [SV399: $i,SV275: $i > $o,SV144: $i > $o] :
( ( ( SV144 @ ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2479]) ).
thf(2540,plain,
! [SV399: $i,SV144: $i > $o,SV275: $i > $o] :
( ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV399
= ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $false )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2480]) ).
thf(2541,plain,
! [SV275: $i > $o,SV440: $i,SV144: $i > $o] :
( ( ( ~ ( ~ ( SV144 @ SV440 )
| ~ ! [SY1745: $i] :
( ~ ( SV144 @ SY1745 )
| ( SV440 = SY1745 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(2544,plain,
! [SV275: $i > $o,SV429: $i,SV144: $i > $o] :
( ( ( ~ ( SV144 @ SV429 ) )
= $true )
| ( ( ~ ! [SY1731: $i] :
( ~ ( SV144 @ SY1731 )
| ( SV429 = SY1731 ) ) )
= $true )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2484]) ).
thf(2545,plain,
! [SV180: $i,SV349: $i > $o,SV29: $i,SV367: $i > $o] :
( ( ( SV367 @ ( sK50_SY1686 @ SV29 @ SV349 @ SV367 @ SV180 ) )
= $true )
| ( ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV29 ) )
= $true )
| ( ( ( dsetconstr @ SV29
@ ^ [SY1648: $i] : ( SV349 @ SY1648 ) )
= ( dsetconstr @ SV180
@ ^ [SY1672: $i] : ( SV367 @ SY1672 ) ) )
= $true )
| ( ( SV29 = SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2488]) ).
thf(2546,plain,
! [SV407: $i,SV35: $i,SV418: $i] :
( ( ( in @ SV418 @ SV35 )
= $false )
| ( ( in @ SV407 @ SV35 )
= $false )
| ( ( ~ ! [SY1715: $i] :
( ~ ( in @ SY1715 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SV407 @ SY1715 )
| ( in @ SV418 @ SY1715 ) )
| ~ ( ~ ( in @ SV418 @ SY1715 )
| ( in @ SV407 @ SY1715 ) ) ) )
| ( SV407 = SV418 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2491]) ).
thf(2547,plain,
! [SV35: $i,SV395: $i,SV391: $i,SV441: $i] :
( ( ( ~ ( in @ SV441 @ SV391 ) )
= $true )
| ( ( in @ SV441 @ SV395 )
= $true )
| ( ( ! [SY1697: $i] :
( ~ ( in @ SY1697 @ SV395 )
| ( in @ SY1697 @ SV391 ) ) )
= $true )
| ( ( in @ SV391 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( in @ SV395 @ ( sK2_SY1109 @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2492]) ).
thf(2548,plain,
! [SV434: $i,SV384: $i,SV35: $i] :
( ( ( ! [SY1679: $i] :
~ ~ ! [SY1680: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1679 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1680 @ SV384 ) )
| ~ ~ ~ ! [SY1681: $i] :
~ ~ ( ~ ( in @ SY1681 @ SY1679 )
| ~ ( in @ SY1681 @ SV384 ) ) )
| ~ ! [SY1616: $i] :
( ~ ( in @ SY1616 @ ( sK2_SY1109 @ SV35 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1616 )
| ( in @ SX6 @ SY1679 ) )
| ( in @ SY1680 @ SY1616 ) ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(2549,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( ~ ~ ! [SY1754: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1754 @ SV384 ) )
| ~ ~ ~ ! [SY1755: $i] :
~ ~ ( ~ ( in @ SY1755 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
| ~ ( in @ SY1755 @ SV384 ) ) )
| ~ ! [SY1756: $i] :
( ~ ( in @ SY1756 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1757: $i] :
( ~ ( in @ SY1757 @ SY1756 )
| ( in @ SY1757 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) ) )
| ( in @ SY1754 @ SY1756 ) ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2494]) ).
thf(2550,plain,
! [SV352: $i,SV442: $i,SV50: $i > $o] :
( ( ( ~ ( SV50 @ SV442 ) )
= $true )
| ( ( ( sK72_SY1160 @ SV352 @ SV50 )
= SV442 )
= $true )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV50 @ ( sK52_SY1651 @ SV352 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2495]) ).
thf(2551,plain,
! [SV352: $i,SV435: $i,SV50: $i > $o] :
( ( ( SV50 @ SV435 )
= $false )
| ( ( ( sK63_SY1160 @ SV352 @ SV50 )
= SV435 )
= $true )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV352
= ( sK52_SY1651 @ SV352 @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2496]) ).
thf(2552,plain,
! [SV210: $i,SV64: $i > $i > $o,SV392: $i] :
( ( ( ~ ( in @ ( sK83_SY1694 @ SV392 @ SV64 @ SV210 ) @ SV210 ) )
= $false )
| ( ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
= $false )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2497]) ).
thf(2553,plain,
! [SV210: $i,SV392: $i,SV64: $i > $i > $o] :
( ( ( ~ ( SV64 @ ( sK83_SY1694 @ SV392 @ SV64 @ SV210 ) @ SV392 ) )
= $false )
| ( ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
= $false )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2497]) ).
thf(2554,plain,
! [SV392: $i,SV64: $i > $i > $o,SV210: $i,SV431: $i] :
( ( ( ~ ( in @ SV431 @ SV210 ) )
= $true )
| ( ( ~ ( SV64 @ SV431 @ SV392 ) )
= $true )
| ( ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
= $true )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2498]) ).
thf(2555,plain,
! [SV210: $i,SV64: $i > $i > $o,SV385: $i,SV443: $i] :
( ( ( ~ ( ~ ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
| ~ ! [SY1746: $i] :
~ ~ ( ~ ( in @ SY1746 @ SV210 )
| ~ ( SV64 @ SY1746 @ SV443 ) ) )
| ~ ( ~ ~ ! [SY1747: $i] :
~ ~ ( ~ ( in @ SY1747 @ SV210 )
| ~ ( SV64 @ SY1747 @ SV443 ) )
| ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) ) ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2499]) ).
thf(2556,plain,
! [SV210: $i,SV64: $i > $i > $o,SV385: $i,SV436: $i] :
( ( ( ~ ( ~ ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
| ~ ! [SY1741: $i] :
~ ~ ( ~ ( in @ SY1741 @ SV210 )
| ~ ( SV64 @ SY1741 @ SV436 ) ) ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2500]) ).
thf(2557,plain,
! [SV385: $i,SV436: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ~ ( ~ ~ ! [SY1742: $i] :
~ ~ ( ~ ( in @ SY1742 @ SV210 )
| ~ ( SV64 @ SY1742 @ SV436 ) )
| ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) ) ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2500]) ).
thf(2558,plain,
! [SV70: $i,SV216: $i > $o,SV393: $i] :
( ( ( ~ ( in @ ( sK85_SY1495 @ SV393 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) ) )
= $false )
| ( ( in @ SV393 @ SV70 )
= $false )
| ( ( SV216 @ SV393 )
= $false )
| ( ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2501]) ).
thf(2559,plain,
! [SV393: $i,SV216: $i > $o,SV70: $i] :
( ( ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK85_SY1495 @ SV393 @ SV216 @ SV70 ) @ emptyset ) )
= $false )
| ( ( in @ SV393 @ SV70 )
= $false )
| ( ( SV216 @ SV393 )
= $false )
| ( ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2501]) ).
thf(2560,plain,
! [SV70: $i,SV216: $i > $o,SV403: $i] :
( ( ( ~ ( ~ ( in @ ( sK89_SY1495 @ SV403 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK89_SY1495 @ SV403 @ SV216 @ SV70 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV403 @ SV70 )
= $false )
| ( ( SV216 @ SV403 )
= $false )
| ( ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2502]) ).
thf(2561,plain,
! [SV70: $i,SV216: $i > $o,SV410: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK92_SY1495 @ SV410 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK92_SY1495 @ SV410 @ SV216 @ SV70 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV410 @ SV70 )
= $false )
| ( ( SV216 @ SV410 )
= $false )
| ( ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2503]) ).
thf(2562,plain,
! [SV420: $i,SV216: $i > $o,SV70: $i] :
( ( ( ! [SY1495: $i] :
~ ~ ( ~ ( in @ SY1495
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ SY1495 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV420 @ SV70 )
= $false )
| ( ( SV216 @ SV420 )
= $false )
| ( ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2504]) ).
thf(2563,plain,
! [SV70: $i,SV216: $i > $o,SV411: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK93_SY1495 @ SV411 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK93_SY1495 @ SV411 @ SV216 @ SV70 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV411 @ SV70 )
= $false )
| ( ( SV216 @ SV411 )
= $false )
| ( ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2505]) ).
thf(2564,plain,
! [SV421: $i,SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
| ( SV421
= ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) ) )
= $false )
| ( ( SV85 @ SV421 )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2506]) ).
thf(2565,plain,
! [SV422: $i,SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
| ( SV422
= ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) ) )
= $false )
| ( ( SV228 @ SV422 )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2507]) ).
thf(2566,plain,
! [SV228: $i > $o,SV85: $i > $o] :
( ( ( ! [SY1247: $i] :
~ ~ ( ~ ( SV85 @ SY1247 )
| ~ ! [SY1248: $i] :
( ~ ( SV85 @ SY1248 )
| ( SY1247 = SY1248 ) ) ) )
= $true )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2508]) ).
thf(2567,plain,
! [SV85: $i > $o,SV228: $i > $o] :
( ( ( ! [SY1519: $i] :
~ ~ ( ~ ( SV228 @ SY1519 )
| ~ ! [SY1520: $i] :
( ~ ( SV228 @ SY1520 )
| ( SY1519 = SY1520 ) ) ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2509]) ).
thf(2572,plain,
! [SV228: $i > $o,SV444: $i,SV85: $i > $o] :
( ( ( ~ ( ~ ( SV85 @ SV444 )
| ~ ! [SY1750: $i] :
( ~ ( SV85 @ SY1750 )
| ( SV444 = SY1750 ) ) ) )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(2573,plain,
! [SV85: $i > $o,SV445: $i,SV228: $i > $o] :
( ( ( ~ ( ~ ( SV228 @ SV445 )
| ~ ! [SY1751: $i] :
( ~ ( SV228 @ SY1751 )
| ( SV445 = SY1751 ) ) ) )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2515]) ).
thf(2574,plain,
! [SV356: $i,SV428: $i,SV90: $i > $o] :
( ( ( ~ ( SV90 @ SV428 ) )
= $true )
| ( ( SV428
= ( sK73_SY1266 @ SV356 @ SV90 ) )
= $true )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV90 @ ( sK53_SY1659 @ SV356 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2516]) ).
thf(2575,plain,
! [SV90: $i > $o,SV356: $i,SV428: $i] :
( ( ( SV428
!= ( sK73_SY1266 @ SV356 @ SV90 ) )
= $true )
| ( ( SV90 @ SV428 )
= $true )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV90 @ ( sK53_SY1659 @ SV356 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2517]) ).
thf(2576,plain,
! [SV356: $i,SV426: $i,SV90: $i > $o] :
( ( ( SV90 @ SV426 )
= $false )
| ( ( SV426
= ( sK65_SY1266 @ SV356 @ SV90 ) )
= $true )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV356
= ( sK53_SY1659 @ SV356 @ SV90 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2577,plain,
! [SV90: $i > $o,SV356: $i,SV426: $i] :
( ( ( SV426
= ( sK65_SY1266 @ SV356 @ SV90 ) )
= $false )
| ( ( SV90 @ SV426 )
= $true )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV356
= ( sK53_SY1659 @ SV356 @ SV90 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2519]) ).
thf(2578,plain,
! [SV92: $i,SV234: $i > $o,SV394: $i] :
( ( ( ~ ( in @ ( sK86_SY1533 @ SV394 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) ) )
= $false )
| ( ( in @ SV394 @ SV92 )
= $false )
| ( ( SV234 @ SV394 )
= $false )
| ( ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2520]) ).
thf(2579,plain,
! [SV394: $i,SV234: $i > $o,SV92: $i] :
( ( ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK86_SY1533 @ SV394 @ SV234 @ SV92 ) @ emptyset ) )
= $false )
| ( ( in @ SV394 @ SV92 )
= $false )
| ( ( SV234 @ SV394 )
= $false )
| ( ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2520]) ).
thf(2580,plain,
! [SV92: $i,SV234: $i > $o,SV404: $i] :
( ( ( ~ ( ~ ( in @ ( sK90_SY1533 @ SV404 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK90_SY1533 @ SV404 @ SV234 @ SV92 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV404 @ SV92 )
= $false )
| ( ( SV234 @ SV404 )
= $false )
| ( ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2521]) ).
thf(2581,plain,
! [SV92: $i,SV234: $i > $o,SV412: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK96_SY1533 @ SV412 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK96_SY1533 @ SV412 @ SV234 @ SV92 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV412 @ SV92 )
= $false )
| ( ( SV234 @ SV412 )
= $false )
| ( ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2522]) ).
thf(2582,plain,
! [SV423: $i,SV234: $i > $o,SV92: $i] :
( ( ( ! [SY1533: $i] :
~ ~ ( ~ ( in @ SY1533
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ SY1533 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV423 @ SV92 )
= $false )
| ( ( SV234 @ SV423 )
= $false )
| ( ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2523]) ).
thf(2583,plain,
! [SV92: $i,SV234: $i > $o,SV413: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK97_SY1533 @ SV413 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK97_SY1533 @ SV413 @ SV234 @ SV92 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV413 @ SV92 )
= $false )
| ( ( SV234 @ SV413 )
= $false )
| ( ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2524]) ).
thf(2584,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( SV98 @ ( sK82_SY1292 @ SV357 @ SV98 ) )
= $true )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $true )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2525]) ).
thf(2585,plain,
! [SV357: $i,SV98: $i > $o] :
( ( ( ! [SY1730: $i] :
( ~ ( SV98 @ SY1730 )
| ( ( sK82_SY1292 @ SV357 @ SV98 )
= SY1730 ) ) )
= $true )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $true )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2526]) ).
thf(2588,plain,
! [SV357: $i,SV446: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ SV446 ) )
= $true )
| ( ( ( sK74_SY1292 @ SV357 @ SV98 )
= SV446 )
= $true )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $false )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2531]) ).
thf(2589,plain,
! [SV108: $i,SV358: $i,SV398: $i] :
( ( ( ~ ( in @ ( sK88_SY1316 @ SV398 @ SV358 @ SV108 )
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
| ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ ( sK88_SY1316 @ SV398 @ SV358 @ SV108 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV358 @ ( setunion @ SV108 ) )
= $false )
| ( ( in @ SV398 @ ( setunion @ SV108 ) )
= $false )
| ( ( SV108
= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2532]) ).
thf(2590,plain,
! [SV360: $i,SV447: $i,SV124: $i > $o] :
( ( ( ~ ( SV124 @ SV447 ) )
= $true )
| ( ( ( sK75_SY1348 @ SV360 @ SV124 )
= SV447 )
= $true )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV124 @ ( sK54_SY1664 @ SV360 @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2533]) ).
thf(2591,plain,
! [SV360: $i,SV437: $i,SV124: $i > $o] :
( ( ( SV124 @ SV437 )
= $false )
| ( ( ( sK66_SY1348 @ SV360 @ SV124 )
= SV437 )
= $true )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV360
= ( sK54_SY1664 @ SV360 @ SV124 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2534]) ).
thf(2592,plain,
! [SV362: $i,SV438: $i,SV130: $i > $o] :
( ( ( SV130 @ SV438 )
= $false )
| ( ( ( sK67_SY1361 @ SV362 @ SV130 )
= SV438 )
= $true )
| ( ( SV130 @ ( sK42_SY1359 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2535]) ).
thf(2593,plain,
! [SV362: $i,SV448: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ SV448 ) )
= $true )
| ( ( ( sK76_SY1361 @ SV362 @ SV130 )
= SV448 )
= $true )
| ( ( SV130 @ ( sK48_SY1690 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2536]) ).
thf(2594,plain,
! [SV362: $i,SV439: $i,SV130: $i > $o] :
( ( ( SV130 @ SV439 )
= $false )
| ( ( ( sK68_SY1361 @ SV362 @ SV130 )
= SV439 )
= $true )
| ( ( ( sK42_SY1359 @ SV362 @ SV130 )
= ( sK48_SY1690 @ SV362 @ SV130 ) )
= $false )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2537]) ).
thf(2595,plain,
! [SV399: $i,SV144: $i > $o,SV275: $i > $o] :
( ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV144 @ ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2539]) ).
thf(2596,plain,
! [SV399: $i,SV144: $i > $o,SV275: $i > $o] :
( ( ( ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV399
= ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $false )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2540]) ).
thf(2597,plain,
! [SV275: $i > $o,SV440: $i,SV144: $i > $o] :
( ( ( ~ ( SV144 @ SV440 )
| ~ ! [SY1745: $i] :
( ~ ( SV144 @ SY1745 )
| ( SV440 = SY1745 ) ) )
= $true )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2541]) ).
thf(2600,plain,
! [SV275: $i > $o,SV429: $i,SV144: $i > $o] :
( ( ( SV144 @ SV429 )
= $false )
| ( ( ~ ! [SY1731: $i] :
( ~ ( SV144 @ SY1731 )
| ( SV429 = SY1731 ) ) )
= $true )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2544]) ).
thf(2601,plain,
! [SV418: $i,SV407: $i,SV35: $i] :
( ( ( ~ ! [SY1715: $i] :
( ~ ( in @ SY1715 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SV407 @ SY1715 )
| ( in @ SV418 @ SY1715 ) )
| ~ ( ~ ( in @ SV418 @ SY1715 )
| ( in @ SV407 @ SY1715 ) ) ) ) )
= $true )
| ( ( SV407 = SV418 )
= $true )
| ( ( in @ SV407 @ SV35 )
= $false )
| ( ( in @ SV418 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2546]) ).
thf(2602,plain,
! [SV35: $i,SV395: $i,SV391: $i,SV441: $i] :
( ( ( in @ SV441 @ SV391 )
= $false )
| ( ( in @ SV441 @ SV395 )
= $true )
| ( ( ! [SY1697: $i] :
( ~ ( in @ SY1697 @ SV395 )
| ( in @ SY1697 @ SV391 ) ) )
= $true )
| ( ( in @ SV391 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( in @ SV395 @ ( sK2_SY1109 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2547]) ).
thf(2603,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( ~ ~ ! [SY1770: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1770 @ SV384 ) )
| ~ ~ ~ ! [SY1771: $i] :
~ ~ ( ~ ( in @ SY1771 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
| ~ ( in @ SY1771 @ SV384 ) ) )
| ~ ! [SY1772: $i] :
( ~ ( in @ SY1772 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1773: $i] :
( ~ ( in @ SY1773 @ SY1772 )
| ( in @ SY1773 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) ) )
| ( in @ SY1770 @ SY1772 ) ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2548]) ).
thf(2604,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( ~ ! [SY1754: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1754 @ SV384 ) )
| ~ ~ ~ ! [SY1755: $i] :
~ ~ ( ~ ( in @ SY1755 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
| ~ ( in @ SY1755 @ SV384 ) ) )
| ~ ! [SY1756: $i] :
( ~ ( in @ SY1756 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1757: $i] :
( ~ ( in @ SY1757 @ SY1756 )
| ( in @ SY1757 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) ) )
| ( in @ SY1754 @ SY1756 ) ) ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2549]) ).
thf(2605,plain,
! [SV352: $i,SV442: $i,SV50: $i > $o] :
( ( ( SV50 @ SV442 )
= $false )
| ( ( ( sK72_SY1160 @ SV352 @ SV50 )
= SV442 )
= $true )
| ( ( SV50 @ SV352 )
= $false )
| ( ( SV50 @ ( sK52_SY1651 @ SV352 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2550]) ).
thf(2606,plain,
! [SV210: $i,SV64: $i > $i > $o,SV392: $i] :
( ( ( in @ ( sK83_SY1694 @ SV392 @ SV64 @ SV210 ) @ SV210 )
= $true )
| ( ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
= $false )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2552]) ).
thf(2607,plain,
! [SV210: $i,SV392: $i,SV64: $i > $i > $o] :
( ( ( SV64 @ ( sK83_SY1694 @ SV392 @ SV64 @ SV210 ) @ SV392 )
= $true )
| ( ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
= $false )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2553]) ).
thf(2608,plain,
! [SV392: $i,SV64: $i > $i > $o,SV210: $i,SV431: $i] :
( ( ( in @ SV431 @ SV210 )
= $false )
| ( ( ~ ( SV64 @ SV431 @ SV392 ) )
= $true )
| ( ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
= $true )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2554]) ).
thf(2609,plain,
! [SV210: $i,SV64: $i > $i > $o,SV385: $i,SV443: $i] :
( ( ( ~ ( ~ ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
| ~ ! [SY1746: $i] :
~ ~ ( ~ ( in @ SY1746 @ SV210 )
| ~ ( SV64 @ SY1746 @ SV443 ) ) ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2555]) ).
thf(2610,plain,
! [SV385: $i,SV443: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ~ ( ~ ~ ! [SY1747: $i] :
~ ~ ( ~ ( in @ SY1747 @ SV210 )
| ~ ( SV64 @ SY1747 @ SV443 ) )
| ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) ) ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2555]) ).
thf(2611,plain,
! [SV210: $i,SV64: $i > $i > $o,SV385: $i,SV436: $i] :
( ( ( ~ ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
| ~ ! [SY1741: $i] :
~ ~ ( ~ ( in @ SY1741 @ SV210 )
| ~ ( SV64 @ SY1741 @ SV436 ) ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2556]) ).
thf(2612,plain,
! [SV385: $i,SV436: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ~ ~ ! [SY1742: $i] :
~ ~ ( ~ ( in @ SY1742 @ SV210 )
| ~ ( SV64 @ SY1742 @ SV436 ) )
| ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2557]) ).
thf(2613,plain,
! [SV70: $i,SV216: $i > $o,SV393: $i] :
( ( ( in @ ( sK85_SY1495 @ SV393 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
= $true )
| ( ( in @ SV393 @ SV70 )
= $false )
| ( ( SV216 @ SV393 )
= $false )
| ( ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2558]) ).
thf(2614,plain,
! [SV393: $i,SV216: $i > $o,SV70: $i] :
( ( ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
= ( setadjoin @ ( sK85_SY1495 @ SV393 @ SV216 @ SV70 ) @ emptyset ) )
= $true )
| ( ( in @ SV393 @ SV70 )
= $false )
| ( ( SV216 @ SV393 )
= $false )
| ( ( in @ ( sK12_SY1492 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2559]) ).
thf(2615,plain,
! [SV70: $i,SV216: $i > $o,SV403: $i] :
( ( ( ~ ( in @ ( sK89_SY1495 @ SV403 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK89_SY1495 @ SV403 @ SV216 @ SV70 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV403 @ SV70 )
= $false )
| ( ( SV216 @ SV403 )
= $false )
| ( ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2560]) ).
thf(2616,plain,
! [SV70: $i,SV216: $i > $o,SV410: $i] :
( ( ( ~ ( ~ ( in @ ( sK92_SY1495 @ SV410 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK92_SY1495 @ SV410 @ SV216 @ SV70 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV410 @ SV70 )
= $false )
| ( ( SV216 @ SV410 )
= $false )
| ( ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2561]) ).
thf(2617,plain,
! [SV70: $i,SV216: $i > $o,SV420: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK99_SY1495 @ SV420 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK99_SY1495 @ SV420 @ SV216 @ SV70 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV420 @ SV70 )
= $false )
| ( ( SV216 @ SV420 )
= $false )
| ( ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2562]) ).
thf(2618,plain,
! [SV70: $i,SV216: $i > $o,SV411: $i] :
( ( ( ~ ( ~ ( in @ ( sK93_SY1495 @ SV411 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK93_SY1495 @ SV411 @ SV216 @ SV70 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV411 @ SV70 )
= $false )
| ( ( SV216 @ SV411 )
= $false )
| ( ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2563]) ).
thf(2619,plain,
! [SV421: $i,SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) ) )
= $false )
| ( ( SV85 @ SV421 )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2564]) ).
thf(2620,plain,
! [SV85: $i > $o,SV228: $i > $o,SV421: $i] :
( ( ( SV421
= ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $false )
| ( ( SV85 @ SV421 )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2564]) ).
thf(2621,plain,
! [SV422: $i,SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) ) )
= $false )
| ( ( SV228 @ SV422 )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2565]) ).
thf(2622,plain,
! [SV228: $i > $o,SV85: $i > $o,SV422: $i] :
( ( ( SV422
= ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $false )
| ( ( SV228 @ SV422 )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2565]) ).
thf(2623,plain,
! [SV228: $i > $o,SV455: $i,SV85: $i > $o] :
( ( ( ~ ~ ( ~ ( SV85 @ SV455 )
| ~ ! [SY1776: $i] :
( ~ ( SV85 @ SY1776 )
| ( SV455 = SY1776 ) ) ) )
= $true )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(2624,plain,
! [SV85: $i > $o,SV456: $i,SV228: $i > $o] :
( ( ( ~ ~ ( ~ ( SV228 @ SV456 )
| ~ ! [SY1777: $i] :
( ~ ( SV228 @ SY1777 )
| ( SV456 = SY1777 ) ) ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(2629,plain,
! [SV228: $i > $o,SV444: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ SV444 )
| ~ ! [SY1750: $i] :
( ~ ( SV85 @ SY1750 )
| ( SV444 = SY1750 ) ) )
= $true )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2572]) ).
thf(2630,plain,
! [SV85: $i > $o,SV445: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ SV445 )
| ~ ! [SY1751: $i] :
( ~ ( SV228 @ SY1751 )
| ( SV445 = SY1751 ) ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2573]) ).
thf(2631,plain,
! [SV356: $i,SV428: $i,SV90: $i > $o] :
( ( ( SV90 @ SV428 )
= $false )
| ( ( SV428
= ( sK73_SY1266 @ SV356 @ SV90 ) )
= $true )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV90 @ ( sK53_SY1659 @ SV356 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2632,plain,
! [SV90: $i > $o,SV356: $i,SV428: $i] :
( ( ( SV428
= ( sK73_SY1266 @ SV356 @ SV90 ) )
= $false )
| ( ( SV90 @ SV428 )
= $true )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV90 @ ( sK53_SY1659 @ SV356 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2633,plain,
! [SV92: $i,SV234: $i > $o,SV394: $i] :
( ( ( in @ ( sK86_SY1533 @ SV394 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
= $true )
| ( ( in @ SV394 @ SV92 )
= $false )
| ( ( SV234 @ SV394 )
= $false )
| ( ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2578]) ).
thf(2634,plain,
! [SV394: $i,SV234: $i > $o,SV92: $i] :
( ( ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
= ( setadjoin @ ( sK86_SY1533 @ SV394 @ SV234 @ SV92 ) @ emptyset ) )
= $true )
| ( ( in @ SV394 @ SV92 )
= $false )
| ( ( SV234 @ SV394 )
= $false )
| ( ( in @ ( sK15_SY1530 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2579]) ).
thf(2635,plain,
! [SV92: $i,SV234: $i > $o,SV404: $i] :
( ( ( ~ ( in @ ( sK90_SY1533 @ SV404 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK90_SY1533 @ SV404 @ SV234 @ SV92 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV404 @ SV92 )
= $false )
| ( ( SV234 @ SV404 )
= $false )
| ( ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2580]) ).
thf(2636,plain,
! [SV92: $i,SV234: $i > $o,SV412: $i] :
( ( ( ~ ( ~ ( in @ ( sK96_SY1533 @ SV412 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK96_SY1533 @ SV412 @ SV234 @ SV92 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV412 @ SV92 )
= $false )
| ( ( SV234 @ SV412 )
= $false )
| ( ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2581]) ).
thf(2637,plain,
! [SV92: $i,SV234: $i > $o,SV423: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK100_SY1533 @ SV423 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK100_SY1533 @ SV423 @ SV234 @ SV92 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV423 @ SV92 )
= $false )
| ( ( SV234 @ SV423 )
= $false )
| ( ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2582]) ).
thf(2638,plain,
! [SV92: $i,SV234: $i > $o,SV413: $i] :
( ( ( ~ ( ~ ( in @ ( sK97_SY1533 @ SV413 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK97_SY1533 @ SV413 @ SV234 @ SV92 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV413 @ SV92 )
= $false )
| ( ( SV234 @ SV413 )
= $false )
| ( ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2583]) ).
thf(2639,plain,
! [SV357: $i,SV457: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ SV457 )
| ( ( sK82_SY1292 @ SV357 @ SV98 )
= SV457 ) )
= $true )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $true )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2585]) ).
thf(2642,plain,
! [SV357: $i,SV446: $i,SV98: $i > $o] :
( ( ( SV98 @ SV446 )
= $false )
| ( ( ( sK74_SY1292 @ SV357 @ SV98 )
= SV446 )
= $true )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $false )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2588]) ).
thf(2643,plain,
! [SV108: $i,SV358: $i,SV398: $i] :
( ( ( ~ ( in @ ( sK88_SY1316 @ SV398 @ SV358 @ SV108 )
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) ) )
= $false )
| ( ( in @ SV358 @ ( setunion @ SV108 ) )
= $false )
| ( ( in @ SV398 @ ( setunion @ SV108 ) )
= $false )
| ( ( SV108
= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2589]) ).
thf(2644,plain,
! [SV358: $i,SV398: $i,SV108: $i] :
( ( ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
!= ( setadjoin @ ( sK88_SY1316 @ SV398 @ SV358 @ SV108 ) @ emptyset ) )
= $false )
| ( ( in @ SV358 @ ( setunion @ SV108 ) )
= $false )
| ( ( in @ SV398 @ ( setunion @ SV108 ) )
= $false )
| ( ( SV108
= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2589]) ).
thf(2645,plain,
! [SV360: $i,SV447: $i,SV124: $i > $o] :
( ( ( SV124 @ SV447 )
= $false )
| ( ( ( sK75_SY1348 @ SV360 @ SV124 )
= SV447 )
= $true )
| ( ( SV124 @ SV360 )
= $false )
| ( ( SV124 @ ( sK54_SY1664 @ SV360 @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2590]) ).
thf(2646,plain,
! [SV362: $i,SV448: $i,SV130: $i > $o] :
( ( ( SV130 @ SV448 )
= $false )
| ( ( ( sK76_SY1361 @ SV362 @ SV130 )
= SV448 )
= $true )
| ( ( SV130 @ ( sK48_SY1690 @ SV362 @ SV130 ) )
= $true )
| ( ( SV130 @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2593]) ).
thf(2647,plain,
! [SV399: $i,SV144: $i > $o,SV275: $i > $o] :
( ( ( ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV144 @ ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2595]) ).
thf(2648,plain,
! [SV399: $i,SV144: $i > $o,SV275: $i > $o] :
( ( ( ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV399
= ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $false )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2596]) ).
thf(2649,plain,
! [SV275: $i > $o,SV440: $i,SV144: $i > $o] :
( ( ( ~ ( SV144 @ SV440 ) )
= $true )
| ( ( ~ ! [SY1745: $i] :
( ~ ( SV144 @ SY1745 )
| ( SV440 = SY1745 ) ) )
= $true )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2597]) ).
thf(2652,plain,
! [SV275: $i > $o,SV429: $i,SV144: $i > $o] :
( ( ( ! [SY1731: $i] :
( ~ ( SV144 @ SY1731 )
| ( SV429 = SY1731 ) ) )
= $false )
| ( ( SV144 @ SV429 )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2600]) ).
thf(2653,plain,
! [SV418: $i,SV407: $i,SV35: $i] :
( ( ( ! [SY1715: $i] :
( ~ ( in @ SY1715 @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SV407 @ SY1715 )
| ( in @ SV418 @ SY1715 ) )
| ~ ( ~ ( in @ SV418 @ SY1715 )
| ( in @ SV407 @ SY1715 ) ) ) ) )
= $false )
| ( ( SV407 = SV418 )
= $true )
| ( ( in @ SV407 @ SV35 )
= $false )
| ( ( in @ SV418 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2601]) ).
thf(2654,plain,
! [SV35: $i,SV441: $i,SV391: $i,SV395: $i,SV458: $i] :
( ( ( ~ ( in @ SV458 @ SV395 )
| ( in @ SV458 @ SV391 ) )
= $true )
| ( ( in @ SV441 @ SV395 )
= $true )
| ( ( in @ SV441 @ SV391 )
= $false )
| ( ( in @ SV391 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( in @ SV395 @ ( sK2_SY1109 @ SV35 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2602]) ).
thf(2655,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( ~ ! [SY1770: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1770 @ SV384 ) )
| ~ ~ ~ ! [SY1771: $i] :
~ ~ ( ~ ( in @ SY1771 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
| ~ ( in @ SY1771 @ SV384 ) ) )
| ~ ! [SY1772: $i] :
( ~ ( in @ SY1772 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1773: $i] :
( ~ ( in @ SY1773 @ SY1772 )
| ( in @ SY1773 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) ) )
| ( in @ SY1770 @ SY1772 ) ) ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2603]) ).
thf(2656,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( ! [SY1754: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1754 @ SV384 ) )
| ~ ~ ~ ! [SY1755: $i] :
~ ~ ( ~ ( in @ SY1755 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
| ~ ( in @ SY1755 @ SV384 ) ) )
| ~ ! [SY1756: $i] :
( ~ ( in @ SY1756 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1757: $i] :
( ~ ( in @ SY1757 @ SY1756 )
| ( in @ SY1757 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) ) )
| ( in @ SY1754 @ SY1756 ) ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2604]) ).
thf(2657,plain,
! [SV210: $i,SV392: $i,SV431: $i,SV64: $i > $i > $o] :
( ( ( SV64 @ SV431 @ SV392 )
= $false )
| ( ( in @ SV431 @ SV210 )
= $false )
| ( ( in @ SV392 @ ( sK40_SY1483 @ SV64 @ SV210 ) )
= $true )
| ( ( in @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV210 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2608]) ).
thf(2658,plain,
! [SV210: $i,SV64: $i > $i > $o,SV385: $i,SV443: $i] :
( ( ( ~ ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
| ~ ! [SY1746: $i] :
~ ~ ( ~ ( in @ SY1746 @ SV210 )
| ~ ( SV64 @ SY1746 @ SV443 ) ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2609]) ).
thf(2659,plain,
! [SV385: $i,SV443: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ~ ~ ! [SY1747: $i] :
~ ~ ( ~ ( in @ SY1747 @ SV210 )
| ~ ( SV64 @ SY1747 @ SV443 ) )
| ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2610]) ).
thf(2660,plain,
! [SV210: $i,SV64: $i > $i > $o,SV385: $i,SV436: $i] :
( ( ( ~ ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) ) )
= $true )
| ( ( ~ ! [SY1741: $i] :
~ ~ ( ~ ( in @ SY1741 @ SV210 )
| ~ ( SV64 @ SY1741 @ SV436 ) ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2611]) ).
thf(2661,plain,
! [SV385: $i,SV436: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ~ ~ ! [SY1742: $i] :
~ ~ ( ~ ( in @ SY1742 @ SV210 )
| ~ ( SV64 @ SY1742 @ SV436 ) ) )
= $true )
| ( ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2612]) ).
thf(2662,plain,
! [SV70: $i,SV216: $i > $o,SV403: $i] :
( ( ( ~ ( in @ ( sK89_SY1495 @ SV403 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) ) )
= $false )
| ( ( in @ SV403 @ SV70 )
= $false )
| ( ( SV216 @ SV403 )
= $false )
| ( ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2615]) ).
thf(2663,plain,
! [SV403: $i,SV216: $i > $o,SV70: $i] :
( ( ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK89_SY1495 @ SV403 @ SV216 @ SV70 ) @ emptyset ) )
= $false )
| ( ( in @ SV403 @ SV70 )
= $false )
| ( ( SV216 @ SV403 )
= $false )
| ( ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2615]) ).
thf(2664,plain,
! [SV70: $i,SV216: $i > $o,SV410: $i] :
( ( ( ~ ( in @ ( sK92_SY1495 @ SV410 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK92_SY1495 @ SV410 @ SV216 @ SV70 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV410 @ SV70 )
= $false )
| ( ( SV216 @ SV410 )
= $false )
| ( ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2616]) ).
thf(2665,plain,
! [SV70: $i,SV216: $i > $o,SV420: $i] :
( ( ( ~ ( ~ ( in @ ( sK99_SY1495 @ SV420 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK99_SY1495 @ SV420 @ SV216 @ SV70 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV420 @ SV70 )
= $false )
| ( ( SV216 @ SV420 )
= $false )
| ( ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2617]) ).
thf(2666,plain,
! [SV70: $i,SV216: $i > $o,SV411: $i] :
( ( ( ~ ( in @ ( sK93_SY1495 @ SV411 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK93_SY1495 @ SV411 @ SV216 @ SV70 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV411 @ SV70 )
= $false )
| ( ( SV216 @ SV411 )
= $false )
| ( ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2618]) ).
thf(2667,plain,
! [SV421: $i,SV228: $i > $o,SV85: $i > $o] :
( ( ( SV85 @ ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $true )
| ( ( SV85 @ SV421 )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2619]) ).
thf(2668,plain,
! [SV421: $i,SV85: $i > $o,SV228: $i > $o] :
( ( ( ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $false )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV421
= ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2620]) ).
thf(2669,plain,
! [SV422: $i,SV85: $i > $o,SV228: $i > $o] :
( ( ( SV228 @ ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $true )
| ( ( SV228 @ SV422 )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2621]) ).
thf(2670,plain,
! [SV422: $i,SV228: $i > $o,SV85: $i > $o] :
( ( ( ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $false )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV422
= ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2622]) ).
thf(2671,plain,
! [SV228: $i > $o,SV455: $i,SV85: $i > $o] :
( ( ( ~ ( ~ ( SV85 @ SV455 )
| ~ ! [SY1776: $i] :
( ~ ( SV85 @ SY1776 )
| ( SV455 = SY1776 ) ) ) )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2623]) ).
thf(2672,plain,
! [SV85: $i > $o,SV456: $i,SV228: $i > $o] :
( ( ( ~ ( ~ ( SV228 @ SV456 )
| ~ ! [SY1777: $i] :
( ~ ( SV228 @ SY1777 )
| ( SV456 = SY1777 ) ) ) )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2624]) ).
thf(2677,plain,
! [SV228: $i > $o,SV444: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ SV444 ) )
= $true )
| ( ( ~ ! [SY1750: $i] :
( ~ ( SV85 @ SY1750 )
| ( SV444 = SY1750 ) ) )
= $true )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2629]) ).
thf(2678,plain,
! [SV85: $i > $o,SV445: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ SV445 ) )
= $true )
| ( ( ~ ! [SY1751: $i] :
( ~ ( SV228 @ SY1751 )
| ( SV445 = SY1751 ) ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2630]) ).
thf(2679,plain,
! [SV92: $i,SV234: $i > $o,SV404: $i] :
( ( ( ~ ( in @ ( sK90_SY1533 @ SV404 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) ) )
= $false )
| ( ( in @ SV404 @ SV92 )
= $false )
| ( ( SV234 @ SV404 )
= $false )
| ( ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2635]) ).
thf(2680,plain,
! [SV404: $i,SV234: $i > $o,SV92: $i] :
( ( ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK90_SY1533 @ SV404 @ SV234 @ SV92 ) @ emptyset ) )
= $false )
| ( ( in @ SV404 @ SV92 )
= $false )
| ( ( SV234 @ SV404 )
= $false )
| ( ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2635]) ).
thf(2681,plain,
! [SV92: $i,SV234: $i > $o,SV412: $i] :
( ( ( ~ ( in @ ( sK96_SY1533 @ SV412 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK96_SY1533 @ SV412 @ SV234 @ SV92 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV412 @ SV92 )
= $false )
| ( ( SV234 @ SV412 )
= $false )
| ( ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2636]) ).
thf(2682,plain,
! [SV92: $i,SV234: $i > $o,SV423: $i] :
( ( ( ~ ( ~ ( in @ ( sK100_SY1533 @ SV423 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK100_SY1533 @ SV423 @ SV234 @ SV92 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV423 @ SV92 )
= $false )
| ( ( SV234 @ SV423 )
= $false )
| ( ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2637]) ).
thf(2683,plain,
! [SV92: $i,SV234: $i > $o,SV413: $i] :
( ( ( ~ ( in @ ( sK97_SY1533 @ SV413 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK97_SY1533 @ SV413 @ SV234 @ SV92 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV413 @ SV92 )
= $false )
| ( ( SV234 @ SV413 )
= $false )
| ( ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2638]) ).
thf(2684,plain,
! [SV357: $i,SV457: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ SV457 ) )
= $true )
| ( ( ( sK82_SY1292 @ SV357 @ SV98 )
= SV457 )
= $true )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $true )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2639]) ).
thf(2687,plain,
! [SV108: $i,SV358: $i,SV398: $i] :
( ( ( in @ ( sK88_SY1316 @ SV398 @ SV358 @ SV108 )
@ ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1317: $i] : ( in @ ( setadjoin @ SY1317 @ emptyset ) @ SV108 ) ) )
= $true )
| ( ( in @ SV358 @ ( setunion @ SV108 ) )
= $false )
| ( ( in @ SV398 @ ( setunion @ SV108 ) )
= $false )
| ( ( SV108
= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2643]) ).
thf(2688,plain,
! [SV358: $i,SV398: $i,SV108: $i] :
( ( ( ( dsetconstr @ ( setunion @ SV108 )
@ ^ [SY1318: $i] : ( in @ ( setadjoin @ SY1318 @ emptyset ) @ SV108 ) )
= ( setadjoin @ ( sK88_SY1316 @ SV398 @ SV358 @ SV108 ) @ emptyset ) )
= $true )
| ( ( in @ SV358 @ ( setunion @ SV108 ) )
= $false )
| ( ( in @ SV398 @ ( setunion @ SV108 ) )
= $false )
| ( ( SV108
= ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2644]) ).
thf(2689,plain,
! [SV399: $i,SV144: $i > $o,SV275: $i > $o] :
( ( ( ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV144 @ ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2647]) ).
thf(2690,plain,
! [SV399: $i,SV144: $i > $o,SV459: $i,SV275: $i > $o] :
( ( ( ~ ~ ( ~ ( SV275 @ SV459 )
| ~ ! [SY1780: $i] :
( ~ ( SV275 @ SY1780 )
| ( SV459 = SY1780 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV399
= ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $false )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2648]) ).
thf(2691,plain,
! [SV275: $i > $o,SV440: $i,SV144: $i > $o] :
( ( ( SV144 @ SV440 )
= $false )
| ( ( ~ ! [SY1745: $i] :
( ~ ( SV144 @ SY1745 )
| ( SV440 = SY1745 ) ) )
= $true )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2649]) ).
thf(2694,plain,
! [SV429: $i,SV275: $i > $o,SV144: $i > $o] :
( ( ( ~ ( SV144 @ ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
| ( SV429
= ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) ) )
= $false )
| ( ( SV144 @ SV429 )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2652]) ).
thf(2695,plain,
! [SV35: $i,SV407: $i,SV418: $i] :
( ( ( ~ ( in @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( ~ ( ~ ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
| ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) ) )
| ~ ( ~ ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
| ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) ) ) ) )
= $false )
| ( ( SV407 = SV418 )
= $true )
| ( ( in @ SV407 @ SV35 )
= $false )
| ( ( in @ SV418 @ SV35 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2653]) ).
thf(2696,plain,
! [SV35: $i,SV441: $i,SV391: $i,SV395: $i,SV458: $i] :
( ( ( ~ ( in @ SV458 @ SV395 ) )
= $true )
| ( ( in @ SV458 @ SV391 )
= $true )
| ( ( in @ SV441 @ SV395 )
= $true )
| ( ( in @ SV441 @ SV391 )
= $false )
| ( ( in @ SV391 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( in @ SV395 @ ( sK2_SY1109 @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2654]) ).
thf(2697,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( ! [SY1770: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ SY1770 @ SV384 ) )
| ~ ~ ~ ! [SY1771: $i] :
~ ~ ( ~ ( in @ SY1771 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
| ~ ( in @ SY1771 @ SV384 ) ) )
| ~ ! [SY1772: $i] :
( ~ ( in @ SY1772 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1773: $i] :
( ~ ( in @ SY1773 @ SY1772 )
| ( in @ SY1773 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) ) )
| ( in @ SY1770 @ SY1772 ) ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2655]) ).
thf(2698,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SV384 ) )
| ~ ~ ~ ! [SY1755: $i] :
~ ~ ( ~ ( in @ SY1755 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
| ~ ( in @ SY1755 @ SV384 ) ) )
| ~ ! [SY1782: $i] :
( ~ ( in @ SY1782 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1757: $i] :
( ~ ( in @ SY1757 @ SY1782 )
| ( in @ SY1757 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) ) )
| ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SY1782 ) ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2656]) ).
thf(2699,plain,
! [SV210: $i,SV64: $i > $i > $o,SV385: $i,SV443: $i] :
( ( ( ~ ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) ) )
= $true )
| ( ( ~ ! [SY1746: $i] :
~ ~ ( ~ ( in @ SY1746 @ SV210 )
| ~ ( SV64 @ SY1746 @ SV443 ) ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2658]) ).
thf(2700,plain,
! [SV385: $i,SV443: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ~ ~ ! [SY1747: $i] :
~ ~ ( ~ ( in @ SY1747 @ SV210 )
| ~ ( SV64 @ SY1747 @ SV443 ) ) )
= $true )
| ( ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2659]) ).
thf(2701,plain,
! [SV210: $i,SV64: $i > $i > $o,SV385: $i,SV436: $i] :
( ( ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $false )
| ( ( ~ ! [SY1741: $i] :
~ ~ ( ~ ( in @ SY1741 @ SV210 )
| ~ ( SV64 @ SY1741 @ SV436 ) ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2660]) ).
thf(2702,plain,
! [SV385: $i,SV436: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ~ ! [SY1742: $i] :
~ ~ ( ~ ( in @ SY1742 @ SV210 )
| ~ ( SV64 @ SY1742 @ SV436 ) ) )
= $false )
| ( ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2661]) ).
thf(2703,plain,
! [SV70: $i,SV216: $i > $o,SV403: $i] :
( ( ( in @ ( sK89_SY1495 @ SV403 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
= $true )
| ( ( in @ SV403 @ SV70 )
= $false )
| ( ( SV216 @ SV403 )
= $false )
| ( ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2662]) ).
thf(2704,plain,
! [SV403: $i,SV216: $i > $o,SV70: $i] :
( ( ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
= ( setadjoin @ ( sK89_SY1495 @ SV403 @ SV216 @ SV70 ) @ emptyset ) )
= $true )
| ( ( in @ SV403 @ SV70 )
= $false )
| ( ( SV216 @ SV403 )
= $false )
| ( ( in @ ( sK25_SY1654 @ SV216 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2663]) ).
thf(2705,plain,
! [SV70: $i,SV216: $i > $o,SV410: $i] :
( ( ( ~ ( in @ ( sK92_SY1495 @ SV410 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) ) )
= $false )
| ( ( in @ SV410 @ SV70 )
= $false )
| ( ( SV216 @ SV410 )
= $false )
| ( ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2664]) ).
thf(2706,plain,
! [SV410: $i,SV216: $i > $o,SV70: $i] :
( ( ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK92_SY1495 @ SV410 @ SV216 @ SV70 ) @ emptyset ) )
= $false )
| ( ( in @ SV410 @ SV70 )
= $false )
| ( ( SV216 @ SV410 )
= $false )
| ( ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2664]) ).
thf(2707,plain,
! [SV70: $i,SV216: $i > $o,SV420: $i] :
( ( ( ~ ( in @ ( sK99_SY1495 @ SV420 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
| ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK99_SY1495 @ SV420 @ SV216 @ SV70 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV420 @ SV70 )
= $false )
| ( ( SV216 @ SV420 )
= $false )
| ( ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2665]) ).
thf(2708,plain,
! [SV70: $i,SV216: $i > $o,SV411: $i] :
( ( ( ~ ( in @ ( sK93_SY1495 @ SV411 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) ) )
= $false )
| ( ( in @ SV411 @ SV70 )
= $false )
| ( ( SV216 @ SV411 )
= $false )
| ( ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2666]) ).
thf(2709,plain,
! [SV411: $i,SV216: $i > $o,SV70: $i] :
( ( ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK93_SY1495 @ SV411 @ SV216 @ SV70 ) @ emptyset ) )
= $false )
| ( ( in @ SV411 @ SV70 )
= $false )
| ( ( SV216 @ SV411 )
= $false )
| ( ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2666]) ).
thf(2710,plain,
! [SV421: $i,SV85: $i > $o,SV228: $i > $o] :
( ( ( ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $false )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV85 @ ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2667]) ).
thf(2711,plain,
! [SV85: $i > $o,SV421: $i,SV228: $i > $o] :
( ( ( ~ ~ ( ~ ( SV228 @ ( sK104_SY1517 @ SV421 @ SV85 @ SV228 ) )
| ~ ! [SY1784: $i] :
( ~ ( SV228 @ SY1784 )
| ( ( sK104_SY1517 @ SV421 @ SV85 @ SV228 )
= SY1784 ) ) ) )
= $false )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV421
= ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2668]) ).
thf(2712,plain,
! [SV422: $i,SV228: $i > $o,SV85: $i > $o] :
( ( ( ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $false )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV228 @ ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2669]) ).
thf(2713,plain,
! [SV228: $i > $o,SV422: $i,SV85: $i > $o] :
( ( ( ~ ~ ( ~ ( SV85 @ ( sK105_SY1253 @ SV422 @ SV228 @ SV85 ) )
| ~ ! [SY1785: $i] :
( ~ ( SV85 @ SY1785 )
| ( ( sK105_SY1253 @ SV422 @ SV228 @ SV85 )
= SY1785 ) ) ) )
= $false )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV422
= ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2670]) ).
thf(2714,plain,
! [SV228: $i > $o,SV455: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ SV455 )
| ~ ! [SY1776: $i] :
( ~ ( SV85 @ SY1776 )
| ( SV455 = SY1776 ) ) )
= $true )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2671]) ).
thf(2715,plain,
! [SV85: $i > $o,SV456: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ SV456 )
| ~ ! [SY1777: $i] :
( ~ ( SV228 @ SY1777 )
| ( SV456 = SY1777 ) ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2672]) ).
thf(2720,plain,
! [SV228: $i > $o,SV444: $i,SV85: $i > $o] :
( ( ( SV85 @ SV444 )
= $false )
| ( ( ~ ! [SY1750: $i] :
( ~ ( SV85 @ SY1750 )
| ( SV444 = SY1750 ) ) )
= $true )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2677]) ).
thf(2721,plain,
! [SV85: $i > $o,SV445: $i,SV228: $i > $o] :
( ( ( SV228 @ SV445 )
= $false )
| ( ( ~ ! [SY1751: $i] :
( ~ ( SV228 @ SY1751 )
| ( SV445 = SY1751 ) ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2678]) ).
thf(2722,plain,
! [SV92: $i,SV234: $i > $o,SV404: $i] :
( ( ( in @ ( sK90_SY1533 @ SV404 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
= $true )
| ( ( in @ SV404 @ SV92 )
= $false )
| ( ( SV234 @ SV404 )
= $false )
| ( ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2679]) ).
thf(2723,plain,
! [SV404: $i,SV234: $i > $o,SV92: $i] :
( ( ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
= ( setadjoin @ ( sK90_SY1533 @ SV404 @ SV234 @ SV92 ) @ emptyset ) )
= $true )
| ( ( in @ SV404 @ SV92 )
= $false )
| ( ( SV234 @ SV404 )
= $false )
| ( ( in @ ( sK27_SY1660 @ SV234 @ SV92 ) @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2680]) ).
thf(2724,plain,
! [SV92: $i,SV234: $i > $o,SV412: $i] :
( ( ( ~ ( in @ ( sK96_SY1533 @ SV412 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) ) )
= $false )
| ( ( in @ SV412 @ SV92 )
= $false )
| ( ( SV234 @ SV412 )
= $false )
| ( ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2681]) ).
thf(2725,plain,
! [SV412: $i,SV234: $i > $o,SV92: $i] :
( ( ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK96_SY1533 @ SV412 @ SV234 @ SV92 ) @ emptyset ) )
= $false )
| ( ( in @ SV412 @ SV92 )
= $false )
| ( ( SV234 @ SV412 )
= $false )
| ( ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2681]) ).
thf(2726,plain,
! [SV92: $i,SV234: $i > $o,SV423: $i] :
( ( ( ~ ( in @ ( sK100_SY1533 @ SV423 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
| ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK100_SY1533 @ SV423 @ SV234 @ SV92 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV423 @ SV92 )
= $false )
| ( ( SV234 @ SV423 )
= $false )
| ( ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2682]) ).
thf(2727,plain,
! [SV92: $i,SV234: $i > $o,SV413: $i] :
( ( ( ~ ( in @ ( sK97_SY1533 @ SV413 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) ) )
= $false )
| ( ( in @ SV413 @ SV92 )
= $false )
| ( ( SV234 @ SV413 )
= $false )
| ( ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2683]) ).
thf(2728,plain,
! [SV413: $i,SV234: $i > $o,SV92: $i] :
( ( ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK97_SY1533 @ SV413 @ SV234 @ SV92 ) @ emptyset ) )
= $false )
| ( ( in @ SV413 @ SV92 )
= $false )
| ( ( SV234 @ SV413 )
= $false )
| ( ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2683]) ).
thf(2729,plain,
! [SV357: $i,SV457: $i,SV98: $i > $o] :
( ( ( SV98 @ SV457 )
= $false )
| ( ( ( sK82_SY1292 @ SV357 @ SV98 )
= SV457 )
= $true )
| ( ( SV98 @ ( sK28_SY1661 @ SV357 @ SV98 ) )
= $true )
| ( ( ( sK28_SY1661 @ SV357 @ SV98 )
= SV357 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2684]) ).
thf(2730,plain,
! [SV399: $i,SV144: $i > $o,SV460: $i,SV275: $i > $o] :
( ( ( ~ ~ ( ~ ( SV275 @ SV460 )
| ~ ! [SY1786: $i] :
( ~ ( SV275 @ SY1786 )
| ( SV460 = SY1786 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV144 @ ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2689]) ).
thf(2731,plain,
! [SV399: $i,SV144: $i > $o,SV459: $i,SV275: $i > $o] :
( ( ( ~ ( ~ ( SV275 @ SV459 )
| ~ ! [SY1780: $i] :
( ~ ( SV275 @ SY1780 )
| ( SV459 = SY1780 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV399
= ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $false )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2690]) ).
thf(2732,plain,
! [SV275: $i > $o,SV440: $i,SV144: $i > $o] :
( ( ( ! [SY1745: $i] :
( ~ ( SV144 @ SY1745 )
| ( SV440 = SY1745 ) ) )
= $false )
| ( ( SV144 @ SV440 )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2691]) ).
thf(2735,plain,
! [SV429: $i,SV275: $i > $o,SV144: $i > $o] :
( ( ( ~ ( SV144 @ ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) ) )
= $false )
| ( ( SV144 @ SV429 )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2694]) ).
thf(2736,plain,
! [SV144: $i > $o,SV275: $i > $o,SV429: $i] :
( ( ( SV429
= ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $false )
| ( ( SV144 @ SV429 )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2694]) ).
thf(2737,plain,
! [SV35: $i,SV407: $i,SV418: $i] :
( ( ( ~ ( in @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) ) )
= $false )
| ( ( SV407 = SV418 )
= $true )
| ( ( in @ SV407 @ SV35 )
= $false )
| ( ( in @ SV418 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2695]) ).
thf(2738,plain,
! [SV35: $i,SV418: $i,SV407: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
| ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) ) )
| ~ ( ~ ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
| ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) ) ) ) )
= $false )
| ( ( SV407 = SV418 )
= $true )
| ( ( in @ SV407 @ SV35 )
= $false )
| ( ( in @ SV418 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2695]) ).
thf(2739,plain,
! [SV35: $i,SV441: $i,SV391: $i,SV395: $i,SV458: $i] :
( ( ( in @ SV458 @ SV395 )
= $false )
| ( ( in @ SV458 @ SV391 )
= $true )
| ( ( in @ SV441 @ SV395 )
= $true )
| ( ( in @ SV441 @ SV391 )
= $false )
| ( ( in @ SV391 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( in @ SV395 @ ( sK2_SY1109 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2696]) ).
thf(2740,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SV384 ) )
| ~ ~ ~ ! [SY1771: $i] :
~ ~ ( ~ ( in @ SY1771 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
| ~ ( in @ SY1771 @ SV384 ) ) )
| ~ ! [SY1788: $i] :
( ~ ( in @ SY1788 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1773: $i] :
( ~ ( in @ SY1773 @ SY1788 )
| ( in @ SY1773 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) ) )
| ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SY1788 ) ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2697]) ).
thf(2741,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SV384 ) )
| ~ ~ ~ ! [SY1755: $i] :
~ ~ ( ~ ( in @ SY1755 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
| ~ ( in @ SY1755 @ SV384 ) ) )
| ~ ! [SY1782: $i] :
( ~ ( in @ SY1782 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1757: $i] :
( ~ ( in @ SY1757 @ SY1782 )
| ( in @ SY1757 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) ) )
| ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SY1782 ) ) ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2698]) ).
thf(2742,plain,
! [SV210: $i,SV64: $i > $i > $o,SV385: $i,SV443: $i] :
( ( ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $false )
| ( ( ~ ! [SY1746: $i] :
~ ~ ( ~ ( in @ SY1746 @ SV210 )
| ~ ( SV64 @ SY1746 @ SV443 ) ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(2743,plain,
! [SV385: $i,SV443: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ~ ! [SY1747: $i] :
~ ~ ( ~ ( in @ SY1747 @ SV210 )
| ~ ( SV64 @ SY1747 @ SV443 ) ) )
= $false )
| ( ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2700]) ).
thf(2744,plain,
! [SV385: $i,SV436: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ! [SY1741: $i] :
~ ~ ( ~ ( in @ SY1741 @ SV210 )
| ~ ( SV64 @ SY1741 @ SV436 ) ) )
= $false )
| ( ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2701]) ).
thf(2745,plain,
! [SV385: $i,SV436: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ! [SY1742: $i] :
~ ~ ( ~ ( in @ SY1742 @ SV210 )
| ~ ( SV64 @ SY1742 @ SV436 ) ) )
= $true )
| ( ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2702]) ).
thf(2746,plain,
! [SV70: $i,SV216: $i > $o,SV410: $i] :
( ( ( in @ ( sK92_SY1495 @ SV410 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
= $true )
| ( ( in @ SV410 @ SV70 )
= $false )
| ( ( SV216 @ SV410 )
= $false )
| ( ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2705]) ).
thf(2747,plain,
! [SV410: $i,SV216: $i > $o,SV70: $i] :
( ( ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
= ( setadjoin @ ( sK92_SY1495 @ SV410 @ SV216 @ SV70 ) @ emptyset ) )
= $true )
| ( ( in @ SV410 @ SV70 )
= $false )
| ( ( SV216 @ SV410 )
= $false )
| ( ( SV216 @ ( sK12_SY1492 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2706]) ).
thf(2748,plain,
! [SV70: $i,SV216: $i > $o,SV420: $i] :
( ( ( ~ ( in @ ( sK99_SY1495 @ SV420 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) ) )
= $false )
| ( ( in @ SV420 @ SV70 )
= $false )
| ( ( SV216 @ SV420 )
= $false )
| ( ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2707]) ).
thf(2749,plain,
! [SV420: $i,SV216: $i > $o,SV70: $i] :
( ( ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
!= ( setadjoin @ ( sK99_SY1495 @ SV420 @ SV216 @ SV70 ) @ emptyset ) )
= $false )
| ( ( in @ SV420 @ SV70 )
= $false )
| ( ( SV216 @ SV420 )
= $false )
| ( ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2707]) ).
thf(2750,plain,
! [SV70: $i,SV216: $i > $o,SV411: $i] :
( ( ( in @ ( sK93_SY1495 @ SV411 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
= $true )
| ( ( in @ SV411 @ SV70 )
= $false )
| ( ( SV216 @ SV411 )
= $false )
| ( ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2708]) ).
thf(2751,plain,
! [SV411: $i,SV216: $i > $o,SV70: $i] :
( ( ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
= ( setadjoin @ ( sK93_SY1495 @ SV411 @ SV216 @ SV70 ) @ emptyset ) )
= $true )
| ( ( in @ SV411 @ SV70 )
= $false )
| ( ( SV216 @ SV411 )
= $false )
| ( ( ( sK12_SY1492 @ SV216 @ SV70 )
= ( sK25_SY1654 @ SV216 @ SV70 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2709]) ).
thf(2752,plain,
! [SV85: $i > $o,SV421: $i,SV228: $i > $o] :
( ( ( ~ ~ ( ~ ( SV228 @ ( sK109_SY1517 @ SV421 @ SV85 @ SV228 ) )
| ~ ! [SY1790: $i] :
( ~ ( SV228 @ SY1790 )
| ( ( sK109_SY1517 @ SV421 @ SV85 @ SV228 )
= SY1790 ) ) ) )
= $false )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV85 @ ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2710]) ).
thf(2753,plain,
! [SV85: $i > $o,SV421: $i,SV228: $i > $o] :
( ( ( ~ ( ~ ( SV228 @ ( sK104_SY1517 @ SV421 @ SV85 @ SV228 ) )
| ~ ! [SY1784: $i] :
( ~ ( SV228 @ SY1784 )
| ( ( sK104_SY1517 @ SV421 @ SV85 @ SV228 )
= SY1784 ) ) ) )
= $true )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV421
= ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2711]) ).
thf(2754,plain,
! [SV228: $i > $o,SV422: $i,SV85: $i > $o] :
( ( ( ~ ~ ( ~ ( SV85 @ ( sK110_SY1253 @ SV422 @ SV228 @ SV85 ) )
| ~ ! [SY1791: $i] :
( ~ ( SV85 @ SY1791 )
| ( ( sK110_SY1253 @ SV422 @ SV228 @ SV85 )
= SY1791 ) ) ) )
= $false )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV228 @ ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2712]) ).
thf(2755,plain,
! [SV228: $i > $o,SV422: $i,SV85: $i > $o] :
( ( ( ~ ( ~ ( SV85 @ ( sK105_SY1253 @ SV422 @ SV228 @ SV85 ) )
| ~ ! [SY1785: $i] :
( ~ ( SV85 @ SY1785 )
| ( ( sK105_SY1253 @ SV422 @ SV228 @ SV85 )
= SY1785 ) ) ) )
= $true )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV422
= ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2713]) ).
thf(2756,plain,
! [SV228: $i > $o,SV455: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ SV455 ) )
= $true )
| ( ( ~ ! [SY1776: $i] :
( ~ ( SV85 @ SY1776 )
| ( SV455 = SY1776 ) ) )
= $true )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2714]) ).
thf(2757,plain,
! [SV85: $i > $o,SV456: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ SV456 ) )
= $true )
| ( ( ~ ! [SY1777: $i] :
( ~ ( SV228 @ SY1777 )
| ( SV456 = SY1777 ) ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2715]) ).
thf(2762,plain,
! [SV228: $i > $o,SV444: $i,SV85: $i > $o] :
( ( ( ! [SY1750: $i] :
( ~ ( SV85 @ SY1750 )
| ( SV444 = SY1750 ) ) )
= $false )
| ( ( SV85 @ SV444 )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2720]) ).
thf(2763,plain,
! [SV85: $i > $o,SV445: $i,SV228: $i > $o] :
( ( ( ! [SY1751: $i] :
( ~ ( SV228 @ SY1751 )
| ( SV445 = SY1751 ) ) )
= $false )
| ( ( SV228 @ SV445 )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2721]) ).
thf(2764,plain,
! [SV92: $i,SV234: $i > $o,SV412: $i] :
( ( ( in @ ( sK96_SY1533 @ SV412 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
= $true )
| ( ( in @ SV412 @ SV92 )
= $false )
| ( ( SV234 @ SV412 )
= $false )
| ( ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2724]) ).
thf(2765,plain,
! [SV412: $i,SV234: $i > $o,SV92: $i] :
( ( ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
= ( setadjoin @ ( sK96_SY1533 @ SV412 @ SV234 @ SV92 ) @ emptyset ) )
= $true )
| ( ( in @ SV412 @ SV92 )
= $false )
| ( ( SV234 @ SV412 )
= $false )
| ( ( SV234 @ ( sK15_SY1530 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2725]) ).
thf(2766,plain,
! [SV92: $i,SV234: $i > $o,SV423: $i] :
( ( ( ~ ( in @ ( sK100_SY1533 @ SV423 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) ) )
= $false )
| ( ( in @ SV423 @ SV92 )
= $false )
| ( ( SV234 @ SV423 )
= $false )
| ( ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2726]) ).
thf(2767,plain,
! [SV423: $i,SV234: $i > $o,SV92: $i] :
( ( ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
!= ( setadjoin @ ( sK100_SY1533 @ SV423 @ SV234 @ SV92 ) @ emptyset ) )
= $false )
| ( ( in @ SV423 @ SV92 )
= $false )
| ( ( SV234 @ SV423 )
= $false )
| ( ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2726]) ).
thf(2768,plain,
! [SV92: $i,SV234: $i > $o,SV413: $i] :
( ( ( in @ ( sK97_SY1533 @ SV413 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
= $true )
| ( ( in @ SV413 @ SV92 )
= $false )
| ( ( SV234 @ SV413 )
= $false )
| ( ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2727]) ).
thf(2769,plain,
! [SV413: $i,SV234: $i > $o,SV92: $i] :
( ( ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
= ( setadjoin @ ( sK97_SY1533 @ SV413 @ SV234 @ SV92 ) @ emptyset ) )
= $true )
| ( ( in @ SV413 @ SV92 )
= $false )
| ( ( SV234 @ SV413 )
= $false )
| ( ( ( sK15_SY1530 @ SV234 @ SV92 )
= ( sK27_SY1660 @ SV234 @ SV92 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2728]) ).
thf(2770,plain,
! [SV399: $i,SV144: $i > $o,SV460: $i,SV275: $i > $o] :
( ( ( ~ ( ~ ( SV275 @ SV460 )
| ~ ! [SY1786: $i] :
( ~ ( SV275 @ SY1786 )
| ( SV460 = SY1786 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV144 @ ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2730]) ).
thf(2771,plain,
! [SV399: $i,SV144: $i > $o,SV459: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ SV459 )
| ~ ! [SY1780: $i] :
( ~ ( SV275 @ SY1780 )
| ( SV459 = SY1780 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV399
= ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $false )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2731]) ).
thf(2772,plain,
! [SV440: $i,SV275: $i > $o,SV144: $i > $o] :
( ( ( ~ ( SV144 @ ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
| ( SV440
= ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) ) )
= $false )
| ( ( SV144 @ SV440 )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2732]) ).
thf(2777,plain,
! [SV429: $i,SV275: $i > $o,SV144: $i > $o] :
( ( ( SV144 @ ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2735]) ).
thf(2778,plain,
! [SV429: $i,SV144: $i > $o,SV275: $i > $o] :
( ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV429
= ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $false )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2736]) ).
thf(2779,plain,
! [SV35: $i,SV407: $i,SV418: $i] :
( ( ( in @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
= $true )
| ( ( SV407 = SV418 )
= $true )
| ( ( in @ SV407 @ SV35 )
= $false )
| ( ( in @ SV418 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2737]) ).
thf(2780,plain,
! [SV35: $i,SV418: $i,SV407: $i] :
( ( ( ~ ( ~ ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
| ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) ) )
| ~ ( ~ ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
| ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) ) ) )
= $true )
| ( ( SV407 = SV418 )
= $true )
| ( ( in @ SV407 @ SV35 )
= $false )
| ( ( in @ SV418 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2738]) ).
thf(2781,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SV384 ) )
| ~ ~ ~ ! [SY1771: $i] :
~ ~ ( ~ ( in @ SY1771 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
| ~ ( in @ SY1771 @ SV384 ) ) )
| ~ ! [SY1788: $i] :
( ~ ( in @ SY1788 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1773: $i] :
( ~ ( in @ SY1773 @ SY1788 )
| ( in @ SY1773 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) ) )
| ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SY1788 ) ) ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2740]) ).
thf(2782,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SV384 ) )
| ~ ~ ~ ! [SY1755: $i] :
~ ~ ( ~ ( in @ SY1755 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
| ~ ( in @ SY1755 @ SV384 ) ) )
| ~ ! [SY1782: $i] :
( ~ ( in @ SY1782 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1757: $i] :
( ~ ( in @ SY1757 @ SY1782 )
| ( in @ SY1757 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) ) )
| ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SY1782 ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2741]) ).
thf(2783,plain,
! [SV385: $i,SV443: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ! [SY1746: $i] :
~ ~ ( ~ ( in @ SY1746 @ SV210 )
| ~ ( SV64 @ SY1746 @ SV443 ) ) )
= $false )
| ( ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2742]) ).
thf(2784,plain,
! [SV385: $i,SV443: $i,SV64: $i > $i > $o,SV210: $i] :
( ( ( ! [SY1747: $i] :
~ ~ ( ~ ( in @ SY1747 @ SV210 )
| ~ ( SV64 @ SY1747 @ SV443 ) ) )
= $true )
| ( ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2743]) ).
thf(2785,plain,
! [SV210: $i,SV64: $i > $i > $o,SV436: $i,SV385: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK112_SY1741 @ SV385 @ SV436 @ SV64 @ SV210 ) @ SV210 )
| ~ ( SV64 @ ( sK112_SY1741 @ SV385 @ SV436 @ SV64 @ SV210 ) @ SV436 ) ) )
= $false )
| ( ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2744]) ).
thf(2786,plain,
! [SV385: $i,SV436: $i,SV64: $i > $i > $o,SV210: $i,SV461: $i] :
( ( ( ~ ~ ( ~ ( in @ SV461 @ SV210 )
| ~ ( SV64 @ SV461 @ SV436 ) ) )
= $true )
| ( ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2745]) ).
thf(2787,plain,
! [SV70: $i,SV216: $i > $o,SV420: $i] :
( ( ( in @ ( sK99_SY1495 @ SV420 @ SV216 @ SV70 )
@ ( dsetconstr @ SV70
@ ^ [SY1496: $i] : ( SV216 @ SY1496 ) ) )
= $true )
| ( ( in @ SV420 @ SV70 )
= $false )
| ( ( SV216 @ SV420 )
= $false )
| ( ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2748]) ).
thf(2788,plain,
! [SV420: $i,SV216: $i > $o,SV70: $i] :
( ( ( ( dsetconstr @ SV70
@ ^ [SY1497: $i] : ( SV216 @ SY1497 ) )
= ( setadjoin @ ( sK99_SY1495 @ SV420 @ SV216 @ SV70 ) @ emptyset ) )
= $true )
| ( ( in @ SV420 @ SV70 )
= $false )
| ( ( SV216 @ SV420 )
= $false )
| ( ( SV216 @ ( sK25_SY1654 @ SV216 @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2749]) ).
thf(2789,plain,
! [SV85: $i > $o,SV421: $i,SV228: $i > $o] :
( ( ( ~ ( ~ ( SV228 @ ( sK109_SY1517 @ SV421 @ SV85 @ SV228 ) )
| ~ ! [SY1790: $i] :
( ~ ( SV228 @ SY1790 )
| ( ( sK109_SY1517 @ SV421 @ SV85 @ SV228 )
= SY1790 ) ) ) )
= $true )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV85 @ ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2752]) ).
thf(2790,plain,
! [SV85: $i > $o,SV421: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK104_SY1517 @ SV421 @ SV85 @ SV228 ) )
| ~ ! [SY1784: $i] :
( ~ ( SV228 @ SY1784 )
| ( ( sK104_SY1517 @ SV421 @ SV85 @ SV228 )
= SY1784 ) ) )
= $false )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV421
= ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(2791,plain,
! [SV228: $i > $o,SV422: $i,SV85: $i > $o] :
( ( ( ~ ( ~ ( SV85 @ ( sK110_SY1253 @ SV422 @ SV228 @ SV85 ) )
| ~ ! [SY1791: $i] :
( ~ ( SV85 @ SY1791 )
| ( ( sK110_SY1253 @ SV422 @ SV228 @ SV85 )
= SY1791 ) ) ) )
= $true )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV228 @ ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2754]) ).
thf(2792,plain,
! [SV228: $i > $o,SV422: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK105_SY1253 @ SV422 @ SV228 @ SV85 ) )
| ~ ! [SY1785: $i] :
( ~ ( SV85 @ SY1785 )
| ( ( sK105_SY1253 @ SV422 @ SV228 @ SV85 )
= SY1785 ) ) )
= $false )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV422
= ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2755]) ).
thf(2793,plain,
! [SV228: $i > $o,SV455: $i,SV85: $i > $o] :
( ( ( SV85 @ SV455 )
= $false )
| ( ( ~ ! [SY1776: $i] :
( ~ ( SV85 @ SY1776 )
| ( SV455 = SY1776 ) ) )
= $true )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2756]) ).
thf(2794,plain,
! [SV85: $i > $o,SV456: $i,SV228: $i > $o] :
( ( ( SV228 @ SV456 )
= $false )
| ( ( ~ ! [SY1777: $i] :
( ~ ( SV228 @ SY1777 )
| ( SV456 = SY1777 ) ) )
= $true )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2757]) ).
thf(2799,plain,
! [SV444: $i,SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
| ( SV444
= ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) ) )
= $false )
| ( ( SV85 @ SV444 )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2762]) ).
thf(2800,plain,
! [SV445: $i,SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
| ( SV445
= ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) ) )
= $false )
| ( ( SV228 @ SV445 )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2763]) ).
thf(2801,plain,
! [SV92: $i,SV234: $i > $o,SV423: $i] :
( ( ( in @ ( sK100_SY1533 @ SV423 @ SV234 @ SV92 )
@ ( dsetconstr @ SV92
@ ^ [SY1534: $i] : ( SV234 @ SY1534 ) ) )
= $true )
| ( ( in @ SV423 @ SV92 )
= $false )
| ( ( SV234 @ SV423 )
= $false )
| ( ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2766]) ).
thf(2802,plain,
! [SV423: $i,SV234: $i > $o,SV92: $i] :
( ( ( ( dsetconstr @ SV92
@ ^ [SY1535: $i] : ( SV234 @ SY1535 ) )
= ( setadjoin @ ( sK100_SY1533 @ SV423 @ SV234 @ SV92 ) @ emptyset ) )
= $true )
| ( ( in @ SV423 @ SV92 )
= $false )
| ( ( SV234 @ SV423 )
= $false )
| ( ( SV234 @ ( sK27_SY1660 @ SV234 @ SV92 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2767]) ).
thf(2803,plain,
! [SV399: $i,SV144: $i > $o,SV460: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ SV460 )
| ~ ! [SY1786: $i] :
( ~ ( SV275 @ SY1786 )
| ( SV460 = SY1786 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV144 @ ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2770]) ).
thf(2804,plain,
! [SV399: $i,SV144: $i > $o,SV459: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ SV459 ) )
= $true )
| ( ( ~ ! [SY1780: $i] :
( ~ ( SV275 @ SY1780 )
| ( SV459 = SY1780 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV399
= ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $false )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2771]) ).
thf(2805,plain,
! [SV440: $i,SV275: $i > $o,SV144: $i > $o] :
( ( ( ~ ( SV144 @ ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) ) )
= $false )
| ( ( SV144 @ SV440 )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2772]) ).
thf(2806,plain,
! [SV144: $i > $o,SV275: $i > $o,SV440: $i] :
( ( ( SV440
= ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $false )
| ( ( SV144 @ SV440 )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2772]) ).
thf(2811,plain,
! [SV429: $i,SV144: $i > $o,SV275: $i > $o] :
( ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV144 @ ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2777]) ).
thf(2812,plain,
! [SV429: $i,SV144: $i > $o,SV275: $i > $o] :
( ( ( ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV429
= ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $false )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2778]) ).
thf(2813,plain,
! [SV35: $i,SV418: $i,SV407: $i] :
( ( ( ~ ( ~ ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
| ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
| ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) ) ) )
= $true )
| ( ( SV407 = SV418 )
= $true )
| ( ( in @ SV407 @ SV35 )
= $false )
| ( ( in @ SV418 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2780]) ).
thf(2814,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SV384 ) )
| ~ ~ ~ ! [SY1771: $i] :
~ ~ ( ~ ( in @ SY1771 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
| ~ ( in @ SY1771 @ SV384 ) ) )
| ~ ! [SY1788: $i] :
( ~ ( in @ SY1788 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1773: $i] :
( ~ ( in @ SY1773 @ SY1788 )
| ( in @ SY1773 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) ) )
| ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SY1788 ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2781]) ).
thf(2815,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SV384 ) )
| ~ ~ ~ ! [SY1755: $i] :
~ ~ ( ~ ( in @ SY1755 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
| ~ ( in @ SY1755 @ SV384 ) ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2782]) ).
thf(2816,plain,
! [SV384: $i,SV430: $i,SV35: $i] :
( ( ( ~ ! [SY1782: $i] :
( ~ ( in @ SY1782 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1757: $i] :
( ~ ( in @ SY1757 @ SY1782 )
| ( in @ SY1757 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) ) )
| ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SY1782 ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2782]) ).
thf(2817,plain,
! [SV210: $i,SV64: $i > $i > $o,SV443: $i,SV385: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK115_SY1746 @ SV385 @ SV443 @ SV64 @ SV210 ) @ SV210 )
| ~ ( SV64 @ ( sK115_SY1746 @ SV385 @ SV443 @ SV64 @ SV210 ) @ SV443 ) ) )
= $false )
| ( ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2783]) ).
thf(2818,plain,
! [SV385: $i,SV443: $i,SV64: $i > $i > $o,SV210: $i,SV462: $i] :
( ( ( ~ ~ ( ~ ( in @ SV462 @ SV210 )
| ~ ( SV64 @ SV462 @ SV443 ) ) )
= $true )
| ( ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2784]) ).
thf(2819,plain,
! [SV210: $i,SV64: $i > $i > $o,SV436: $i,SV385: $i] :
( ( ( ~ ( ~ ( in @ ( sK112_SY1741 @ SV385 @ SV436 @ SV64 @ SV210 ) @ SV210 )
| ~ ( SV64 @ ( sK112_SY1741 @ SV385 @ SV436 @ SV64 @ SV210 ) @ SV436 ) ) )
= $true )
| ( ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2785]) ).
thf(2820,plain,
! [SV385: $i,SV436: $i,SV64: $i > $i > $o,SV210: $i,SV461: $i] :
( ( ( ~ ( ~ ( in @ SV461 @ SV210 )
| ~ ( SV64 @ SV461 @ SV436 ) ) )
= $false )
| ( ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2786]) ).
thf(2821,plain,
! [SV85: $i > $o,SV421: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK109_SY1517 @ SV421 @ SV85 @ SV228 ) )
| ~ ! [SY1790: $i] :
( ~ ( SV228 @ SY1790 )
| ( ( sK109_SY1517 @ SV421 @ SV85 @ SV228 )
= SY1790 ) ) )
= $false )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV85 @ ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(2822,plain,
! [SV85: $i > $o,SV421: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK104_SY1517 @ SV421 @ SV85 @ SV228 ) ) )
= $false )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV421
= ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2790]) ).
thf(2823,plain,
! [SV85: $i > $o,SV421: $i,SV228: $i > $o] :
( ( ( ~ ! [SY1784: $i] :
( ~ ( SV228 @ SY1784 )
| ( ( sK104_SY1517 @ SV421 @ SV85 @ SV228 )
= SY1784 ) ) )
= $false )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV421
= ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2790]) ).
thf(2824,plain,
! [SV228: $i > $o,SV422: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK110_SY1253 @ SV422 @ SV228 @ SV85 ) )
| ~ ! [SY1791: $i] :
( ~ ( SV85 @ SY1791 )
| ( ( sK110_SY1253 @ SV422 @ SV228 @ SV85 )
= SY1791 ) ) )
= $false )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV228 @ ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(2825,plain,
! [SV228: $i > $o,SV422: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK105_SY1253 @ SV422 @ SV228 @ SV85 ) ) )
= $false )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV422
= ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2792]) ).
thf(2826,plain,
! [SV228: $i > $o,SV422: $i,SV85: $i > $o] :
( ( ( ~ ! [SY1785: $i] :
( ~ ( SV85 @ SY1785 )
| ( ( sK105_SY1253 @ SV422 @ SV228 @ SV85 )
= SY1785 ) ) )
= $false )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV422
= ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2792]) ).
thf(2827,plain,
! [SV228: $i > $o,SV455: $i,SV85: $i > $o] :
( ( ( ! [SY1776: $i] :
( ~ ( SV85 @ SY1776 )
| ( SV455 = SY1776 ) ) )
= $false )
| ( ( SV85 @ SV455 )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2793]) ).
thf(2828,plain,
! [SV85: $i > $o,SV456: $i,SV228: $i > $o] :
( ( ( ! [SY1777: $i] :
( ~ ( SV228 @ SY1777 )
| ( SV456 = SY1777 ) ) )
= $false )
| ( ( SV228 @ SV456 )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2794]) ).
thf(2833,plain,
! [SV444: $i,SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) ) )
= $false )
| ( ( SV85 @ SV444 )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2799]) ).
thf(2834,plain,
! [SV85: $i > $o,SV228: $i > $o,SV444: $i] :
( ( ( SV444
= ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $false )
| ( ( SV85 @ SV444 )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2799]) ).
thf(2835,plain,
! [SV445: $i,SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) ) )
= $false )
| ( ( SV228 @ SV445 )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2800]) ).
thf(2836,plain,
! [SV228: $i > $o,SV85: $i > $o,SV445: $i] :
( ( ( SV445
= ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $false )
| ( ( SV228 @ SV445 )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2800]) ).
thf(2837,plain,
! [SV399: $i,SV144: $i > $o,SV460: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ SV460 ) )
= $true )
| ( ( ~ ! [SY1786: $i] :
( ~ ( SV275 @ SY1786 )
| ( SV460 = SY1786 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV144 @ ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2803]) ).
thf(2838,plain,
! [SV399: $i,SV144: $i > $o,SV459: $i,SV275: $i > $o] :
( ( ( SV275 @ SV459 )
= $false )
| ( ( ~ ! [SY1780: $i] :
( ~ ( SV275 @ SY1780 )
| ( SV459 = SY1780 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV399
= ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $false )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2804]) ).
thf(2839,plain,
! [SV440: $i,SV275: $i > $o,SV144: $i > $o] :
( ( ( SV144 @ ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) )
| ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2805]) ).
thf(2840,plain,
! [SV440: $i,SV144: $i > $o,SV275: $i > $o] :
( ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV440
= ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2806]) ).
thf(2845,plain,
! [SV429: $i,SV144: $i > $o,SV275: $i > $o] :
( ( ( ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV144 @ ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2811]) ).
thf(2846,plain,
! [SV429: $i,SV144: $i > $o,SV275: $i > $o] :
( ( ( ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV429
= ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $false )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2812]) ).
thf(2847,plain,
! [SV35: $i,SV418: $i,SV407: $i] :
( ( ( ~ ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
| ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
| ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) ) ) )
= $true )
| ( ( SV407 = SV418 )
= $true )
| ( ( in @ SV407 @ SV35 )
= $false )
| ( ( in @ SV418 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2813]) ).
thf(2848,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SV384 ) )
| ~ ~ ~ ! [SY1771: $i] :
~ ~ ( ~ ( in @ SY1771 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
| ~ ( in @ SY1771 @ SV384 ) ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2814]) ).
thf(2849,plain,
! [SV384: $i,SV434: $i,SV35: $i] :
( ( ( ~ ! [SY1788: $i] :
( ~ ( in @ SY1788 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1773: $i] :
( ~ ( in @ SY1773 @ SY1788 )
| ( in @ SY1773 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) ) )
| ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SY1788 ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2814]) ).
thf(2850,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SV384 ) )
| ~ ~ ~ ! [SY1755: $i] :
~ ~ ( ~ ( in @ SY1755 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
| ~ ( in @ SY1755 @ SV384 ) ) ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2815]) ).
thf(2851,plain,
! [SV384: $i,SV430: $i,SV35: $i] :
( ( ( ! [SY1782: $i] :
( ~ ( in @ SY1782 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1757: $i] :
( ~ ( in @ SY1757 @ SY1782 )
| ( in @ SY1757 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) ) )
| ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SY1782 ) ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2816]) ).
thf(2852,plain,
! [SV210: $i,SV64: $i > $i > $o,SV443: $i,SV385: $i] :
( ( ( ~ ( ~ ( in @ ( sK115_SY1746 @ SV385 @ SV443 @ SV64 @ SV210 ) @ SV210 )
| ~ ( SV64 @ ( sK115_SY1746 @ SV385 @ SV443 @ SV64 @ SV210 ) @ SV443 ) ) )
= $true )
| ( ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2817]) ).
thf(2853,plain,
! [SV385: $i,SV443: $i,SV64: $i > $i > $o,SV210: $i,SV462: $i] :
( ( ( ~ ( ~ ( in @ SV462 @ SV210 )
| ~ ( SV64 @ SV462 @ SV443 ) ) )
= $false )
| ( ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2818]) ).
thf(2854,plain,
! [SV210: $i,SV64: $i > $i > $o,SV436: $i,SV385: $i] :
( ( ( ~ ( in @ ( sK112_SY1741 @ SV385 @ SV436 @ SV64 @ SV210 ) @ SV210 )
| ~ ( SV64 @ ( sK112_SY1741 @ SV385 @ SV436 @ SV64 @ SV210 ) @ SV436 ) )
= $false )
| ( ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2819]) ).
thf(2855,plain,
! [SV385: $i,SV436: $i,SV64: $i > $i > $o,SV210: $i,SV461: $i] :
( ( ( ~ ( in @ SV461 @ SV210 )
| ~ ( SV64 @ SV461 @ SV436 ) )
= $true )
| ( ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2820]) ).
thf(2856,plain,
! [SV85: $i > $o,SV421: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK109_SY1517 @ SV421 @ SV85 @ SV228 ) ) )
= $false )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV85 @ ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2821]) ).
thf(2857,plain,
! [SV85: $i > $o,SV421: $i,SV228: $i > $o] :
( ( ( ~ ! [SY1790: $i] :
( ~ ( SV228 @ SY1790 )
| ( ( sK109_SY1517 @ SV421 @ SV85 @ SV228 )
= SY1790 ) ) )
= $false )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV85 @ ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2821]) ).
thf(2858,plain,
! [SV85: $i > $o,SV421: $i,SV228: $i > $o] :
( ( ( SV228 @ ( sK104_SY1517 @ SV421 @ SV85 @ SV228 ) )
= $true )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV421
= ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2822]) ).
thf(2859,plain,
! [SV85: $i > $o,SV421: $i,SV228: $i > $o] :
( ( ( ! [SY1784: $i] :
( ~ ( SV228 @ SY1784 )
| ( ( sK104_SY1517 @ SV421 @ SV85 @ SV228 )
= SY1784 ) ) )
= $true )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV421
= ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2823]) ).
thf(2860,plain,
! [SV228: $i > $o,SV422: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK110_SY1253 @ SV422 @ SV228 @ SV85 ) ) )
= $false )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV228 @ ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2824]) ).
thf(2861,plain,
! [SV228: $i > $o,SV422: $i,SV85: $i > $o] :
( ( ( ~ ! [SY1791: $i] :
( ~ ( SV85 @ SY1791 )
| ( ( sK110_SY1253 @ SV422 @ SV228 @ SV85 )
= SY1791 ) ) )
= $false )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV228 @ ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2824]) ).
thf(2862,plain,
! [SV228: $i > $o,SV422: $i,SV85: $i > $o] :
( ( ( SV85 @ ( sK105_SY1253 @ SV422 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV422
= ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2825]) ).
thf(2863,plain,
! [SV228: $i > $o,SV422: $i,SV85: $i > $o] :
( ( ( ! [SY1785: $i] :
( ~ ( SV85 @ SY1785 )
| ( ( sK105_SY1253 @ SV422 @ SV228 @ SV85 )
= SY1785 ) ) )
= $true )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV422
= ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2826]) ).
thf(2864,plain,
! [SV455: $i,SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
| ( SV455
= ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) ) )
= $false )
| ( ( SV85 @ SV455 )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2827]) ).
thf(2865,plain,
! [SV456: $i,SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
| ( SV456
= ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) ) )
= $false )
| ( ( SV228 @ SV456 )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2828]) ).
thf(2874,plain,
! [SV444: $i,SV228: $i > $o,SV85: $i > $o] :
( ( ( SV85 @ ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $true )
| ( ( SV85 @ SV444 )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2833]) ).
thf(2875,plain,
! [SV444: $i,SV85: $i > $o,SV228: $i > $o] :
( ( ( ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $false )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV444
= ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2834]) ).
thf(2876,plain,
! [SV445: $i,SV85: $i > $o,SV228: $i > $o] :
( ( ( SV228 @ ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $true )
| ( ( SV228 @ SV445 )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2835]) ).
thf(2877,plain,
! [SV445: $i,SV228: $i > $o,SV85: $i > $o] :
( ( ( ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $false )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV445
= ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2836]) ).
thf(2878,plain,
! [SV399: $i,SV144: $i > $o,SV460: $i,SV275: $i > $o] :
( ( ( SV275 @ SV460 )
= $false )
| ( ( ~ ! [SY1786: $i] :
( ~ ( SV275 @ SY1786 )
| ( SV460 = SY1786 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV144 @ ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2837]) ).
thf(2879,plain,
! [SV399: $i,SV144: $i > $o,SV459: $i,SV275: $i > $o] :
( ( ( ! [SY1780: $i] :
( ~ ( SV275 @ SY1780 )
| ( SV459 = SY1780 ) ) )
= $false )
| ( ( SV275 @ SV459 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV399
= ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $false )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2838]) ).
thf(2880,plain,
! [SV440: $i,SV144: $i > $o,SV275: $i > $o] :
( ( ( ~ ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV144 @ ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2839]) ).
thf(2881,plain,
! [SV440: $i,SV144: $i > $o,SV275: $i > $o] :
( ( ( ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV440
= ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2840]) ).
thf(2886,plain,
! [SV429: $i,SV144: $i > $o,SV275: $i > $o] :
( ( ( ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV144 @ ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2845]) ).
thf(2887,plain,
! [SV429: $i,SV144: $i > $o,SV463: $i,SV275: $i > $o] :
( ( ( ~ ~ ( ~ ( SV275 @ SV463 )
| ~ ! [SY1792: $i] :
( ~ ( SV275 @ SY1792 )
| ( SV463 = SY1792 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV429
= ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $false )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2846]) ).
thf(2888,plain,
! [SV35: $i,SV418: $i,SV407: $i] :
( ( ( ~ ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
| ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) ) ) )
= $true )
| ( ( SV407 = SV418 )
= $true )
| ( ( in @ SV407 @ SV35 )
= $false )
| ( ( in @ SV418 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2847]) ).
thf(2889,plain,
! [SV35: $i,SV407: $i,SV418: $i] :
( ( ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
| ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) ) ) )
= $true )
| ( ( SV407 = SV418 )
= $true )
| ( ( in @ SV407 @ SV35 )
= $false )
| ( ( in @ SV418 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2847]) ).
thf(2890,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SV384 ) )
| ~ ~ ~ ! [SY1771: $i] :
~ ~ ( ~ ( in @ SY1771 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
| ~ ( in @ SY1771 @ SV384 ) ) ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2848]) ).
thf(2891,plain,
! [SV384: $i,SV434: $i,SV35: $i] :
( ( ( ! [SY1788: $i] :
( ~ ( in @ SY1788 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1773: $i] :
( ~ ( in @ SY1773 @ SY1788 )
| ( in @ SY1773 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) ) )
| ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SY1788 ) ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2849]) ).
thf(2892,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SV384 ) )
| ~ ~ ~ ! [SY1755: $i] :
~ ~ ( ~ ( in @ SY1755 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
| ~ ( in @ SY1755 @ SV384 ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2850]) ).
thf(2893,plain,
! [SV384: $i,SV430: $i,SV35: $i,SV464: $i] :
( ( ( ~ ( in @ SV464 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1793: $i] :
( ~ ( in @ SY1793 @ SV464 )
| ( in @ SY1793 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) ) )
| ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SV464 ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2851]) ).
thf(2894,plain,
! [SV210: $i,SV64: $i > $i > $o,SV443: $i,SV385: $i] :
( ( ( ~ ( in @ ( sK115_SY1746 @ SV385 @ SV443 @ SV64 @ SV210 ) @ SV210 )
| ~ ( SV64 @ ( sK115_SY1746 @ SV385 @ SV443 @ SV64 @ SV210 ) @ SV443 ) )
= $false )
| ( ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2852]) ).
thf(2895,plain,
! [SV385: $i,SV443: $i,SV64: $i > $i > $o,SV210: $i,SV462: $i] :
( ( ( ~ ( in @ SV462 @ SV210 )
| ~ ( SV64 @ SV462 @ SV443 ) )
= $true )
| ( ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2853]) ).
thf(2896,plain,
! [SV210: $i,SV64: $i > $i > $o,SV436: $i,SV385: $i] :
( ( ( ~ ( in @ ( sK112_SY1741 @ SV385 @ SV436 @ SV64 @ SV210 ) @ SV210 ) )
= $false )
| ( ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2854]) ).
thf(2897,plain,
! [SV210: $i,SV436: $i,SV385: $i,SV64: $i > $i > $o] :
( ( ( ~ ( SV64 @ ( sK112_SY1741 @ SV385 @ SV436 @ SV64 @ SV210 ) @ SV436 ) )
= $false )
| ( ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2854]) ).
thf(2898,plain,
! [SV385: $i,SV436: $i,SV64: $i > $i > $o,SV210: $i,SV461: $i] :
( ( ( ~ ( in @ SV461 @ SV210 ) )
= $true )
| ( ( ~ ( SV64 @ SV461 @ SV436 ) )
= $true )
| ( ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2855]) ).
thf(2899,plain,
! [SV85: $i > $o,SV421: $i,SV228: $i > $o] :
( ( ( SV228 @ ( sK109_SY1517 @ SV421 @ SV85 @ SV228 ) )
= $true )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV85 @ ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2856]) ).
thf(2900,plain,
! [SV85: $i > $o,SV421: $i,SV228: $i > $o] :
( ( ( ! [SY1790: $i] :
( ~ ( SV228 @ SY1790 )
| ( ( sK109_SY1517 @ SV421 @ SV85 @ SV228 )
= SY1790 ) ) )
= $true )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV85 @ ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2857]) ).
thf(2901,plain,
! [SV85: $i > $o,SV421: $i,SV465: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ SV465 )
| ( ( sK104_SY1517 @ SV421 @ SV85 @ SV228 )
= SV465 ) )
= $true )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV421
= ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(2902,plain,
! [SV228: $i > $o,SV422: $i,SV85: $i > $o] :
( ( ( SV85 @ ( sK110_SY1253 @ SV422 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV228 @ ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2860]) ).
thf(2903,plain,
! [SV228: $i > $o,SV422: $i,SV85: $i > $o] :
( ( ( ! [SY1791: $i] :
( ~ ( SV85 @ SY1791 )
| ( ( sK110_SY1253 @ SV422 @ SV228 @ SV85 )
= SY1791 ) ) )
= $true )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV228 @ ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2861]) ).
thf(2904,plain,
! [SV228: $i > $o,SV422: $i,SV466: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ SV466 )
| ( ( sK105_SY1253 @ SV422 @ SV228 @ SV85 )
= SV466 ) )
= $true )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV422
= ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2863]) ).
thf(2905,plain,
! [SV455: $i,SV228: $i > $o,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) ) )
= $false )
| ( ( SV85 @ SV455 )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2864]) ).
thf(2906,plain,
! [SV85: $i > $o,SV228: $i > $o,SV455: $i] :
( ( ( SV455
= ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $false )
| ( ( SV85 @ SV455 )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2864]) ).
thf(2907,plain,
! [SV456: $i,SV85: $i > $o,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) ) )
= $false )
| ( ( SV228 @ SV456 )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2865]) ).
thf(2908,plain,
! [SV228: $i > $o,SV85: $i > $o,SV456: $i] :
( ( ( SV456
= ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $false )
| ( ( SV228 @ SV456 )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2865]) ).
thf(2917,plain,
! [SV444: $i,SV85: $i > $o,SV228: $i > $o] :
( ( ( ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $false )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV85 @ ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(2918,plain,
! [SV85: $i > $o,SV444: $i,SV228: $i > $o] :
( ( ( ~ ~ ( ~ ( SV228 @ ( sK122_SY1517 @ SV444 @ SV85 @ SV228 ) )
| ~ ! [SY1794: $i] :
( ~ ( SV228 @ SY1794 )
| ( ( sK122_SY1517 @ SV444 @ SV85 @ SV228 )
= SY1794 ) ) ) )
= $false )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV444
= ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2875]) ).
thf(2919,plain,
! [SV445: $i,SV228: $i > $o,SV85: $i > $o] :
( ( ( ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $false )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV228 @ ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2876]) ).
thf(2920,plain,
! [SV228: $i > $o,SV445: $i,SV85: $i > $o] :
( ( ( ~ ~ ( ~ ( SV85 @ ( sK123_SY1253 @ SV445 @ SV228 @ SV85 ) )
| ~ ! [SY1795: $i] :
( ~ ( SV85 @ SY1795 )
| ( ( sK123_SY1253 @ SV445 @ SV228 @ SV85 )
= SY1795 ) ) ) )
= $false )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV445
= ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2877]) ).
thf(2921,plain,
! [SV399: $i,SV144: $i > $o,SV460: $i,SV275: $i > $o] :
( ( ( ! [SY1786: $i] :
( ~ ( SV275 @ SY1786 )
| ( SV460 = SY1786 ) ) )
= $false )
| ( ( SV275 @ SV460 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV144 @ ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2878]) ).
thf(2922,plain,
! [SV459: $i,SV144: $i > $o,SV399: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ ( sK124_SY1780 @ SV399 @ SV144 @ SV459 @ SV275 ) )
| ( SV459
= ( sK124_SY1780 @ SV399 @ SV144 @ SV459 @ SV275 ) ) )
= $false )
| ( ( SV275 @ SV459 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV399
= ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $false )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2879]) ).
thf(2923,plain,
! [SV440: $i,SV144: $i > $o,SV275: $i > $o] :
( ( ( ~ ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV144 @ ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2880]) ).
thf(2924,plain,
! [SV440: $i,SV144: $i > $o,SV275: $i > $o] :
( ( ( ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV440
= ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2881]) ).
thf(2929,plain,
! [SV429: $i,SV144: $i > $o,SV469: $i,SV275: $i > $o] :
( ( ( ~ ~ ( ~ ( SV275 @ SV469 )
| ~ ! [SY1798: $i] :
( ~ ( SV275 @ SY1798 )
| ( SV469 = SY1798 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV144 @ ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2886]) ).
thf(2930,plain,
! [SV429: $i,SV144: $i > $o,SV463: $i,SV275: $i > $o] :
( ( ( ~ ( ~ ( SV275 @ SV463 )
| ~ ! [SY1792: $i] :
( ~ ( SV275 @ SY1792 )
| ( SV463 = SY1792 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV429
= ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $false )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2887]) ).
thf(2931,plain,
! [SV35: $i,SV418: $i,SV407: $i] :
( ( ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
| ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) ) ) )
= $true )
| ( ( SV407 = SV418 )
= $true )
| ( ( in @ SV407 @ SV35 )
= $false )
| ( ( in @ SV418 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2888]) ).
thf(2932,plain,
! [SV35: $i,SV407: $i,SV418: $i] :
( ( ( ~ ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
| ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) ) )
= $false )
| ( ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
= $false )
| ( ( SV407 = SV418 )
= $true )
| ( ( in @ SV407 @ SV35 )
= $false )
| ( ( in @ SV418 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2889]) ).
thf(2933,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SV384 ) )
| ~ ~ ~ ! [SY1771: $i] :
~ ~ ( ~ ( in @ SY1771 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
| ~ ( in @ SY1771 @ SV384 ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2890]) ).
thf(2934,plain,
! [SV384: $i,SV434: $i,SV35: $i,SV470: $i] :
( ( ( ~ ( in @ SV470 @ ( sK2_SY1109 @ SV35 ) )
| ! [SY1799: $i] :
( ~ ( in @ SY1799 @ SV470 )
| ( in @ SY1799 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) ) )
| ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SV470 ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(2935,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SV384 ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2892]) ).
thf(2936,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( ~ ~ ~ ! [SY1755: $i] :
~ ~ ( ~ ( in @ SY1755 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
| ~ ( in @ SY1755 @ SV384 ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2892]) ).
thf(2937,plain,
! [SV384: $i,SV430: $i,SV35: $i,SV464: $i] :
( ( ( ~ ( in @ SV464 @ ( sK2_SY1109 @ SV35 ) ) )
= $true )
| ( ( ! [SY1793: $i] :
( ~ ( in @ SY1793 @ SV464 )
| ( in @ SY1793 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) ) )
| ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SV464 ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2893]) ).
thf(2938,plain,
! [SV210: $i,SV64: $i > $i > $o,SV443: $i,SV385: $i] :
( ( ( ~ ( in @ ( sK115_SY1746 @ SV385 @ SV443 @ SV64 @ SV210 ) @ SV210 ) )
= $false )
| ( ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2894]) ).
thf(2939,plain,
! [SV210: $i,SV443: $i,SV385: $i,SV64: $i > $i > $o] :
( ( ( ~ ( SV64 @ ( sK115_SY1746 @ SV385 @ SV443 @ SV64 @ SV210 ) @ SV443 ) )
= $false )
| ( ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2894]) ).
thf(2940,plain,
! [SV385: $i,SV443: $i,SV64: $i > $i > $o,SV210: $i,SV462: $i] :
( ( ( ~ ( in @ SV462 @ SV210 ) )
= $true )
| ( ( ~ ( SV64 @ SV462 @ SV443 ) )
= $true )
| ( ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2895]) ).
thf(2941,plain,
! [SV210: $i,SV64: $i > $i > $o,SV436: $i,SV385: $i] :
( ( ( in @ ( sK112_SY1741 @ SV385 @ SV436 @ SV64 @ SV210 ) @ SV210 )
= $true )
| ( ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2896]) ).
thf(2942,plain,
! [SV210: $i,SV436: $i,SV385: $i,SV64: $i > $i > $o] :
( ( ( SV64 @ ( sK112_SY1741 @ SV385 @ SV436 @ SV64 @ SV210 ) @ SV436 )
= $true )
| ( ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2897]) ).
thf(2943,plain,
! [SV385: $i,SV436: $i,SV64: $i > $i > $o,SV210: $i,SV461: $i] :
( ( ( in @ SV461 @ SV210 )
= $false )
| ( ( ~ ( SV64 @ SV461 @ SV436 ) )
= $true )
| ( ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2898]) ).
thf(2944,plain,
! [SV85: $i > $o,SV421: $i,SV471: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ SV471 )
| ( ( sK109_SY1517 @ SV421 @ SV85 @ SV228 )
= SV471 ) )
= $true )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV85 @ ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(2945,plain,
! [SV85: $i > $o,SV421: $i,SV465: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ SV465 ) )
= $true )
| ( ( ( sK104_SY1517 @ SV421 @ SV85 @ SV228 )
= SV465 )
= $true )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV421
= ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2901]) ).
thf(2946,plain,
! [SV228: $i > $o,SV422: $i,SV472: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ SV472 )
| ( ( sK110_SY1253 @ SV422 @ SV228 @ SV85 )
= SV472 ) )
= $true )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV228 @ ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2903]) ).
thf(2947,plain,
! [SV228: $i > $o,SV422: $i,SV466: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ SV466 ) )
= $true )
| ( ( ( sK105_SY1253 @ SV422 @ SV228 @ SV85 )
= SV466 )
= $true )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV422
= ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2904]) ).
thf(2948,plain,
! [SV455: $i,SV228: $i > $o,SV85: $i > $o] :
( ( ( SV85 @ ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $true )
| ( ( SV85 @ SV455 )
= $false )
| ( ( ~ ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2905]) ).
thf(2949,plain,
! [SV455: $i,SV85: $i > $o,SV228: $i > $o] :
( ( ( ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $false )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV455
= ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2906]) ).
thf(2950,plain,
! [SV456: $i,SV85: $i > $o,SV228: $i > $o] :
( ( ( SV228 @ ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $true )
| ( ( SV228 @ SV456 )
= $false )
| ( ( ~ ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2907]) ).
thf(2951,plain,
! [SV456: $i,SV228: $i > $o,SV85: $i > $o] :
( ( ( ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $false )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV456
= ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2908]) ).
thf(2960,plain,
! [SV85: $i > $o,SV444: $i,SV228: $i > $o] :
( ( ( ~ ~ ( ~ ( SV228 @ ( sK129_SY1517 @ SV444 @ SV85 @ SV228 ) )
| ~ ! [SY1804: $i] :
( ~ ( SV228 @ SY1804 )
| ( ( sK129_SY1517 @ SV444 @ SV85 @ SV228 )
= SY1804 ) ) ) )
= $false )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV85 @ ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2917]) ).
thf(2961,plain,
! [SV85: $i > $o,SV444: $i,SV228: $i > $o] :
( ( ( ~ ( ~ ( SV228 @ ( sK122_SY1517 @ SV444 @ SV85 @ SV228 ) )
| ~ ! [SY1794: $i] :
( ~ ( SV228 @ SY1794 )
| ( ( sK122_SY1517 @ SV444 @ SV85 @ SV228 )
= SY1794 ) ) ) )
= $true )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV444
= ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2918]) ).
thf(2962,plain,
! [SV228: $i > $o,SV445: $i,SV85: $i > $o] :
( ( ( ~ ~ ( ~ ( SV85 @ ( sK130_SY1253 @ SV445 @ SV228 @ SV85 ) )
| ~ ! [SY1805: $i] :
( ~ ( SV85 @ SY1805 )
| ( ( sK130_SY1253 @ SV445 @ SV228 @ SV85 )
= SY1805 ) ) ) )
= $false )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV228 @ ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2919]) ).
thf(2963,plain,
! [SV228: $i > $o,SV445: $i,SV85: $i > $o] :
( ( ( ~ ( ~ ( SV85 @ ( sK123_SY1253 @ SV445 @ SV228 @ SV85 ) )
| ~ ! [SY1795: $i] :
( ~ ( SV85 @ SY1795 )
| ( ( sK123_SY1253 @ SV445 @ SV228 @ SV85 )
= SY1795 ) ) ) )
= $true )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV445
= ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2920]) ).
thf(2964,plain,
! [SV460: $i,SV144: $i > $o,SV399: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ ( sK131_SY1786 @ SV399 @ SV144 @ SV460 @ SV275 ) )
| ( SV460
= ( sK131_SY1786 @ SV399 @ SV144 @ SV460 @ SV275 ) ) )
= $false )
| ( ( SV275 @ SV460 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV144 @ ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2921]) ).
thf(2965,plain,
! [SV459: $i,SV144: $i > $o,SV399: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ ( sK124_SY1780 @ SV399 @ SV144 @ SV459 @ SV275 ) ) )
= $false )
| ( ( SV275 @ SV459 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV399
= ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $false )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2922]) ).
thf(2966,plain,
! [SV275: $i > $o,SV144: $i > $o,SV399: $i,SV459: $i] :
( ( ( SV459
= ( sK124_SY1780 @ SV399 @ SV144 @ SV459 @ SV275 ) )
= $false )
| ( ( SV275 @ SV459 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV399
= ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $false )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2922]) ).
thf(2967,plain,
! [SV440: $i,SV144: $i > $o,SV275: $i > $o] :
( ( ( ! [SY1580: $i] :
~ ~ ( ~ ( SV275 @ SY1580 )
| ~ ! [SY1581: $i] :
( ~ ( SV275 @ SY1581 )
| ( SY1580 = SY1581 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV144 @ ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2923]) ).
thf(2968,plain,
! [SV440: $i,SV144: $i > $o,SV473: $i,SV275: $i > $o] :
( ( ( ~ ~ ( ~ ( SV275 @ SV473 )
| ~ ! [SY1806: $i] :
( ~ ( SV275 @ SY1806 )
| ( SV473 = SY1806 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV440
= ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2924]) ).
thf(2973,plain,
! [SV429: $i,SV144: $i > $o,SV469: $i,SV275: $i > $o] :
( ( ( ~ ( ~ ( SV275 @ SV469 )
| ~ ! [SY1798: $i] :
( ~ ( SV275 @ SY1798 )
| ( SV469 = SY1798 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV144 @ ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2929]) ).
thf(2974,plain,
! [SV429: $i,SV144: $i > $o,SV463: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ SV463 )
| ~ ! [SY1792: $i] :
( ~ ( SV275 @ SY1792 )
| ( SV463 = SY1792 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV429
= ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $false )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2930]) ).
thf(2975,plain,
! [SV35: $i,SV407: $i,SV418: $i] :
( ( ( ~ ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
| ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) ) )
= $false )
| ( ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
= $true )
| ( ( SV407 = SV418 )
= $true )
| ( ( in @ SV407 @ SV35 )
= $false )
| ( ( in @ SV418 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2931]) ).
thf(2977,plain,
! [SV35: $i,SV418: $i,SV407: $i] :
( ( ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
= $false )
| ( ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
= $false )
| ( ( SV407 = SV418 )
= $true )
| ( ( in @ SV407 @ SV35 )
= $false )
| ( ( in @ SV418 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2932]) ).
thf(2978,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SV384 ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2933]) ).
thf(2979,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( ~ ~ ~ ! [SY1771: $i] :
~ ~ ( ~ ( in @ SY1771 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
| ~ ( in @ SY1771 @ SV384 ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2933]) ).
thf(2980,plain,
! [SV384: $i,SV434: $i,SV35: $i,SV470: $i] :
( ( ( ~ ( in @ SV470 @ ( sK2_SY1109 @ SV35 ) ) )
= $true )
| ( ( ! [SY1799: $i] :
( ~ ( in @ SY1799 @ SV470 )
| ( in @ SY1799 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) ) )
| ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SV470 ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2934]) ).
thf(2981,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( ~ ( ~ ( in @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SV384 ) ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2935]) ).
thf(2982,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( ~ ~ ! [SY1755: $i] :
~ ~ ( ~ ( in @ SY1755 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
| ~ ( in @ SY1755 @ SV384 ) ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2936]) ).
thf(2983,plain,
! [SV384: $i,SV430: $i,SV35: $i,SV464: $i] :
( ( ( in @ SV464 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( ! [SY1793: $i] :
( ~ ( in @ SY1793 @ SV464 )
| ( in @ SY1793 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) ) )
| ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SV464 ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2937]) ).
thf(2984,plain,
! [SV210: $i,SV64: $i > $i > $o,SV443: $i,SV385: $i] :
( ( ( in @ ( sK115_SY1746 @ SV385 @ SV443 @ SV64 @ SV210 ) @ SV210 )
= $true )
| ( ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2938]) ).
thf(2985,plain,
! [SV210: $i,SV443: $i,SV385: $i,SV64: $i > $i > $o] :
( ( ( SV64 @ ( sK115_SY1746 @ SV385 @ SV443 @ SV64 @ SV210 ) @ SV443 )
= $true )
| ( ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2939]) ).
thf(2986,plain,
! [SV385: $i,SV443: $i,SV64: $i > $i > $o,SV210: $i,SV462: $i] :
( ( ( in @ SV462 @ SV210 )
= $false )
| ( ( ~ ( SV64 @ SV462 @ SV443 ) )
= $true )
| ( ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2940]) ).
thf(2987,plain,
! [SV385: $i,SV210: $i,SV436: $i,SV461: $i,SV64: $i > $i > $o] :
( ( ( SV64 @ SV461 @ SV436 )
= $false )
| ( ( in @ SV461 @ SV210 )
= $false )
| ( ( in @ SV436 @ ( sK81_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV385
= ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2943]) ).
thf(2988,plain,
! [SV85: $i > $o,SV421: $i,SV471: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ SV471 ) )
= $true )
| ( ( ( sK109_SY1517 @ SV421 @ SV85 @ SV228 )
= SV471 )
= $true )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV85 @ ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2944]) ).
thf(2989,plain,
! [SV85: $i > $o,SV421: $i,SV465: $i,SV228: $i > $o] :
( ( ( SV228 @ SV465 )
= $false )
| ( ( ( sK104_SY1517 @ SV421 @ SV85 @ SV228 )
= SV465 )
= $true )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV421
= ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2945]) ).
thf(2990,plain,
! [SV228: $i > $o,SV422: $i,SV472: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ SV472 ) )
= $true )
| ( ( ( sK110_SY1253 @ SV422 @ SV228 @ SV85 )
= SV472 )
= $true )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV228 @ ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2946]) ).
thf(2991,plain,
! [SV228: $i > $o,SV422: $i,SV466: $i,SV85: $i > $o] :
( ( ( SV85 @ SV466 )
= $false )
| ( ( ( sK105_SY1253 @ SV422 @ SV228 @ SV85 )
= SV466 )
= $true )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV422
= ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $false )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2947]) ).
thf(2992,plain,
! [SV455: $i,SV85: $i > $o,SV228: $i > $o] :
( ( ( ! [SY1517: $i] :
~ ~ ( ~ ( SV228 @ SY1517 )
| ~ ! [SY1518: $i] :
( ~ ( SV228 @ SY1518 )
| ( SY1517 = SY1518 ) ) ) )
= $false )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV85 @ ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2948]) ).
thf(2993,plain,
! [SV85: $i > $o,SV455: $i,SV228: $i > $o] :
( ( ( ~ ~ ( ~ ( SV228 @ ( sK132_SY1517 @ SV455 @ SV85 @ SV228 ) )
| ~ ! [SY1809: $i] :
( ~ ( SV228 @ SY1809 )
| ( ( sK132_SY1517 @ SV455 @ SV85 @ SV228 )
= SY1809 ) ) ) )
= $false )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV455
= ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2949]) ).
thf(2994,plain,
! [SV456: $i,SV228: $i > $o,SV85: $i > $o] :
( ( ( ! [SY1253: $i] :
~ ~ ( ~ ( SV85 @ SY1253 )
| ~ ! [SY1254: $i] :
( ~ ( SV85 @ SY1254 )
| ( SY1253 = SY1254 ) ) ) )
= $false )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV228 @ ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2950]) ).
thf(2995,plain,
! [SV228: $i > $o,SV456: $i,SV85: $i > $o] :
( ( ( ~ ~ ( ~ ( SV85 @ ( sK133_SY1253 @ SV456 @ SV228 @ SV85 ) )
| ~ ! [SY1810: $i] :
( ~ ( SV85 @ SY1810 )
| ( ( sK133_SY1253 @ SV456 @ SV228 @ SV85 )
= SY1810 ) ) ) )
= $false )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV456
= ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2951]) ).
thf(3004,plain,
! [SV85: $i > $o,SV444: $i,SV228: $i > $o] :
( ( ( ~ ( ~ ( SV228 @ ( sK129_SY1517 @ SV444 @ SV85 @ SV228 ) )
| ~ ! [SY1804: $i] :
( ~ ( SV228 @ SY1804 )
| ( ( sK129_SY1517 @ SV444 @ SV85 @ SV228 )
= SY1804 ) ) ) )
= $true )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV85 @ ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2960]) ).
thf(3005,plain,
! [SV85: $i > $o,SV444: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK122_SY1517 @ SV444 @ SV85 @ SV228 ) )
| ~ ! [SY1794: $i] :
( ~ ( SV228 @ SY1794 )
| ( ( sK122_SY1517 @ SV444 @ SV85 @ SV228 )
= SY1794 ) ) )
= $false )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV444
= ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(3006,plain,
! [SV228: $i > $o,SV445: $i,SV85: $i > $o] :
( ( ( ~ ( ~ ( SV85 @ ( sK130_SY1253 @ SV445 @ SV228 @ SV85 ) )
| ~ ! [SY1805: $i] :
( ~ ( SV85 @ SY1805 )
| ( ( sK130_SY1253 @ SV445 @ SV228 @ SV85 )
= SY1805 ) ) ) )
= $true )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV228 @ ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2962]) ).
thf(3007,plain,
! [SV228: $i > $o,SV445: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK123_SY1253 @ SV445 @ SV228 @ SV85 ) )
| ~ ! [SY1795: $i] :
( ~ ( SV85 @ SY1795 )
| ( ( sK123_SY1253 @ SV445 @ SV228 @ SV85 )
= SY1795 ) ) )
= $false )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV445
= ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2963]) ).
thf(3008,plain,
! [SV460: $i,SV144: $i > $o,SV399: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ ( sK131_SY1786 @ SV399 @ SV144 @ SV460 @ SV275 ) ) )
= $false )
| ( ( SV275 @ SV460 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV144 @ ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2964]) ).
thf(3009,plain,
! [SV275: $i > $o,SV144: $i > $o,SV399: $i,SV460: $i] :
( ( ( SV460
= ( sK131_SY1786 @ SV399 @ SV144 @ SV460 @ SV275 ) )
= $false )
| ( ( SV275 @ SV460 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV144 @ ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2964]) ).
thf(3010,plain,
! [SV459: $i,SV144: $i > $o,SV399: $i,SV275: $i > $o] :
( ( ( SV275 @ ( sK124_SY1780 @ SV399 @ SV144 @ SV459 @ SV275 ) )
= $true )
| ( ( SV275 @ SV459 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV399
= ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $false )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2965]) ).
thf(3011,plain,
! [SV440: $i,SV144: $i > $o,SV476: $i,SV275: $i > $o] :
( ( ( ~ ~ ( ~ ( SV275 @ SV476 )
| ~ ! [SY1815: $i] :
( ~ ( SV275 @ SY1815 )
| ( SV476 = SY1815 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV144 @ ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2967]) ).
thf(3012,plain,
! [SV440: $i,SV144: $i > $o,SV473: $i,SV275: $i > $o] :
( ( ( ~ ( ~ ( SV275 @ SV473 )
| ~ ! [SY1806: $i] :
( ~ ( SV275 @ SY1806 )
| ( SV473 = SY1806 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV440
= ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2968]) ).
thf(3017,plain,
! [SV429: $i,SV144: $i > $o,SV469: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ SV469 )
| ~ ! [SY1798: $i] :
( ~ ( SV275 @ SY1798 )
| ( SV469 = SY1798 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV144 @ ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2973]) ).
thf(3018,plain,
! [SV429: $i,SV144: $i > $o,SV463: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ SV463 ) )
= $true )
| ( ( ~ ! [SY1792: $i] :
( ~ ( SV275 @ SY1792 )
| ( SV463 = SY1792 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV429
= ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $false )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2974]) ).
thf(3019,plain,
! [SV35: $i,SV407: $i,SV418: $i] :
( ( ( ~ ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) ) )
= $false )
| ( ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
= $true )
| ( ( SV407 = SV418 )
= $true )
| ( ( in @ SV407 @ SV35 )
= $false )
| ( ( in @ SV418 @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2975]) ).
thf(3022,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( ~ ( ~ ( in @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SV384 ) ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2978]) ).
thf(3023,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( ~ ~ ! [SY1771: $i] :
~ ~ ( ~ ( in @ SY1771 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
| ~ ( in @ SY1771 @ SV384 ) ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2979]) ).
thf(3024,plain,
! [SV384: $i,SV434: $i,SV35: $i,SV470: $i] :
( ( ( in @ SV470 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( ! [SY1799: $i] :
( ~ ( in @ SY1799 @ SV470 )
| ( in @ SY1799 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) ) )
| ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SV470 ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2980]) ).
thf(3025,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( ~ ( in @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SV384 ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2981]) ).
thf(3026,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( ~ ! [SY1755: $i] :
~ ~ ( ~ ( in @ SY1755 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
| ~ ( in @ SY1755 @ SV384 ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2982]) ).
thf(3027,plain,
! [SV35: $i,SV384: $i,SV430: $i,SV464: $i] :
( ( ( ! [SY1793: $i] :
( ~ ( in @ SY1793 @ SV464 )
| ( in @ SY1793 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) ) ) )
= $true )
| ( ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SV464 )
= $true )
| ( ( in @ SV464 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2983]) ).
thf(3028,plain,
! [SV385: $i,SV210: $i,SV443: $i,SV462: $i,SV64: $i > $i > $o] :
( ( ( SV64 @ SV462 @ SV443 )
= $false )
| ( ( in @ SV462 @ SV210 )
= $false )
| ( ( in @ SV443 @ ( sK84_SY1483 @ SV385 @ SV64 @ SV210 ) )
= $true )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ SV385 )
= $false )
| ( ( SV64 @ ( sK11_SY1480 @ SV64 @ SV210 ) @ ( sK64_SY1684 @ SV385 @ SV210 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2986]) ).
thf(3029,plain,
! [SV85: $i > $o,SV421: $i,SV471: $i,SV228: $i > $o] :
( ( ( SV228 @ SV471 )
= $false )
| ( ( ( sK109_SY1517 @ SV421 @ SV85 @ SV228 )
= SV471 )
= $true )
| ( ( SV85 @ SV421 )
= $false )
| ( ( SV85 @ ( sK94_SY1717 @ SV228 @ SV421 @ SV85 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2988]) ).
thf(3030,plain,
! [SV228: $i > $o,SV422: $i,SV472: $i,SV85: $i > $o] :
( ( ( SV85 @ SV472 )
= $false )
| ( ( ( sK110_SY1253 @ SV422 @ SV228 @ SV85 )
= SV472 )
= $true )
| ( ( SV228 @ SV422 )
= $false )
| ( ( SV228 @ ( sK95_SY1718 @ SV85 @ SV422 @ SV228 ) )
= $true )
| ( ( ( sK13_SY1513 @ SV228 @ SV85 )
= ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2990]) ).
thf(3031,plain,
! [SV85: $i > $o,SV455: $i,SV228: $i > $o] :
( ( ( ~ ~ ( ~ ( SV228 @ ( sK138_SY1517 @ SV455 @ SV85 @ SV228 ) )
| ~ ! [SY1816: $i] :
( ~ ( SV228 @ SY1816 )
| ( ( sK138_SY1517 @ SV455 @ SV85 @ SV228 )
= SY1816 ) ) ) )
= $false )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV85 @ ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2992]) ).
thf(3032,plain,
! [SV85: $i > $o,SV455: $i,SV228: $i > $o] :
( ( ( ~ ( ~ ( SV228 @ ( sK132_SY1517 @ SV455 @ SV85 @ SV228 ) )
| ~ ! [SY1809: $i] :
( ~ ( SV228 @ SY1809 )
| ( ( sK132_SY1517 @ SV455 @ SV85 @ SV228 )
= SY1809 ) ) ) )
= $true )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV455
= ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2993]) ).
thf(3033,plain,
! [SV228: $i > $o,SV456: $i,SV85: $i > $o] :
( ( ( ~ ~ ( ~ ( SV85 @ ( sK139_SY1253 @ SV456 @ SV228 @ SV85 ) )
| ~ ! [SY1817: $i] :
( ~ ( SV85 @ SY1817 )
| ( ( sK139_SY1253 @ SV456 @ SV228 @ SV85 )
= SY1817 ) ) ) )
= $false )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV228 @ ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2994]) ).
thf(3034,plain,
! [SV228: $i > $o,SV456: $i,SV85: $i > $o] :
( ( ( ~ ( ~ ( SV85 @ ( sK133_SY1253 @ SV456 @ SV228 @ SV85 ) )
| ~ ! [SY1810: $i] :
( ~ ( SV85 @ SY1810 )
| ( ( sK133_SY1253 @ SV456 @ SV228 @ SV85 )
= SY1810 ) ) ) )
= $true )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV456
= ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2995]) ).
thf(3043,plain,
! [SV85: $i > $o,SV444: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK129_SY1517 @ SV444 @ SV85 @ SV228 ) )
| ~ ! [SY1804: $i] :
( ~ ( SV228 @ SY1804 )
| ( ( sK129_SY1517 @ SV444 @ SV85 @ SV228 )
= SY1804 ) ) )
= $false )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV85 @ ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3004]) ).
thf(3044,plain,
! [SV85: $i > $o,SV444: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK122_SY1517 @ SV444 @ SV85 @ SV228 ) ) )
= $false )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV444
= ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3005]) ).
thf(3045,plain,
! [SV85: $i > $o,SV444: $i,SV228: $i > $o] :
( ( ( ~ ! [SY1794: $i] :
( ~ ( SV228 @ SY1794 )
| ( ( sK122_SY1517 @ SV444 @ SV85 @ SV228 )
= SY1794 ) ) )
= $false )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV444
= ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3005]) ).
thf(3046,plain,
! [SV228: $i > $o,SV445: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK130_SY1253 @ SV445 @ SV228 @ SV85 ) )
| ~ ! [SY1805: $i] :
( ~ ( SV85 @ SY1805 )
| ( ( sK130_SY1253 @ SV445 @ SV228 @ SV85 )
= SY1805 ) ) )
= $false )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV228 @ ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3006]) ).
thf(3047,plain,
! [SV228: $i > $o,SV445: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK123_SY1253 @ SV445 @ SV228 @ SV85 ) ) )
= $false )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV445
= ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3007]) ).
thf(3048,plain,
! [SV228: $i > $o,SV445: $i,SV85: $i > $o] :
( ( ( ~ ! [SY1795: $i] :
( ~ ( SV85 @ SY1795 )
| ( ( sK123_SY1253 @ SV445 @ SV228 @ SV85 )
= SY1795 ) ) )
= $false )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV445
= ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3007]) ).
thf(3049,plain,
! [SV460: $i,SV144: $i > $o,SV399: $i,SV275: $i > $o] :
( ( ( SV275 @ ( sK131_SY1786 @ SV399 @ SV144 @ SV460 @ SV275 ) )
= $true )
| ( ( SV275 @ SV460 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV399 )
= $false )
| ( ( SV144 @ ( sK87_SY1698 @ SV275 @ SV399 @ SV144 ) )
= $true )
| ( ( ( sK18_SY1576 @ SV275 @ SV144 )
= ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3008]) ).
thf(3050,plain,
! [SV440: $i,SV144: $i > $o,SV476: $i,SV275: $i > $o] :
( ( ( ~ ( ~ ( SV275 @ SV476 )
| ~ ! [SY1815: $i] :
( ~ ( SV275 @ SY1815 )
| ( SV476 = SY1815 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV144 @ ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3011]) ).
thf(3051,plain,
! [SV440: $i,SV144: $i > $o,SV473: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ SV473 )
| ~ ! [SY1806: $i] :
( ~ ( SV275 @ SY1806 )
| ( SV473 = SY1806 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV440
= ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3012]) ).
thf(3056,plain,
! [SV429: $i,SV144: $i > $o,SV469: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ SV469 ) )
= $true )
| ( ( ~ ! [SY1798: $i] :
( ~ ( SV275 @ SY1798 )
| ( SV469 = SY1798 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV144 @ ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3017]) ).
thf(3057,plain,
! [SV429: $i,SV144: $i > $o,SV463: $i,SV275: $i > $o] :
( ( ( SV275 @ SV463 )
= $false )
| ( ( ~ ! [SY1792: $i] :
( ~ ( SV275 @ SY1792 )
| ( SV463 = SY1792 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV429
= ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $false )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3018]) ).
thf(3058,plain,
! [SV35: $i,SV407: $i,SV418: $i] :
( ( ( in @ SV418 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
= $true )
| ( ( in @ SV407 @ ( sK102_SY1715 @ SV418 @ SV407 @ SV35 ) )
= $true )
| ( ( SV407 = SV418 )
= $true )
| ( ( in @ SV407 @ SV35 )
= $false )
| ( ( in @ SV418 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3019]) ).
thf(3059,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( ~ ( in @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
| ~ ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SV384 ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3022]) ).
thf(3060,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( ~ ! [SY1771: $i] :
~ ~ ( ~ ( in @ SY1771 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
| ~ ( in @ SY1771 @ SV384 ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3023]) ).
thf(3061,plain,
! [SV35: $i,SV384: $i,SV434: $i,SV470: $i] :
( ( ( ! [SY1799: $i] :
( ~ ( in @ SY1799 @ SV470 )
| ( in @ SY1799 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) ) ) )
= $true )
| ( ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SV470 )
= $true )
| ( ( in @ SV470 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3024]) ).
thf(3062,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( ~ ( in @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3025]) ).
thf(3063,plain,
! [SV430: $i,SV384: $i,SV35: $i] :
( ( ( ~ ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SV384 ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3025]) ).
thf(3064,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( ! [SY1755: $i] :
~ ~ ( ~ ( in @ SY1755 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
| ~ ( in @ SY1755 @ SV384 ) ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3026]) ).
thf(3065,plain,
! [SV35: $i,SV384: $i,SV430: $i,SV464: $i,SV477: $i] :
( ( ( ~ ( in @ SV477 @ SV464 )
| ( in @ SV477 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) ) )
= $true )
| ( ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SV464 )
= $true )
| ( ( in @ SV464 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3027]) ).
thf(3066,plain,
! [SV85: $i > $o,SV455: $i,SV228: $i > $o] :
( ( ( ~ ( ~ ( SV228 @ ( sK138_SY1517 @ SV455 @ SV85 @ SV228 ) )
| ~ ! [SY1816: $i] :
( ~ ( SV228 @ SY1816 )
| ( ( sK138_SY1517 @ SV455 @ SV85 @ SV228 )
= SY1816 ) ) ) )
= $true )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV85 @ ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3031]) ).
thf(3067,plain,
! [SV85: $i > $o,SV455: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK132_SY1517 @ SV455 @ SV85 @ SV228 ) )
| ~ ! [SY1809: $i] :
( ~ ( SV228 @ SY1809 )
| ( ( sK132_SY1517 @ SV455 @ SV85 @ SV228 )
= SY1809 ) ) )
= $false )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV455
= ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3032]) ).
thf(3068,plain,
! [SV228: $i > $o,SV456: $i,SV85: $i > $o] :
( ( ( ~ ( ~ ( SV85 @ ( sK139_SY1253 @ SV456 @ SV228 @ SV85 ) )
| ~ ! [SY1817: $i] :
( ~ ( SV85 @ SY1817 )
| ( ( sK139_SY1253 @ SV456 @ SV228 @ SV85 )
= SY1817 ) ) ) )
= $true )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV228 @ ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3033]) ).
thf(3069,plain,
! [SV228: $i > $o,SV456: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK133_SY1253 @ SV456 @ SV228 @ SV85 ) )
| ~ ! [SY1810: $i] :
( ~ ( SV85 @ SY1810 )
| ( ( sK133_SY1253 @ SV456 @ SV228 @ SV85 )
= SY1810 ) ) )
= $false )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV456
= ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3034]) ).
thf(3082,plain,
! [SV85: $i > $o,SV444: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK129_SY1517 @ SV444 @ SV85 @ SV228 ) ) )
= $false )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV85 @ ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3043]) ).
thf(3083,plain,
! [SV85: $i > $o,SV444: $i,SV228: $i > $o] :
( ( ( ~ ! [SY1804: $i] :
( ~ ( SV228 @ SY1804 )
| ( ( sK129_SY1517 @ SV444 @ SV85 @ SV228 )
= SY1804 ) ) )
= $false )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV85 @ ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3043]) ).
thf(3084,plain,
! [SV85: $i > $o,SV444: $i,SV228: $i > $o] :
( ( ( SV228 @ ( sK122_SY1517 @ SV444 @ SV85 @ SV228 ) )
= $true )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV444
= ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3044]) ).
thf(3085,plain,
! [SV85: $i > $o,SV444: $i,SV228: $i > $o] :
( ( ( ! [SY1794: $i] :
( ~ ( SV228 @ SY1794 )
| ( ( sK122_SY1517 @ SV444 @ SV85 @ SV228 )
= SY1794 ) ) )
= $true )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV444
= ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3045]) ).
thf(3086,plain,
! [SV228: $i > $o,SV445: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK130_SY1253 @ SV445 @ SV228 @ SV85 ) ) )
= $false )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV228 @ ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3046]) ).
thf(3087,plain,
! [SV228: $i > $o,SV445: $i,SV85: $i > $o] :
( ( ( ~ ! [SY1805: $i] :
( ~ ( SV85 @ SY1805 )
| ( ( sK130_SY1253 @ SV445 @ SV228 @ SV85 )
= SY1805 ) ) )
= $false )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV228 @ ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3046]) ).
thf(3088,plain,
! [SV228: $i > $o,SV445: $i,SV85: $i > $o] :
( ( ( SV85 @ ( sK123_SY1253 @ SV445 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV445
= ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3047]) ).
thf(3089,plain,
! [SV228: $i > $o,SV445: $i,SV85: $i > $o] :
( ( ( ! [SY1795: $i] :
( ~ ( SV85 @ SY1795 )
| ( ( sK123_SY1253 @ SV445 @ SV228 @ SV85 )
= SY1795 ) ) )
= $true )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV445
= ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3048]) ).
thf(3090,plain,
! [SV440: $i,SV144: $i > $o,SV476: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ SV476 )
| ~ ! [SY1815: $i] :
( ~ ( SV275 @ SY1815 )
| ( SV476 = SY1815 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV144 @ ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3050]) ).
thf(3091,plain,
! [SV440: $i,SV144: $i > $o,SV473: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ SV473 ) )
= $true )
| ( ( ~ ! [SY1806: $i] :
( ~ ( SV275 @ SY1806 )
| ( SV473 = SY1806 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV440
= ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3051]) ).
thf(3096,plain,
! [SV429: $i,SV144: $i > $o,SV469: $i,SV275: $i > $o] :
( ( ( SV275 @ SV469 )
= $false )
| ( ( ~ ! [SY1798: $i] :
( ~ ( SV275 @ SY1798 )
| ( SV469 = SY1798 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV144 @ ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3056]) ).
thf(3097,plain,
! [SV429: $i,SV144: $i > $o,SV463: $i,SV275: $i > $o] :
( ( ( ! [SY1792: $i] :
( ~ ( SV275 @ SY1792 )
| ( SV463 = SY1792 ) ) )
= $false )
| ( ( SV275 @ SV463 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV429
= ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $false )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3057]) ).
thf(3098,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( ~ ( in @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3059]) ).
thf(3099,plain,
! [SV434: $i,SV384: $i,SV35: $i] :
( ( ( ~ ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SV384 ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3059]) ).
thf(3100,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( ! [SY1771: $i] :
~ ~ ( ~ ( in @ SY1771 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
| ~ ( in @ SY1771 @ SV384 ) ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3060]) ).
thf(3101,plain,
! [SV35: $i,SV384: $i,SV434: $i,SV470: $i,SV478: $i] :
( ( ( ~ ( in @ SV478 @ SV470 )
| ( in @ SV478 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) ) )
= $true )
| ( ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SV470 )
= $true )
| ( ( in @ SV470 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3061]) ).
thf(3102,plain,
! [SV35: $i,SV384: $i,SV430: $i] :
( ( ( in @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3062]) ).
thf(3103,plain,
! [SV430: $i,SV384: $i,SV35: $i] :
( ( ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SV384 )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3063]) ).
thf(3104,plain,
! [SV35: $i,SV384: $i,SV430: $i,SV479: $i] :
( ( ( ~ ~ ( ~ ( in @ SV479 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
| ~ ( in @ SV479 @ SV384 ) ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3064]) ).
thf(3105,plain,
! [SV35: $i,SV384: $i,SV430: $i,SV464: $i,SV477: $i] :
( ( ( ~ ( in @ SV477 @ SV464 ) )
= $true )
| ( ( in @ SV477 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
= $true )
| ( ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SV464 )
= $true )
| ( ( in @ SV464 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3065]) ).
thf(3106,plain,
! [SV85: $i > $o,SV455: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK138_SY1517 @ SV455 @ SV85 @ SV228 ) )
| ~ ! [SY1816: $i] :
( ~ ( SV228 @ SY1816 )
| ( ( sK138_SY1517 @ SV455 @ SV85 @ SV228 )
= SY1816 ) ) )
= $false )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV85 @ ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3066]) ).
thf(3107,plain,
! [SV85: $i > $o,SV455: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK132_SY1517 @ SV455 @ SV85 @ SV228 ) ) )
= $false )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV455
= ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3067]) ).
thf(3108,plain,
! [SV85: $i > $o,SV455: $i,SV228: $i > $o] :
( ( ( ~ ! [SY1809: $i] :
( ~ ( SV228 @ SY1809 )
| ( ( sK132_SY1517 @ SV455 @ SV85 @ SV228 )
= SY1809 ) ) )
= $false )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV455
= ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3067]) ).
thf(3109,plain,
! [SV228: $i > $o,SV456: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK139_SY1253 @ SV456 @ SV228 @ SV85 ) )
| ~ ! [SY1817: $i] :
( ~ ( SV85 @ SY1817 )
| ( ( sK139_SY1253 @ SV456 @ SV228 @ SV85 )
= SY1817 ) ) )
= $false )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV228 @ ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3068]) ).
thf(3110,plain,
! [SV228: $i > $o,SV456: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK133_SY1253 @ SV456 @ SV228 @ SV85 ) ) )
= $false )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV456
= ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3069]) ).
thf(3111,plain,
! [SV228: $i > $o,SV456: $i,SV85: $i > $o] :
( ( ( ~ ! [SY1810: $i] :
( ~ ( SV85 @ SY1810 )
| ( ( sK133_SY1253 @ SV456 @ SV228 @ SV85 )
= SY1810 ) ) )
= $false )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV456
= ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3069]) ).
thf(3128,plain,
! [SV85: $i > $o,SV444: $i,SV228: $i > $o] :
( ( ( SV228 @ ( sK129_SY1517 @ SV444 @ SV85 @ SV228 ) )
= $true )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV85 @ ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3082]) ).
thf(3129,plain,
! [SV85: $i > $o,SV444: $i,SV228: $i > $o] :
( ( ( ! [SY1804: $i] :
( ~ ( SV228 @ SY1804 )
| ( ( sK129_SY1517 @ SV444 @ SV85 @ SV228 )
= SY1804 ) ) )
= $true )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV85 @ ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3083]) ).
thf(3130,plain,
! [SV85: $i > $o,SV444: $i,SV480: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ SV480 )
| ( ( sK122_SY1517 @ SV444 @ SV85 @ SV228 )
= SV480 ) )
= $true )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV444
= ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3085]) ).
thf(3131,plain,
! [SV228: $i > $o,SV445: $i,SV85: $i > $o] :
( ( ( SV85 @ ( sK130_SY1253 @ SV445 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV228 @ ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3086]) ).
thf(3132,plain,
! [SV228: $i > $o,SV445: $i,SV85: $i > $o] :
( ( ( ! [SY1805: $i] :
( ~ ( SV85 @ SY1805 )
| ( ( sK130_SY1253 @ SV445 @ SV228 @ SV85 )
= SY1805 ) ) )
= $true )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV228 @ ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3087]) ).
thf(3133,plain,
! [SV228: $i > $o,SV445: $i,SV481: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ SV481 )
| ( ( sK123_SY1253 @ SV445 @ SV228 @ SV85 )
= SV481 ) )
= $true )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV445
= ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3089]) ).
thf(3134,plain,
! [SV440: $i,SV144: $i > $o,SV476: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ SV476 ) )
= $true )
| ( ( ~ ! [SY1815: $i] :
( ~ ( SV275 @ SY1815 )
| ( SV476 = SY1815 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV144 @ ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3090]) ).
thf(3135,plain,
! [SV440: $i,SV144: $i > $o,SV473: $i,SV275: $i > $o] :
( ( ( SV275 @ SV473 )
= $false )
| ( ( ~ ! [SY1806: $i] :
( ~ ( SV275 @ SY1806 )
| ( SV473 = SY1806 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV440
= ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3091]) ).
thf(3140,plain,
! [SV429: $i,SV144: $i > $o,SV469: $i,SV275: $i > $o] :
( ( ( ! [SY1798: $i] :
( ~ ( SV275 @ SY1798 )
| ( SV469 = SY1798 ) ) )
= $false )
| ( ( SV275 @ SV469 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV144 @ ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3096]) ).
thf(3141,plain,
! [SV463: $i,SV144: $i > $o,SV429: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ ( sK140_SY1792 @ SV429 @ SV144 @ SV463 @ SV275 ) )
| ( SV463
= ( sK140_SY1792 @ SV429 @ SV144 @ SV463 @ SV275 ) ) )
= $false )
| ( ( SV275 @ SV463 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV429
= ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $false )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3097]) ).
thf(3142,plain,
! [SV35: $i,SV384: $i,SV434: $i] :
( ( ( in @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) @ ( sK2_SY1109 @ SV35 ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3098]) ).
thf(3143,plain,
! [SV434: $i,SV384: $i,SV35: $i] :
( ( ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SV384 )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3099]) ).
thf(3144,plain,
! [SV35: $i,SV384: $i,SV434: $i,SV482: $i] :
( ( ( ~ ~ ( ~ ( in @ SV482 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
| ~ ( in @ SV482 @ SV384 ) ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3100]) ).
thf(3145,plain,
! [SV35: $i,SV384: $i,SV434: $i,SV470: $i,SV478: $i] :
( ( ( ~ ( in @ SV478 @ SV470 ) )
= $true )
| ( ( in @ SV478 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
= $true )
| ( ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SV470 )
= $true )
| ( ( in @ SV470 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3101]) ).
thf(3146,plain,
! [SV35: $i,SV384: $i,SV430: $i,SV479: $i] :
( ( ( ~ ( ~ ( in @ SV479 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
| ~ ( in @ SV479 @ SV384 ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3104]) ).
thf(3147,plain,
! [SV35: $i,SV384: $i,SV430: $i,SV464: $i,SV477: $i] :
( ( ( in @ SV477 @ SV464 )
= $false )
| ( ( in @ SV477 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
= $true )
| ( ( in @ ( sK103_SY1754 @ SV35 @ SV384 @ SV430 ) @ SV464 )
= $true )
| ( ( in @ SV464 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3105]) ).
thf(3148,plain,
! [SV85: $i > $o,SV455: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ ( sK138_SY1517 @ SV455 @ SV85 @ SV228 ) ) )
= $false )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV85 @ ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3106]) ).
thf(3149,plain,
! [SV85: $i > $o,SV455: $i,SV228: $i > $o] :
( ( ( ~ ! [SY1816: $i] :
( ~ ( SV228 @ SY1816 )
| ( ( sK138_SY1517 @ SV455 @ SV85 @ SV228 )
= SY1816 ) ) )
= $false )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV85 @ ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3106]) ).
thf(3150,plain,
! [SV85: $i > $o,SV455: $i,SV228: $i > $o] :
( ( ( SV228 @ ( sK132_SY1517 @ SV455 @ SV85 @ SV228 ) )
= $true )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV455
= ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3107]) ).
thf(3151,plain,
! [SV85: $i > $o,SV455: $i,SV228: $i > $o] :
( ( ( ! [SY1809: $i] :
( ~ ( SV228 @ SY1809 )
| ( ( sK132_SY1517 @ SV455 @ SV85 @ SV228 )
= SY1809 ) ) )
= $true )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV455
= ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3108]) ).
thf(3152,plain,
! [SV228: $i > $o,SV456: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ ( sK139_SY1253 @ SV456 @ SV228 @ SV85 ) ) )
= $false )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV228 @ ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3109]) ).
thf(3153,plain,
! [SV228: $i > $o,SV456: $i,SV85: $i > $o] :
( ( ( ~ ! [SY1817: $i] :
( ~ ( SV85 @ SY1817 )
| ( ( sK139_SY1253 @ SV456 @ SV228 @ SV85 )
= SY1817 ) ) )
= $false )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV228 @ ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3109]) ).
thf(3154,plain,
! [SV228: $i > $o,SV456: $i,SV85: $i > $o] :
( ( ( SV85 @ ( sK133_SY1253 @ SV456 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV456
= ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3110]) ).
thf(3155,plain,
! [SV228: $i > $o,SV456: $i,SV85: $i > $o] :
( ( ( ! [SY1810: $i] :
( ~ ( SV85 @ SY1810 )
| ( ( sK133_SY1253 @ SV456 @ SV228 @ SV85 )
= SY1810 ) ) )
= $true )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV456
= ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3111]) ).
thf(3168,plain,
! [SV85: $i > $o,SV444: $i,SV487: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ SV487 )
| ( ( sK129_SY1517 @ SV444 @ SV85 @ SV228 )
= SV487 ) )
= $true )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV85 @ ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3129]) ).
thf(3169,plain,
! [SV85: $i > $o,SV444: $i,SV480: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ SV480 ) )
= $true )
| ( ( ( sK122_SY1517 @ SV444 @ SV85 @ SV228 )
= SV480 )
= $true )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV444
= ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3130]) ).
thf(3170,plain,
! [SV228: $i > $o,SV445: $i,SV488: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ SV488 )
| ( ( sK130_SY1253 @ SV445 @ SV228 @ SV85 )
= SV488 ) )
= $true )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV228 @ ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3132]) ).
thf(3171,plain,
! [SV228: $i > $o,SV445: $i,SV481: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ SV481 ) )
= $true )
| ( ( ( sK123_SY1253 @ SV445 @ SV228 @ SV85 )
= SV481 )
= $true )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV445
= ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3133]) ).
thf(3172,plain,
! [SV440: $i,SV144: $i > $o,SV476: $i,SV275: $i > $o] :
( ( ( SV275 @ SV476 )
= $false )
| ( ( ~ ! [SY1815: $i] :
( ~ ( SV275 @ SY1815 )
| ( SV476 = SY1815 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV144 @ ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3134]) ).
thf(3173,plain,
! [SV440: $i,SV144: $i > $o,SV473: $i,SV275: $i > $o] :
( ( ( ! [SY1806: $i] :
( ~ ( SV275 @ SY1806 )
| ( SV473 = SY1806 ) ) )
= $false )
| ( ( SV275 @ SV473 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV440
= ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3135]) ).
thf(3178,plain,
! [SV469: $i,SV144: $i > $o,SV429: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ ( sK143_SY1798 @ SV429 @ SV144 @ SV469 @ SV275 ) )
| ( SV469
= ( sK143_SY1798 @ SV429 @ SV144 @ SV469 @ SV275 ) ) )
= $false )
| ( ( SV275 @ SV469 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV144 @ ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3140]) ).
thf(3179,plain,
! [SV463: $i,SV144: $i > $o,SV429: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ ( sK140_SY1792 @ SV429 @ SV144 @ SV463 @ SV275 ) ) )
= $false )
| ( ( SV275 @ SV463 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV429
= ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $false )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3141]) ).
thf(3180,plain,
! [SV275: $i > $o,SV144: $i > $o,SV429: $i,SV463: $i] :
( ( ( SV463
= ( sK140_SY1792 @ SV429 @ SV144 @ SV463 @ SV275 ) )
= $false )
| ( ( SV275 @ SV463 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV429
= ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $false )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3141]) ).
thf(3181,plain,
! [SV35: $i,SV384: $i,SV434: $i,SV482: $i] :
( ( ( ~ ( ~ ( in @ SV482 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
| ~ ( in @ SV482 @ SV384 ) ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3144]) ).
thf(3182,plain,
! [SV35: $i,SV384: $i,SV434: $i,SV470: $i,SV478: $i] :
( ( ( in @ SV478 @ SV470 )
= $false )
| ( ( in @ SV478 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
= $true )
| ( ( in @ ( sK108_SY1770 @ SV35 @ SV384 @ SV434 ) @ SV470 )
= $true )
| ( ( in @ SV470 @ ( sK2_SY1109 @ SV35 ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3145]) ).
thf(3183,plain,
! [SV35: $i,SV384: $i,SV430: $i,SV479: $i] :
( ( ( ~ ( in @ SV479 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
| ~ ( in @ SV479 @ SV384 ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3146]) ).
thf(3184,plain,
! [SV85: $i > $o,SV455: $i,SV228: $i > $o] :
( ( ( SV228 @ ( sK138_SY1517 @ SV455 @ SV85 @ SV228 ) )
= $true )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV85 @ ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3148]) ).
thf(3185,plain,
! [SV85: $i > $o,SV455: $i,SV228: $i > $o] :
( ( ( ! [SY1816: $i] :
( ~ ( SV228 @ SY1816 )
| ( ( sK138_SY1517 @ SV455 @ SV85 @ SV228 )
= SY1816 ) ) )
= $true )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV85 @ ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3149]) ).
thf(3186,plain,
! [SV85: $i > $o,SV455: $i,SV489: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ SV489 )
| ( ( sK132_SY1517 @ SV455 @ SV85 @ SV228 )
= SV489 ) )
= $true )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV455
= ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3151]) ).
thf(3187,plain,
! [SV228: $i > $o,SV456: $i,SV85: $i > $o] :
( ( ( SV85 @ ( sK139_SY1253 @ SV456 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV228 @ ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3152]) ).
thf(3188,plain,
! [SV228: $i > $o,SV456: $i,SV85: $i > $o] :
( ( ( ! [SY1817: $i] :
( ~ ( SV85 @ SY1817 )
| ( ( sK139_SY1253 @ SV456 @ SV228 @ SV85 )
= SY1817 ) ) )
= $true )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV228 @ ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3153]) ).
thf(3189,plain,
! [SV228: $i > $o,SV456: $i,SV490: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ SV490 )
| ( ( sK133_SY1253 @ SV456 @ SV228 @ SV85 )
= SV490 ) )
= $true )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV456
= ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3155]) ).
thf(3198,plain,
! [SV85: $i > $o,SV444: $i,SV487: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ SV487 ) )
= $true )
| ( ( ( sK129_SY1517 @ SV444 @ SV85 @ SV228 )
= SV487 )
= $true )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV85 @ ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3168]) ).
thf(3199,plain,
! [SV85: $i > $o,SV444: $i,SV480: $i,SV228: $i > $o] :
( ( ( SV228 @ SV480 )
= $false )
| ( ( ( sK122_SY1517 @ SV444 @ SV85 @ SV228 )
= SV480 )
= $true )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV444
= ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3169]) ).
thf(3200,plain,
! [SV228: $i > $o,SV445: $i,SV488: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ SV488 ) )
= $true )
| ( ( ( sK130_SY1253 @ SV445 @ SV228 @ SV85 )
= SV488 )
= $true )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV228 @ ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3170]) ).
thf(3201,plain,
! [SV228: $i > $o,SV445: $i,SV481: $i,SV85: $i > $o] :
( ( ( SV85 @ SV481 )
= $false )
| ( ( ( sK123_SY1253 @ SV445 @ SV228 @ SV85 )
= SV481 )
= $true )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV445
= ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $false )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3171]) ).
thf(3202,plain,
! [SV440: $i,SV144: $i > $o,SV476: $i,SV275: $i > $o] :
( ( ( ! [SY1815: $i] :
( ~ ( SV275 @ SY1815 )
| ( SV476 = SY1815 ) ) )
= $false )
| ( ( SV275 @ SV476 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV144 @ ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3172]) ).
thf(3203,plain,
! [SV473: $i,SV144: $i > $o,SV440: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ ( sK144_SY1806 @ SV440 @ SV144 @ SV473 @ SV275 ) )
| ( SV473
= ( sK144_SY1806 @ SV440 @ SV144 @ SV473 @ SV275 ) ) )
= $false )
| ( ( SV275 @ SV473 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV440
= ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3173]) ).
thf(3210,plain,
! [SV469: $i,SV144: $i > $o,SV429: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ ( sK143_SY1798 @ SV429 @ SV144 @ SV469 @ SV275 ) ) )
= $false )
| ( ( SV275 @ SV469 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV144 @ ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3178]) ).
thf(3211,plain,
! [SV275: $i > $o,SV144: $i > $o,SV429: $i,SV469: $i] :
( ( ( SV469
= ( sK143_SY1798 @ SV429 @ SV144 @ SV469 @ SV275 ) )
= $false )
| ( ( SV275 @ SV469 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV144 @ ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3178]) ).
thf(3212,plain,
! [SV463: $i,SV144: $i > $o,SV429: $i,SV275: $i > $o] :
( ( ( SV275 @ ( sK140_SY1792 @ SV429 @ SV144 @ SV463 @ SV275 ) )
= $true )
| ( ( SV275 @ SV463 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV429
= ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $false )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3179]) ).
thf(3213,plain,
! [SV35: $i,SV384: $i,SV434: $i,SV482: $i] :
( ( ( ~ ( in @ SV482 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
| ~ ( in @ SV482 @ SV384 ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3181]) ).
thf(3214,plain,
! [SV35: $i,SV384: $i,SV430: $i,SV479: $i] :
( ( ( ~ ( in @ SV479 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) ) )
= $true )
| ( ( ~ ( in @ SV479 @ SV384 ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3183]) ).
thf(3215,plain,
! [SV85: $i > $o,SV455: $i,SV495: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ SV495 )
| ( ( sK138_SY1517 @ SV455 @ SV85 @ SV228 )
= SV495 ) )
= $true )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV85 @ ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3185]) ).
thf(3216,plain,
! [SV85: $i > $o,SV455: $i,SV489: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ SV489 ) )
= $true )
| ( ( ( sK132_SY1517 @ SV455 @ SV85 @ SV228 )
= SV489 )
= $true )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV455
= ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3186]) ).
thf(3217,plain,
! [SV228: $i > $o,SV456: $i,SV496: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ SV496 )
| ( ( sK139_SY1253 @ SV456 @ SV228 @ SV85 )
= SV496 ) )
= $true )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV228 @ ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3188]) ).
thf(3218,plain,
! [SV228: $i > $o,SV456: $i,SV490: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ SV490 ) )
= $true )
| ( ( ( sK133_SY1253 @ SV456 @ SV228 @ SV85 )
= SV490 )
= $true )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV456
= ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3189]) ).
thf(3227,plain,
! [SV85: $i > $o,SV444: $i,SV487: $i,SV228: $i > $o] :
( ( ( SV228 @ SV487 )
= $false )
| ( ( ( sK129_SY1517 @ SV444 @ SV85 @ SV228 )
= SV487 )
= $true )
| ( ( SV85 @ SV444 )
= $false )
| ( ( SV85 @ ( sK113_SY1750 @ SV228 @ SV444 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3198]) ).
thf(3228,plain,
! [SV228: $i > $o,SV445: $i,SV488: $i,SV85: $i > $o] :
( ( ( SV85 @ SV488 )
= $false )
| ( ( ( sK130_SY1253 @ SV445 @ SV228 @ SV85 )
= SV488 )
= $true )
| ( ( SV228 @ SV445 )
= $false )
| ( ( SV228 @ ( sK114_SY1751 @ SV85 @ SV445 @ SV228 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3200]) ).
thf(3229,plain,
! [SV476: $i,SV144: $i > $o,SV440: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ ( sK147_SY1815 @ SV440 @ SV144 @ SV476 @ SV275 ) )
| ( SV476
= ( sK147_SY1815 @ SV440 @ SV144 @ SV476 @ SV275 ) ) )
= $false )
| ( ( SV275 @ SV476 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV144 @ ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3202]) ).
thf(3230,plain,
! [SV473: $i,SV144: $i > $o,SV440: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ ( sK144_SY1806 @ SV440 @ SV144 @ SV473 @ SV275 ) ) )
= $false )
| ( ( SV275 @ SV473 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV440
= ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3203]) ).
thf(3231,plain,
! [SV275: $i > $o,SV144: $i > $o,SV440: $i,SV473: $i] :
( ( ( SV473
= ( sK144_SY1806 @ SV440 @ SV144 @ SV473 @ SV275 ) )
= $false )
| ( ( SV275 @ SV473 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV440
= ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3203]) ).
thf(3238,plain,
! [SV469: $i,SV144: $i > $o,SV429: $i,SV275: $i > $o] :
( ( ( SV275 @ ( sK143_SY1798 @ SV429 @ SV144 @ SV469 @ SV275 ) )
= $true )
| ( ( SV275 @ SV469 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV429 )
= $false )
| ( ( SV144 @ ( sK101_SY1731 @ SV275 @ SV429 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3210]) ).
thf(3239,plain,
! [SV35: $i,SV384: $i,SV434: $i,SV482: $i] :
( ( ( ~ ( in @ SV482 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) ) )
= $true )
| ( ( ~ ( in @ SV482 @ SV384 ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3213]) ).
thf(3240,plain,
! [SV35: $i,SV384: $i,SV430: $i,SV479: $i] :
( ( ( in @ SV479 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
= $false )
| ( ( ~ ( in @ SV479 @ SV384 ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3214]) ).
thf(3241,plain,
! [SV85: $i > $o,SV455: $i,SV495: $i,SV228: $i > $o] :
( ( ( ~ ( SV228 @ SV495 ) )
= $true )
| ( ( ( sK138_SY1517 @ SV455 @ SV85 @ SV228 )
= SV495 )
= $true )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV85 @ ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3215]) ).
thf(3242,plain,
! [SV85: $i > $o,SV455: $i,SV489: $i,SV228: $i > $o] :
( ( ( SV228 @ SV489 )
= $false )
| ( ( ( sK132_SY1517 @ SV455 @ SV85 @ SV228 )
= SV489 )
= $true )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV455
= ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3216]) ).
thf(3243,plain,
! [SV228: $i > $o,SV456: $i,SV496: $i,SV85: $i > $o] :
( ( ( ~ ( SV85 @ SV496 ) )
= $true )
| ( ( ( sK139_SY1253 @ SV456 @ SV228 @ SV85 )
= SV496 )
= $true )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV228 @ ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3217]) ).
thf(3244,plain,
! [SV228: $i > $o,SV456: $i,SV490: $i,SV85: $i > $o] :
( ( ( SV85 @ SV490 )
= $false )
| ( ( ( sK133_SY1253 @ SV456 @ SV228 @ SV85 )
= SV490 )
= $true )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV456
= ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $false )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3218]) ).
thf(3249,plain,
! [SV476: $i,SV144: $i > $o,SV440: $i,SV275: $i > $o] :
( ( ( ~ ( SV275 @ ( sK147_SY1815 @ SV440 @ SV144 @ SV476 @ SV275 ) ) )
= $false )
| ( ( SV275 @ SV476 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV144 @ ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3229]) ).
thf(3250,plain,
! [SV275: $i > $o,SV144: $i > $o,SV440: $i,SV476: $i] :
( ( ( SV476
= ( sK147_SY1815 @ SV440 @ SV144 @ SV476 @ SV275 ) )
= $false )
| ( ( SV275 @ SV476 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV144 @ ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3229]) ).
thf(3251,plain,
! [SV473: $i,SV144: $i > $o,SV440: $i,SV275: $i > $o] :
( ( ( SV275 @ ( sK144_SY1806 @ SV440 @ SV144 @ SV473 @ SV275 ) )
= $true )
| ( ( SV275 @ SV473 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV440
= ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $false )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3230]) ).
thf(3254,plain,
! [SV35: $i,SV384: $i,SV434: $i,SV482: $i] :
( ( ( in @ SV482 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
= $false )
| ( ( ~ ( in @ SV482 @ SV384 ) )
= $true )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3239]) ).
thf(3255,plain,
! [SV35: $i,SV430: $i,SV384: $i,SV479: $i] :
( ( ( in @ SV479 @ SV384 )
= $false )
| ( ( in @ SV479 @ ( sK91_SY1679 @ SV430 @ SV384 @ SV35 ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV35 )
= $false )
| ( ( in @ SV430 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3240]) ).
thf(3256,plain,
! [SV85: $i > $o,SV455: $i,SV495: $i,SV228: $i > $o] :
( ( ( SV228 @ SV495 )
= $false )
| ( ( ( sK138_SY1517 @ SV455 @ SV85 @ SV228 )
= SV495 )
= $true )
| ( ( SV85 @ SV455 )
= $false )
| ( ( SV85 @ ( sK120_SY1776 @ SV228 @ SV455 @ SV85 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3241]) ).
thf(3257,plain,
! [SV228: $i > $o,SV456: $i,SV496: $i,SV85: $i > $o] :
( ( ( SV85 @ SV496 )
= $false )
| ( ( ( sK139_SY1253 @ SV456 @ SV228 @ SV85 )
= SV496 )
= $true )
| ( ( SV228 @ SV456 )
= $false )
| ( ( SV228 @ ( sK121_SY1777 @ SV85 @ SV456 @ SV228 ) )
= $true )
| ( ( SV85 @ ( sK13_SY1513 @ SV228 @ SV85 ) )
= $true )
| ( ( SV228 @ ( sK20_SY1658 @ SV85 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3243]) ).
thf(3258,plain,
! [SV476: $i,SV144: $i > $o,SV440: $i,SV275: $i > $o] :
( ( ( SV275 @ ( sK147_SY1815 @ SV440 @ SV144 @ SV476 @ SV275 ) )
= $true )
| ( ( SV275 @ SV476 )
= $false )
| ( ( ( descr
@ ^ [SY1393: $i] : ( SV144 @ SY1393 ) )
= ( descr
@ ^ [SY1583: $i] : ( SV275 @ SY1583 ) ) )
= $true )
| ( ( SV144 @ SV440 )
= $false )
| ( ( SV144 @ ( sK111_SY1745 @ SV275 @ SV440 @ SV144 ) )
= $true )
| ( ( SV144 @ ( sK18_SY1576 @ SV275 @ SV144 ) )
= $true )
| ( ( SV275 @ ( sK22_SY1666 @ SV144 @ SV275 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3249]) ).
thf(3259,plain,
! [SV35: $i,SV434: $i,SV384: $i,SV482: $i] :
( ( ( in @ SV482 @ SV384 )
= $false )
| ( ( in @ SV482 @ ( sK98_SY1679 @ SV434 @ SV384 @ SV35 ) )
= $false )
| ( ( in @ ( sK61_SY1677 @ SV35 @ SV384 ) @ SV384 )
= $true )
| ( ( in @ SV434 @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3254]) ).
thf(3260,plain,
! [SV356: $i,SV426: $i] :
( ( ( SV426
= ( sK65_SY1266 @ SV356
@ ^ [SX0: $i] : ( SX0 = SV356 ) ) )
= $false )
| ( ( SV426 = SV356 )
= $true )
| ( ( SV356 = SV356 )
= $false )
| ( ( SV356
= ( sK53_SY1659 @ SV356
@ ^ [SX0: $i] : ( SX0 = SV356 ) ) )
= $false ) ),
inference(replace_leibnizEQ,[status(thm)],[2577:[bind(SV90,$thf( ^ [SV497: $i] : ( SV497 = SV356 ) ))]]) ).
thf(3261,plain,
! [SV356: $i,SV426: $i] :
( ( ( SV426
= ( sK65_SY1266 @ SV356
@ ^ [SX0: $i] : ( SX0 = SV356 ) ) )
= $false )
| ( ( SV426 = SV356 )
= $true )
| ( ( SV356
= ( sK53_SY1659 @ SV356
@ ^ [SX0: $i] : ( SX0 = SV356 ) ) )
= $false ) ),
inference(sim,[status(thm)],[3260]) ).
thf(3262,plain,
! [SV356: $i,SV428: $i] :
( ( ( SV428
= ( sK73_SY1266 @ SV356
@ ^ [SX0: $i] : ( SX0 = SV356 ) ) )
= $false )
| ( ( SV428 = SV356 )
= $true )
| ( ( SV356 = SV356 )
= $false )
| ( ( ( sK53_SY1659 @ SV356
@ ^ [SX0: $i] : ( SX0 = SV356 ) )
= SV356 )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[2632:[bind(SV90,$thf( ^ [SV498: $i] : ( SV498 = SV356 ) ))]]) ).
thf(3263,plain,
! [SV356: $i,SV428: $i] :
( ( ( SV428
= ( sK73_SY1266 @ SV356
@ ^ [SX0: $i] : ( SX0 = SV356 ) ) )
= $false )
| ( ( SV428 = SV356 )
= $true )
| ( ( ( sK53_SY1659 @ SV356
@ ^ [SX0: $i] : ( SX0 = SV356 ) )
= SV356 )
= $true ) ),
inference(sim,[status(thm)],[3262]) ).
thf(3264,plain,
! [SV73: $o] :
( ( SV73 = $false )
| ( ( SV73
= ( ~ ( in @ emptyset @ ( prop2set @ SV73 ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[849]) ).
thf(3265,plain,
! [SV133: $o] :
( ( SV133 = $false )
| ( ( SV133
= ( ~ ( set2prop @ ( prop2set @ SV133 ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[913]) ).
thf(3266,plain,
! [SV84: $i,SV348: $o] :
( ( SV348 = $true )
| ( ( SV348
= ( ~ ( in @ SV84 @ emptyset ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1002]) ).
thf(3267,plain,
! [SV112: $o,SV251: $i] :
( ( SV112 = $true )
| ( ( SV112
= ( ~ ( in @ SV251 @ ( prop2set @ SV112 ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1032]) ).
thf(3268,plain,
! [SV134: $i > $o,SV269: $i] :
( ( ( SV134 @ SV269 )
= $true )
| ( ( ( SV134 @ SV269 )
= ( ~ ( in @ SV269 @ emptyset ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1055]) ).
thf(3269,plain,
! [SV235: $i > $o,SV93: $i,SV316: $i] :
( ( ( SV235 @ SV316 )
= $true )
| ( ( ( SV235 @ SV316 )
= ( ~ ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SY1537: $i] : ( SV235 @ SY1537 ) ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1139]) ).
thf(3270,plain,
! [SV110: $i] :
( ( ( SV110 = emptyset )
= $true )
| ( ( ( in @ ( sK6_SY1321 @ SV110 ) @ SV110 )
= ( SV110 = emptyset ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1156]) ).
thf(3271,plain,
! [SV129: $i] :
( ( ( SV129 = emptyset )
= $true )
| ( ( ( in @ ( sK7_SY1357 @ SV129 ) @ SV129 )
= ( SV129 = emptyset ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1170]) ).
thf(3272,plain,
! [SV236: $i,SV94: $i,SV317: $i] :
( ( ( in @ SV317 @ SV236 )
= $false )
| ( ( ( in @ SV317 @ ( setminus @ SV94 @ SV236 ) )
= ( in @ SV317 @ SV236 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1256]) ).
thf(3273,plain,
! [SV106: $i,SV247: $i,SV326: $i] :
( ( ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) )
= $false )
| ( ( ( in @ SV326 @ SV247 )
= ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1265]) ).
thf(3274,plain,
! [SV52: $i] :
( ( ( SV52 = emptyset )
= $true )
| ( ( ( in @ ( sK19_SY1165 @ SV52 ) @ SV52 )
= ( SV52 = emptyset ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1323]) ).
thf(3275,plain,
! [SV86: $i,SV229: $i] :
( ( ( subset @ SV86 @ SV229 )
= $true )
| ( ( ( in @ ( sK14_SY1523 @ SV229 @ SV86 ) @ SV86 )
= ( subset @ SV86 @ SV229 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1354]) ).
thf(3276,plain,
! [SV260: $i,SV120: $i] :
( ( ( in @ SV260 @ ( powerset @ SV120 ) )
= $true )
| ( ( ( in @ ( sK16_SY1565 @ SV120 @ SV260 ) @ SV260 )
= ( in @ SV260 @ ( powerset @ SV120 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1380]) ).
thf(3277,plain,
! [SV361: $i,SV127: $i] :
( ( ( in @ SV361 @ SV127 )
= $false )
| ( ( ( SV127 = emptyset )
= ( in @ SV361 @ SV127 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1386]) ).
thf(3278,plain,
! [SV141: $i,SV274: $i] :
( ( ( subset @ SV141 @ SV274 )
= $true )
| ( ( ( in @ ( sK17_SY1575 @ SV274 @ SV141 ) @ SV141 )
= ( subset @ SV141 @ SV274 ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1394]) ).
thf(3279,plain,
! [SV273: $i,SV140: $i] :
( ( ( in @ SV273 @ ( powerset @ SV140 ) )
= $true )
| ( ( ( in @ ( sK36_SY1574 @ SV140 @ SV273 ) @ SV273 )
= ( in @ SV273 @ ( powerset @ SV140 ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1684]) ).
thf(3280,plain,
! [SV143: $i] :
( ( ( SV143 = emptyset )
= $true )
| ( ( ( in @ ( sK21_SY1385 @ SV143 ) @ SV143 )
= ( SV143 = emptyset ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1686]) ).
thf(3282,plain,
! [SV89: $i,SV232: $i] :
( ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true )
| ( ( ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV89 )
= ( ( binintersect @ SV89 @ SV232 )
= emptyset ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1742]) ).
thf(3283,plain,
! [SV89: $i,SV232: $i] :
( ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true )
| ( ( ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV232 )
= ( ( binintersect @ SV89 @ SV232 )
= emptyset ) )
= $false ) ),
inference(fac_restr,[status(thm)],[1743]) ).
thf(3284,plain,
! [SV73: $o] :
( ( ( ~ ( SV73
| ~ ( in @ emptyset @ ( prop2set @ SV73 ) ) )
| ~ ( ~ SV73
| ~ ~ ( in @ emptyset @ ( prop2set @ SV73 ) ) ) )
= $false )
| ( SV73 = $false ) ),
inference(extcnf_equal_neg,[status(thm)],[3264]) ).
thf(3286,plain,
! [SV133: $o] :
( ( ( ~ ( SV133
| ~ ( set2prop @ ( prop2set @ SV133 ) ) )
| ~ ( ~ SV133
| ~ ~ ( set2prop @ ( prop2set @ SV133 ) ) ) )
= $false )
| ( SV133 = $false ) ),
inference(extcnf_equal_neg,[status(thm)],[3265]) ).
thf(3288,plain,
! [SV84: $i,SV348: $o] :
( ( ( ~ ( SV348
| ~ ( in @ SV84 @ emptyset ) )
| ~ ( ~ SV348
| ~ ~ ( in @ SV84 @ emptyset ) ) )
= $false )
| ( SV348 = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[3266]) ).
thf(3289,plain,
! [SV84: $i,SV348: $o] :
( ( ( SV348
= ( ~ ( in @ SV84 @ emptyset ) ) )
= $false )
| ( SV348 = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[3266]) ).
thf(3290,plain,
! [SV251: $i,SV112: $o] :
( ( ( ~ ( SV112
| ~ ( in @ SV251 @ ( prop2set @ SV112 ) ) )
| ~ ( ~ SV112
| ~ ~ ( in @ SV251 @ ( prop2set @ SV112 ) ) ) )
= $false )
| ( SV112 = $true ) ),
inference(extcnf_equal_neg,[status(thm)],[3267]) ).
thf(3292,plain,
! [SV269: $i,SV134: $i > $o] :
( ( ( ~ ( ( SV134 @ SV269 )
| ~ ( in @ SV269 @ emptyset ) )
| ~ ( ~ ( SV134 @ SV269 )
| ~ ~ ( in @ SV269 @ emptyset ) ) )
= $false )
| ( ( SV134 @ SV269 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[3268]) ).
thf(3293,plain,
! [SV269: $i,SV134: $i > $o] :
( ( ( ( SV134 @ SV269 )
= ( ~ ( in @ SV269 @ emptyset ) ) )
= $false )
| ( ( SV134 @ SV269 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[3268]) ).
thf(3294,plain,
! [SV93: $i,SV316: $i,SV235: $i > $o] :
( ( ( ~ ( ( SV235 @ SV316 )
| ~ ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SY1537: $i] : ( SV235 @ SY1537 ) ) ) )
| ~ ( ~ ( SV235 @ SV316 )
| ~ ~ ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SY1537: $i] : ( SV235 @ SY1537 ) ) ) ) )
= $false )
| ( ( SV235 @ SV316 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[3269]) ).
thf(3295,plain,
! [SV93: $i,SV316: $i,SV235: $i > $o] :
( ( ( ( SV235 @ SV316 )
= ( ~ ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SY1537: $i] : ( SV235 @ SY1537 ) ) ) ) )
= $false )
| ( ( SV235 @ SV316 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[3269]) ).
thf(3296,plain,
! [SV110: $i] :
( ( ( ~ ( ( in @ ( sK6_SY1321 @ SV110 ) @ SV110 )
| ( SV110 = emptyset ) )
| ~ ( ~ ( in @ ( sK6_SY1321 @ SV110 ) @ SV110 )
| ( SV110 != emptyset ) ) )
= $false )
| ( ( SV110 = emptyset )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[3270]) ).
thf(3298,plain,
! [SV129: $i] :
( ( ( ~ ( ( in @ ( sK7_SY1357 @ SV129 ) @ SV129 )
| ( SV129 = emptyset ) )
| ~ ( ~ ( in @ ( sK7_SY1357 @ SV129 ) @ SV129 )
| ( SV129 != emptyset ) ) )
= $false )
| ( ( SV129 = emptyset )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[3271]) ).
thf(3300,plain,
! [SV236: $i,SV94: $i,SV317: $i] :
( ( ( ~ ( ( in @ SV317 @ ( setminus @ SV94 @ SV236 ) )
| ( in @ SV317 @ SV236 ) )
| ~ ( ~ ( in @ SV317 @ ( setminus @ SV94 @ SV236 ) )
| ~ ( in @ SV317 @ SV236 ) ) )
= $false )
| ( ( in @ SV317 @ SV236 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[3272]) ).
thf(3302,plain,
! [SV106: $i,SV247: $i,SV326: $i] :
( ( ( ~ ( ( in @ SV326 @ SV247 )
| ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) ) )
| ~ ( ~ ( in @ SV326 @ SV247 )
| ~ ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) ) ) )
= $false )
| ( ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[3273]) ).
thf(3304,plain,
! [SV52: $i] :
( ( ( ~ ( ( in @ ( sK19_SY1165 @ SV52 ) @ SV52 )
| ( SV52 = emptyset ) )
| ~ ( ~ ( in @ ( sK19_SY1165 @ SV52 ) @ SV52 )
| ( SV52 != emptyset ) ) )
= $false )
| ( ( SV52 = emptyset )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[3274]) ).
thf(3306,plain,
! [SV86: $i,SV229: $i] :
( ( ( ~ ( ( in @ ( sK14_SY1523 @ SV229 @ SV86 ) @ SV86 )
| ( subset @ SV86 @ SV229 ) )
| ~ ( ~ ( in @ ( sK14_SY1523 @ SV229 @ SV86 ) @ SV86 )
| ~ ( subset @ SV86 @ SV229 ) ) )
= $false )
| ( ( subset @ SV86 @ SV229 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[3275]) ).
thf(3308,plain,
! [SV260: $i,SV120: $i] :
( ( ( ~ ( ( in @ ( sK16_SY1565 @ SV120 @ SV260 ) @ SV260 )
| ( in @ SV260 @ ( powerset @ SV120 ) ) )
| ~ ( ~ ( in @ ( sK16_SY1565 @ SV120 @ SV260 ) @ SV260 )
| ~ ( in @ SV260 @ ( powerset @ SV120 ) ) ) )
= $false )
| ( ( in @ SV260 @ ( powerset @ SV120 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[3276]) ).
thf(3310,plain,
! [SV361: $i,SV127: $i] :
( ( ( ~ ( ( SV127 = emptyset )
| ( in @ SV361 @ SV127 ) )
| ~ ( ( SV127 != emptyset )
| ~ ( in @ SV361 @ SV127 ) ) )
= $false )
| ( ( in @ SV361 @ SV127 )
= $false ) ),
inference(extcnf_equal_neg,[status(thm)],[3277]) ).
thf(3312,plain,
! [SV141: $i,SV274: $i] :
( ( ( ~ ( ( in @ ( sK17_SY1575 @ SV274 @ SV141 ) @ SV141 )
| ( subset @ SV141 @ SV274 ) )
| ~ ( ~ ( in @ ( sK17_SY1575 @ SV274 @ SV141 ) @ SV141 )
| ~ ( subset @ SV141 @ SV274 ) ) )
= $false )
| ( ( subset @ SV141 @ SV274 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[3278]) ).
thf(3314,plain,
! [SV273: $i,SV140: $i] :
( ( ( ~ ( ( in @ ( sK36_SY1574 @ SV140 @ SV273 ) @ SV273 )
| ( in @ SV273 @ ( powerset @ SV140 ) ) )
| ~ ( ~ ( in @ ( sK36_SY1574 @ SV140 @ SV273 ) @ SV273 )
| ~ ( in @ SV273 @ ( powerset @ SV140 ) ) ) )
= $false )
| ( ( in @ SV273 @ ( powerset @ SV140 ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[3279]) ).
thf(3316,plain,
! [SV143: $i] :
( ( ( ~ ( ( in @ ( sK21_SY1385 @ SV143 ) @ SV143 )
| ( SV143 = emptyset ) )
| ~ ( ~ ( in @ ( sK21_SY1385 @ SV143 ) @ SV143 )
| ( SV143 != emptyset ) ) )
= $false )
| ( ( SV143 = emptyset )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[3280]) ).
thf(3320,plain,
! [SV89: $i,SV232: $i] :
( ( ( ~ ( ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV89 )
| ( ( binintersect @ SV89 @ SV232 )
= emptyset ) )
| ~ ( ~ ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV89 )
| ( ( binintersect @ SV89 @ SV232 )
!= emptyset ) ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[3282]) ).
thf(3322,plain,
! [SV89: $i,SV232: $i] :
( ( ( ~ ( ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV232 )
| ( ( binintersect @ SV89 @ SV232 )
= emptyset ) )
| ~ ( ~ ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV232 )
| ( ( binintersect @ SV89 @ SV232 )
!= emptyset ) ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[3283]) ).
thf(3325,plain,
! [SV73: $o] :
( ( ( ~ ( ~ SV73
| ~ ~ ( in @ emptyset @ ( prop2set @ SV73 ) ) ) )
= $false )
| ( SV73 = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3284]) ).
thf(3327,plain,
! [SV133: $o] :
( ( ( ~ ( ~ SV133
| ~ ~ ( set2prop @ ( prop2set @ SV133 ) ) ) )
= $false )
| ( SV133 = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3286]) ).
thf(3328,plain,
! [SV84: $i,SV348: $o] :
( ( ( ~ ( SV348
| ~ ( in @ SV84 @ emptyset ) ) )
= $false )
| ( SV348 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[3288]) ).
thf(3330,plain,
! [SV251: $i,SV112: $o] :
( ( ( ~ ( SV112
| ~ ( in @ SV251 @ ( prop2set @ SV112 ) ) ) )
= $false )
| ( SV112 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[3290]) ).
thf(3332,plain,
! [SV269: $i,SV134: $i > $o] :
( ( ( ~ ( ( SV134 @ SV269 )
| ~ ( in @ SV269 @ emptyset ) ) )
= $false )
| ( ( SV134 @ SV269 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3292]) ).
thf(3334,plain,
! [SV93: $i,SV316: $i,SV235: $i > $o] :
( ( ( ~ ( ( SV235 @ SV316 )
| ~ ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SY1537: $i] : ( SV235 @ SY1537 ) ) ) ) )
= $false )
| ( ( SV235 @ SV316 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3294]) ).
thf(3336,plain,
! [SV110: $i] :
( ( ( ~ ( ( in @ ( sK6_SY1321 @ SV110 ) @ SV110 )
| ( SV110 = emptyset ) ) )
= $false )
| ( ( SV110 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3296]) ).
thf(3338,plain,
! [SV129: $i] :
( ( ( ~ ( ( in @ ( sK7_SY1357 @ SV129 ) @ SV129 )
| ( SV129 = emptyset ) ) )
= $false )
| ( ( SV129 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3298]) ).
thf(3341,plain,
! [SV236: $i,SV94: $i,SV317: $i] :
( ( ( ~ ( ~ ( in @ SV317 @ ( setminus @ SV94 @ SV236 ) )
| ~ ( in @ SV317 @ SV236 ) ) )
= $false )
| ( ( in @ SV317 @ SV236 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3300]) ).
thf(3343,plain,
! [SV106: $i,SV247: $i,SV326: $i] :
( ( ( ~ ( ~ ( in @ SV326 @ SV247 )
| ~ ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) ) ) )
= $false )
| ( ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3302]) ).
thf(3344,plain,
! [SV52: $i] :
( ( ( ~ ( ( in @ ( sK19_SY1165 @ SV52 ) @ SV52 )
| ( SV52 = emptyset ) ) )
= $false )
| ( ( SV52 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3304]) ).
thf(3346,plain,
! [SV86: $i,SV229: $i] :
( ( ( ~ ( ( in @ ( sK14_SY1523 @ SV229 @ SV86 ) @ SV86 )
| ( subset @ SV86 @ SV229 ) ) )
= $false )
| ( ( subset @ SV86 @ SV229 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3306]) ).
thf(3348,plain,
! [SV260: $i,SV120: $i] :
( ( ( ~ ( ( in @ ( sK16_SY1565 @ SV120 @ SV260 ) @ SV260 )
| ( in @ SV260 @ ( powerset @ SV120 ) ) ) )
= $false )
| ( ( in @ SV260 @ ( powerset @ SV120 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3308]) ).
thf(3351,plain,
! [SV361: $i,SV127: $i] :
( ( ( ~ ( ( SV127 != emptyset )
| ~ ( in @ SV361 @ SV127 ) ) )
= $false )
| ( ( in @ SV361 @ SV127 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3310]) ).
thf(3352,plain,
! [SV141: $i,SV274: $i] :
( ( ( ~ ( ( in @ ( sK17_SY1575 @ SV274 @ SV141 ) @ SV141 )
| ( subset @ SV141 @ SV274 ) ) )
= $false )
| ( ( subset @ SV141 @ SV274 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3312]) ).
thf(3354,plain,
! [SV273: $i,SV140: $i] :
( ( ( ~ ( ( in @ ( sK36_SY1574 @ SV140 @ SV273 ) @ SV273 )
| ( in @ SV273 @ ( powerset @ SV140 ) ) ) )
= $false )
| ( ( in @ SV273 @ ( powerset @ SV140 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3314]) ).
thf(3356,plain,
! [SV143: $i] :
( ( ( ~ ( ( in @ ( sK21_SY1385 @ SV143 ) @ SV143 )
| ( SV143 = emptyset ) ) )
= $false )
| ( ( SV143 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3316]) ).
thf(3360,plain,
! [SV89: $i,SV232: $i] :
( ( ( ~ ( ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV89 )
| ( ( binintersect @ SV89 @ SV232 )
= emptyset ) ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3320]) ).
thf(3362,plain,
! [SV89: $i,SV232: $i] :
( ( ( ~ ( ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV232 )
| ( ( binintersect @ SV89 @ SV232 )
= emptyset ) ) )
= $false )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3322]) ).
thf(3365,plain,
! [SV73: $o] :
( ( ( ~ SV73
| ~ ~ ( in @ emptyset @ ( prop2set @ SV73 ) ) )
= $true )
| ( SV73 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3325]) ).
thf(3367,plain,
! [SV133: $o] :
( ( ( ~ SV133
| ~ ~ ( set2prop @ ( prop2set @ SV133 ) ) )
= $true )
| ( SV133 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3327]) ).
thf(3368,plain,
! [SV84: $i,SV348: $o] :
( ( ( SV348
| ~ ( in @ SV84 @ emptyset ) )
= $true )
| ( SV348 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[3328]) ).
thf(3370,plain,
! [SV251: $i,SV112: $o] :
( ( ( SV112
| ~ ( in @ SV251 @ ( prop2set @ SV112 ) ) )
= $true )
| ( SV112 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[3330]) ).
thf(3372,plain,
! [SV269: $i,SV134: $i > $o] :
( ( ( ( SV134 @ SV269 )
| ~ ( in @ SV269 @ emptyset ) )
= $true )
| ( ( SV134 @ SV269 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3332]) ).
thf(3374,plain,
! [SV93: $i,SV316: $i,SV235: $i > $o] :
( ( ( ( SV235 @ SV316 )
| ~ ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SY1537: $i] : ( SV235 @ SY1537 ) ) ) )
= $true )
| ( ( SV235 @ SV316 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3334]) ).
thf(3376,plain,
! [SV110: $i] :
( ( ( ( in @ ( sK6_SY1321 @ SV110 ) @ SV110 )
| ( SV110 = emptyset ) )
= $true )
| ( ( SV110 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3336]) ).
thf(3378,plain,
! [SV129: $i] :
( ( ( ( in @ ( sK7_SY1357 @ SV129 ) @ SV129 )
| ( SV129 = emptyset ) )
= $true )
| ( ( SV129 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3338]) ).
thf(3381,plain,
! [SV236: $i,SV94: $i,SV317: $i] :
( ( ( ~ ( in @ SV317 @ ( setminus @ SV94 @ SV236 ) )
| ~ ( in @ SV317 @ SV236 ) )
= $true )
| ( ( in @ SV317 @ SV236 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3341]) ).
thf(3383,plain,
! [SV106: $i,SV247: $i,SV326: $i] :
( ( ( ~ ( in @ SV326 @ SV247 )
| ~ ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) ) )
= $true )
| ( ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3343]) ).
thf(3384,plain,
! [SV52: $i] :
( ( ( ( in @ ( sK19_SY1165 @ SV52 ) @ SV52 )
| ( SV52 = emptyset ) )
= $true )
| ( ( SV52 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3344]) ).
thf(3386,plain,
! [SV86: $i,SV229: $i] :
( ( ( ( in @ ( sK14_SY1523 @ SV229 @ SV86 ) @ SV86 )
| ( subset @ SV86 @ SV229 ) )
= $true )
| ( ( subset @ SV86 @ SV229 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3346]) ).
thf(3388,plain,
! [SV260: $i,SV120: $i] :
( ( ( ( in @ ( sK16_SY1565 @ SV120 @ SV260 ) @ SV260 )
| ( in @ SV260 @ ( powerset @ SV120 ) ) )
= $true )
| ( ( in @ SV260 @ ( powerset @ SV120 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3348]) ).
thf(3391,plain,
! [SV361: $i,SV127: $i] :
( ( ( ( SV127 != emptyset )
| ~ ( in @ SV361 @ SV127 ) )
= $true )
| ( ( in @ SV361 @ SV127 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3351]) ).
thf(3392,plain,
! [SV141: $i,SV274: $i] :
( ( ( ( in @ ( sK17_SY1575 @ SV274 @ SV141 ) @ SV141 )
| ( subset @ SV141 @ SV274 ) )
= $true )
| ( ( subset @ SV141 @ SV274 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3352]) ).
thf(3394,plain,
! [SV273: $i,SV140: $i] :
( ( ( ( in @ ( sK36_SY1574 @ SV140 @ SV273 ) @ SV273 )
| ( in @ SV273 @ ( powerset @ SV140 ) ) )
= $true )
| ( ( in @ SV273 @ ( powerset @ SV140 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3354]) ).
thf(3396,plain,
! [SV143: $i] :
( ( ( ( in @ ( sK21_SY1385 @ SV143 ) @ SV143 )
| ( SV143 = emptyset ) )
= $true )
| ( ( SV143 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3356]) ).
thf(3400,plain,
! [SV89: $i,SV232: $i] :
( ( ( ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV89 )
| ( ( binintersect @ SV89 @ SV232 )
= emptyset ) )
= $true )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3360]) ).
thf(3402,plain,
! [SV89: $i,SV232: $i] :
( ( ( ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV232 )
| ( ( binintersect @ SV89 @ SV232 )
= emptyset ) )
= $true )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3362]) ).
thf(3405,plain,
! [SV73: $o] :
( ( ( ~ SV73 ) = $true )
| ( ( ~ ~ ( in @ emptyset @ ( prop2set @ SV73 ) ) )
= $true )
| ( SV73 = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3365]) ).
thf(3407,plain,
! [SV133: $o] :
( ( ( ~ SV133 ) = $true )
| ( ( ~ ~ ( set2prop @ ( prop2set @ SV133 ) ) )
= $true )
| ( SV133 = $false ) ),
inference(extcnf_or_pos,[status(thm)],[3367]) ).
thf(3408,plain,
! [SV84: $i,SV348: $o] :
( ( SV348 = $true )
| ( ( ~ ( in @ SV84 @ emptyset ) )
= $true )
| ( SV348 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[3368]) ).
thf(3410,plain,
! [SV251: $i,SV112: $o] :
( ( SV112 = $true )
| ( ( ~ ( in @ SV251 @ ( prop2set @ SV112 ) ) )
= $true )
| ( SV112 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[3370]) ).
thf(3412,plain,
! [SV269: $i,SV134: $i > $o] :
( ( ( SV134 @ SV269 )
= $true )
| ( ( ~ ( in @ SV269 @ emptyset ) )
= $true )
| ( ( SV134 @ SV269 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3372]) ).
thf(3414,plain,
! [SV93: $i,SV316: $i,SV235: $i > $o] :
( ( ( SV235 @ SV316 )
= $true )
| ( ( ~ ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SY1537: $i] : ( SV235 @ SY1537 ) ) ) )
= $true )
| ( ( SV235 @ SV316 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3374]) ).
thf(3416,plain,
! [SV110: $i] :
( ( ( in @ ( sK6_SY1321 @ SV110 ) @ SV110 )
= $true )
| ( ( SV110 = emptyset )
= $true )
| ( ( SV110 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3376]) ).
thf(3418,plain,
! [SV129: $i] :
( ( ( in @ ( sK7_SY1357 @ SV129 ) @ SV129 )
= $true )
| ( ( SV129 = emptyset )
= $true )
| ( ( SV129 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3378]) ).
thf(3421,plain,
! [SV236: $i,SV94: $i,SV317: $i] :
( ( ( ~ ( in @ SV317 @ ( setminus @ SV94 @ SV236 ) ) )
= $true )
| ( ( ~ ( in @ SV317 @ SV236 ) )
= $true )
| ( ( in @ SV317 @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3381]) ).
thf(3423,plain,
! [SV106: $i,SV247: $i,SV326: $i] :
( ( ( ~ ( in @ SV326 @ SV247 ) )
= $true )
| ( ( ~ ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) ) )
= $true )
| ( ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3383]) ).
thf(3424,plain,
! [SV52: $i] :
( ( ( in @ ( sK19_SY1165 @ SV52 ) @ SV52 )
= $true )
| ( ( SV52 = emptyset )
= $true )
| ( ( SV52 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3384]) ).
thf(3426,plain,
! [SV86: $i,SV229: $i] :
( ( ( in @ ( sK14_SY1523 @ SV229 @ SV86 ) @ SV86 )
= $true )
| ( ( subset @ SV86 @ SV229 )
= $true )
| ( ( subset @ SV86 @ SV229 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3386]) ).
thf(3428,plain,
! [SV260: $i,SV120: $i] :
( ( ( in @ ( sK16_SY1565 @ SV120 @ SV260 ) @ SV260 )
= $true )
| ( ( in @ SV260 @ ( powerset @ SV120 ) )
= $true )
| ( ( in @ SV260 @ ( powerset @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3388]) ).
thf(3431,plain,
! [SV361: $i,SV127: $i] :
( ( ( SV127 != emptyset )
= $true )
| ( ( ~ ( in @ SV361 @ SV127 ) )
= $true )
| ( ( in @ SV361 @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3391]) ).
thf(3432,plain,
! [SV141: $i,SV274: $i] :
( ( ( in @ ( sK17_SY1575 @ SV274 @ SV141 ) @ SV141 )
= $true )
| ( ( subset @ SV141 @ SV274 )
= $true )
| ( ( subset @ SV141 @ SV274 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3392]) ).
thf(3434,plain,
! [SV273: $i,SV140: $i] :
( ( ( in @ ( sK36_SY1574 @ SV140 @ SV273 ) @ SV273 )
= $true )
| ( ( in @ SV273 @ ( powerset @ SV140 ) )
= $true )
| ( ( in @ SV273 @ ( powerset @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3394]) ).
thf(3436,plain,
! [SV143: $i] :
( ( ( in @ ( sK21_SY1385 @ SV143 ) @ SV143 )
= $true )
| ( ( SV143 = emptyset )
= $true )
| ( ( SV143 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3396]) ).
thf(3440,plain,
! [SV89: $i,SV232: $i] :
( ( ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV89 )
= $true )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3400]) ).
thf(3442,plain,
! [SV89: $i,SV232: $i] :
( ( ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV232 )
= $true )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3402]) ).
thf(3445,plain,
! [SV73: $o] :
( ( SV73 = $false )
| ( ( ~ ~ ( in @ emptyset @ ( prop2set @ SV73 ) ) )
= $true )
| ( SV73 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3405]) ).
thf(3447,plain,
! [SV133: $o] :
( ( SV133 = $false )
| ( ( ~ ~ ( set2prop @ ( prop2set @ SV133 ) ) )
= $true )
| ( SV133 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3407]) ).
thf(3448,plain,
! [SV348: $o,SV84: $i] :
( ( ( in @ SV84 @ emptyset )
= $false )
| ( SV348 = $true )
| ( SV348 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[3408]) ).
thf(3450,plain,
! [SV112: $o,SV251: $i] :
( ( ( in @ SV251 @ ( prop2set @ SV112 ) )
= $false )
| ( SV112 = $true )
| ( SV112 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[3410]) ).
thf(3452,plain,
! [SV134: $i > $o,SV269: $i] :
( ( ( in @ SV269 @ emptyset )
= $false )
| ( ( SV134 @ SV269 )
= $true )
| ( ( SV134 @ SV269 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3412]) ).
thf(3454,plain,
! [SV235: $i > $o,SV93: $i,SV316: $i] :
( ( ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SY1537: $i] : ( SV235 @ SY1537 ) ) )
= $false )
| ( ( SV235 @ SV316 )
= $true )
| ( ( SV235 @ SV316 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3414]) ).
thf(3458,plain,
! [SV236: $i,SV94: $i,SV317: $i] :
( ( ( in @ SV317 @ ( setminus @ SV94 @ SV236 ) )
= $false )
| ( ( ~ ( in @ SV317 @ SV236 ) )
= $true )
| ( ( in @ SV317 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3421]) ).
thf(3459,plain,
! [SV106: $i,SV247: $i,SV326: $i] :
( ( ( in @ SV326 @ SV247 )
= $false )
| ( ( ~ ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) ) )
= $true )
| ( ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3423]) ).
thf(3463,plain,
! [SV361: $i,SV127: $i] :
( ( ( SV127 = emptyset )
= $false )
| ( ( ~ ( in @ SV361 @ SV127 ) )
= $true )
| ( ( in @ SV361 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3431]) ).
thf(3470,plain,
! [SV73: $o] :
( ( ( ~ ( in @ emptyset @ ( prop2set @ SV73 ) ) )
= $false )
| ( SV73 = $false )
| ( SV73 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3445]) ).
thf(3471,plain,
! [SV133: $o] :
( ( ( ~ ( set2prop @ ( prop2set @ SV133 ) ) )
= $false )
| ( SV133 = $false )
| ( SV133 = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3447]) ).
thf(3478,plain,
! [SV94: $i,SV236: $i,SV317: $i] :
( ( ( in @ SV317 @ SV236 )
= $false )
| ( ( in @ SV317 @ ( setminus @ SV94 @ SV236 ) )
= $false )
| ( ( in @ SV317 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3458]) ).
thf(3479,plain,
! [SV247: $i,SV106: $i,SV326: $i] :
( ( ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) )
= $false )
| ( ( in @ SV326 @ SV247 )
= $false )
| ( ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3459]) ).
thf(3483,plain,
! [SV127: $i,SV361: $i] :
( ( ( in @ SV361 @ SV127 )
= $false )
| ( ( SV127 = emptyset )
= $false )
| ( ( in @ SV361 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3463]) ).
thf(3490,plain,
! [SV73: $o] :
( ( ( in @ emptyset @ ( prop2set @ SV73 ) )
= $true )
| ( SV73 = $false )
| ( SV73 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3470]) ).
thf(3491,plain,
! [SV133: $o] :
( ( ( set2prop @ ( prop2set @ SV133 ) )
= $true )
| ( SV133 = $false )
| ( SV133 = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3471]) ).
thf(3496,plain,
! [SV84: $i] :
( ( ~ ( in @ SV84 @ emptyset ) )
= $true ),
inference(extuni,[status(esa)],[3289:[bind(SV348,$thf( ~ ( in @ SV84 @ emptyset ) ))]]) ).
thf(3498,plain,
! [SV505: $i > $i,SV269: $i,SV504: $i > $i] :
( ( ( ~ ( in @ ( SV504 @ SV269 ) @ ( SV505 @ SV269 ) ) )
= $true )
| ( ( in @ ( SV504 @ SV269 ) @ ( SV505 @ SV269 ) )
= $false )
| ( ( in @ SV269 @ emptyset )
= $false ) ),
inference(extuni,[status(esa)],[3293:[bind(SV134,$thf( ^ [SX0: $i] : ~ ( in @ ( SV504 @ SX0 ) @ ( SV505 @ SX0 ) ) ))]]) ).
thf(3499,plain,
! [SV269: $i,SV501: $i > $o] :
( ( ( ~ ( SV501 @ SV269 ) )
= $true )
| ( ( ~ ( SV501 @ SV269 ) )
= $true )
| ( ( ~ ( in @ SV269 @ emptyset ) )
= $true ) ),
inference(extuni,[status(esa)],[3293:[bind(SV134,$thf( ^ [SX0: $i] : ~ ( SV501 @ SX0 ) ))]]) ).
thf(3502,plain,
! [SV93: $i,SV512: $i > $i,SV316: $i,SV511: $i > $i] :
( ( ( ~ ( in @ ( SV511 @ SV316 ) @ ( SV512 @ SV316 ) ) )
= $true )
| ( ( in @ ( SV511 @ SV316 ) @ ( SV512 @ SV316 ) )
= $false )
| ( ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SX0: $i] :
~ ( in @ ( SV511 @ SX0 ) @ ( SV512 @ SX0 ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[3295:[bind(SV235,$thf( ^ [SX0: $i] : ~ ( in @ ( SV511 @ SX0 ) @ ( SV512 @ SX0 ) ) ))]]) ).
thf(3503,plain,
! [SV93: $i,SV316: $i,SV508: $i > $o] :
( ( ( ~ ( SV508 @ SV316 ) )
= $true )
| ( ( ~ ( SV508 @ SV316 ) )
= $true )
| ( ( ~ ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SX0: $i] :
~ ( SV508 @ SX0 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[3295:[bind(SV235,$thf( ^ [SX0: $i] : ~ ( SV508 @ SX0 ) ))]]) ).
thf(3508,plain,
! [SV361: $i] :
( ( ( in @ SV361 @ emptyset )
= $false )
| ( ( in @ SV361 @ emptyset )
= $false ) ),
inference(extuni,[status(esa)],[3483:[bind(SV127,$thf( emptyset ))]]) ).
thf(3511,plain,
! [SV189: $i] :
( ( subset @ SV189 @ SV189 )
= $true ),
inference(extuni,[status(esa)],[957:[bind(SV41,$thf( SV189 ))]]) ).
thf(3514,plain,
( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK3_SY1491 @ emptyset ) ) @ emptyset )
= emptyset )
= $false ),
inference(extuni,[status(esa)],[988]) ).
thf(3515,plain,
! [SV215: $i] :
( ( subset @ SV215 @ SV215 )
= $true ),
inference(extuni,[status(esa)],[989:[bind(SV69,$thf( SV215 ))]]) ).
thf(3516,plain,
! [SV226: $i] :
( ( ( setadjoin @ SV226 @ ( setadjoin @ SV226 @ emptyset ) )
= ( setadjoin @ SV226 @ emptyset ) )
= $true ),
inference(extuni,[status(esa)],[1000:[bind(SV82,$thf( SV226 ))]]) ).
thf(3518,plain,
! [SV268: $i] :
( ( in @ SV268 @ ( setadjoin @ SV268 @ emptyset ) )
= $true ),
inference(extuni,[status(esa)],[1054:[bind(SV132,$thf( SV268 ))]]) ).
thf(3525,plain,
! [SV345: $i,SV190: $i,SV297: $i,SV42: $i] :
( ( ( SV42 = SV297 )
= $true )
| ( ( ( setadjoin @ SV42 @ ( setadjoin @ SV190 @ emptyset ) )
= ( setadjoin @ SV297 @ ( setadjoin @ SV345 @ emptyset ) ) )
= $false )
| ( ( ( setadjoin @ SV42 @ emptyset )
= ( setadjoin @ SV297 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[1207]) ).
thf(3526,plain,
! [SV345: $i,SV190: $i,SV297: $i,SV42: $i] :
( ( ( SV42 = SV297 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV42 @ ( setadjoin @ SV190 @ emptyset ) ) @ emptyset )
= ( setadjoin @ ( setadjoin @ SV297 @ ( setadjoin @ SV345 @ emptyset ) ) @ emptyset ) )
= $false )
| ( ( ( setadjoin @ SV42 @ emptyset )
= ( setadjoin @ SV297 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[1207]) ).
thf(3533,plain,
! [SV347: $i,SV212: $i,SV308: $i,SV66: $i] :
( ( ( SV66 = SV308 )
= $true )
| ( ( ( setadjoin @ SV66 @ ( setadjoin @ SV212 @ emptyset ) )
= ( setadjoin @ SV308 @ ( setadjoin @ SV347 @ emptyset ) ) )
= $false )
| ( ( ( setadjoin @ SV66 @ emptyset )
= ( setadjoin @ SV308 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[1231]) ).
thf(3534,plain,
! [SV347: $i,SV212: $i,SV308: $i,SV66: $i] :
( ( ( SV66 = SV308 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV66 @ ( setadjoin @ SV212 @ emptyset ) ) @ emptyset )
= ( setadjoin @ ( setadjoin @ SV308 @ ( setadjoin @ SV347 @ emptyset ) ) @ emptyset ) )
= $false )
| ( ( ( setadjoin @ SV66 @ emptyset )
= ( setadjoin @ SV308 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[1231]) ).
thf(3535,plain,
! [SV214: $i] :
( ( subset @ SV214 @ SV214 )
= $true ),
inference(extuni,[status(esa)],[1233:[bind(SV68,$thf( SV214 ))]]) ).
thf(3536,plain,
! [SV361: $i] :
( ( in @ SV361 @ emptyset )
= $false ),
inference(extuni,[status(esa)],[1386:[bind(SV127,$thf( emptyset ))]]) ).
thf(3538,plain,
! [SV238: $i,SV96: $i] :
( ( in @ SV96 @ ( setadjoin @ SV96 @ SV238 ) )
= $true ),
inference(extuni,[status(esa)],[1552:[bind(SV319,$thf( SV96 ))]]) ).
thf(3540,plain,
! [SV350: $i] :
( ( ( in @ ( setunion @ ( setadjoin @ SV350 @ emptyset ) ) @ ( setadjoin @ SV350 @ emptyset ) )
= $true )
| ( ( in @ SV350 @ ( setadjoin @ SV350 @ emptyset ) )
= $false ) ),
inference(extuni,[status(esa)],[1595:[bind(SV30,$thf( setadjoin @ SV350 @ emptyset ))]]) ).
thf(3542,plain,
! [SV367: $i > $o,SV349: $i > $o,SV180: $i] :
( ( ( ( dsetconstr @ SV180
@ ^ [SX0: $i] : ( SV349 @ SX0 ) )
= ( dsetconstr @ SV180
@ ^ [SX0: $i] : ( SV367 @ SX0 ) ) )
= $true )
| ( ( in @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV180 ) @ SV180 )
= $true ) ),
inference(extuni,[status(esa)],[1699:[bind(SV29,$thf( SV180 ))]]) ).
thf(3543,plain,
! [SV367: $i > $o,SV349: $i > $o,SV180: $i] :
( ( ( ( dsetconstr @ SV180
@ ^ [SX0: $i] : ( SV349 @ SX0 ) )
= ( dsetconstr @ SV180
@ ^ [SX0: $i] : ( SV367 @ SX0 ) ) )
= $true )
| ( ( in @ ( sK50_SY1686 @ SV180 @ SV349 @ SV367 @ SV180 ) @ SV180 )
= $true ) ),
inference(extuni,[status(esa)],[1898:[bind(SV29,$thf( SV180 ))]]) ).
thf(3546,plain,
! [SV367: $i > $o,SV349: $i > $o,SV180: $i] :
( ( ( ( dsetconstr @ SV180
@ ^ [SX0: $i] : ( SV349 @ SX0 ) )
= ( dsetconstr @ SV180
@ ^ [SX0: $i] : ( SV367 @ SX0 ) ) )
= $true )
| ( ( ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV180 )
= ( sK50_SY1686 @ SV180 @ SV349 @ SV367 @ SV180 ) )
= $true ) ),
inference(extuni,[status(esa)],[2011:[bind(SV29,$thf( SV180 ))]]) ).
thf(3547,plain,
! [SV367: $i > $o,SV349: $i > $o,SV180: $i] :
( ( ( ( dsetconstr @ SV180
@ ^ [SX0: $i] : ( SV349 @ SX0 ) )
= ( dsetconstr @ SV180
@ ^ [SX0: $i] : ( SV367 @ SX0 ) ) )
= $true )
| ( ( SV367 @ ( sK50_SY1686 @ SV180 @ SV349 @ SV367 @ SV180 ) )
= $false )
| ( ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV180 ) )
= $false ) ),
inference(extuni,[status(esa)],[2425:[bind(SV29,$thf( SV180 ))]]) ).
thf(3550,plain,
! [SV367: $i > $o,SV349: $i > $o,SV180: $i] :
( ( ( ( dsetconstr @ SV180
@ ^ [SX0: $i] : ( SV349 @ SX0 ) )
= ( dsetconstr @ SV180
@ ^ [SX0: $i] : ( SV367 @ SX0 ) ) )
= $true )
| ( ( SV349 @ ( sK38_SY1669 @ SV367 @ SV349 @ SV180 @ SV180 ) )
= $true )
| ( ( SV367 @ ( sK50_SY1686 @ SV180 @ SV349 @ SV367 @ SV180 ) )
= $true ) ),
inference(extuni,[status(esa)],[2545:[bind(SV29,$thf( SV180 ))]]) ).
thf(3551,plain,
! [SV356: $i,SV90: $i > $o] :
( ( ( SV90 @ ( sK53_SY1659 @ SV356 @ SV90 ) )
= $true )
| ( ( SV90 @ SV356 )
= $false )
| ( ( SV90 @ ( sK73_SY1266 @ SV356 @ SV90 ) )
= $true ) ),
inference(extuni,[status(esa)],[2632:[bind(SV428,$thf( sK73_SY1266 @ SV356 @ SV90 ))]]) ).
thf(3552,plain,
! [SV356: $i] :
( ( ( ( sK53_SY1659 @ SV356
@ ^ [SX0: $i] : ( SX0 = SV356 ) )
= SV356 )
= $true )
| ( ( ( sK73_SY1266 @ SV356
@ ^ [SX0: $i] : ( SX0 = SV356 ) )
= SV356 )
= $true ) ),
inference(extuni,[status(esa)],[3263:[bind(SV428,$thf( sK73_SY1266 @ SV356 @ ^ [SX0: $i] : ( SX0 = SV356 ) ))]]) ).
thf(3553,plain,
! [SV358: $i,SV398: $i] :
( ( ( in @ SV398 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV358 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ ( sK88_SY1316 @ SV398 @ SV358 @ ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) )
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) )
@ ^ [SX0: $i] : ( in @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[2687:[bind(SV108,$thf( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ))]]) ).
thf(3554,plain,
! [SV358: $i,SV398: $i] :
( ( ( in @ SV398 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV358 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) )
@ ^ [SX0: $i] : ( in @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( sK88_SY1316 @ SV398 @ SV358 @ ( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) )
= $true ) ),
inference(extuni,[status(esa)],[2688:[bind(SV108,$thf( setadjoin @ ( setadjoin @ SV358 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV358 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ))]]) ).
thf(3555,plain,
! [SV84: $i] :
( ( in @ SV84 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3496]) ).
thf(3557,plain,
! [SV269: $i,SV501: $i > $o] :
( ( ( SV501 @ SV269 )
= $false )
| ( ( ~ ( SV501 @ SV269 ) )
= $true )
| ( ( ~ ( in @ SV269 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3499]) ).
thf(3558,plain,
! [SV505: $i > $i,SV269: $i,SV504: $i > $i] :
( ( ( in @ ( SV504 @ SV269 ) @ ( SV505 @ SV269 ) )
= $false )
| ( ( in @ ( SV504 @ SV269 ) @ ( SV505 @ SV269 ) )
= $false )
| ( ( in @ SV269 @ emptyset )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3498]) ).
thf(3561,plain,
! [SV93: $i,SV316: $i,SV508: $i > $o] :
( ( ( SV508 @ SV316 )
= $false )
| ( ( ~ ( SV508 @ SV316 ) )
= $true )
| ( ( ~ ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SX0: $i] :
~ ( SV508 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3503]) ).
thf(3562,plain,
! [SV93: $i,SV512: $i > $i,SV316: $i,SV511: $i > $i] :
( ( ( in @ ( SV511 @ SV316 ) @ ( SV512 @ SV316 ) )
= $false )
| ( ( in @ ( SV511 @ SV316 ) @ ( SV512 @ SV316 ) )
= $false )
| ( ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SX0: $i] :
~ ( in @ ( SV511 @ SX0 ) @ ( SV512 @ SX0 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3502]) ).
thf(3565,plain,
! [SV269: $i,SV501: $i > $o] :
( ( ( SV501 @ SV269 )
= $false )
| ( ( SV501 @ SV269 )
= $false )
| ( ( ~ ( in @ SV269 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3557]) ).
thf(3567,plain,
! [SV93: $i,SV316: $i,SV508: $i > $o] :
( ( ( SV508 @ SV316 )
= $false )
| ( ( SV508 @ SV316 )
= $false )
| ( ( ~ ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SX0: $i] :
~ ( SV508 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3561]) ).
thf(3569,plain,
! [SV501: $i > $o,SV269: $i] :
( ( ( in @ SV269 @ emptyset )
= $false )
| ( ( SV501 @ SV269 )
= $false )
| ( ( SV501 @ SV269 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3565]) ).
thf(3571,plain,
! [SV508: $i > $o,SV93: $i,SV316: $i] :
( ( ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SX0: $i] :
~ ( SV508 @ SX0 ) ) )
= $false )
| ( ( SV508 @ SV316 )
= $false )
| ( ( SV508 @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3567]) ).
thf(3572,plain,
( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ),
inference(sim,[status(thm)],[850]) ).
thf(3573,plain,
! [SV76: $i] :
( ( in @ SV76 @ emptyset )
= $false ),
inference(sim,[status(thm)],[854]) ).
thf(3574,plain,
( ( set2prop @ ( prop2set @ $true ) )
= $true ),
inference(sim,[status(thm)],[914]) ).
thf(3575,plain,
! [SV84: $i] :
( ( in @ SV84 @ emptyset )
= $false ),
inference(sim,[status(thm)],[1004]) ).
thf(3576,plain,
! [SV253: $i] :
( ( in @ SV253 @ ( prop2set @ $false ) )
= $false ),
inference(sim,[status(thm)],[1034]) ).
thf(3577,plain,
! [SV72: $i,SV218: $i] :
( ( ( in @ SV218 @ ( sK34_SX0 @ SV72 @ SV218 ) )
= $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(sim,[status(thm)],[1634]) ).
thf(3578,plain,
! [SV218: $i,SV72: $i] :
( ( ( in @ ( sK34_SX0 @ SV72 @ SV218 ) @ SV72 )
= $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(sim,[status(thm)],[1736]) ).
thf(3579,plain,
! [SV368: $i,SV181: $i > $o,SV31: $i] :
( ( ( ( dsetconstr @ SV31
@ ^ [SY1444: $i] : ( SV181 @ SY1444 ) )
= emptyset )
= $false )
| ( ( in @ SV368 @ SV31 )
= $false )
| ( ( SV181 @ SV368 )
= $false ) ),
inference(sim,[status(thm)],[1901]) ).
thf(3580,plain,
! [SV60: $i,SV206: $i,SV306: $i] :
( ( ( in @ SV306 @ SV206 )
= $true )
| ( ( in @ SV306 @ SV60 )
= $true )
| ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false ) ),
inference(sim,[status(thm)],[2029]) ).
thf(3581,plain,
! [SV91: $i,SV233: $i,SV315: $i] :
( ( ( in @ SV315 @ SV233 )
= $true )
| ( ( SV315 = SV91 )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(sim,[status(thm)],[2053]) ).
thf(3582,plain,
! [SV113: $i,SV254: $i,SV329: $i] :
( ( ( in @ SV329 @ SV254 )
= $true )
| ( ( in @ SV329 @ SV113 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(sim,[status(thm)],[2174]) ).
thf(3583,plain,
! [SV254: $i,SV113: $i,SV329: $i] :
( ( ( in @ SV329 @ SV113 )
= $false )
| ( ( in @ SV329 @ SV254 )
= $false )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(sim,[status(thm)],[2330]) ).
thf(3584,plain,
! [SV73: $o] :
( ( ( in @ emptyset @ ( prop2set @ SV73 ) )
= $true )
| ( SV73 = $false ) ),
inference(sim,[status(thm)],[3490]) ).
thf(3585,plain,
! [SV133: $o] :
( ( ( set2prop @ ( prop2set @ SV133 ) )
= $true )
| ( SV133 = $false ) ),
inference(sim,[status(thm)],[3491]) ).
thf(3586,plain,
! [SV348: $o,SV84: $i] :
( ( ( in @ SV84 @ emptyset )
= $false )
| ( SV348 = $true ) ),
inference(sim,[status(thm)],[3448]) ).
thf(3587,plain,
! [SV112: $o,SV251: $i] :
( ( ( in @ SV251 @ ( prop2set @ SV112 ) )
= $false )
| ( SV112 = $true ) ),
inference(sim,[status(thm)],[3450]) ).
thf(3588,plain,
! [SV134: $i > $o,SV269: $i] :
( ( ( in @ SV269 @ emptyset )
= $false )
| ( ( SV134 @ SV269 )
= $true ) ),
inference(sim,[status(thm)],[3452]) ).
thf(3589,plain,
! [SV501: $i > $o,SV269: $i] :
( ( ( in @ SV269 @ emptyset )
= $false )
| ( ( SV501 @ SV269 )
= $false ) ),
inference(sim,[status(thm)],[3569]) ).
thf(3590,plain,
! [SV505: $i > $i,SV269: $i,SV504: $i > $i] :
( ( ( in @ ( SV504 @ SV269 ) @ ( SV505 @ SV269 ) )
= $false )
| ( ( in @ SV269 @ emptyset )
= $false ) ),
inference(sim,[status(thm)],[3558]) ).
thf(3591,plain,
! [SV235: $i > $o,SV93: $i,SV316: $i] :
( ( ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SY1537: $i] : ( SV235 @ SY1537 ) ) )
= $false )
| ( ( SV235 @ SV316 )
= $true ) ),
inference(sim,[status(thm)],[3454]) ).
thf(3592,plain,
! [SV508: $i > $o,SV93: $i,SV316: $i] :
( ( ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SX0: $i] :
~ ( SV508 @ SX0 ) ) )
= $false )
| ( ( SV508 @ SV316 )
= $false ) ),
inference(sim,[status(thm)],[3571]) ).
thf(3593,plain,
! [SV93: $i,SV512: $i > $i,SV316: $i,SV511: $i > $i] :
( ( ( in @ ( SV511 @ SV316 ) @ ( SV512 @ SV316 ) )
= $false )
| ( ( in @ SV316
@ ( dsetconstr @ SV93
@ ^ [SX0: $i] :
~ ( in @ ( SV511 @ SX0 ) @ ( SV512 @ SX0 ) ) ) )
= $false ) ),
inference(sim,[status(thm)],[3562]) ).
thf(3594,plain,
! [SV110: $i] :
( ( ( in @ ( sK6_SY1321 @ SV110 ) @ SV110 )
= $true )
| ( ( SV110 = emptyset )
= $true ) ),
inference(sim,[status(thm)],[3416]) ).
thf(3595,plain,
! [SV129: $i] :
( ( ( in @ ( sK7_SY1357 @ SV129 ) @ SV129 )
= $true )
| ( ( SV129 = emptyset )
= $true ) ),
inference(sim,[status(thm)],[3418]) ).
thf(3596,plain,
! [SV94: $i,SV236: $i,SV317: $i] :
( ( ( in @ SV317 @ SV236 )
= $false )
| ( ( in @ SV317 @ ( setminus @ SV94 @ SV236 ) )
= $false ) ),
inference(sim,[status(thm)],[3478]) ).
thf(3597,plain,
! [SV247: $i,SV106: $i,SV326: $i] :
( ( ( in @ SV326 @ ( setminus @ SV106 @ SV247 ) )
= $false )
| ( ( in @ SV326 @ SV247 )
= $false ) ),
inference(sim,[status(thm)],[3479]) ).
thf(3598,plain,
! [SV52: $i] :
( ( ( in @ ( sK19_SY1165 @ SV52 ) @ SV52 )
= $true )
| ( ( SV52 = emptyset )
= $true ) ),
inference(sim,[status(thm)],[3424]) ).
thf(3599,plain,
! [SV86: $i,SV229: $i] :
( ( ( in @ ( sK14_SY1523 @ SV229 @ SV86 ) @ SV86 )
= $true )
| ( ( subset @ SV86 @ SV229 )
= $true ) ),
inference(sim,[status(thm)],[3426]) ).
thf(3600,plain,
! [SV260: $i,SV120: $i] :
( ( ( in @ ( sK16_SY1565 @ SV120 @ SV260 ) @ SV260 )
= $true )
| ( ( in @ SV260 @ ( powerset @ SV120 ) )
= $true ) ),
inference(sim,[status(thm)],[3428]) ).
thf(3601,plain,
! [SV361: $i] :
( ( in @ SV361 @ emptyset )
= $false ),
inference(sim,[status(thm)],[3508]) ).
thf(3602,plain,
! [SV141: $i,SV274: $i] :
( ( ( in @ ( sK17_SY1575 @ SV274 @ SV141 ) @ SV141 )
= $true )
| ( ( subset @ SV141 @ SV274 )
= $true ) ),
inference(sim,[status(thm)],[3432]) ).
thf(3603,plain,
! [SV273: $i,SV140: $i] :
( ( ( in @ ( sK36_SY1574 @ SV140 @ SV273 ) @ SV273 )
= $true )
| ( ( in @ SV273 @ ( powerset @ SV140 ) )
= $true ) ),
inference(sim,[status(thm)],[3434]) ).
thf(3604,plain,
! [SV143: $i] :
( ( ( in @ ( sK21_SY1385 @ SV143 ) @ SV143 )
= $true )
| ( ( SV143 = emptyset )
= $true ) ),
inference(sim,[status(thm)],[3436]) ).
thf(3605,plain,
! [SV89: $i,SV232: $i] :
( ( ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV89 )
= $true )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(sim,[status(thm)],[3440]) ).
thf(3606,plain,
! [SV89: $i,SV232: $i] :
( ( ( in @ ( sK26_SY1527 @ SV232 @ SV89 ) @ SV232 )
= $true )
| ( ( ( binintersect @ SV89 @ SV232 )
= emptyset )
= $true ) ),
inference(sim,[status(thm)],[3442]) ).
thf(3607,plain,
( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ),
inference(sim,[status(thm)],[850]) ).
thf(3608,plain,
! [SV76: $i] :
( ( in @ SV76 @ emptyset )
= $false ),
inference(sim,[status(thm)],[854]) ).
thf(3609,plain,
( ( set2prop @ ( prop2set @ $true ) )
= $true ),
inference(sim,[status(thm)],[914]) ).
thf(3610,plain,
! [SV84: $i] :
( ( in @ SV84 @ emptyset )
= $false ),
inference(sim,[status(thm)],[1004]) ).
thf(3611,plain,
! [SV253: $i] :
( ( in @ SV253 @ ( prop2set @ $false ) )
= $false ),
inference(sim,[status(thm)],[1034]) ).
thf(3612,plain,
! [SV72: $i,SV218: $i] :
( ( ( in @ SV218 @ ( sK34_SX0 @ SV72 @ SV218 ) )
= $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(sim,[status(thm)],[1634]) ).
thf(3613,plain,
! [SV218: $i,SV72: $i] :
( ( ( in @ ( sK34_SX0 @ SV72 @ SV218 ) @ SV72 )
= $true )
| ( ( in @ SV218 @ ( setunion @ SV72 ) )
= $false ) ),
inference(sim,[status(thm)],[1736]) ).
thf(3614,plain,
! [SV60: $i,SV206: $i,SV306: $i] :
( ( ( in @ SV306 @ SV206 )
= $true )
| ( ( in @ SV306 @ SV60 )
= $true )
| ( ( in @ SV306 @ ( binunion @ SV60 @ SV206 ) )
= $false ) ),
inference(sim,[status(thm)],[2029]) ).
thf(3615,plain,
! [SV91: $i,SV233: $i,SV315: $i] :
( ( ( in @ SV315 @ SV233 )
= $true )
| ( ( SV315 = SV91 )
= $true )
| ( ( in @ SV315 @ ( setadjoin @ SV91 @ SV233 ) )
= $false ) ),
inference(sim,[status(thm)],[2053]) ).
thf(3616,plain,
! [SV113: $i,SV254: $i,SV329: $i] :
( ( ( in @ SV329 @ SV254 )
= $true )
| ( ( in @ SV329 @ SV113 )
= $true )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(sim,[status(thm)],[2174]) ).
thf(3617,plain,
! [SV254: $i,SV113: $i,SV329: $i] :
( ( ( in @ SV329 @ SV113 )
= $false )
| ( ( in @ SV329 @ SV254 )
= $false )
| ( ( in @ SV329 @ ( symdiff @ SV113 @ SV254 ) )
= $false ) ),
inference(sim,[status(thm)],[2330]) ).
thf(3618,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[308,3617,3616,3615,3614,3613,3612,3611,3610,3609,3608,3607,3606,3605,3604,3603,3602,3601,3600,3599,3598,3597,3596,3595,3594,3593,3592,3591,3590,3589,3588,3587,3586,3585,3584,3583,3582,3581,3580,3579,3578,3577,3576,3575,3574,3573,3572,3555,3554,3553,3552,3551,3550,3547,3546,3543,3542,3540,3538,3536,3535,3534,3533,3526,3525,3518,3516,3515,3514,3511,3263,3261,3259,3258,3257,3256,3255,3251,3250,3244,3242,3238,3231,3228,3227,3212,3211,3201,3199,3187,3184,3182,3180,3154,3150,3147,3143,3142,3131,3128,3103,3102,3088,3084,3058,3049,3030,3029,3028,3010,3009,2991,2989,2987,2985,2984,2977,2966,2942,2941,2902,2899,2862,2858,2802,2801,2788,2787,2779,2769,2768,2765,2764,2751,2750,2747,2746,2739,2729,2723,2722,2704,2703,2688,2687,2657,2646,2645,2642,2634,2633,2632,2631,2614,2613,2607,2606,2605,2594,2592,2591,2584,2577,2576,2551,2545,2538,2487,2486,2485,2475,2471,2468,2432,2431,2426,2425,2422,2421,2418,2417,2416,2407,2403,2401,2364,2361,2326,2324,2323,2301,2300,2290,2289,2265,2264,2263,2210,2196,2195,2186,2179,2162,2159,2158,2128,2127,2123,2122,2092,2088,2051,2031,2030,2027,2025,2024,2020,2011,2003,1989,1988,1983,1982,1916,1898,1890,1884,1883,1807,1758,1743,1742,1734,1717,1713,1711,1710,1699,1697,1696,1691,1690,1686,1684,1683,1679,1675,1637,1628,1606,1595,1579,1559,1556,1553,1552,1551,1505,1475,1469,1462,1459,1450,1447,1446,1445,1436,1430,1423,1422,1418,1415,1414,1403,1394,1391,1386,1380,1377,1354,1343,1328,1327,1323,1318,1309,1302,1301,1299,1292,1277,1266,1265,1256,1247,1233,1231,1220,1207,1199,1193,1188,1184,1172,1170,1159,1156,1151,1148,1147,1139,1134,1120,1116,1089,1077,1072,1071,1067,1056,1055,1054,1050,1044,1043,1038,1032,1019,1002,1001,1000,999,996,989,988,981,965,963,959,957,952,939,913,894,849,803,661,660,659,658,657,656,655,654,653,652,651,650,649,647,646,645,644,643,498,497,496,493,492,490,477,476,475,332]) ).
thf(3619,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3618]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU650^1 : 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
% 0.08/0.21 % Computer : n016.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Oct 6 15:34:59 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 219.11/36.82
% 219.11/36.82 No.of.Axioms: 0
% 219.11/36.82
% 219.11/36.82 Length.of.Defs: 36024
% 219.11/36.82
% 219.11/36.82 Contains.Choice.Funs: true
% 219.11/36.82 .......................................................................................................................eprover: CPU time limit exceeded, terminating
% 219.11/36.82 ..............................
% 219.11/36.82
% 219.11/36.82 ********************************
% 219.11/36.82 * All subproblems solved! *
% 219.11/36.82 ********************************
% 219.11/36.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:166,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:3618,loop_count:0,foatp_calls:2,translation:fof_full)
% 219.11/36.82
% 219.11/36.82 %**** Beginning of derivation protocol ****
% 219.11/36.82 % SZS output start CNFRefutation
% See solution above
% 219.11/36.86
% 219.11/36.86 %**** End of derivation protocol ****
% 219.11/36.86 %**** no. of clauses in derivation: 3030 ****
% 219.11/36.86 %**** clause counter: 3618 ****
% 219.11/36.86
% 219.11/36.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:166,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:3618,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------